ABSTRACT 
 
Title of Document: IMPROVEMENT OF DYNAMIC PROPERTIES 
AND SEISMIC RESPONSE OF CLAY USING 
FIBER REINFORCEMENT   
  
 Behzad Amir Faryar, Doctor of Philosophy, 2012 
  
Directed By: Professor M. Sherif Aggour, Department of Civil 
and Environmental Engineering 
 
 In recent years, earthquakes have caused heavy damage to buildings and 
infrastructure. One of the causes of heavy damage due to earthquake motions is the role 
of soft clay in amplifying bedrock ground motions. Improving the soil conditions at a site 
in order to mitigate earthquake damage can be one of the methods of modifying site 
conditions and thus reduce its effects on the seismic site response. The inclusion of 
randomly distributed short virgin polypropylene fibers (C3H6) in clay has proven to 
significantly improve the static geotechnical properties of clay such as shear, 
compression, tensile strengths, and so on. These improvements have triggered great 
interest in the possibility of mixing fibers with clay to improve the clay?s dynamic 
properties. Because the percentage of fibers is currently arbitrarily chosen by users, a 
procedure was set up in this study to determine the optimum fiber content for a fiber-clay 
composite. 
 
 
Experimental testing was performed using the Resonant Column Method to obtain 
both the shear modulus and the material damping for a clay and the fiber-clay composite 
to determine the effect of fiber inclusion on the dynamic properties of clayey soil. The 
research showed that the inclusion of fiber at optimum fiber content as a ground 
improvement technique can improve the dynamic properties of soft clayey soils at low 
shear strain. Test results indicated that both the shear modulus and damping increased. 
Hence, the inclusion of fiber in clay can provide a double benefit for the dynamic 
response of a site by increasing the stiffness of the site and reducing its amplitude of 
vibration. General formulas for shear modulus and damping were developed as functions 
of the shear strain amplitude for the clay and for fiber reinforced clay. 
The effect of fiber inclusion on the seismic site response using two different 
earthquake motions was also studied. One-dimensional wave propagation analysis was 
performed to investigate the effect of the modification of the clay dynamic properties 
using fibrillated fiber reinforcements on the site response. The results indicated that by 
modifying the clayey soil using fiber, the seismic site response can be improved. 
 
 
 
 
 
 
 
 
 
 
IMPROVEMENT OF DYNAMIC PROPERTIES AND SEISMIC RESPONSE OF 
CLAY USING FIBER REINFORCEMENT 
 
By 
Behzad Amir Faryar 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the 
University of Maryland in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2012 
 
Advisory Committee: 
 
Professor M. Sherif Aggour, Chair 
Professor Amde M. Amde 
Associate Professor Peter C. Chang 
Associate Professor Dimitrios G. Goulias 
Professor Sung Lee 
 
         
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Behzad Amir Faryar 
2012 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ii 
 
Dedication 
 
To my:  
 Mother, Mrs. Mahsa Hariri 
 Father, Mr. M. Reza Amir-Faryar 
 Brother, Mr. Farzad Amir Faryar, P.E. 
 Late Grandfather, Mr. Jafar Hariri 
 Late Grandfather, Mr. Reza Amirfaryar 
 Late Grandmother, Mrs. Sedigheh Zendehrokh 
 Late Grandmother, Mrs. Ashraf Tassouji 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
iii 
 
Acknowledgements 
 
It looked so far-fetched one day! 
The author wishes to express his thanks to the following people who helped him 
achieve his research?s mammoth tasks and get to this very page of his dissertation and his 
life: 
- The chairman of his doctoral committee, Professor M. Sherif Aggour, for his 
continued guidance, generosity, and constant support, and for the time he 
generously shared with the author. His objective and invaluable criticism of the 
manuscript was of great assistance in the preparation of this dissertation. It has 
been an extreme pleasure learning from and working with him.  
- Member of his doctoral committee, Professors Amde M. Amde, Peter C. Chang, 
Dimitrios G. Goulias, and Sung Lee, for accepting to be part of his dissertation 
committee. 
- The Civil and Environmental Engineering Department of the University of 
Maryland for allowing me to use the facilities in the Geotechnical Laboratory. 
- The technical personnel at the Civil and Environmental Engineering Laboratory, 
University of Maryland, especially Mr. Alfred Bituin, for assisting in connecting 
water and air pipes to the test apparatus and providing assistance during the 
experimental stage of the work. 
- Colleague, Mr. Robert S. Woodke, professor at Northern Virginia Community 
College (NVCC), who helped machine laboratory pieces required for testing. 
 
iv 
 
- Colleague, Dr. Donald R. Goral, professor in Department of Mathematics of 
NVCC, who provided valuable suggestions about nonlinear curve fitting. 
- Colleagues at Professional Service Industries, Inc. (PSI), Mr. Daniel P. 
O?Connell, P.E., G.E., Mr. James Kline, P.G., Mr. Karl E. Suter, P.E., Mr. 
Richard E. Finnen, Jr., P.E., Mr. Dana K. Eddy, P.E., and Dr. James Meng, P.E. 
for our general discussions, their suggestions, proof-reading, and editing this 
manuscript. 
- Ex-colleague, Mr. Ross Cutts with Maryland State Highway Administration 
(SHA) for his suggestions about the analytical approach of the research. 
- Colleagues and friends in the Department of Civil and Environmental Engineering 
at the University of Maryland, Dr. Bora Cetin, Ms. Sadaf Khosravifar, and Mr. 
Kareem Ali (visiting scholar) for performing some of the compaction tests. 
The author wishes to express his deepest gratitude to his family, especially his 
mother, Mrs. Mahsa Hariri whom he is greatly indebted to, for her unconditional support 
and encouragement throughout his entire education. 
The author wishes to express his appreciation to his brother Mr. Farzad Amir Faryar, 
P.E. and good friends Mr. Arash Aghvami, P.E. with SK&A, Mr. M. Hossein Alikhani, 
P.E., Mr. Gholamreza Fahimi, Mr. Karim Jafarqomi, USPTO Examiner Mr. M. Ray 
Sedighian, Mr. Saeed Fallah Balani, P.E. with ECS-Mid Atlantic, and Mr. David Sadri 
for their constructive feedback in preparing the dissertation. 
I am very grateful to Mrs. Aggour for her help with final manuscript. 
 
v 
 
And above all his thanks goes to the Lord of the Universe without whose help this 
work could not have been accomplished. 
 Behzad Amir Faryar, P.E. - Fall 2012 
A. James Clark School of Engineering, 
University of Maryland, College Park 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
vi 
 
 
TABLE OF CONTENTS 
List of Figures ..................................................................................................................... x 
List of Tables ................................................................................................................... xvi 
Chapter 1 Research Background & Literature Review............................................... ??1 
1.1 Introduction?????????????????????????...1 
1.2 Methods Used in the Determination of Shear Modulus and Damping???..3 
1.3  Laboratory Methods??????????????????????..5 
1.3.1 Cyclic Triaxial Test??????????????????????...6 
1.3.2 Cyclic Direct Simple Shear Test?????????????????...8 
1.3.3 Cyclic Torsional Shear Test???????????????????10 
1.3.4 Piezoelectric Bender Element Test????????????????..11 
1.3.5 Resonant Column Test?????????????????????.14 
1.3.6 Shake Table Test???????????????????????.19 
1.3.7 Ultrasonic Wave Propagation Test????????????????..21 
1.4 Field Methods????????????????????????..22 
1.4.1 Geophysical Tests???????????????????????24 
1.4.2 Surface Vibrator Test?????????????????????...26 
1.4.3 Plate Bearing Tests??????????????????????..27 
1.5 Cohesive Soils????????????????????????.27 
1.5.1 Introduction?????????????????????????.27 
1.5.2 Clay Mineralogy???????????????????????..28 
1.6 Expansive Soils????????????????????????30 
1.7 Lime Stabilization???????????????????????35 
1.7.1 Mechanism of Lime-Soil Chemical Reactions????????????36 
1.7.1.1 Short Term/Immediate Reactions?????????????????36 
1.7.1.2 Long Term Reactions?????????????????????..38 
1.7.2 Soil-Lime Mixture Design???????????????????...39 
1.8 Fiber Reinforcement??????????????????????42 
1.8.1 Discrete Geofibers??????????????????????...44 
 
vii 
 
1.8.2 Description of Geofibers????????????????????.47 
1.8.3 Geotechnical and Dynamic Properties of Clayey Soils Stabilized with 
Polypropylene Fibers?????????????????????????.47 
1.8.4 Mechanism of Fiber Reinforced Clayey Soil (Geofiber Composite)???..49 
1.8.5 Fiber Geometry????????????????????????50 
1.8.6 Fiber Orientation???????????????????????..52 
1.8.7 Fiber Material Properties????????????????????.53 
1.9 Dynamic Properties of Soil???????????????????..56 
1.9.1 Dynamic Properties of Cohesive Soils???????????????58 
1.9.2 Shear Modulus and Damping Equations??????????????.64 
1.9.2.1 Hardin and Drnevich Design Equations??????????????..64 
1.9.2.2 Modified Hyperbolic Model???????????????????66 
1.9.2.3 Ramberg-Osgood Model????????????????????.67 
1.9.2.4 Borden Equation???????????????????????..67 
1.9.2.5 Modified Masing Behavior for Damping Ratio???????????..68 
 
Chapter 2 Test Equipment ................................................................................................ 72 
2.1 Introduction?????????????????????????.72 
2.2 The Drnevich Resonant Column Apparatus and Attached Equipment??...72 
2.3 Calibration of the Test Equipment????????????????...82 
2.3.1 Resonant Column Apparatus Calibration??????????????83 
2.3.2 Acceleration Transducers and Charge Amplifiers??????????...85 
2.3.3 Linear Variable Differential Transformer (LVDT) and LVDT Readout??87 
2.4 Coupling between Soil Specimen and Top Platen??????????...88 
2.5 Resonant Column Data Reduction Calculations???????????.88 
2.5.1 Calculation of Shear Modulus??????????????????.89 
2.5.2 Calculation of Damping Ratio??????????????????.91 
2.5.3 Calculation of Shear Strain???????????????????..92 
 
Chapter 3 Determination of Optimum Fiber Content ....................................................... 93 
3.1 Current State of the Research??????????????????..93 
3.2 Density and Compaction????????????????????.98 
 
viii 
 
3.2.1 Soil and Fiber Materials????????????????????..98 
3.2.2 Sample Preparation and Compaction Criteria???????????...101 
3.2.3 Compaction Data and Discussion????????????????..104 
3.2.4 Conclusion?????????????????????????.111 
 
Chapter 4 Dynamic Testing Program and Results .......................................................... 113 
4.1 Introduction????????????????????????...113 
4.2 Testing Apparatus??????????????????????..114 
4.3 Low-Amplitude Moduli of Fiber Reinforced Clay??????????116 
4.4 Sample Preparation??????????????????????116 
4.5 Dynamic Testing Procedure??????????????????..122 
4.5 Dynamic Testing Results for Fibrillated Fiber Reinforced Clay????...124 
4.5.1 Effect of Fibrillated Fiber Inclusion and Fiber Content on Shear Modulus of 
Clay ?????????????????????????????...124 
4.5.2 Effect of Fibrillated Fiber Inclusion and Fiber Content on Damping Ratio of 
Clay ?????????????????????????????...126 
4.6 Dynamic Testing Results for Monofilament Fiber Reinforced Clay???128 
4.6.1 Effect of Monofilament Fiber Inclusion and Fiber Content on Shear Modulus 
of Clay ?????????????????????????????...128 
4.6.1 Effect of Monofilament Fiber Inclusion and Fiber Content on Damping Ratio 
of Clay ?????????????????????????????...130 
4.7 Effect of Fiber Types on the Dynamic Properties of Clay???????132 
4.8 Comparison of the Dynamic Response of Clay with Published Data??...134 
4.9 Repeatability????????????????????????..135 
4.10 Mathematical Modeling of Empirical Data????????????...137 
4.10.1 Non-linear Least Square Method????????????????...138 
4.10.2 Normalized Shear Modulus Equations??????????????..142 
4.10.3 General Material Damping Formula for Soils???????????...146 
4.11 Damping Formula Evaluation Using Verification Data????????150 
4.12 Conclusions????????????????????????...156 
 
Chapter 5 Effect of Fiber Reinforcement of Clay on Seismic Site Response ................ 158 
5.1 Seismic Response of Horizontally Layered Soil??????????...159 
 
ix 
 
5.1.1 Seismic Site Response Evaluation Procedure???????????...159 
5.1.2 Equivalent Linear Approach??????????????????..161 
5.1.3 Analysis using DEEPSOIL Software Program???????????.162 
5.2 Design Earthquake Parameters?????????????????..167 
5.2.1 Earthquake Motions?????????????????????...167 
5.3 Factors Affecting Ground Shake????????????????...169 
5.4 Materials Used in the Analysis?????????????????..170 
5.5 Dynamic Properties of Clay and Fiber Modified Clay Used in the Analysis170 
5.6 Effect of Fiber Reinforcement on Dynamic Response of a Clayey Site?...172 
5.6.1 Seismic Site Response of 60 feet Column of Soil??????????.173 
5.6.2 Analysis for 60 feet Column of Soil???????????????..180 
5.7 Effect of Depth to Bedrock on Seismic Response of Clayey Sites???...183 
5.7.1 Seismic Site Response of 20 feet Column of Soil??????????.184 
5.7.2 Analysis for 20 feet Column of Soil???????????????..190 
5.8 Effect of Thickness of Fiber Improvement on Seismic Site Response of   
Clayey Sites????????????????????????????.194 
5.9 Effect of Fiber Improvement on Natural Period of Clayey Site?????208 
5.10 Conclusions????????????????????????...215 
 
Chapter 6 Summary, Conclusions, and Recommendations for Further Research .......... 216 
6.1 Summary?????????????????????????...216 
6.2 Conclusions????????????????????????...217 
6.3 Recommendations??????????????????????.219 
6.3.1 Recommendations for Further Research?????????????...219 
6.3.2 Recommendations for Modifying the Equipment??????????.219 
 
References ....................................................................................................................... 221 
 
 
 
x 
 
LIST OF FIGURES 
 
 
Figure 1-1: Stress?strain relationship in cyclic loading (Shannon & Wilson, 1972) ......... 4 
Figure 1-2: shear strain amplitude capacities of laboratory apparatus (Woods, 1978) ...... 6 
Figure 1-3: Piezoelectric bender elements.  Positive and negative voltage charges cause 
the element to bend (Kramer, 1996) ................................................................................. 12 
Figure 1-4: Specimen in the resonant column apparatus without the confining chamber 
(Kim & Stokoe, 1992)....................................................................................................... 15 
Figure 1-5: Schematic illustration of the free-free resonant column device  
(Stokoe, et al., 1994) ......................................................................................................... 17 
Figure 1-6: Schematic configuration for the new free-free resonant column device 
(Kalinski & Thummaluru, 2005) ...................................................................................... 18 
Figure 1-7: Shake table test set up (Wilson & Associates, 1972) ..................................... 19 
Figure 1-8: Response curve under forced vibration (Hoadley, 1985) .............................. 23 
Figure 1-9: Geophysical test setup (Shannon & Wilson, 1972) ....................................... 24 
Figure 1-10: Parallel arrangements of natural clay particles (Carmeuse Technical 
Training, 2002) ................................................................................................................. 37 
Figure 1-11: Edge to face contacts of lime-treated clay particles (Carmeuse Technical 
Training, 2002) ................................................................................................................. 37 
Figure 1-12: Shear stress versus shear strain cyclic graph ............................................... 57 
Figure 1-13: Effect of PI on normalized shear modulus (a) and damping (b)  
versus cyclic shear strain curves of clay (Vucetic & Dorby, 1991) .................................. 60 
Figure 1-14: Effect of varying frequency content on the shear modulus of Clay  
(Aggour, et al., 1987) ........................................................................................................ 62 
Figure 1-15: Effect of varying frequency content on damping ratio of clay  
(Aggour, et al., 1987) ........................................................................................................ 63 
Figure 1-16: Darendeli?s shifted damping curve (Darendeli, 2001) ................................. 70 
Figure 2-1: Drnevich Resonant Column Apparatus .......................................................... 73 
Figure 2-2: Torsional Coils set up .................................................................................... 75 
Figure 2-3: Voltage test set up .......................................................................................... 77 
Figure 2-4: Set up of the resonant column attached devices ............................................ 79 
Figure 2-5: Wiring diagram for control box ..................................................................... 80 
Figure 2-6: Schematic diagram of the resonant column testing system  (Red lines are 
input lines; Green lines are output lines) .......................................................................... 81 
Figure 2-7: Digital pressure gauge and water separator ................................................... 82 
Figure 2-8: Approximate cross section of RC apparatus showing the calibration rod in 
blue .................................................................................................................................... 84 
Figure 2-9 Set-up diagram for calibration of transducer and charge amplifier ................ 86 
Figure 3-1: Schematic graph of density of matrix versus fiber volume fraction .............. 95 
Figure 3-2: Schematic graph of soil composition ............................................................. 96 
Figure 3-3: Schematic graph of fiber reinforced soil composition ................................... 97 
Figure 3-4: Polypropylene fibers used in the experiments. a) Fibrillated fiber b) 
Monofilament fiber ......................................................................................................... 100 
Figure 3-5: Mixing using mechanical mixer ................................................................... 102 
 
xi 
 
Figure 3-6: Mixture of kaolinite soil and fibrillated fibers (FC = 0.6%) ........................ 103 
Figure 3-7: Compacted soil-fiber composite being extruded from the standard mold ... 104 
Figure 3-8: Compaction curves for composites of kaolinite soil and monofilament  
fibers with various fiber contents (fiber length = 0.75 in) .............................................. 105 
Figure 3-9: Compaction curves for composites of kaolinite soil and monofilament  
fibers with various fiber contents (fiber length = 0.5 in) ................................................ 106 
Figure 3-10: Compaction curves for composites of kaolinite soil and fibrillated fibers 
with various fiber contents (fiber length = 0.75 in) ........................................................ 106 
Figure 3-11: Compaction curves for composites of kaolinite soil and fibrillated fibers 
with various fiber contents (fiber length = 0.5 in) .......................................................... 107 
Figure 3-12: Change in ?d max with various fiber contents (fiber length = 0.75 in) ......... 108 
Figure 3-13: Change in ?d max with various fiber contents (fiber length = 0.5 in) ........... 108 
Figure 3-14: Change in OMC with various fiber contents (fiber length = 0.75 in) ........ 109 
Figure 3-15: Change in OMC with various fiber contents (fiber length = 0.5 in) .......... 109 
Figure 3-16: Change in MDD with various fiber lengths and types ............................... 110 
Figure 4-1: Hollow brass cylinder with clay sample inside ............................................ 117 
Figure 4-2: Hollow brass cylinder pushed into the compacted soil ................................ 118 
Figure 4-3: Filled cylinder .............................................................................................. 119 
Figure 4-4: Soil specimen held inside a lidded jar .......................................................... 120 
Figure 4-5: Membrane wrapped around soil specimen. Two o?rings can be seen in the 
picture ............................................................................................................................. 121 
Figure 4-6: Observed Lissajous figure on oscilloscope .................................................. 123 
Figure 4-7: Maximum shear modulus versus fiber content graph (fibrillated fiber) ...... 125 
Figure 4-8: Normalized shear modulus versus shear strain graph for different fiber 
contents (Fibrillated fiber) .............................................................................................. 126 
Figure 4-9: Minimum damping ratio versus fiber content graph (fibrillated fiber) ........ 127 
Figure 4-10: Damping versus shear strain graph for different fiber contents (fibrillated 
fiber) ................................................................................................................................ 128 
Figure 4-11: Maximum shear modulus versus fiber content graph (monofilament fiber)
 ......................................................................................................................................... 129 
Figure 4-12: Normalized shear modulus versus shear strain graph for different fiber 
contents (monofilament fiber)......................................................................................... 130 
Figure 4-13: Minimum damping ratio versus fiber content graph (monofilament fiber) 131 
Figure 4-14: Damping versus shear strain graph for different fiber contents 
(monofilament fiber) ....................................................................................................... 132 
Figure 4-15: Normalized shear modulus versus shear strain comparison graph ............ 134 
Figure 4-16: Damping versus shear strain comparison graph ........................................ 135 
Figure 4-17: Normalized shear modulus versus shear strain series of data .................... 136 
Figure 4-18: Damping ratio versus shear strain series of data ........................................ 136 
Figure 4-19: Modeling of damping ratio as function of shear strain .............................. 137 
Figure 4-20: Schematic sketch showing the curve fitting approach ............................... 141 
Figure 4-21: Graph of shear modulus versus shear strain for clay and fiber-reinforced 
clay (FC = 0.2% & 0.4%) ............................................................................................... 143 
Figure 4-22: Graph of measured G/Gmax versus predicted G/Gmax for clay  
(FC = 0.0%) .................................................................................................................... 144 
 
xii 
 
Figure 4-23: Graph of measured G/Gmax versus predicted G/Gmax for  
fiber-reinforced clay (FC = 0.2%) .................................................................................. 145 
Figure 4-24: Graph of measured G/Gmax versus predicted G/Gmax for  
fiber-reinforced clay (FC = 0.4%) .................................................................................. 145 
Figure 4-25: Graph of damping ratio versus shear strain for clay and fiber-reinforced  
clay (FC = 0.2%) ............................................................................................................. 148 
Figure 4-26: Graph of measured damping ratio versus predicted damping ratio for clay 
(FC = 0.0%) .................................................................................................................... 149 
Figure 4-27: Graph of measured damping ratio versus predicted damping ratio for  
fiber-reinforced clay (FC = 0.2%) .................................................................................. 149 
Figure 4-28: Graph of normalized shear modulus versus shear strain for sand, after  
Seed and Idriss 1991 ....................................................................................................... 152 
Figure 4-29: Graph of damping ratio versus shear strain for sand, after Seed and Idriss 
1991................................................................................................................................. 152 
Figure 4-30: Graph of measured damping ratio versus predicted damping ratio for  
lower limit sand, after Seed and Idriss, 1991 .................................................................. 153 
Figure 4-31: Graph of measured damping ratio versus predicted damping ratio for  
mean limit sand, after Seed and Idriss, 1991 .................................................................. 154 
Figure 4-32: Graph of measured damping ratio versus predicted damping ratio for  
upper limit sand, after Seed and Idriss, 1991 .................................................................. 154 
Figure 4-33: Graph of measured damping ratio versus predicted damping ratio for  
clay, after Vucetic and Dorby 1991 ................................................................................ 155 
Figure 5-1: Schematic figure showing the upward propagation of a shear wave from 
bedrock ............................................................................................................................ 159 
Figure 5-2: Input graphical interface of DEEPSOIL software ....................................... 163 
Figure 5-3: Graph of Imperial Valley motion and Parkfield acceleration versus time  
are shown on the left and right, respectively. ................................................................. 169 
Figure 5-4: Normalized shear modulus versus shear strain for clay and fiber-clay 
composite with FC = 0.2% ............................................................................................. 171 
Figure 5-5: Damping ratio versus shear strain for clay and fiber-clay composite with  
FC = 0.2% ....................................................................................................................... 172 
Figure 5-6: Site profile sketch - soil column = 60 ft ....................................................... 173 
Figure 5-7: Acceleration versus time graph for all-clay condition, 60 ft column of soil, 
Imperial Valley motion (case 1) ..................................................................................... 174 
Figure 5-8: Amplitude ratio versus frequency graph for all-clay condition, 60 ft column 
of soil, Imperial Valley motion (case 1) ......................................................................... 174 
Figure 5-9: Response spectra versus period graph for all-clay condition, 60 ft column of 
soil, Imperial Valley motion (case 1) .............................................................................. 175 
Figure 5-10: Acceleration versus time graph for all-clay condition, 60 ft column of soil, 
Parkfield motion (case 1) ................................................................................................ 175 
Figure 5-11: Amplitude ratio versus frequency graph for all-clay condition, 60 ft  
column of soil, Parkfield motion (case 1) ....................................................................... 176 
Figure 5-12: Response spectra versus period graph for all-clay condition, 60 ft  
column of soil, Parkfield motion (case 1) ....................................................................... 176 
Figure 5-13: Acceleration versus time graph, 60 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft (case 2) ............................................. 177 
 
xiii 
 
Figure 5-14: Amplitude ratio versus frequency graph, 60 ft column of soil, Imperial 
Valley motion, thickness of fiber modified layer is 10 ft (case 2) .................................. 177 
Figure 5-15: Response spectra versus period graph, 60 ft column of soil,  
Imperial Valley motion, thickness of fiber modified layer is 10 ft (case 2) ................... 178 
Figure 5-16: Acceleration versus time graph, 60 ft column of soil, Parkfield motion, 
thickness of fiber modified layer is 10 ft (case 2) ........................................................... 178 
Figure 5-17: Amplitude ratio versus frequency graph, 60 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft (case 2) ............................................. 179 
Figure 5-18: Response spectra versus period graph, 60 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft (case 2) ............................................. 179 
Figure 5-19: Maximum PGA comparison graph, 60 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 180 
Figure 5-20: Amplitude ratio comparison graph, 60 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 180 
Figure 5-21: Maximum PSA comparison graph, 60 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 181 
Figure 5-22: Maximum PGA comparison graph, 60 ft column of soil, Parkfield motion
 ......................................................................................................................................... 181 
Figure 5-23: Amplitude ratio comparison graph, 60 ft column of soil, Parkfield motion
 ......................................................................................................................................... 182 
Figure 5-24: Maximum PSA comparison graph, 60 ft column of soil, Parkfield motion
 ......................................................................................................................................... 182 
Figure 5-25: Site profile sketch- soil column = 20 ft ...................................................... 184 
Figure 5-26: Acceleration versus time graph for all-clay condition, 20 ft column of  
soil, Imperial Valley motion ........................................................................................... 185 
Figure 5-27: Amplitude ratio versus frequency graph for all-clay condition, 20 ft  
column of soil, Imperial Valley motion .......................................................................... 185 
Figure 5-28: Response spectra versus period graph for all-clay condition, 20 ft  
column of soil, Imperial Valley motion .......................................................................... 186 
Figure 5-29: Acceleration versus time graph for all-clay condition, 20 ft column of  
soil, Parkfield motion ...................................................................................................... 186 
Figure 5-30: Amplitude ratio versus frequency graph for all-clay condition, 20 ft  
column of soil, Parkfield motion .................................................................................... 187 
Figure 5-31: Response spectra versus frequency graph for all-clay condition, 20 ft 
column of soil, Parkfield motion .................................................................................... 187 
Figure 5-32: Acceleration versus time graph, 20 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft ........................................................... 188 
Figure 5-33: Amplitude ratio versus frequency graph, 20 ft column of soil, Imperial 
Valley motion, thickness of fiber modified layer is 10 ft ............................................... 188 
Figure 5-34: Response spectra versus period graph, 20 ft column of soil,  
Imperial Valley motion, thickness of fiber modified layer is 10 ft ................................. 189 
Figure 5-35: Acceleration versus time graph, 20 ft column of soil, Parkfield motion, 
thickness of fiber modified layer is 10 ft ........................................................................ 189 
Figure 5-36: Amplitude ratio versus frequency graph, 20 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft ........................................................... 190 
 
xiv 
 
Figure 5-37: Response spectra versus period graph, 20 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft ........................................................... 190 
Figure 5-38: Maximum PGA comparison graph, 20 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 191 
Figure 5-39: Amplitude ratio comparison graph, 20 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 191 
Figure 5-40: Maximum PSA comparison graph, 20 ft column of soil, Imperial Valley 
motion ............................................................................................................................. 192 
Figure 5-41: Maximum PGA comparison graph, 20 ft column of soil, Parkfield motion
 ......................................................................................................................................... 192 
Figure 5-42: Amplitude Ratio comparison graph, 20 ft column of soil, Parkfield motion
 ......................................................................................................................................... 193 
Figure 5-43: Maximum PSA comparison graph, 20 ft column of soil, Parkfield motion
 ......................................................................................................................................... 193 
Figure 5-44: Site profile sketch, soil column = 20 ft (fiber improvement increment  
is 5 feet)........................................................................................................................... 195 
Figure 5-45: Acceleration versus time graph for case 2 (5 feet of fiber improvement) 
, 20 ft column of soil, Imperial Valley motion ............................................................... 196 
Figure 5-46: Amplitude ratio versus frequency graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion ......................................... 196 
Figure 5-47: Response spectra versus period graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion ......................................... 197 
Figure 5-48: Acceleration versus time graph for case 2 (5 feet of fiber improvement) 
, 20 ft column of soil, Parkfield motion .......................................................................... 197 
Figure 5-49: Amplitude ratio versus frequency graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion ................................................... 198 
Figure 5-50: Response spectra versus Period graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion ................................................... 198 
Figure 5-51: Acceleration versus time graph for case 4 (15 feet of fiber improvement) 
, 20 ft column of soil, Imperial Valley motion ............................................................... 199 
Figure 5-52: Amplitude ratio versus frequency graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion ......................................... 199 
Figure 5-53: Response spectra versus period graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion ......................................... 200 
Figure 5-54: Acceleration versus time graph for case 4 (15 feet of fiber improvement) 
, 20 ft column of soil, Parkfield motion .......................................................................... 200 
Figure 5-55: Amplitude ratio versus frequency graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion ................................................... 201 
Figure 5-56: Response spectra versus period graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion ................................................... 201 
Figure 5-57: Acceleration versus time graph for case 5 (all fiber modified), 20 ft  
column of soil, Imperial Valley motion .......................................................................... 202 
Figure 5-58: Amplitude ratio versus frequency graph for case 5 (all fiber modified) 
, 20 ft column of soil, Imperial Valley motion ............................................................... 202 
Figure 5-59: Response spectra versus period graph for case 5 (all fiber modified) 
, 20 ft column of soil, Imperial Valley motion ............................................................... 203 
 
xv 
 
Figure 5-60: Acceleration versus time graph for case 5 (all fiber modified), 20 ft  
column of soil, Parkfield motion .................................................................................... 203 
Figure 5-61: Amplitude ratio versus frequency graph for case 5 (all fiber modified),  
20 ft column of soil, Parkfield motion ............................................................................ 204 
Figure 5-62: Response spectra versus period graph for case 5 (all fiber modified),  
20 ft column of soil, Parkfield motion ............................................................................ 204 
Figure 5-63: Peak ground acceleration change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Imperial Valley motion .................................. 205 
Figure 5-64: Amplitude ratio change versus thickness of soil improvement graph  
for all cases, 20 ft column of soil, Imperial Valley motion ............................................ 205 
Figure 5-65: Maximum response spectra change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Imperial Valley motion .................................. 206 
Figure 5-66: Peak ground acceleration change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Parkfield motion ............................................. 206 
Figure 5-67: Amplitude ratio change versus thickness of soil improvement graph  
for all cases, 20 ft column of soil, Parkfield motion ....................................................... 207 
Figure 5-68: Maximum response spectra change versus thickness of soil  
improvement graph for all cases, 20 ft column of soil, Parkfield motion ...................... 207 
Figure 5-69: Natural period versus depth to bedrock for 20 ft and 60 ft columns  
of soil. Blue bar: fiber modified condition (thickness of improvement = 10 ft),  
red bar: all-clay condition ............................................................................................... 210 
Figure 5-70: Natural frequency versus depth to bedrock for 20 ft and 60 ft columns  
of soil. Blue bar: fiber modified condition (thickness of improvement = 10 ft),  
red bar: all-clay condition ............................................................................................... 210 
Figure 5-71: Natural period change versus depth to bedrock for 20 ft and 60 ft  
columns of soil ................................................................................................................ 211 
Figure 5-72: Natural frequency change versus depth to bedrock for 20 ft and 60 ft 
columns of soil ................................................................................................................ 211 
Figure 5-73: Site natural frequency versus thickness of fiber reinforced layer for  
20 ft soil column ............................................................................................................. 212 
Figure 5-74: Natural period versus thickness of fiber reinforced layer for 20 ft soil 
column............................................................................................................................. 213 
Figure 5-75: Site natural frequency change versus thickness of fiber reinforced  
layer for 20 ft soil column ............................................................................................... 213 
Figure 5-76: Natural period change versus thickness of fiber reinforced layer for  
20 ft soil column ............................................................................................................. 214 
 
  
 
xvi 
 
LIST OF TABLES 
 
Table 1-1: Advantages and disadvantages of laboratory and field testing methods 
(Tawfiq, 1986) .................................................................................................................... 5 
Table 1-2: Diagram and properties of clay minerals (Gromoko, 1974) ........................... 30 
Table 1-3: Typical activity values for three clay minerals (Bowles, 1979) ...................... 33 
Table 1-4: Degree of expansion classification of clayey soils based on swell potential 
(Seed, Woodward, & Lundgren, 1962) ............................................................................. 34 
Table 1-5: Equations for predicting swell potential of clayey soils using plasticity  
index (Seed, et al., 1962) .................................................................................................. 34 
Table 1-6: Properties of fibers commonly used in civil engineering materials  
(Hannant, 1978) ................................................................................................................ 46 
Table 1-7: Advantages of using commercially available short virgin PP fiber 
reinforcements in clayey soils ........................................................................................... 49 
Table 1-8: Typical fiber material properties, after (Hoover, 1982) .................................. 55 
Table 2-1: Electronic equipment used with the resonant column apparatus .................... 78 
Table 3-1: Chemical properties of Kaolinite Soil ............................................................. 99 
Table 3-2: Properties of polypropylene fibers ................................................................ 101 
Table 3-3: Composition of mixtures ............................................................................... 103 
Table 3-4: Compaction test result for various fiber contents .......................................... 107 
Table 4-1: Upper, mean, and lower limits data, after Seed and Idriss, 1991 .................. 151 
Table 5-1: Earthquake motions data used in the analysis (Hashash, et al., 2011) .......... 168 
Table 5-2: Properties of materials ................................................................................... 170 
Table 5-3: The results of site response analyses for all-clay and fiber modified  
conditions (60 ft column) ................................................................................................ 183 
Table 5-4: The results of site response analyses for 20 ft soil column ........................... 194 
Table 5-5: The results of site response analyses to investigate the effect of thickness  
of soil improvement ........................................................................................................ 208 
Table 5-6: The results of natural frequency and natural period for all-clay and fiber 
modified conditions ........................................................................................................ 212 
Table 5-7: The results of site response analyses for all-clay and fiber modified  
conditions ........................................................................................................................ 214 
 
 
 
1 
 
CHAPTER 1  
RESEARCH BACKGROUND & LITERATURE REVIEW 
1.1 Introduction 
In recent years, earthquakes have caused heavy damages to buildings and 
infrastructure. One of the causes of heavy damages due to earthquake motions are the 
role of soft clay in amplifying bedrock ground motions. Modifying the soil conditions of 
sites in order to mitigate earthquake damages can be one of the methods of enhancing site 
conditions and its effects on seismic site response.  
Every once in a while a revolutionary idea or method comes along that changes 
everything. The idea of using reinforcement steel in concrete is one of those ideas. It 
changed the entire construction industry. Nowadays, barely any concrete structure is 
constructed without using reinforced steel in the concrete. The idea of using fiber as 
reinforcement for clayey soil follows a similar idea to reinforced steel-concrete. The 
inclusion of randomly distributed short virgin polypropylene fibers (C3H6) in clay has 
proven to significantly improve geotechnical properties of clay such as shear, 
compressive, tensile strength, and so on. These improvements have triggered great 
attention on the possibility of mixing fibers with clay to from a desirable composite.  
In Chapter one, a brief overview of dynamic field and laboratory test equipment, 
clayey soils and different modification techniques, descriptions and properties of 
geofibers, dynamic properties of cohesive soils, and shear modulus and damping ratio 
equations are presented.  
 
2 
 
A general overview of the dynamic test equipment used in this study along with 
calibration of the test equipment and resonant column data reduction calculations are 
described in Chapter Two. The preliminary work and testing involved in determining the 
right mix design for fiber-clay composite is discussed in Chapter Three.  In that chapter, a 
new compaction procedure was developed for finding the optimum fiber content (OFC) 
and its compaction test data. The recommended mix design was used to prepare soil and 
composite specimens in Chapter Four?s dynamic test program.  
Dynamic experimental testing was performed using the Resonant Column Method 
to obtain the shear modulus and material damping ratio for clay and fiber-clay 
composites to investigate the dynamic effect of fiber inclusion in clayey soil. The results 
of the dynamic experimental testing are shown in the Chapter Four. The research 
presented in Chapter Four has been performed for four main purposes: (1) investigate the 
effect of fiber inclusion on the dynamic properties of clay; (2) study the effect of fiber 
content on the dynamic properties of the composite; (3) further investigate the effect of 
type of fibers on the dynamic properties of clay; (4) determine an analytical relationship 
between shear modulus and shear strain and also between material damping and shear 
strain of the composite; and (5) develop a general formula correlating material damping 
to shear strain of soil. The developed formula in Chapter Four can be applied to all soil 
types and fiber-reinforced soil composites. 
The effect of fiber inclusion on the seismic site response using two different 
earthquake motions was also presented in Chapter Five. One dimensional wave 
propagation analysis was performed using DEEPSOIL software (Hashash, et al., 2011) to 
investigate the effect of modification of clay using fibrillated fiber reinforcements on the 
 
3 
 
site response. Two different material types, clay and fibrillated fiber reinforced clay, were 
used for different soil columns. The research presented in Chapter Five was performed to 
study the following: (1) investigate the effect of modification of clay using fibrillated 
fiber reinforcements on the site response; (2) study the effect of depth to bedrock on the 
site response of the fiber reinforced site; (3) investigate the effect of the thickness of the 
soil reinforced layer; and (4) study the effect of different earthquake motions on the site 
response. 
A summary of the study and conclusions along with recommendations for further 
research was summarized in Chapter Six. 
1.2 Methods Used in the Determination of Shear Modulus and Damping 
 With recent advances in the analytical and testing methods, the behavior of soils 
subjected to various types of dynamic loading; such as, earthquakes, ocean waves, 
machine vibrations, and blasts, are being better understood. The measurement of dynamic 
soil properties is a vital task in the solution of geotechnical earthquake engineering 
problems. Any analysis of dynamic engineering problems requires the determination of 
the shear modulus and damping ratio. These two parameters are usually determined using 
laboratory or field methods. The selection of testing methods for measurement of 
dynamic soil properties requires thorough consideration and understanding of the specific 
problem at hand. 
The shear modulus (G) and damping ratio (D) are the two variable properties in 
the dynamic response analysis of soils. They are the reason that soils are not considered a 
linear-elastic material. The shear modulus, and damping of soils are strain dependent. 
 
4 
 
 The vibratory motion of shear waves can cause shear strains on a soil element. 
The stress-strain curve forms a closed loop, called hysteresis loop, as shown below.  
 
Figure 1-1: Stress?strain relationship in cyclic loading (Shannon & Wilson, 1972) 
Shear modulus and damping can be directly obtained from Figure 1-1. The damping ratio 
increases with increasing strains while the shear modulus decreases. The shear modulus 
and damping can be obtained both in the laboratory and field. Each technique has an 
associated strain range in which the test is conducted. A summary of the laboratory and 
field tests for soil dynamics, along with the advantages and disadvantages of the testing 
methods are tabulated in Table 1-1 (Tawfiq, 1986). 
 
Shear 
Stress 
Shear
 Strain 
1 
G2.?2 
?2 
Shear 
Stress 
Shear 
Strain 
?1 
1 
G1.?1 
 
5 
 
Table 1-1: Advantages and disadvantages of laboratory and field testing methods 
(Tawfiq, 1986) 
Laboratory Techniques Field Techniques 
1 ? Cyclic Triaxial 1 ? In-Hole Methods 
2 ? Cyclic Simple Shear - Cross Hole 
3 ? Cyclic Torsional Shear - Down Hole 
4 ? Resonant Column - Up Hole 
5 ? Ultrasonic 2 ? Surface Wave Methods 
6 ? Shaking Table  
  
Advantages Advantages 
1 ? Better control of boundary conditions 1 ? Measure large masses 
2 ? Evaluate different parameters of soil 
behavior 
2 ? Less soil disturbance 
3 ? Provide wide ranges of strain 
amplitudes 
3 ? Measurements under actual field 
conditions 
4 ? Evaluate damping characteristics  
  
Disadvantages Disadvantages 
1 ? Sample disturbance 1 ? Low strain amplitude 
2 ? In general, the advantages and 
disadvantages of laboratory testing 
methods depend on the minimum criteria 
for obtaining adequate values of soil 
behavior 
2 ? Damping characteristics cannot be 
measured 
 
A comprehensive review of laboratory and field techniques and procedures to obtain 
dynamic soil properties are given by Woods, 1978; Hoadley, 1985; Kramer ,1996; 
Towhata, 2008. 
1.3  Laboratory Methods 
 Laboratory tests are typically performed on relatively small soil specimens that 
are assumed to be representative of a larger body of soil. The ability of laboratory tests to 
provide accurate rather than precise measurements of soil properties depends on their 
ability to simulate the initial conditions and loading conditions of the problem of interest 
 
6 
 
on a smaller scale. The proficiency of the laboratory technician also factors into the 
results.   
Laboratory tests provide an opportunity to determine the dynamic properties of soils 
under dynamic loading for a wide range of strain levels. Figure 1-2 shows the strain 
levels induced in soils under different loading conditions and the strain amplitude 
capacities of each laboratory testing procedure.
 110
 -1
 10
 -2
 10
 -3
 10
 -4
 110101010
 -1-2-3-4
 Close-in
 nuclear
 explosion
 Strong ground shaking
 from earthquake
 Properly designed
 machine foundation
 Shearing strain amplitude (%)
 Resonant Column (Hollow samples)
 Torsional Shear (Hollow samples)
 Typical Motion Characteristics
 Shake Table
 Cyclic Simple Shear
 Cyclic Triaxial
 Resonant Column (Solid samples)
 Pulse Methods 
 
Figure 1-2: shear strain amplitude capacities of laboratory apparatus (Woods, 1978) 
1.3.1 Cyclic Triaxial Test 
 The cyclic triaxial test has been the most regularly used experiment for the 
measurement of dynamic properties of soil at high strain levels. In a triaxial test, a 
cylindrical soil sample is situated between top and bottom loading platens and surrounded 
by a relatively thin rubber membrane. The soil specimen is subjected to a radial stress and 
 
7 
 
an axial stress, which are pneumatically applied. The difference between the radial and 
axial stresses is called the deviator stress. The deviator stress, in cyclic triaxial testing, is 
applied cyclically (Kramer, 1996). Since soil characteristics are governed by effective 
stresses, all methods of testing soils at high strain levels must be capable of controlling 
the porewater pressure of the specimen and also the porewater drainage from the soil 
sample to determine volume change and porewater pressures in the soil sample.  
 There has been extensive research conducted on dynamic properties of clay using 
cyclic triaxial testing. Moreover, the use of lime as a stabilizer in clayey soils has been 
studied and dynamic properties of lime stabilized clay are determined (Fahoum, 1994). 
 To determine the shear modulus and damping ratio in this method, the sample is 
first consolidated under a confining and all-around pressure, ?3, and subsequently a 
vertical predetermined cyclic stress (stress controlled) or strain (strain controlled) is 
applied. A typical axial stress-strain curve (hysteresis loop) from a triaxial test is obtained 
from a special data acquisition device. From such a loop the elastic modulus, E, is 
calculated by having the slope of the straight line connecting the two extreme points of 
the hysteresis loop. 
  (1.1)  
where: ??a = ?dp; a: maximum axial strain. 
The shear modulus can also be calculated using:  
  (1.2)  
 
8 
 
where: G: shear modulus; ?: Poisson?s ratio. 
The damping ratio can be determined from the hysteresis stress-strain graph using: 
  (1.3)  
where: D: damping ratio. 
This equation shows how much energy is dissipated in each cycle of loading. Shear strain 
can also be measured by: 
  (1.4)  
where: ?s: shear strain. 
To determine shear stress, ?, the following equation can be used: 
 
 
(1.5)  
1.3.2 Cyclic Direct Simple Shear Test 
The cyclic direct simple shear test is more accurate in terms of reproducing 
earthquake stress conditions compared to the cyclic triaxial test. In this test, a short, 
prismatic soil sample is kept under restriction against lateral expansion by a rigid 
boundary platen. The test soil sample is deformed when cyclic horizontal shear stresses 
are applied to the top or bottom of the soil sample (Kramer, 1996). 
The drawback of the cyclic direct simple shear test is that shear stresses are only 
applied on the top and bottom surfaces of the specimen. It creates nonuniformity of 
stresses on the vertical side. The effects of nonuniformity of stresses are intensified by 
 
9 
 
decreasing the diameter/height ratio of the soil sample (Kramer, 1996). These effects are 
small at diameter/height ratios greater than about 8:1 (Kovacs & Leo, 1981). 
The shear modulus is calculated directly from a shear stress vs. shear strain 
diagram. The equation used to calculate the shear modulus is given by: 
  (1.6)  
where: G: shear modulus (the slope of the line connecting the two extreme end points of 
the hysteresis loop); ?max: maximum shear stress; ?max: maximum shear strain. 
The damping ratio is also directly calculated from the stress-strain diagram using the 
same equation in the cyclic triaxial test. It also can be determined using the free vibration 
method. In this method, the soil sample is subjected to a predetermined strain in the 
horizontal direction then released to vibrate freely. The displacement decay is then 
measured with time by a linear variable differential transformer (LVDT) to determine the 
damping using: 
 
 
(1.7)  
where: ? f: percent of critical damping in free vibration; Xn: the ordinate of the nth cycle 
Xn+1: the ordinate of the nth+1 cycle. 
The shear modulus is determined using the theory of transverse vibration of shear beams 
by: 
  (1.8)  
 
10 
 
where: H: height of soil block; g: gravity acceleration; T: period of free vibration;  
?: unit weight of soil. 
1.3.3 Cyclic Torsional Shear Test 
 By loading cylindrical soil samples in torsion, many problems associated with the 
cyclic triaxial and cyclic direct simple shear tests can be resolved. Both isotropic and 
anisotropic initial stress conditions are allowed using the cyclic torsional shear test. This 
test is mostly used to determine stiffness and damping characteristics over a wide range 
of strain levels. This test has two methods of forced and free vibration (Kramer, 1996).  
 Solid or hollow samples can be used in the forced vibration method. Solid 
samples have the drawback of nonuniform shear strains (being zero at the center and 
maximum at the edges). Therefore, hollow cylinders are introduced to resolve this 
problem (Kramer, 1996). 
 In the free vibrating method, a solid cylindrical soil sample is initially twisted at 
one free end and then released to vibrate freely. A relatively heavy weight is placed on 
the free end of the soil sample making a one degree of freedom system, with the stiffness 
given by the soil and the inertia offered by the weight (Kramer, 1996). The resulting 
frequency and shear modulus of the soil sample is then determined using the following 
equation for a single degree of freedom system (Shannon & Wilson, 1972). 
  (1.9)  
 
 
(1.10)  
 
11 
 
 
 
(1.11)  
where: K: constant characteristic dependent upon the geometry of the system; Wn: the 
natural frequency of either the apparatus (i) or the entire system (n); D: the critical 
damping ratio of either the apparatus (i) or the entire system (n). 
The damping ratio of soil is measured the same way it was measured in the large scale 
free vibration simple shear test. The cyclic torsional shear test has almost the same 
limitations as the cyclic triaxial test due to their similar configurations. 
1.3.4 Piezoelectric Bender Element Test 
This type of test allows measurement of shear wave velocity on laboratory 
specimens using piezoelectric bender elements (Shirley & Anderson, 1975); (Dyvik & 
Madshus, 1985); and (De Alba & Pyke, 1987). Bender elements are made by bonding 
two piezoelectric materials together in such a way that a voltage applied to their faces 
causes one to expand while the other contracts forcing the entire element to bend as 
shown in Figure 1-3 (Kramer, 1996). In the same way, a lateral disturbance of the bender 
element will generate a voltage, so the bender elements can be used as both s-wave 
transmitters and receivers (Kramer, 1996). 
 
12 
 
Direction of elements tip and
    soil particle movement
 Zero Voltage
 - Voltage
 + Voltage
 Bearing Plate
 Direction of
 shear wave
 propagation
  
Figure 1-3: Piezoelectric bender elements.  
Positive and negative voltage charges cause the element to bend (Kramer, 1996) 
 In most setups, the bender elements are installed in opposite ends of a soil 
specimen. A voltage pulse is applied to the transmitter element, which causes it to 
generate an S-wave (Kramer, 1996). The transmitter element shakes at high frequencies 
in the horizontal direction and generates s-wave propagation from one end towards the 
other end of a soil sample where it is picked up by the receiver element (Towhata, 2008). 
When the S-wave arrives at the other end of the specimen, distortion of the receiver 
element generates another voltage pulse. The time difference between the two voltage 
pulses is measured with an oscilloscope and divided into the distance between the tips of 
the bender elements (tip to tip/end to end distance) to give the s-wave velocity of the 
specimen (Kramer, 1996).   
 
 
(1.12)  
The piezoelectric bender elements test can be performed in conjunction with 
running other tests on a specimen at the same time. It has been run with conventional and 
cubical triaxial devices, direct simple shear devices, oedometers, model tests (Arulnathan, 
 
13 
 
et al., 2000), and resonant column tests. The benefit of using it with a high voltage type 
of testing is that it can provide a value for maximum shear modulus (Gmax) of soil 
specimens. It is also used with a low voltage type of testing, i.e., resonant column testing 
(RC) to increase the accuracy of test results. The operator can compare the Gmax obtained 
from RC with the one obtained from bender elements. 
Shear wave velocity is measured in triaxial specimens using piezoceramic bender 
elements (Bates, 1989); (Brignoli, et al., 1996); (Blewett, et al., 2000); (Pennington, et 
al., 2001); (Greening & Nash, 2004); (Leong, at al., 2005). Small strain stiffness, Gmax, of 
soil specimens is determined in resonant column (Dyvik & Madshus, 1985), oedometer 
(Dyvik & Madshus, 1985); (Kawaguchi, et al., 2001), and direct simple shear (Dyvik & 
Madshus, 1985) apparatuses using piezoelectric bender elements. Finally, a bender 
element device is used in a triaxial cell material to calculate the damping ratio (Karl, et 
al., 2008).  
To date, the bender element test has yet to be standardized. This is due to the fact 
that differences arise with respect to method of interpretation (Viana da Fonseca, et al., 
2008) and some uncertainties; such as, not being clear whether the travel distance is the 
distance between two ends of the specimen, the distance between tips of bender elements, 
etc. Furthermore, the time traveled is supposed to be the time difference between 
transmitted wave and arrived wave. The arrived wave cannot be clearly defined to be the 
arrival of initial shaking or the arrival of the wave peak (Towhata, 2008). This 
uncertainty is due to the fact that the wave field is not one-dimensional but is subjected to 
a more complex near-field effect (Brignoli, et al., 1996). 
 
14 
 
1.3.5 Resonant Column Test 
The resonant column test is the most frequently used laboratory soil test for 
measuring low strain properties 10-6 to10-4 (10-4 % to10-2 %). The method of resonant 
column testing was first developed by K. Iida in 1939s. It has become well accepted 
worldwide since the 1950s. In the beginning, Ishimoto and Iida (1936, 1937) established 
both a theory and a device for resonant column tests, in which the loading frequency was 
used to determine the elastic properties of soils. During that time period, they were not 
able to apply confining pressure to consolidate the specimen; thus, soil samples with fines 
and moisture that could maintain shape without pressure application, were put into 
testing. Afterward, Iida (1938) performed tests on dry sand, which was supported by 
cellophane sheets (Towhata, 2008). The test is used to indirectly measure the shear 
modulus or elastic modulus and damping of soils based on the theory of wave 
propagation in prismatic rods by Richart el al. 1970 (Woods, 1978). It can be run on both 
solid and hollow specimens. 
Resonant column testing has been gaining popularity in soil dynamics laboratory 
studies since it was first used by Japanese engineers. It is modified based on the needs of 
different research purposes. There are two methods, a Fixed-Free and a Free-Free method 
to determine dynamic properties of soil. 
Vincent P. Drnevich patented the most commonly used fixed free resonant 
column apparatus on December 9, 19751. As shown in Figure 1-4, the apparatus is used 
                                                 
1 United States Patent, Patent#: 3,924,451, Inventor: Vincent P. Drnevich, Resonant Column Testing 
Apparatus 
 
15 
 
for testing the behavior of a column of soil placed between a pair of platens within a 
pressurized chamber in which torsional or longitudinal vibrations can be applied. 
Coil
 Support
 System
 Drive Coil
 Counter
 Weight
 Drive
 Plate
 Accelerometer
 Fixed Base
 Top Cap
 Soil Specimen
 Harmonic
 Torsional
 Excitation
  
                       Figure 1-4: Specimen in the resonant column apparatus without the 
confining chamber (Kim & Stokoe, 1992) 
Harmonic loads are usually the most common loading system for which the frequency 
and amplitude are controlled. However, random loading (Al-Sanad, et al., 1983); (Al-
 Sanad & Aggour, 1984); (Amini, et al., 1988); (Aggour, et al., 1989) and impulse loading 
(Tawfiq, 1986); (Tawfiq, et al., 1988) have also been used as a loading system in 
resonant column devices. The effect of coupled loading on the dynamic properties of 
clayey (Tawfiq, 1986) and sandy (Aggour & Zhang, 2006) soils has also been examined. 
 A relatively new Non-Resonance method (NR) has been introduced to determine 
dynamic properties of soils at low strains over a broad range of frequencies (Rix & Meng, 
2005). The NR method can be implemented using conventional resonant column or 
torsional shear apparatus. The advantage of the NR method is that continuous 
 
16 
 
measurements can be taken over a broader input frequency range. Frequency dependent 
behavior of the soil dynamic properties was studied using the method (Meng, 2007). 
In the conventional method, the elastic or shear modulus, depending on the 
vibration directions, can be indirectly calculated in terms of the resonant frequency.  
Shear modulus can be calculated in terms of specimen dimensions and testing apparatus 
condition using the following equation: 
 
 
(1.13)  
where: G: shear modulus; ?: mass density of soil specimen; L: height of specimen 
F: dimensionless frequency2; fr: resonant frequency of the system. 
Damping is determined by switching off the driving power at resonance and recording 
the decaying vibration from which the logarithmic decrement is calculated using the 
following equation: 
 
 
(1.14)  
where: ?s: logarithmic decrement (damping); A1: initial value of amplitude; An + 1: 
amplitude after  oscillations. 
Damping ratio is also calculated using following equation: 
 
 
(1.15)  
where: ?A: logarithmic decrement of the apparatus without specimen; S: system energy 
ratio; D: damping ratio; ?s: logarithmic decrement (damping). 
                                                 
2 It is dependent on the apparatus used in the experiment. 
 
17 
 
Another type of testing for measurements of Gmax and Dmin is called the free-free 
resonant column method, which was developed by Stokoe et al. in 1994. Using the free-
 free configuration, the soil specimen is oriented horizontally inside a latex membrane 
with end caps as shown in Figure 1-5. 
 
                     Figure 1-5: Schematic illustration of the free-free resonant column device 
(Stokoe, et al., 1994) 
The traditional free-free device was limited to a maximum attainable vacuum pressure of 
around 80 kPa. This was due to the fact that the test had not been configured in a 
pressurized cell. Therefore, a new free-free device was developed to allow measurements 
in a pressurized cell with confining pressures greater than 80 kPa that are more 
representative of in situ conditions. Figure 1-6 shows the schematic configuration for a 
new free-free device (Kalinski & Thummaluru, 2005). 
 
18 
 
 
Figure 1-6: Schematic configuration for the new free-free resonant column device (Kalinski & 
Thummaluru, 2005) 
 There have been researches conducted on natural clayey soils (Hardcastle & 
Sharma, 1998); (Hoyos, et al., 2008); (Kallioglou, et al., 2008) and synthetic clay 
(Tawfiq, et al., 1988); (Chepkoit, 1999); (Amir-Faryar & Aggour, 2012b) using the fixed-
 free resonant column apparatus. In addition, Bentonite3 has been blended with the soils to 
create samples with higher plasticity index (PI) for experimental investigation (Inci, et 
al., 2003). 
                                                 
3 Bentonite is an absorbent aluminum phyllosilicate, generally impure clay made up of mostly 
Montmorillonite.  
 
19 
 
1.3.6 Shake Table Test 
This technique uses large size material samples benefiting the free vibration 
method. 1-G Shaking table research has provided helpful insight into liquefaction, post-
 earthquake settlement, foundation response, and lateral earth pressure problems (Kramer, 
1996). The current version of shaking tables uses multiple degrees of freedom compared 
to old single-degree-of-freedom4 devices.  
Forcing Motion
 Table (moving)
 SOIL BED
 3' to 10'
 3" to 12"
 Unrestrained
 motion
 1' to 
10'
  
Figure 1-7: Shake table test set up (Wilson & Associates, 1972) 
Figure 1-7 shows a typical shake table set up. 
The benefit of 1-G shaking table testing comparing to a centrifugal model is that 
preparation of a model is easier due to its practically larger size. It also has a lower 
maintenance cost (Towhata, 2008). For a bigger size device like a shaking table, soils can 
be simply placed, compacted, and instrumented. In addition shaking table models can be 
viewed without difficulty from different perspectives during tests (Kramer, 1996). 
                                                 
4 Horizontal translation 
 
20 
 
On the contrary, high gravitational stresses cannot be generated in a 1-G shaking 
table test. (Kramer, 1996). It also cannot replicate the field stress level and accordingly 
the stress-strain behavior of tested soil under low-effective stress (Towhata, 2008). Thus, 
correction procedures have been developed to modify shaking table test results (Hettler & 
Gudehus, 1985); (Iai, 1989). 
Different materials including clayey (Kovacs, et al., 1971) and sandy (Seed, et al., 
1977) soils have been tested using this method. The procedure in which shear modulus 
and damping ratio of soils are determined involved firstly exciting the base of the soil 
specimen and then measuring the vibration response when the excitation is stopped. 
Afterwards, the frequency of the first mode is measured and the shear modulus is 
obtained using the following formula: 
 
 
 
(1.16)  
where: ?: shear strain (%); H: thickness of soil sample; f: frequency of oscillation (1st 
mode); g: gravity acceleration. 
? is calculated as the soil being vibrated in the steady state condition prior to stopping the 
excitation. By measuring the frequency of oscillation (f) and acceleration (a) of the steady 
state vibration, ? can be obtained using the following equation: 
  (1.17)  
The damping ratio is computed using a similar approach to that using free vibration 
excitation. 
 
21 
 
1.3.7 Ultrasonic Wave Propagation Test 
 In the laboratory, wave propagation velocities can be measured by means of an 
ultrasonic pulse test (Lawrence, 1963); (Naccy & Taylor, 1967). An ultrasonic pulse of 
either compression or shear waves can be produced and received by a piezoelectric5 
material (Hoadley, 1985). By measuring the travel time of the waves over a known 
distance, the wave velocity and shear modulus can be calculated. This technique has also 
been used to determine Young?s modulus and shear modulus of silty clay (Stephenson, 
1978). It has also been used for the ultrasonic assessment of highly plastic clay stabilized 
with lime, cement, and lime-fly ash class F mixtures (Yesiller, et al., 2001). 
 A relationship between the wave amplitude of the compression and shear waves 
and the speed of propagation can be measured as:  
  (1.18)  
  (1.19)  
 
 
(1.20)  
 
 
(1.21)  
where: Vc: compression wave velocity; Vs: shear wave velocity; ?: Poisson?s ratio; E: 
Young?s modulus; : logarithmic decrement (damping); G: shear modulus; ?: mass 
density; A0: initial value of amplitude; An: amplitude after  oscillations. 
                                                 
5 some materials, notably crystals and certain ceramics, that can generate an electric field (Holler & Skoog, 
2006) 
 
22 
 
 
 Not being able to identify and interpret the exact wave arrival time is one of the 
major weaknesses of this technique (Woods, 1978). This method is only suitable for low 
amplitude vibrations such as vehicular traffic vibrations because of its low range of strain 
amplitudes over which the test is conducted. The damping ratio is difficult to determine 
from this test because of difficulties in obtaining the arrival times of reflecting waves. 
1.4 Field Methods 
 Field techniques are used in the determination of dynamic soil properties and 
depend mainly on either the measurements of wave velocities (shear or compression), or 
on the response of soil structure systems (Woods, 1978). There are two types of waves 
that can propagate through soils, body and surface waves. Body waves are made up of 
compression waves (P waves) and shear waves (S waves), while the surface waves 
consist of Raleigh waves (R waves) and Love waves (L waves) (Hoadley, 1985). 
 Damping measurements are not very reliable if performed in the field. This is due 
to the fact that the field techniques involve small strain amplitudes. Therefore, the 
damping values are more reliable if they are obtained from lab experiments. Damping 
values can be theoretically obtained in the field by observing the decay of the wave 
motion amplitude with distance from an energy source using the following equation 
(Shannon & Wilson, 1972): 
 
 
(1.22)  
where A1 and A2 are the vibration amplitudes at successive peaks of the decay curve. 
Figure 1-8 shows a typical displacement-frequency curve.  
 
23 
 
 
Figure 1-8: Response curve under forced vibration (Hoadley, 1985) 
By using such a curve, it is possible to calculate damping by the following equation: 
 
 
(1.23)  
where: ?f: width of response curve at an amplitude equal to ; Amax: maximum 
amplitude; fr: resonant frequency. 
Equation 1.23 is valid when a constant force oscillator is used. Therefore, the values 
obtained from this method cannot be directly applied to soil problems induced by a strong 
earthquake motion. This is due to the much larger shear strain associated with 
earthquakes (Hoadley, 1985). A brief summary of the popular field methods used to 
determine dynamic soil properties is described in the following sections. 
 
24 
 
1.4.1 Geophysical Tests 
 In-hole geophysical testing is a widely used technique among the various field 
methods. It depends on the measurements of the arrival of shear waves generated by a 
small explosion or a hammer and collected by one or more geophones6. As shown in 
Figure 1-9, three configurations of the test procedure can be set up based on the 
placement of energy source and geophones (Hoadley, 1985). 
 
Figure 1-9: Geophysical test setup (Shannon & Wilson, 1972) 
Seismic cross-hole tests use two or more boreholes to determine wave propagation 
velocities at an equivalent depth. The simplest cross-hole test consists of two boreholes, 
one of which contains an energy source and the other a receiver (Kramer, 1996). To 
measure the average shear velocity in the up-hole technique, the energy source is placed 
in the hole while the geophone is placed at the ground surface, contrary to the down-hole 
technique, where the energy source is placed at the ground surface and the geophone is 
placed in the hole (Hoadley, 1985). 
                                                 
6 A Geophone is a device that converts ground movement (displacement) into voltage, which may be 
recorded at a recording station. 
 
25 
 
 In all the geophysical tests, the shear wave velocity is measured in the field, from 
which the shear modulus is calculated using the following equation: 
  (1.24)  
where: G: shear modulus; ?: mass density; Vs: shear wave velocity. 
It is also possible to measure the compression wave velocity of soil using these 
geophysical methods. The elastic modulus is obtained in terms of compression wave 
velocity by using the following equation: 
  (1.25)  
where: E: elastic modulus; Vc: compression wave velocity; ?: Poisson?s ratio. 
 One major difficulty of the geophysical technique is filtering the slower shear 
waves from the compression waves. This problem can be resolved by reversing the 
polarity of the energy source in the down-hole technique (Shannon & Wilson, 1972). 
Another difficulty arises when water table is present. Presence of water table affects the 
speed of the compression wave, unlike shear waves. Therefore, it is preferable to utilize 
the shear wave velocity measurements to determine the corresponding shear modulus 
values. 
Another drawback is the low strain amplitude ranges through which these 
techniques are utilized. Some different techniques can be utilized to increase the strain 
amplitude range, such as loading the soil cyclically with an in-hole (up-hole technique) 
anchor connected by a heavy pipe to a large surface vibrator. Difficulties in equipment 
design and other factors made the technique unfeasible (Wilson, et al., 1978). 
 
26 
 
 A cylindrical in situ test (CIST) is another technique used to measure field soil 
dynamic properties. The CIST involves deploying accelerometers in the field spaced out 
at various depths and distances from a central borehole in which explosives are placed. 
The explosive charge generates a very high pressure causing failure in close proximity to 
the central borehole and large shear strains at a greater distance from the central borehole. 
Particle velocity-time records are gained from the accelerometers. Following data 
retrieval, an iterative one or two dimensional finite difference analysis, which requires 
initial material properties assumptions, is performed. Adjustments to the initial model are 
made to regenerate the particle-time velocity histories over a range of dynamic strain 
levels for each layer of soil (Hoadley, 1985). 
 One more technique that involves using many boreholes is known as the in situ 
impulse test. This test is very similar to the cross-hole test except in the generation of 
controlled shear waves and the spacing of the boreholes. Smaller shear strains are 
obtained by increasing the distance between the energy source and the boreholes. One of 
the drawbacks of this procedure is the extra cost involved in drilling more boreholes and 
placing sophisticated in-hole recording equipment (Hoadley, 1985). 
1.4.2 Surface Vibrator Test 
 In this method, a mechanical or electromagnetic oscillator is used to generate 
steady-state Raleigh waves. The Raleigh wave velocity can be computed using the 
following equation: 
  (1.26)  
where: VR: Raleigh wave velocity; ?R: Raleigh wavelength; f: frequency. 
 
27 
 
It is assumed that, at low strains, Raleigh wave velocity is approximately equal to 
the shear wave velocity (Richart, 1960). Therefore, the shear modulus can be directly 
measured from the Raleigh wave velocity. About one half of the wavelength is an 
estimate for the effective depth of a Raleigh wave. This introduces a major limitation that 
deep exploration would require large power generating equipment operating at a low 
frequency (Hoadley, 1985). 
1.4.3 Plate Bearing Tests 
 The modulus of soil can be either directly measured from the stress-strain curve 
generated by applying a slow repeated load (Static load test) or by measuring the resonant 
frequency of a small vibrator placed on the soil in situ (Dynamic load test). Major 
drawbacks are associated with these two techniques such as the lack of confinement, the 
modulus being dependent on the size of the plate, and the fact that measurements are 
limited to the near surface soil (Hoadley, 1985). 
1.5 Cohesive Soils 
1.5.1 Introduction 
 Clay is known to be a material whose properties puzzled engineers for centuries. 
There is hardly any type of soil that is likely to cause more exasperating problems in 
connection with engineering projects than clay (Terzaghi, 1928). Engineers are frequently 
required to build a structure on, through, or with clay materials. Therefore, the nature of 
clay particles and engineering properties of this type of soil needs to be investigated. 
Clay is a rock term, and like most rocks it consists of a number of different 
minerals in varying portions. In soil mechanics, Clay also carries the implication of very 
 
28 
 
small particle size. Usually the term clay is used in accordance with what is called fine-
 grained material in soil mechanics. Clay shows plastic behavior when mixed with a small 
amount of water (Klein & Hurlbut Jr., 1985). 
1.5.2 Clay Mineralogy 
 Clays have been shown to be made up of mainly a group of crystalline 
constituents known as the clay minerals. They are all fundamentally hydrous aluminum 
silicates. In some clay minerals, magnesium (Mg) or iron (Fe) substitute in part for 
aluminum (Al) and alkalis7 may exist as essential constituents. Although clay may consist 
of a single clay mineral, there are typically several clay minerals mixed with other 
minerals such as feldspar, quartz, carbonates, and micas (Klein & Hurlbut Jr., 1985). 
Montmorillonite, illite, and kaolinite are the most frequently encountered soils in the field 
(Eades & Grim, 1960). 
Kaolinite (Al2Si2O5 (OH)4) is a two layered mineral that is a combination of a 
silicate sheet with a gibbsite8 sheet. This two layer arrangement can be repeated many 
times and the repeated layers are held together by hydrogen bonding9 and a secondary 
valence force10 (Das, 1983). Kaolinite is a common mineral, the main constituent of 
kaolin or clay. It is always a secondary mineral formed by hydrothermal alteration or 
weathering of aluminum silicates, specifically feldspar. In rocks that are undergoing 
alteration, it can be found mixed with feldspar. Kaolinite is one of the common and 
                                                 
7 Alkaline earths 
 
8 Al(OH)3, is one mineral form of aluminum hydroxide. 
 
9 Hydrogen bond is an attractive interaction of a hydrogen atom with an electronegative atom, such as: 
nitrogen, oxygen or fluorine. The hydrogen must be covalently bonded with another electronegative atom 
to create the bond (Jeffrey, 1997). 
 
10 Valence force fields are used to describe intra-molecular interactions. 
 
29 
 
extensive products of the decomposition of rocks found in soils. It has been transported 
by water and accumulated in lakes in the form of beds of clay deposits. The kaolinite 
mineral can be found mixed with quartz and other materials (Klein & Hurlbut Jr., 1985). 
Illite is a broad term for the mica-like clay minerals (Klein & Hurlbut Jr., 1985). It 
is a three layer sheet mineral that is made up of an octahedral sheet in the middle and 
silica sheet on the top and the bottom. The sheets are connected together by potassium 
ions (Das, 1983). The illites differ from the micas in having less substitution of Al for 
silicon (Si), and in having potassium (K) partly replaced by calcium (Ca) and Mg (having 
less potassium than well-crystallized micas (Gaudette, et al., 1964)). Illite is the main 
constituent in many types of shale (Klein & Hurlbut Jr., 1985).  
Montmorillonite is the main constituent of clay mineral in bentonite. It can be 
formed from altered volcanic ash. Bentonite has the rare property of expanding several 
times its original volume when wetted (Klein & Hurlbut Jr., 1985). Montmorillonite is 
the clay mineral that is known for most expansive soil problems. Structurally, it is the 
same as the illite mineral except that the bonding between the sheets is provided by water 
layers (Das, 1983). 
Talc (Mg3Si4O10(OH)2) is a secondary mineral shaped by the alteration of 
magnesium silicates, such as pyroxenes, olivine, and amphiboles, and may be found as 
pseudomorphs11 after these minerals. It can be seen in massive form, soapstone, or as a 
prominent constituent in schistose rocks (Klein & Hurlbut Jr., 1985).  
                                                 
11 A mineral or mineral compound that appears in an atypical crystal form, resulting from a substitution 
process in which the appearance and dimensions remain constant, but the original mineral is replaced by 
another. The name literally means "false form". 
 
30 
 
The specific surface of the clay mineral is expressed as being the surface area of 
clay particles per unit mass. Table 1-2 shows the symbolic structures of the mentioned 
clay minerals together with their properties.  
Table 1-2: Diagram and properties of clay minerals (Gromoko, 1974) 
 
From Table 1-2, it can be seen that Montmorillonite minerals have the largest specific 
surface values (600 ? 800 m2/gram) and the largest percentage of swelling. 
1.6 Expansive Soils 
 Clayey soils generally experience a volumetric change associated with the change 
in their water content. An increase or decrease in the water content respectively can cause 
heave or shrinkage in clayey soils. The magnitude of such volumetric change depends 
mainly on the clay mineral present in the soils. Three primary clay minerals are identified 
 
31 
 
to exist in most clayey soils. These minerals are illite, montmorillonite, and kaolinite 
(Das, 1983). 
 In engineering practice, soils are considered expansive if they meet all four of the 
following provisions. The tests to show compliance with items 1, 2, and 3 are not 
required if the test prescribed in item 4 is conducted (IBC, 2006). 
1- Plasticity index (PI) of 15 or greater, determined in accordance with ASTM D 
4318. 
2- More than 10 percent of the soil particles pass a No. 200 sieve (75?m), 
determined in accordance with ASTM D 422. 
3- More than 10 percent of the soil particles are less than 5 micrometers in size, 
determined in accordance with ASTM D 422. 
4- Expansion index greater than 20, determined in accordance with ASTM D 4829. 
 Expansive soils occur in different parts of the world. The countries in which 
expansive soils have been reported are as follows: Argentina, Australia, Burma, Canada, 
Cuba, Ethiopia, Ghana, India, Iran, Mexico, Morocco, Rhodesia, South Africa, Spain, 
Turkey, USA, and Venezuela (Chen, 1988). Expansive soils can cause more damage to 
structures, especially light buildings and pavements, than any other natural hazard, 
including earthquakes and floods. In the United States, expansive soils instigate more 
damage than earthquakes, tornadoes, hurricanes, and floods combined (Jones & Holtz, 
1973). The annual costs of these damages are approximated to be about $ 7 billion (Wray 
& Meyer, 2004); excluding Hurricane Katrina that hit in year 2005 and cost $ 25 billion 
alone. 
 
32 
 
 Expansive soils originate from two parent material sources. These two groups are 
soils derived from basic igneous rocks and also soils derived from sedimentary rocks. 
They are derived from the sedimentary rock parent material that contains montmorillonite 
as a constituent. These soils are found in North America (Donaldson, 1969). 
 Clay particles carry a negative charge at their face. In order to balance this 
negative charge in their porewater, they attract positively charged ions from salt (Das, 
1983). Some minerals are attracted more than others and cation exchange takes place 
from left to right as follows: 
Al3+>Ca2+>Mg2+>NH4+>K+>H+>NA+>Li+ 
Two types of water concerning clay minerals exist. The first is the double water layer 
which is electrically attracted and encloses the clay particle. The second one is the 
adsorbed water which is very close and robustly connected to the clay particle. The 
double layer of water brings about the plasticity of clay. The thickness of this double 
layer is different from mineral to mineral, thus, the plasticity of each minerals is different. 
Plasticity is also dependent on the nature and the amount of clay minerals (Bowles, 
1979). 
 The activity of clay is a proposed term used to differentiate clay minerals in terms 
of their swelling potential. Activity is associated with the plasticity index and clay 
percentage that exists in certain soils as in the following equation: 
 
 
(1.27)  
where: A: activity; PI: plasticity index; C: percent of clay size fraction (< 2mm). 
 
33 
 
Typical values of A, for the three clay minerals mentioned above, are given Table 1-3 
(Bowles, 1979): 
Table 1-3: Typical activity values for three clay minerals (Bowles, 1979) 
 Kaolinite 
Illite 
Montmorillonite 
0.4 ? 0.5 
0.5 ? 1.0 
1.0 ? 7.0 
 
Swelling of expansive soils is found to be related to the existence of active clay 
minerals, such as montmorillonite, and the increase in the natural water content (Das, 
1983). Swell potential is defined as the percentage of swell of a laterally confined soil 
specimen, which has been soaked under 1 psi surcharge after being compacted according 
to the AASHTO compaction test (Warner & Brown, 1974). After conducting many tests 
on compacted clay, the following general formula is suggested for predicting swell 
potential (Seed, at al., 1962): 
  (1.28)  
where: S: swell potential; A: activity; C: clay percentage by weight. 
Based on this equation, the following classification is presented for the degree of 
expansion of clayey soils: 
 
 
 
34 
 
 
 
Table 1-4: Degree of expansion classification of clayey soils based on swell potential 
(Seed, Woodward, & Lundgren, 1962) 
 Degree of expansion Swell Potential (S)  
 Low 0.0 ? 1.5  
 Medium 1.5 ? 5.0  
 High 5.0 ? 25.0  
 Very high > 25.0  
The previous equation is further simplified to incorporate plasticity index: 
Table 1-5: Equations for predicting swell potential of clayey soils using plasticity index 
(Seed, et al., 1962) 
19 < C <70 S = 3.6 x 10-3 (PI) 2.44 Error within 20 % S  
40 < C <80 S = 2.16 x 10-3 (PI) 2.44 Error within 30 % S  
There are many other similar equations in the literature to determine the swell potential of 
clay. Swell potential can also be obtained in the laboratory by the following tests 
(Gromoko, 1974): 
1- Free swell index: In this test, the volume change of soils is obtained after they are 
submerged underwater. 
2- Atterberg limits: Liquid limit, plastic limit, plasticity index, and shrinkage limit 
are all determined. Then, swell potentials are calculated using correlations such as 
the one mentioned above. 
3- Colloid content: In this test, percentages of soils having fractions of less than 1-2 
? in diameter are measured. These percentages are deemed to contribute the most 
to soils expansion. 
 
35 
 
4- Consolidation: This procedure depends on the comparison between two samples 
under swell and pressure. One is allowed to swell under a load while the other is 
consolidated under pressure. The void ratio against the logarithm of pressure plot 
is then determined for both samples.  
The Transportation Research Board (TRB) gave a full study of the evaluation and control 
of expansive soils in 1985. 
1.7 Lime Stabilization 
 Lime is an additive used for soil stabilization and improving soil physical and 
mechanical properties such as minimizing swelling, reducing soil plasticity, and 
increasing workability. Lime stabilization has been used since the beginning of clearly 
recorded history and is still being used (McDowell, 1959). The Appian Way12 is believed 
to be the first Roman road to feature the use of lime (Winterkorn & Pamukcu, 1991). 
Lime was extensively utilized during the 2nd world war for roadway and runway 
construction (Bell, 1996). Examples of projects where lime has been used are the 
Dallas/Fort Worth Regional Airport in Dallas, TX constructed in 1973, and the Railroad 
Embankment in Chicago, IL built in 1976 (Boynton & Blacklock, 1986). 
 Various types of lime are available for the purpose of soil stabilization. The most 
common used types are hydrated high calcium lime (Ca (OH)2), monohydrated dolomitic 
lime Ca(OH)2.MgO, and calcitic quicklime CaO.MgO. Since most soils are made up of 
silica and aluminosilicates, the simple addition of lime and water provides the desired 
environment for the chemical composition and ultimately stabilization (Chepkoit, 1999). 
                                                 
12 Appian Way was one of the earliest and most important Roman roads. It connected Rome to Brindisi, 
and Apulia in Southwest of today?s Italy. 
 
36 
 
1.7.1 Mechanism of Lime-Soil Chemical Reactions 
 The chemical reactions between soil constituents and lime can be categorized into 
short term or immediate reactions and also long term reactions. 
1.7.1.1 Short Term/Immediate Reactions 
 When lime is combined in a clay-water system, the calcium cations with a valence 
of two (divalent) replace the cations of single valence (e.g., Na+, K+), which are typically 
adsorbed at the clay surface. The cations exchange because the addition of lime causes 
stabilization of the diffused water layer and a reduction in its size. The clay particles 
move more closely toward each other. Ultimately, attraction of broken bonds at the edge 
of the clay particles to the oppositely charged surfaces of neighboring clay particles takes 
place (Little, 1987). This immediate phase of reaction is termed ?lime modification? of 
soil (Hsay-Yang, 1990). The above reaction (cation exchange and 
flocculation13/agglomeration) takes place within 96 hours of commencement of reaction 
(Little, 1987). These two reactions tend to decrease the liquid limit and the plasticity 
index, increase the plastic limit, the shrinkage limit, and workability, and also improve 
the strength (Das, 1984). 
The effects of short term reactions on the particles are as follows (Little, 1987): 
1- Substantial decline and stabilization of the adsorbed water layer. 
2- Increased internal friction among the flocculates and greater aggregate shear 
strength provided by edge to face contact of the clay particles. 
                                                 
13 As defined by IUPAC (International Union of Pure & Applied Chemistry), flocculation is ?a process of 
contact and adhesion whereby the particles of dispersion form larger-size cluster?. Flocculation is 
synonymous with agglomeration and coagulation. 
 
37 
 
3- Textural change from plastic clay to friable, sand-like material that helps improve 
workability 
Figure 1-10 and 1-11 respectively show parallel arrangements of natural clay particles 
and edge to face contacts of lime-treated clay particles. 
 
Figure 1-10: Parallel arrangements of natural clay particles (Carmeuse Technical 
Training, 2002) 
 
Figure 1-11: Edge to face contacts of lime-treated clay particles (Carmeuse Technical 
Training, 2002) 
The degree of effect and the amount of lime required to cause cation exchange is 
based on the chemical and mineralogical state of the soil and the water environment 
(Little, 1987). 
 
38 
 
1.7.1.2 Long Term Reactions 
 The long term effect is broken down into two phases of Pozzolanic action (long 
term strength gain) and Carbonation. 
 Pozzolanic action is more complex reaction that increases the strength with time. 
It is greatly influenced by soil conditions and mineralogical properties. Clays mostly 
contain finely divided siliceous or aluminous materials, which in the presence of water 
and calcium will shape calcium-silicate-hydrates or calcium-aluminate-hydrates. The 
reactions are shown by the following chemical equations (Carmeuse Technical Training, 
2002): 
Ca++ + OH + Soluble clay silica ? Calcium Silicate Hydrate (CSH) 
Ca++ + OH + Soluble clay alumina ? Calcium Aluminate Hydrate (CAH) 
It is proposed that these two hydrates are the cemented products that contribute to the 
development of a cemented matrix among the soil particles (Little, 1987). Pozzolanic 
reaction is effective at a high PH condition, hence the soil-lime-water system should have 
a pH high enough (about 12.45) to facilitate this reaction. Lime is then used in two ways 
in this phase of the reaction (Carmeuse Technical Training, 2002): 
1- To induce high pH condition, which makes soluble or increases the solubility of 
the silica and alumina. 
2- To supply the residual free calcium, which combines with the silica and alumina 
provided by the clay. 
 
39 
 
In general, cementation is a time dependent reaction. Also, it depends on the soil type and 
amount of lime.  
 Carbonation is an undesirable reaction that takes place when the lime added to the 
soil does not react with the soil, but pulls out carbon-dioxide (CO2) from the air or soil to 
form insoluble calcium carbonate (CaCO3) (Thompson, 1969). Calcium carbonate is a 
plastic material that increases the plasticity of the soil and lime blends and prevents the 
pozzolanic reaction. This undesired situation is obtained when the soil does not contain 
an adequate amount of siliceous and aluminous material, and also when excess lime is 
used (Carmeuse Technical Training, 2002). 
1.7.2 Soil-Lime Mixture Design 
The major objective of the mixture design is to assign the quantity of lime 
required to produce an optimum quality mixture to attain the stabilization objectives and 
anticipated field conditions. The type of lime is an important factor in soil-lime mixture 
design. The US government authorities, despite finding a good result using quicklime, 
has discouraged utilizing it due to possible environmental problems associated with 
quicklime (Chepkoit, 1999).  
 Many researchers have used the lime addition of 2% to 8% by weight 
(Winterkorn & Pamukcu, 1991); (Fahoum, 1994); (Chepkoit, 1999); (He, et al., 2006), 
and also 1% to 7% by weight (Sakr, at al., 2009). It substantially reduces the plasticity 
index of clayey soil and also reduces its expansion potential (Fahoum, 1994). 
 
40 
 
 Many procedures are followed to evaluate the soil-lime mixture. They normally 
include Atterberg Limits tests, California Bearing Ratio test (CBR), R value test14, swell 
tests, unconfined compression, and triaxial testing. In the Atterberg Limits tests, the 
mixture of appropriate amounts of dry soils, lime, and water is generally left for about an 
hour before conducting the test (TRB, 1987). In the various strength tests, soil samples 
are typically compacted at optimum water content and prepared according to ASTM D-
 698 or ASTM D-1557. Afterwards, samples with the required size are extruded and 
wrapped to prevent any possible moisture loss and carbonation reaction. The soil samples 
are then cured. The period and temperature of curing varies considerably from one 
procedure to another. An elevated temperature of 48?C for 48 hours is usually considered 
to be equivalent to the occasionally used 30 day room temperature curing (Thompson, 
1969). Most of empirical tests to this date follow the same curing pattern of 48?C for 48 
hours (Fahoum, 1994); (He, et al., 2006) unless the effect of different curing temperatures 
is studied (Rao & Shivananda, 2005); (Sakr, et al., 2009).  
The addition of lime causes the following effects on soils properties: 
1- Compaction: The addition of lime decreases the maximum dry density and 
increases the optimum water content (Neubauer & Thompson, 1972).  
2- Plasticity and Workability: An immediate change in the Atterberg limits is related 
to the addition of lime and water. It is proven when the amount of colloidal clay 
and the chemo-physical activity of the soils are higher and is more likely to see a 
decrease in liquid limit of the soil (Brandl, 1981). This statement implies that 
                                                 
14 This test is used by Caltran (California Department of Transportation) for pavement design, replacing the 
California Bearing Ratio test. 
 
41 
 
montmorillonite clay, which is very active, would be affected the most and the 
changes in the Atterberg limits would be substantial. 
3- Volumetric Change: One of the measuring indices of swelling potential of 
cohesive soils is the plasticity index. Since this parameter considerably decreases 
with the addition of lime, it is safe to conclude that the swelling potential will also 
decrease (Fahoum, 1994). 
Many tests are conducted on various types of cohesive soils treated with lime and 
cured to 48 hours at 48?C. Consequently, the swelling is reduced to 0% - 0.1% as 
compared to the swelling values, before treatment, of 2.6% - 0.1% for the soils 
tested (Thompson, 1969). 
4- Strength: The strength of compacted samples is generally measured by different 
methods. The most widely used method is the unconfined compression test. Other 
methods include the undrained triaxial test, CBR, and R value. At first, an 
immediate increase in strength is noticed followed by much higher strength with 
time as a result of the pozzolanic reaction (Fahoum, 1994). 
Lime stabilization in the field can be accomplished in three ways (Fahoum, 1994): 
1- Mixing in with original or borrowed materials in the field and then compacting 
with the addition of water. 
2- Soil-lime mixture is attained at the plant and then compacted at the site. 
3- Pressure injecting lime slurry to a depth 2 ? 3.5 m at a spacing of 2 - 2.5 m. 
 
42 
 
A general study of lime-soil mixture with regard to reaction, strength, sample 
preparation, and methods of construction is given by the Transportation Research Board, 
State of the Art Reports, 1987.       
1.8 Fiber Reinforcement 
Use of fiber reinforcement in construction materials can be traced back to 
prehistoric times, when civilizations in Mesopotamia15 added straw to mud bricks (sun-
 dried soil bricks). The goal was to provide strength to a weak matrix by taking control of 
the growth of cracks and improve soil properties. Europeans utilized horse hair for 
reinforcing plastic materials, and civilizations in Australia and New Zealand used 
vegetable fibers as reinforcement for plaster-boards at a much later date. The mentioned 
applications were limited to a fairly small scale. Composite material technology 
continued to remain fairly undeveloped until the early part of the 20th century, when it 
took a giant leap with the development and production of reinforced concrete (Majundar, 
1975). 
Early applications of soil fiber composites were in the area of reinforced earth. In 
the late 1960s, some research investigations were conducted on utilization of galvanized 
steel for reinforcing earth retaining structure backfill (Vidal, 1978).  
In 1966, the evaluation of random fiber reinforced concrete took a new turn since 
the formation of the America Concrete Institute Committee 544 (American Concrete 
Institute Committee, 1973). Determination of design strength and various moduli have 
been determined by taking fiber concentrations, orientation, and geometry into account, 
                                                 
15 Mesopotamia is a toponym for the area of the Tigris and Euphrates rivers system. It largely corresponds 
to modern Iraq, as well as parts of Northeastern Syria, parts of Southeastern Turkey, and parts of Khuzestan 
province in Southwestern Iran (Bottero, 1992). 
 
43 
 
as well as the usual water-cement ratio, air content, density, and other related factors. It 
was concluded that the occurrence and development of bonds between the matrix and 
fiber is of vital importance (Hoff, 1979). In addition, empirical verification of fiber 
reinforced concrete has led to the application of classical composite theory (Hoover, 
1982). 
In the mid-1970s, the idea of using Sulfur treated Bamboo to reinforce earthen 
slopes, dams, and backfill material was introduced and some studies were performed on 
the possibility of using Bamboo for earth retaining structures. The studies indicated that 
Bamboo reinforcement improved the shear strength of soil and could be economical 
when used to reinforce engineered structures. For existing dams and also embankments, it 
was recommended that the Bamboo be vertically placed, with its length extending further 
than the depth of a theoretical failure plane. For new embankments or dams, it was 
recommended that the Bamboo should be horizontally placed, either in the form of strips 
or the form of a mat. It is also noteworthy to mention that Bamboo reinforced earth 
retaining structures have shown better resistance to seismic excitations than non-
 reinforced earth retaining structures (Fang & Meleta, 1979). 
Some research on utilization of fabrics in roadway soils were first conducted in 
the mid-1970s (International Conference on the Use of Fabrics in Geotechnics, 1977). It 
was also shown that non-woven fabrics could increase the stability of aggregate roads as 
well as soil roads (Hoover, et al., 1981). 
The utilization of both natural and synthetic fibers as reinforcements for 
cohesionless soils was investigated at prearranged fiber orientations in the mid-1980s. 
 
44 
 
The study showed that shear strength is a function of fiber type, fiber length (FL), fiber 
orientation, and fiber volume fraction (Gray & Ohashi, 1983). 
The use of randomly reinforced fibers with cohesive soils was examined in 1986. 
It was shown that the inclusion of fiber could result in greater strength as well as 
toughness in compacted fine-grained soil (Freitag, 1986). 
1.8.1 Discrete Geofibers 
Geofibers are defined as any type of fiber material that is mixed with soil for 
improving geotechnical properties of soil. Geofibers are blended into soils to enhance 
geotechnical properties of soil and to create an improved reinforcement-soil system. 
Geofibers, by mixing or meshing with the soil already on site, can help to create a soil 
reinforcement system that work together to improve soil engineering properties. In 
addition, reinforcement of expansive soils with discrete geofibers (flexible polymeric 
fibers) can be an alternative method to chemical stabilization techniques and other 
methods for enhancing geotechnical properties of clayey soil. 
A broad classification of Geofibers in terms of material is as follows: 
1- Synthetic fibers are man-made flexible polymeric fibers, such as: Olefin fibers 
(Polypropylene (PP) fibers, Polyethylene (PE) fibers). 
2- Natural fibers are made from natural (animal, plant) materials, such as: cellulose 
fibers (e.g. Coir fibers), asbestos fibers. 
Various chemical processes are sources for manufacturing synthetic fibers. 
Synthetic fibers are classified into high modulus, high strength fibers, and low modulus, 
high elongation fibers. The former includes fibers composed of materials such as steel, 
 
45 
 
fiberglass, carbon, etc., while the latter comprises fibers such as polypropylene and 
polyethylene (Mangat, 1976).  
Cellulose fibers are reinforcing fibers that can be found in their crystalline form. 
They can be classified according to the part of the plant from which they are obtained 
(Parrat, 1972). Cellulose fibers typically have lower values of elastic modulus and tensile 
strength than most synthetic fibers but are plentifully available in bulk (Krenchel, 1973). 
It is known that natural fibers may be affected by varying environments (Parrat, 1972). 
Furthermore, because natural fibers are not homogeneous, a constant parameter cannot be 
obtained for their geometry; hence, it can complicate any design procedure. Also, another 
drawback in using natural fibers is that they are biodegrade when placed in alkaline 
environments and may also be susceptible to microbiological attack and rotting (Parrat, 
1972); (Krenchel, 1973). 
Asbestos fibers are known to have high chemical resistance and provide good 
mechanical properties, such as high tensile strength and elastic modulus. They can also 
undergo severe pretreatment conditions during mixing and are available at low cost and 
in bulk quantities. These fibers had been extensively used as reinforcement for cement 
mortars, but due to the fact that they are a hazardous material and can cause human 
cancer, the usage of these fibers has been limited (Krenchel, 1973). 
Synthetic fibers have two well-recognized advantages over natural fibers. First, 
these fibers can be manufactured according to users? desired specifications; for example, 
the geometry of fibers can be controlled, and the shape of fibers and surface conditions 
can be modified in order to improve the frictional properties of the fibers. Second, 
 
46 
 
synthetic fibers do not biodegrade when subjected to extreme environments in 
engineering scales such as variability of moisture, cold, heat, or sunlight (Krenchel, 
1973). 
Olefin fiber is a man-made fiber in which the fiber-forming substance is a long-
 chain synthetic polymer made up of at least 85% by weight of ethylene, propylene, or 
other olefin units. Olefin fiber is a broad description that covers thermoplastic fibers 
obtained from olefins, predominately aliphatic16 hydrocarbons17. Olefins can be produced 
from polymerization of propylene and ethylene gases. Polypropylene (PP) and 
Polyethylene (PE) are the two most frequently used members of the Olefin family. 
Polypropylene is extremely versatile as a fiber-forming material, whereas polyethylene is 
not when formed as fiber (Kadolph & Langford, 2002). 
Table 1-6: Properties of fibers commonly used in civil engineering materials (Hannant, 
1978) 
Fiber Type Subcategory Diameter 
(?m) 
Length 
(mm) 
Density 
(kg/m3?103) 
Young?s 
Modulus 
(MN/M2) 
Poisson?s 
Ratio 
Tensile 
Strength 
(MN/M2) 
Elongation 
at Break 
(%) 
Typical 
Volume in 
Composite 
(%) 
Asbestos18 Chysotile 0.02-30 40 2.55 164 0.3 200-1800 2-3 10 
Asbestos Crocidolite 0.1-20 - 3.37 196 - 3500 2-3 - 
Cellulose  - - 1.2 10 - 300-500 - 10-20 
E-Fiberglass  8-10 - 2.54 72 0.25 3500 4.8 - 
Polypropylene Monofilament 100-200 5-50 0.9 5 0.29-0.46 400 18 0.1-6 
Polypropylene Fibrillated 500-4000 20-75 0.9 8 0.29-0.46 400 8 0.1-6 
 
 Fiber content is typically expressed in terms of volume fraction or weight 
fraction, either term characterizing the amount of fiber in a composite as a percentage of 
                                                 
16 In organic chemistry, compounds composed of carbon and hydrogen are classified into two classes: 
aromatic compounds, which contain benzene (C6H6) rings or similar rings of atoms, and aliphatic 
compounds, which do not comprise aromatic rings (Gold, 1995). 
 
17 A hydrocarbon is an organic compound consisting of hydrogen and carbon in its entirety (McMurry, 
2000). 
 
18 Nowadays, the use of Asbestos in the construction industry is limited due to its hazardous nature. 
 
47 
 
total volume or total weight of the composite, respectively (Agrawal, et al., 1980). One of 
the advantages of polypropylene over other types of olefin is its ability to be used in a 
wide range of fibrous forms.  
1.8.2 Description of Geofibers 
Geofibers can be produced in three forms: continuous filaments, staple fibers, and 
slit films. A filament has infinite length and is produced by extruding melted polymer 
through dies19 or spinnerets20. The filament is usually stretched to longitudinally orient its 
molecules after extrusion, resulting in greater strength. Monofilament yarns consist of a 
single filament. Two or more filaments may be arranged in line to form a multifilament 
yarn. Staple fibers are manufactured by cutting filaments in lengths of 1 to 4 inches. A 
spun yarn is produced by inter-connecting and twisting staple fibers together. Slit film 
(plain tape) is produced by cutting a cast film into narrow tapes that are oriented and 
drawn in the machine direction (uniaxially). A fibrillated yarn is a slit film fiber which 
has been partially slit to make a series of connected fibers, and then twisted (Maier & 
Calafut, 1998). 
1.8.3 Geotechnical and Dynamic Properties of Clayey Soils Stabilized with 
Polypropylene Fibers 
In recent years, short virgin monofilament fibers have been added and mixed into 
clayey soils to improve the compressive strength behavior (Freitag, 1986); (Maher & Ho, 
1994); (Tang, at al., 2007); (Harianto, et al., 2008), shear strength (Tang, et al., 2007), 
and also increase their ductility (Maher & Ho, 1994); (Tang, et al., 2007); (Harianto, et 
                                                 
19 A die is a specialized tool used in textile manufacturing industries to cut or shape material using a press. 
 
20 Spinneret refers to a multi-pored textile machine through which a plastic polymer melt is extruded to 
form fibers. 
 
48 
 
al., 2008); (Ple & Le, 2012), tensile strength (Maher & Ho, 1994); (Harianto, et al., 
2008), and flexural toughness (Maher & Ho, 1994).  
The utilization of recycled short monofilament fibers in clayey soil has also 
resulted in increasing the compressive and shear strength characteristics of clay (Akbulut, 
et al., 2007). 
Short fibrillated fiber reinforcements have been observed to increase the 
unconfined compressive strength (Nataraj & McManis, 1997); (Puppala & Musenda, 
2000) and shear strength (Nataraj & McManis, 1997); (Zhang, et al., 2000), and also 
reduce the swelling potential (Puppala & Musenda, 2000) of clayey soils. Tension 
cracking and volume change due to swelling/shrinking in compacted clays are also 
reduced when reinforced with PP fibers (Al Wahab & El-Kedrah, 1995); (Nataraj & 
McManis, 1997).The inclusion of fibrillated fibers can increase the tensile strength of the 
clay and provide a ductile behavior that was not otherwise present (Ziegler, et al., 1998).  
The utilization of recycled short fibrillated fibers in clayey soil has also resulted 
in increasing the unconfined compressive strength characteristics of clay. It is shown that 
fiber reinforcement decreased the vertical shrinkage strains; however, it increased the free 
swell value of raw expansive soils by 2% (Puppala, et al., 2001). 
A summary of advantages of using short virgin fiber reinforcement is shown in 
Table 1-7.  
 
49 
 
Table 1-7: Advantages of using commercially available short virgin PP fiber reinforcements in clayey soils 
Fiber Type Shear Strength 
Tensile 
Strength 
Unconfined 
Compressive 
Strength 
Swelling 
Potential 
Tension 
Cracking 
Monofilament Increased Increased Increased - - 
Fibrillated Increased Increased Increased Decreased Decreased 
 
 Some researchers found that lime treatment is a contributing factor to the soil 
brittleness that results in relatively rapid and great loss in strength when failure occurs 
(Sabry, et al., 1996). PP fibers have recently been used in conjunction with lime as a 
novel stabilization method to reduce the brittle behavior of soil stabilized by lime (Cai, et 
al., 2006) and shrinkage-induced soil cracking (Puppala, et al., 2001). The effects of 
moisture content and confining pressure have also been investigated on the dynamic 
properties of PP reinforced lime modified clayey soil using the resonant column test 
(Hoyos, et al., 2004).  
Furthermore, it has been shown that the inclusion of short PP fiber reinforcement 
in cemented clayey soil, changes cemented soils? brittleness to a more ductile one. It also 
increases the unconfined compressive strength, shear strength, and axial strain at failure 
of cemented clay and decreases the loss of post-peak strength, and the stiffness (Tang, et 
al., 2007). 
1.8.4 Mechanism of Fiber Reinforced Clayey Soil (Geofiber Composite) 
The mechanism by which discrete fibers limits swelling of expansive soil is 
different from using a chemical additive like lime. When swelling occurs in soils, the 
flexible polymeric fibers used as reinforcement in the soil are stretched out and this is 
 
50 
 
when the tensile resistance of the fibers against tension comes into assistance and resists 
further swelling. It is also shown that this resistance to swelling offered by the fibers 
depends upon the contact area between soil and fiber (Viswanadham, et al., 2008). 
The amount of swelling can be reduced in the case of fiber-reinforced swelling clays 
through the following (Viswanadham, et al., 2008): 
1- Tensile resistance offered by the fiber to swelling that depends upon the contact 
area between clay and fiber. 
2- Non-swelling fiber are replaced with swelling clay. 
Some laboratory experiments, such as: swell consolidation tests, volumetric 
shrinkage, and swell pressure tests, have been conducted to assess the feasibility of using 
fibrillated and slit film fibers in an expansive soil to reduce swell potential. The results 
indicate that the fiber reinforcement reduces volumetric shrinkage strains, swell pressure, 
and swell potential of the fiber-soil composite (Puppala & Musenda, 2000); 
(Viswanadham, et al., 2008).  
Swell potential (S%) is reported as the ratio of the increase in the thickness of the 
sample upon inundation (?H) to its initial thickness (H) and swelling pressure (Ps). It is 
determined by inundating the soil and measuring the pressure required to prevent its 
expansion (Sowers, 1979). 
1.8.5 Fiber Geometry 
Length is a main criterion used for fiber classification. Composites produced with 
fibers shorter than 3 inches are generally called ?short fiber composites?. Composites 
consisting of longer fibers are classified as ?continuous fiber composites?. This is due to 
 
51 
 
the fact that in most cases the fibers extend throughout the mass of the matrix (Agrawal, 
et al., 1980). 
The mechanics of stress transfer in both classifications are not similar. In the short 
fiber composite case, applied stresses are first transferred to the matrix material then to 
the fibers through the fiber ends and also the surfaces of fibers near the fiber ends. On the 
contrary, in the continuous fiber composite case, applied stresses to the composite are 
transferred to the fibers and matrix at the same time (Agrawal, et al., 1980). 
For short fiber composites, the length parameters, load transfer length (Lt) and 
critical fiber length (Lcr), can be defined. Load transfer length indicates the minimum 
fiber length in which maximum fiber stress can be attained. It is noted that the maximum 
fiber stress is a function of the stress applied to the composite. For a stress applied to the 
composite, the value of maximum fiber stress can be limited by the stress that would be 
accepted by a fiber of infinite or continuous length. Critical fiber length is defined as the 
minimum fiber length in which the fiber ultimate strength is achieved. The fiber ultimate 
strength is not a function of the stress applied to the composite, and hence the critical 
fiber length is also not a function of applied stress, denoting the maximum value of load 
transfer length (Agrawal, et al., 1980). 
 A widely used parameter related to fiber length is aspect ratio defined by length 
divided by diameter (L/d). The aspect ratio plays an important role in determining the 
magnitude of interfacial accumulated shear during loading. The larger the aspect ratio, 
the smaller the amount of interfacial shear developed during loading and hence the 
stronger the fiber matrix interfacial bond must be (Agrawal, et al., 1980). In the case of a 
 
52 
 
clayey matrix using slit film fibers; it is shown that at shorter lengths or lower aspect 
ratios of the fiber, the contact between clay and fiber would be more pronounced 
resulting in higher resistance to swelling. At longer lengths or higher aspect ratios, the 
fiber would be more susceptible to bending and folding. It can reduce the contact area 
between clay and fiber, leading to lesser resistance to swelling.  
Furthermore, at higher aspect ratios, compaction efficiency could decrease; 
consequently, heave reduction is proven to be less at higher aspect ratios. It has been 
proven when long fibers are randomly mixed, they tend to twist or fold. This reflects in 
the form of loss of effective soil-fiber contact area for limiting swelling (Viswanadham, 
et al., 2008).  
1.8.6 Fiber Orientation 
In fiber-matrix composite fabrication, fibers may be arranged in one, two, or three 
dimensional orientations. In one dimensional orientation, fibers are aligned parallel to 
one another and in the direction of the possible applied stress. For two and three 
dimensional arrangements, fibers maybe either randomly oriented during construction, or 
ordered to be arranged when fabricated. The difference between two and three 
dimensional orientations is that in the two dimensional orientation, fibers are positioned 
almost in a plane; while in the three dimensional, fibers lie in all directions (Allen, 1971).  
The principles of reinforcement are similar in all three cases, except that for two 
and three dimensional orientations some strength reduction factors occur. This is due to 
the fact that, in fiber-matrix composites, only the fibers normally positioned to the 
applied stress can carry the applied stress. Hence, for two and three dimensional 
 
53 
 
orientations, some fibers do not bear any stress at all and this is accounted for by 
applying strength reduction factors. The strength reduction factors are more commonly 
known as efficiency factors (Hoover, 1982). 
 When the application of loading direction and magnitude is known, long fiber 
composites perform well. On the contrary, when the load and its direction can vary or is 
not known, long fiber reinforced composites do not perform as well. In such cases, short, 
randomly oriented fiber reinforced composites are desired (Agrawal, et al., 1980). 
The main advantages in using randomly distributed fiber reinforcement over 
typical geosynthetics used in construction are as follows: First, the inclusion of randomly 
distributed fibers limits any potential planes of weakness that otherwise can develop 
when oriented reinforcement is used. Secondly, the simplicity of using randomly oriented 
fibers in the field using self-propelled rotary mixers or other applicable methods. It is 
used to great extent the same way as other chemical additives such as lime, cement, etc. 
The discrete fibers are simply mixed randomly with soil to make a uniform distribution. 
The above mentioned advantages have made randomly oriented distribution of fibers 
very desirable in recent years (Tang, et al., 2007). 
1.8.7 Fiber Material Properties 
In order to select Synthetic fibers, a degree of familiarity with terminology used 
within the textile and fiber industry is required. A brief summary of the most applicable 
terms follows: 
1- Fiber: A general term used for all filaments, yarns, bristles, staples and non-
 woven entities. 
 
54 
 
2- Filament: An untwisted, individual fiber. Filaments typically have a high 
aspect ratio and are classified as crimped or uncrimped. Crimping is used to 
prevent filament separation when bundles are formed in a fiber production 
plant. 
3- Yarn: Refers to a bundle or series of filaments twisted together to produce a 
single fiber in which the individual filaments cannot be detached. 
4- Tow: A long continuous roll of a single filament, groups of filaments, or 
yarns. 
5- Staple: A cut length of fiber measured and expressed in inches; as an example 
in case, a 0.75-inch staple refers to a cut length of 0.75 inch. 
6- Denier: A term used widely in the textile industry and is defined as the weight 
in grams of 9000 meters (9842.49 yards) of a fiber. As an example in case, if 
9000 meters of nylon filament weigh 100 grams, it is classified as a 100 
denier filament. Denier can also be an indirect measure for fiber diameter 
since it is scaled and measured in a constant length of fiber. 
7- Aspect ratio: In order to present fiber dimensions in a more conventional 
manner, an aspect ratio consisting of length divided by diameter is used. This 
terminology is more applicable to civil engineering and construction than to 
the textile industry. 
8- Tenacity: A measure of tensile strength that can be expressed in terms of 
grams/denier. As an example, a 100 denier filament that breaks under a 250 
gram load is rated at 2.5 grams/denier. 
 
55 
 
9- Elongation at break: Refers to the strain characteristic of the fiber; i.e., a 
gauge to measure the amount of longitudinal deformation that occurs prior to 
failure. Elongation at break is expressed as a percentage. 
10-  Regain: Tendency of the fiber material to absorb moisture. 
Different materials can have a variety of physical and chemical properties. 
Physical properties of typical fiber materials, along with approximate cost associated with 
each fiber type are listed in Table 1-8. 
Table 1-8: Typical fiber material properties, after (Hoover, 1982) 
Fiber Type Specific  
Gravity 
Tensile 
Strength 
(ksi) 
Average 
Tensile 
Modulus 
(psi) 
Elongation 
at Break 
(%) 
Elastic 
Recovery 
 
Survivability Approximate 
Cost 
($/lb) 
Nylon 
(monofilament 0.9 
mm diameter) 
1.14 131.3 6?105 10-15 High Moderate 2-4 
Polypropylene 0.91 64.1 1.1?106 70 High High 0.75-1.5 
Polyester 1.39 103.2 1.6?106 30 Low Moderate 2-7 
Polyester 1.39 92.5 1.6?106 45 Low Moderate 2-7 
Polyester 1.39 71.2 1.6?106 60 Low Moderate 2-7 
Polyester 1.39 58.7 1.6?106 43 Low Moderate 2-7 
Type E Fiberglass 2.54 300 10?106 2-3.5 Low High <1.0 
 
 Another factor to take into account is the availability of these materials in desired 
staple (cut length). All of the synthetic fibers could be commercially made available in 
different staples and denier within the possible range; however, manufacturers require a 
minimal order (eg. 1500-2000 lbs) of fiber in order to justify resetting of their cutters to 
produce specially requested lengths and customized fiber (Hoover, 1982). 
Another consideration in the fiber material selection process is paying attention to 
the range of mechanical properties of the fiber materials. While this consideration in fiber 
selection might normally be of significance, it is not a critical determinant when dealing 
with a soil-fiber composite. By a qualitative analysis, it is determined that the degree of 
 
56 
 
excellent quality of the soil-fiber interfacial bond would be greatly below that normally 
found in fiber reinforced concrete, or reinforced plastics. Hence, it is not very critical to 
match fiber properties to those of the soil as a means of controlling the mode of failure 
that might occur. In other words, the degree of criticality is reduced in soils. Any fiber 
materials, that are ultimately considered, would be able to provide tensile strengths and 
moduli far in excess of any desired properties anticipated in soil systems (Hoover, 1982). 
Table 1-8 shows that the utilization of PP fiber is economically justified because 
of its low purchasing cost compared to other fiber materials. It also has a high rate of 
survivability of the fiber within the soil (Hoover, 1982) and has demonstrated an 
acceptable resistance to biochemical degradation (Halpin & Tsai, 1969). To determine 
the rate of survivability, the varying nature of the soil-water system in regards to 
alkalinity, chemical composition, temperature, and environmental variations are taken 
into consideration (Hoover, 1982). 
1.9 Dynamic Properties of Soil 
Small-strain shear modulus (Gmax) and shear wave velocity (Vs) values of soil are 
indirect measurements of soil stiffness against dynamic shear force.  They are directly 
related to each other by Gmax = ? x Vs
 2, where, ? = mass density of soil (total unit weight 
of the soil divided by the acceleration of gravity).  The values of shear modulus and shear 
wave velocity of soil can be an indicator of resistance of soil to dynamic shear forces. For 
instance, the larger values of shear modulus and shear wave velocity of soil can indicate 
that the soil has a large stiffness to tolerate dynamic shear forces.  
 
57 
 
Secant value of the shear modulus is called the secant shear modulus (G). It is 
used to represent the average soil stiffness at larger strains. The relationship between G, 
Gmax and shear strain (?) and shear stress (?) is shown in Figure 1-12. 
 
Figure 1-12: Shear stress versus shear strain cyclic graph 
The soil damping ratio (D) indicates the dissipated energy in soil. The damping is caused 
by friction taking place between particles, strain rate effect, and nonlinear soil behavior. 
The hysteretic damping ratio can be obtained by the following formula: 
  (1.29)  
 
where, WD =  energy dissipated in one cycle of loading and Ws  = maximum strain stored 
during the cycle.  
 
58 
 
The area of the hysteresis loop is WD and the area of the triangle is Ws. Ideally, there 
should be no loss of energy in the linear elastic range for the hysteretic damping model 
expressed by equation 1.29. However, even at very low strain levels, there is always 
some energy dissipation observed by laboratory testing. The damping ratio at very low 
strain levels is considered to be a constant value and is called the small-strain damping 
ratio (Dmin). At larger strains, the nonlinearity in the stress?strain relationship causes an 
increase in material damping ratio with increasing strain amplitude. 
1.9.1 Dynamic Properties of Cohesive Soils 
Several researchers have studied about dynamic soil properties of cohesive soils 
and factors affecting them (Hardin & Drnevich, 1972a); (Hardin & Drnevich, 1972b), 
(Kokusho, et al., 1982); (Aggour, et al., 1987); (Sun, et al., 1988); (Vucetic & Dorby, 
1991); (Kagawa, 1992); (Ishibashi & Zhang, 1993); (Lanzo, et al., 1997); (Vucetic, et al., 
1998); (Darendeli, 2001); (Stokoe, et al., 2004); (Zhang, et al., 2005); (Nie, 2008); 
(Kallioglou, et al., 2008); (Biglari, 2012). In comparison with non-cohesive soils, 
dynamic materials properties of cohesive soils such as the modulus, the damping ratio 
and their strain dependency are more variable due to the physical and other conditions 
affecting the soils. The most significant factors affecting the shear modulus and damping 
of cohesive soils are discussed below. These factors include shear strain amplitude, 
plasticity index, confining stress, frequency of loading, previous stress history (over-
 consolidation ratio), void ratio, degree of saturation, and geologic age. 
The shear modulus of soils in general and cohesive soils in particular reduces 
sharply with increasing strain amplitude, ?. On the contrary, the damping ratio increases 
as shear strain increases. The modulus versus strain amplitude curves are generally 
 
59 
 
expressed by a normalized reduction curve in which modulus values at any strain are 
normalized by the small strain shear modulus, Gmax or G0. The value of Gmax is 
approximately constant for strains below ? = 1?10-5 or 1?10-3 % where the deformations 
are fully recoverable (linear elastic). In other words the strain-dependent change of shear 
modulus of clay is very small for the strain less than 1?10-5; therefore, it is almost 
negligible. In higher strains, the soil behaves as nonlinear elasto-plastic and consequently 
results in irrecoverable permanent deformations.  
As discussed before, PI is an indirect measure of clay mineralogy. It has been 
shown that the PI of clayey soil has a noticeable influence on the form and location of the 
normalized modulus reduction curves. Hence, it can be noted that PI is one of the main 
factors controlling the variation of shear modulus reduction and damping ratio versus 
shear strain curves. Higher plasticity clays show a slower rate of modulus reduction as 
well as a gradual shift of the curve location to the right (Kokusho, et al., 1982); (Sun, et 
al., 1988); (Vucetic & Dorby, 1991). It has also been determined that at the same shear 
strain value, a clay soil with larger PI has a smaller damping ratio, as shown in the 
damping ratio versus cyclic shear strain curve shown in Figure 1-13. 
 
60 
 
 
Figure 1-13: Effect of PI on normalized shear modulus (a) and damping (b) versus cyclic 
shear strain curves of clay (Vucetic & Dorby, 1991) 
 
61 
 
It is not possible to independently vary both the void ratio and confining pressure 
for normally consolidated samples. It can be seen that recent research performed varied 
confining pressures rather than void ratio. This can be due to the fact that void ratio 
depends on soil structure (fabric and bonding) and composition as well as consolidation 
stress and over consolidation ratio (OCR) (Hwang, 1997). It has been extensively 
determined by researchers that shear modulus of soil can increase when confining stress 
is increased. In addition, the damping ratio of soil decreases as the confining stress is 
increased. 
Stress history also plays an important role in determination of the dynamic 
properties of cohesive soils. The effect of over-consolidation on the small strain shear 
modulus of virgin cohesive soils is to increase the modulus as compared to the normally 
consolidated condition. As the OCR and confining pressure increase, the normalized 
shear modulus - shear strain curves shift upward. However, as the PI of clays increases, 
the effects of OCR and confining pressure become less pronounced and may eventually 
disappear when dealing with high plasticity cohesive soils (Lanzo, et al., 1997). 
Furthermore, damping generally decreases with the OCR and confining pressure. 
However, if the PI and confining pressure increase, these effects become less pronounced 
and may eventually disappear (Vucetic, et al., 1998). 
It was determined that the effect of confining stress is more significant and the 
effect of the PI is less significant than previously thought for virgin clayey soils of 
different geological ages. The research suggests taking into consideration the effect of 
geology and confining pressure (Zhang, et al., 2005). 
 
62 
 
It has been experimented that by varying frequency contents the normalized shear 
modulus curve can be affected. Aggour et al. applied random vibrations with varying cut-
 off frequencies to investigate the effect of loading frequency on the normalized shear 
modulus curves for cohesive soils. In the case of random loading, the soil shear modulus 
were found to increase with higher frequency content and were lower than the shear 
modulus obtained from sinusoidal testing as shown in Figure 1-14 (Aggour, et al., 1987). 
 
Figure 1-14: Effect of varying frequency content on the shear modulus of Clay (Aggour, 
et al., 1987) 
 
63 
 
The effect of varying cut-off frequencies on the damping ratio of clayey soil was 
also investigated using a series of random vibration tests. It was indicated that higher 
frequencies are attributed to lower values of damping, as shown in Figure 1-15. 
 
Figure 1-15: Effect of varying frequency content on damping ratio of clay (Aggour, et al., 
1987) 
It was also shown that the damping curve for conventional sinusoidal loading is located 
below the curve with highest frequency of random vibration as shown in Figure 1-15. It 
indicates that the damping ratio of the soil is greater in a condition of the random 
vibration than sinusoidal vibration. 
 
64 
 
 Because of a wide range of factors affecting dynamic properties of cohesive soils 
engineers are recommended to perform in situ and lab testing of cohesive soil properties 
to evaluate appropriate design values and to avoid significant errors. 
1.9.2 Shear Modulus and Damping Equations 
Empirical curves that represent G/Gmax-Log ? and D- Log ? are broadly used in 
geotechnical earthquake engineering practice. Several researchers have proposed various 
analytical models to predict the nonlinear clay behavior (Hardin & Drnevich, 1972a); 
(Hardin & Drnevich, 1972b); (Anderson, 1974); (Borden, et al., 1996); (Darendeli, 
1997); (Darendeli, 2001). The most widely used models in engineering practice are 
explained in this section.  
1.9.2.1 Hardin and Drnevich Design Equations 
The first design equations with parameters that control soils? nonlinear behavior 
were introduced by Hardin and Drnevich (Hardin & Drnevich, 1972a), (Hardin & 
Drnevich, 1972b). They proposed a hyperbolic relationship that can relate shear stress 
and shear strain in an empirical equation as below: 
 
 
(1.30)  
where: ? is shear stress; ? is shear strain; Gmax is small-strain shear modulus; and ?max is 
shear strength. 
Equation 1.30 can be rephrased by dividing both sides of the equation by ? to obtain the 
secant shear modulus (G) as below: 
 
65 
 
  (1.31)  
A new term was defined as reference strain using following equation: 
  (1.32)  
 
The normalized modulus reduction curve can be evaluated using equation 1.30 and 
rearranging it based on equation 1.31 as follow: 
  (1.33)  
Hardin and Drnevich also proposed an approximate model for the material damping: 
  (1.34)  
where Dmax is the maximum damping ratio of the soil that depends on soil type, confining 
pressure, number of cycles, and loading frequency. 
They also observed that soil type can have an impact on the stress-strain 
relationship. As a result, they proposed to approximately model the observed soil 
behavior by changing the strain scale to logarithmic scale. This change in scale makes the 
measured stress-strain curve have a hyperbolic shape. Hence, they defined a new 
parameter called hyperbolic strain (?h), which replaced the ?/?r term in equations 1.32 and 
1.33. Hyperbolic strain was defined as: 
 
66 
 
 
 
(1.35)  
where ?a? and ?b? are coefficients that control the shape of the stress-strain curve for soil 
type, number of cycles, and loading frequency. The other benefit of using the logarithmic 
scale is that a stress-strain curve can be plotted in one graph covering a very large strain 
range. 
1.9.2.2 Modified Hyperbolic Model 
Many other researchers have been influenced by Harding and Drnevich?s work 
and have made efforts to refine their equations. A modified hyperbolic model was 
introduced by Darendeli as follows (Darendeli, 1997):  
  (1.36)  
where: ?r = reference strain; a = curvilinear coefficient. 
Darendeli utilized a relatively simple approach to fit measured stress-strain 
curves. He introduced a reference strain different from Hardin and Drnevich?s reference 
strain. Darendeli?s reference strain (?r) corresponds to the strain amplitude when the shear 
modulus is reduced to one half of the maximum shear modulus, Gmax. The advantage of 
the modified hyperbolic model is its simplicity. 
 Darendeli (1997) also modeled the relationship between material damping ratio 
and strain using the modified hyperbolic model: 
  (1.37)  
 
67 
 
where, ?rD is the reference strain with respect to normalized material damping ratio. The 
value of Ds equals to 2DS,min at ? = ?rD. It is noteworthy to mention that the value of ?rD is 
different from the value of ?r of most models. 
1.9.2.3 Ramberg-Osgood Model 
The other applicable model is a Ramberg-Osgood model. Anderson used the 
Ramberg-Osgood stress-strain relationship to predict the variation of shear modulus with 
shearing strain (Anderson, 1974). The general form of the Ramberg-Osgood model is 
defined as: 
  (1.38)  
where: ? = shape factor; ? = shear stress at yield; and R = correlation number for 
Ramberg-Osgood curve. 
It was suggested that values of 1.0 and 3.0 are used for ? and R for various clays, 
respectively as below: 
For various clays:  (1.39)  
1.9.2.4 Borden Equation 
Borden presented a curve fitting model function for soils. The function correlates 
the decay rate of G/Gmax with an increase in shear strain amplitude (?). The suggested 
function is (Borden, et al., 1996): 
 
68 
 
  (1.40)  
where, constants a, b, and c represent the decay rate of G/Gmax with an increase in shear 
strain amplitude (?). The advantage of the Borden equation is its simplicity and the 
capability of being adapted for both cohesive and cohesionless soils. An equation similar 
to the Borden equation has been modified and used for modeling the relationship between 
the normalized shear modulus and shear strain of soils in this study. The relationship 
between normalized shear modulus and shear strain of clayey soil and fiber-reinforced 
clayey soil is discussed in Chapter 4. 
The normalized shear modulus and damping ratio were also correlated by Borden using 
the following general equation: 
 
 
(1.41)  
1.9.2.5 Modified Masing Behavior for Damping Ratio 
Material damping increases with increasing strain amplitude. The increasing 
damping in the nonlinear range (large strain range) is a result of increasing nonlinearity at 
particle contacts. This suggests that if the relationship between G/G
 max 
and log ? are 
determined, then the D
  
? log ? curve can be simply defined with the D
  
? G/G
 max 
relationship. Several models have been used to define the relationship between the 
material damping ratio and the normalized shear modulus in the nonlinear range 
(Ishihara, 1996); (Hwang, 1997); (Darendeli, 2001). Because of its simplicity, the 
?Masing behavior? is one of the most commonly used models. The cyclic stress-strain 
 
69 
 
behavior proposed by Masing (1926) and the modification of the ?Masing behavior? 
proposed by Darendeli (2001) are discussed below. 
Masing (1926) proposed that the stress-strain path during cyclic loading could be 
related to the backbone curve or monotonic loading stress-strain path. As illustrated in 
Figure 1-12, Masing suggested that the reloading stress-strain curve follows the same 
scaled backbone curve to the initial point of the unloading curve. These sets of unloading 
and reloading curves are said to follow ?Masing behavior? (Masing, 1926). 
The unloading curve is the backbone curve scaled by two, in terms of absolute 
value.  The initial shear modulus of the unloading curve is assumed to be G
 max
  according 
to the hysteresis loop. This assumption is similar to the behavior of metals rather than 
soils. In a soil specimen, particles deform and move as the specimen is placed under 
loading. At the initial point of the unloading curve, soil particles have deformed from the 
initial condition at loading. Hence, at the initial unloading, the shear modulus is expected 
to be lower than G
 max
 . Since the initial shear modulus is overestimated in Masing 
behavior, the area of the hysteresis loop obtained from Masing behavior is larger than 
those in actual soil behavior. As a result, material damping calculated from Masing 
behavior is larger than those of determined in the laboratory, especially at larger strain 
levels (> 10
 -4
 ). Also, it is noteworthy to mention that damping calculated from Masing 
behavior lacks small-strain damping. 
To overcome the shortcoming of the Masing behavior approximation at larger 
strains, Darendeli (2001) adjusted the material damping ratio determined by assuming 
Masing behavior with a correction function as: 
 
70 
 
 
 
(1.42)  
where: D
 Adjusted 
= scaled and capped material damping, 
b = scaling coefficient (= 0.6329 - 0.0057 ? ln (N)); N = number of cycle; G/G
 max 
= 
normalized shear modulus; and D
 Masing 
= material damping ratio determined from the 
Masing behavior.  
Figure 1-16 shows the comparison between D
 Masing 
and D
 Nonlinear
 .  
 
Figure 1-16: Darendeli?s shifted damping curve (Darendeli, 2001) 
As depicted in Figure 1-16, the amount of adjustment of the material damping 
ratio increases with increasing shear strain, and the actual material damping ratio at a 
shear strain is the summation of scaled Masing damping and D
 min
 , as noted in Figure 1-
 16. 
 
71 
 
The Masing damping, D
 Masing
 , presented in Figure 1-16, is determined from a modified 
hyperbolic G/G
 max 
? log ? curve with ?
 r 
= 0.03% and a = 0.90. The theoretical value of 
D
 Masing 
can be determined, only when a = 1 as: 
  (1.43)  
 
where:  ? = 3.1416. For values of D
 Masing 
with a curvature coefficient ?a? other than 1 
(DMasing
 ?), Darendeli (2001) suggested calculating the values numerically as:  
  (1.44)  
where: C1 = -1.1143a
 2 + 1.8618a + 0.2523; C2 = 0.0805a
 2 ? 0.0710a ? 0.0095; and 
C3 = -0.0005a
 2 + 0.0002a + 0.0003. 
 
 
 
 
 
 
72 
 
CHAPTER 2  
TEST EQUIPMENT 
2.1 Introduction 
Soil dynamics is the study of the dynamic properties of soils including moduli and 
damping ratios under dynamic loadings or deformation. Unlike many structural materials 
the samples of soils, which may be cohesive or cohesionless, do not have a readily 
measurable elasticity and yet the dynamic behavior of the soil specimen needs to be 
tested in accordance with concepts of elasticity. The main objective of this research is to 
study the effect of fiber reinforcement on the dynamic properties of clayey soils using the 
resonant column test. The resonant column testing technique has gained popularity 
among researchers due to its accuracy. It was accepted by ASTM as a standard testing 
method in 1978. This chapter describes in detail the test equipment used in this research. 
2.2 The Drnevich Resonant Column Apparatus and Attached Equipment 
The Drnevich resonant column apparatus, a relatively nondestructive testing 
equipment, was used in this research. The resonant column testing apparatus employs a 
chamber having a lower and a top platen (active platen) confining a column of soil in 
between and with the means to provide water and compressed air into the chamber for 
subjecting the column of soil to conditions representative of in-situ soil. Figure 2.1 shows 
a sketch of the Drnevich resonant column apparatus. 
 
73 
 
 
Figure 2-1: Drnevich Resonant Column Apparatus 
A magnet plate supporting torsional and longitudinal accelerometers, in association 
with fixed coils connected with an electrical circuit, provides for torsional vibration of the 
soil column. A centrally placed coil on the torsional magnet plate in cooperation with a 
vertically adjustable magnet provides for longitudinal vibration of the soil column and a 
 
74 
 
length measuring transducer21 attaching to the upper platen serves to give constant 
readings of the length changes of the soil column resulting from the compaction of that 
column (Drnevich, 1975). According to the specification of the LVDT, the excitation 
signals should be 6 volts peak to peak (4.25 rms) with a frequency equal to 2.5 kHz. 
There are three ways to obtain the length measurements from an LVDT: 
1- Using a conditioning module (e.g., Schaevitz LDM-1000) to excite the LVDT and 
reading the length measurements from a digital multimeter. A calibration chart 
needs to be developed to convert the rms readings of the voltmeter to length units. 
2- Using an audio generator as an excitation source and a power amplifier to amplify 
the signals in accordance with the LVDT specifications. 
3- Using a digital panel meter as a combined readout and conditioning unit. 
All of the above mentioned methods provide the same measurements; hence, it is the 
researchers? decision to choose the method of measurement depending on the availability 
of devices at the laboratory. For this research, a combined LVDT readout and condition 
unit (Digital Panel Meters Model PML-1000) was used as a conditioning module to 
excite the LVDT and reading the response received from the LVDT.  
The excitation system of the resonant column device is an electromagnetic system 
comprising of a permanent magnet and coil that can move in the gap between the North 
and South Poles of the permanent magnet. For longitudinal excitation, the assembly 
comprises one set of a coil and magnet. The magnet is connected to a heavy steel base 
and held up by a bracket, while the coil is housed in the top active platen and penetrates 
                                                 
21 The length change of the soil column is measured with a Measurement Specialties (Schaevitz), type 
300HR displacement transducer (LVDT) that has a linear range of ?0.300 inch and linearity error less than 
0.25%. 
 
75 
 
concentrically into the magnet at least 15 mm (0.5 inch). For the torsional mode, the 
assembly comprises four rectangular coils and horseshoe-shaped magnets. The coils are 
connected to the brackets and the magnets to the top active platen. Equal gaps should be 
maintained between the magnets and the coils to minimize the development of any 
bending forces. The important consideration is that the magnets can move freely within 
each coil without touching it.  
The torsional coils allow movements (0.5 inch) in the vertical direction to accommodate 
the change in length during the consolidation process of clay. Torsional coils are shown 
in the Figure 2-2.  
 
Figure 2-2: Torsional Coils set up 
 
76 
 
By generating an AC current of controlled frequency through the coils, a 
magnetic field would be generated, which in turn develops longitudinal or torsional 
forces on the top of the soil column.  
The polarity of the torsional wiring system should be checked; meaning that the 
polarity of the system should create a moment in the same direction, e.g., clockwise. In 
order to check the polarity, test leads or other convenient temporary connections can be 
used to short out coils 2, 3, and 4. The coils should be slightly loosened (not tightly fixed) 
but still in place. A 6 volt DC current should be connected to the main lead for the 
torsional coils from the Control Box in lieu of the AC voltage provided by the power 
amplifier. This should place a current of less than one amp through coil number 1. That 
current should be sufficient to cause the magnet and top platen system to rotate in either 
clockwise or counter clockwise. The operator should make note of the rotation direction. 
Then, the short from coil 2 should be removed and coils 1, 3, and 4 should be shorted out. 
The same 6 volt DC current should be connected and the system should experience a 
motion in the same direction as noted above. If it is not, the leads to coil 2 should be 
reversed. The procedure should be continued for coils 3 and 4 making sure that 
connections to each coil produce the same rotation motion of the magnet-top platen 
system for the same voltage applied. Figure 2-3 shows the voltage test set up. All the 
shorted connections should be removed and a convenient scheme to code the connections 
to the coils should be sketched and used for the testing program. 
 
77 
 
 
Figure 2-3: Voltage test set up 
The accompanying devices, required for the excitation system, are a wide range 
oscilloscope (Tektronix model T912), a sine wave generator (GW Instek), and an 
amplifier (Bogen Model MT125B). Adjoining equipment is a frequency counter (VC 
2000) used to accurately give the value of the circular frequency and a digital multimeter 
(BK Precision 2831E) utilized to measure the current passing through the drive coils. The 
digital multimeter, operating in true root mean square (rms), also measures the voltage 
drop across an accurate 5 ohm power resistor placed in the control box of the resonant 
column. Table 2-1 is a summary of the specifications for the electronics.  
 
 
78 
 
Table 2-1: Electronic equipment used with the resonant column apparatus 
Equipment Manufacturer Model Function 
Sine Wave 
Generator 
GW Instek GAG-809/810 
Providing sinusoidal 
input voltage for 
driving coils (either 
directly or thru 
power amplifier) 
Frequency Counter TUV VC2000 
Measuring 
frequency of input 
signal 
Power Amplifier Bogen MT125 B 
Amplifying input 
signal from signal 
generator to coils 
Oscilloscope Tektronix 912 
Displayed and stored 
output signal from 
accelerometer 
Charge Amplifier 
Columbia Research 
Lab 
4102 
Exciting transducer 
and conditioning 
output voltage from 
accelerometer 
Digital Multimeter 
&  Frequency 
Counter 
BK Precision 2831E 
Measuring the input 
and output voltage 
to/from transducer 
thru charge 
amplifier. Also, 
measuring frequency 
of input signal 
LVDT Readout 
Measurement 
Specialties 
PML-1000 
Exciting and 
conditioning LVDT 
and measuring the 
output from LVDT 
 
Figure 2-4 shows a setup of the resonant column attached devices. 
 
79 
 
 
Figure 2-4: Set up of the resonant column attached devices 
During each testing routine, the wave oscillator signals are amplified with the power 
amplifier and then input to the drive coils after passing through the power resistor in the 
control box. Figure 2-5 shows the wiring diagram for control box. 
 
80 
 
 
Figure 2-5: Wiring diagram for control box 
The pick-up system comprises of a piezoelectric meter (Columbia Model 200-1-
 H) placed in the active-end platen. The transducer is mounted at a distance of 0.0316 
meter from the axes of rotation. The transducer has a charge sensitivity of 36.3 pk-
 pcmb/pk-g. A charge amplifier (Columbia Model 4102) is used to operate the 
accelerometer by converting the charge into emf22. The output would be 2.5 pk-volts/pk-
 g, 0.25 pk-volts/pk-g, or 0.025 pk-volts/pk-g, depending on whether the left, center, or 
right button is depressed on the panel of the charge amplifier. The digital multimeter and 
oscilloscope are used to record the responses. The digital multimeter gives readings of 
sample acceleration in terms of rms, which in turn can be converted to define the shear 
strain. The oscilloscope monitors the frequency response of the sample. The electrical 
connections are outlined in Figure 2-6. 
                                                 
22 Electromotive force is the energy per unit charge that is converted reversibly from mechanical, chemical, 
or other forms of energy into electrical energy. 
 
81 
 
  
An air pressure regulator unit, Tri-Flex 2, manufactured by ELE International was 
used to maintain the pressure at 5 psi during the consolidation period and during the test.  
The use of an air pressure regulator unit can prevent the air flow from any fluctuation 
during consolidation period and testing. In addition, a water separator was placed in the 
air feeding line with the purpose of keeping the water and moisture out of the air. A 
Wave 
Generator 
Charge 
Amplifier 
X-Y 
Oscilloscope 
LVDT 
Readout 
Unit 
Power 
Amplifier  
 Switch 
Box 
Control 
Box 
Frequency 
Counter 
Digital 
Multimeter 
Air Pressure 
Gauge 
Water 
Separator 
Water 
Unit 
Air Pressure 
Regulator 
Unit 
Figure 2-6: Schematic diagram of the resonant column testing system  
(Red lines are input lines; Green lines are output lines) 
 
82 
 
digital pressure regulator gauge was also installed in the air feeding line prior to the point 
where the air is to enter the resonant column chamber to measure the air pressure at the 
point of air entry. Figure 2-7 shows the digital pressure gauge and water separator. 
 
Figure 2-7: Digital pressure gauge and water separator 
2.3 Calibration of the Test Equipment 
Calibration is a comparison between measurements read from two test equipment, 
one of known magnitude and other not known. The device with the known or assigned 
correctness is called the Standard. The other equipment is the unit under test (test 
equipment). There are two types of calibration, absolute and relative calibrations. The 
absolute calibration is performed at the manufacturer?s factory; whereas, the relative 
 
83 
 
calibration can be conducted by operators at soil mechanics laboratories when Standard 
equipment is available or the magnitude of the expected measurements are known.  
From cost prospective, when a large number of equipment is needed to be 
calibrated, it is more economical to send out one unit to be calibrated at the 
manufacturer?s factory (absolute calibration) and use the newly calibrated unit as the 
Standard equipment for calibrating other equipment (relative calibration) at a laboratory. 
2.3.1 Resonant Column Apparatus Calibration 
To calibrate a resonant column (RC) apparatus, a rod of known torsional stiffness 
properties is needed to calibrate the results obtained from the testing. In order to do that 
the apparatus shall be operated with a slender aluminum calibrating rod in place of the 
specimen. One end of the rod shall be rigidly fixed and the other end shall be rigidly tied 
to the magnet platen after taking out the top platen. The system then approximates a 
single degree of freedom (SDF) system. Figure 2-8 shows an approximate cross section 
of the apparatus showing the placed calibration rod (Drnevich, et al., 1978). 
 
84 
 
Magnet Platen
 Aluminum Calibration Rod
 Lower Specimen Pedestal
  
Figure 2-8: Approximate cross section of RC apparatus showing the calibration rod in 
blue 
With the torsional calibration rod in place, a small current should be sent to the 
torsional coils. The voltage associated with this current should be approximately 0.05 
Vrms. The loading frequency should be adjusted to obtain resonance. The resonant 
frequency (ft) should be recorded and the value of ft and ft should be calculated. A 
large current with voltage of approximately 1.0 Vrms should be applied while the 
frequency of oscillation is set to ft. The corresponding output of the torsional 
accelerometer should be recorded. The same large current now should be applied at ft 
and the corresponding outputs should be recorded. Then, two coefficients, C1 and C2, can 
be calculated from equations 2.1 and 2.2. 
 
 
(2.1)  
 
 
85 
 
 
 
(2.2)  
where: C1 and C2 are calibration coefficients, 
CR1 and CR2 are excitation voltages corresponding to ft and ft frequencies, 
respectively, 
TO1 and TO2 are response voltages corresponding to ft and ft frequencies, 
respectively. 
The values of C1 and C2 should agree within 10 percent otherwise the calibration should 
be repeated (ASTM D4015-07). From C1 and C2 the torsional coils Torque Calibration 
Factor (TCF) can be calculated using equation 2.3. 
  (2.3)  
where, Kcr is spring constant of the calibration rod and is equal to 265.4  , 
TCF is Torsional Calibration Factor in  . 
The torsional calibration factor was calculated to be 7.05 x 10-2  for the apparatus 
using the above mentioned procedure. 
2.3.2 Acceleration Transducers and Charge Amplifiers 
 Prior to starting the test, the acceleration transducer and charge amplifier need to 
be calibrated. To meet this goal, the standard transducer (a recently calibrated transducer) 
and the to-be-calibrated acceleration transducer are symmetrically attached together with 
 
86 
 
wax and are glued on the plate of a shaking table (vibrator), as shown in Figure 2-9. The 
transducer to be calibrated and the standard transducer are respectively connected to the 
charge amplifier to be calibrated and the standard charge amplifier. The shaker vibrates 
sinusoidally from a frequency of 10Hz to 1,000Hz. Although the expected frequencies for 
conducting the resonant column testing are less than 100Hz, responses up to 10 times the 
highest frequency of interest are compared. It is advised by the manufacturer that 
accelerometers should be calibrated in regard to resonant frequencies up to five times the 
highest frequency of interest. 
Standard
 Charge Amplifier
 Frequency
 Analyzer
 Charge Amplifier
 to be calibrated
 Transducer
 to be calibrated
 Standard
 transducer
 Vibrator
  
Figure 2-9 Set-up diagram for calibration of transducer and charge amplifier 
Relative calibration was performed for the transducer and charge amplifier. The 
calibration set up is shown in Figure 2-9. After performing the relative calibration, due to 
the importance of accuracy of the measurements from the charge amplifier and transducer 
(model 200-1-H serial no. 858), both devices were sent to Columbia Research Labs, Inc. 
for absolute calibrations. Charge sensitivity of 36.3   for the frequency ranges 
between 2 Hz to 5 kHz was determined for the transducer. 
 
87 
 
2.3.3 Linear Variable Differential Transformer (LVDT) and LVDT Readout 
The absolute calibration was conducted on the LVDT 300HR by the 
manufacturer. After the calibration, the LVDT was installed on the apparatus and 
connected to an LVDT Readout, PML 1000. Before the LVDT can be used it must first 
be calibrated to the LVDT Readout. Please note that the calibration of LVDT, which was 
performed by the manufacturer, is different from calibrating the LVDT to the LVDT 
readout. The calibration of the LVDT to the LVDT readout is a procedure conducted so 
that the numbers obtained from the LVDT can be defined for the LVDT readout. The 
LVDT was connected to the LVDT Readout at the appropriate input measurement mode 
and correct excitation voltage. Frequency was selected from the input menu. The 
Automatic Gain selection option was used from the input menu and was set to ON. 
It is significant that the LVDT operates around the midpoint of its stroke as this 
gives the best results by minimizing any errors due to non-linearity. A feature of the PML 
1000 is the ability to locate the midpoint of the LVDTs measurement range (null point). 
The LVDT was mounted so that the required measurement range is equally divided by 
the null position. The displayed value started flashing when the LVDT was closer to its 
null position. 
To perform an initial calibration of the LVDT to the PML 1000 the CAL option 
from the main menu was selected. The display showed the message L-iP (low input). At 
this time, the position of the LVDT was set to its minimum displacement position 
(minimum stroke). When the LVDT was set at its low calibration point (displacement of 
0 mm), the Enter key was pressed, the display showed WAit while the PML 1000 
measured the output from the LVDT. This took a few seconds. After a few seconds, the 
 
88 
 
display showed H-iP. This indicated that the PML 1000 was ready to calibrate the high 
point. At this time, the LVDT was set to its high calibration point (maximum 
displacement position of 200 mm) and pressed Enter. The unit displayed the message 
WAit while it was measuring the output from the LVDT. At the end of the calibration 
sequence, the PML 1000 used the two measured output values from the LVDT to 
calculate its own calibration constants that would be utilized in all future measurements. 
2.4 Coupling between Soil Specimen and Top Platen 
Having complete coupling between stiff soil specimens and the top platen could 
be a problem if precautions are not taken. At very low strains, coupling can exist but as 
the strain amplitude increases, shear stresses increase and incomplete coupling may 
occur. Incomplete coupling results in lower shear modulus and higher damping than what 
should be at a given shear-strain amplitude. To ensure a complete coupling, razor blade 
vanes are placed in top platen. The protrusion of the blades should be greater than or 
equal to 1.5 mm (Drnevich, 1978). 
2.5 Resonant Column Data Reduction Calculations 
In the resonant column technique, a column of material is excited either 
longitudinally or torsionally.  The Young?s Modulus (E) or Shear Modulus (G) of the soil 
can be evaluated employing the wave propagation theory. The wave propagation theory 
will depend on the specimen configuration. In this research a ?Fixed-Free? configuration 
resonant column was used for studying the shear modulus properties of clay and fiber 
reinforced clay. In the following section the equations used to calculate shear modulus, 
damping, and shear strain from resonant column testing are presented. 
 
89 
 
2.5.1 Calculation of Shear Modulus 
In the resonant column tests where soil specimens are subjected to torsional 
vibration with fixed-free conditions, the wave propagation is expressed as follows: 
 
 (2.4)  
where:  = angle of twist (rad), 
Is = polar moment of inertia of the soil specimen (m
 4), 
JT = polar mass moment of inertia of the top platen (kg-m
 2), 
Vs = shear wave velocity in soil specimen (m/s). 
The wave velocity Vs can be calculated from equation 1.19. The solution to the wave 
equations for short bars or soil column vibrating in a natural mode can be written in the 
general form as equations 2.5 and 2.6. 
  (2.5) 
where  is the undamped natural circular frequency; A1 and A2 are constants; and U(x) 
is the amplitude of displacement along the length of the soil column and is independent 
of time, and 
  (2.6) 
where B1 and B2 are constants. These constants may be determined by the end condition 
to which the rod or soil column may be subjected. 
 
90 
 
Using the boundary conditions for the fixed-free case, at x = 0 (fixed end), U(x) = 0 and 
at X = L (free end),  and U(x) is: 
  (2.7) 
The inertia force (F) on the soil column under torsion can be expressed in equation 2.8 in 
terms of polar mass moment of inertia (JT) and the shear strain at x = L. 
 
 (2.8) 
It can also be rephrased in terms of polar moment of inertia as: 
 
 (2.9) 
 
The following can be obtained by substituting second derivatives of combined equations 
2.5 and 2.7 in equations 2.8 and 2.9.  
  (2.10) 
 
 
(2.11) 
Equating equations 2.10 and 2.11 and expressing G in terms of mass density and shear 
wave velocity the following solution can be obtained. 
  (2.12) 
and  
 
91 
 
  (2.13) 
where FT = dimensionless frequency factor, which can be calculated from the following 
equation: 
  (2.14) 
And , and Js = polar mass moment of inertia of soil specimen (kg-m
 2) and is equal 
to 
 
 (2.15) 
where d = diameter of the soil specimen (m), 
Ms = mass of the soil specimen. 
With the value of FT, shear modulus (G) of the soil specimen can be determined from: 
 
 (2.16) 
where fnT = resonant frequency in torsional vibration (Hz). 
2.5.2 Calculation of Damping Ratio 
The Resonant Response Method was used to calculate the damping ratio using the 
following equation (Drnevich, 1978): 
  (2.17) 
where A = 2 (TL + 0.405) and MMF is calculated from the following equation: 
 
92 
 
 
 (2.18) 
where, RCF = rotational calibration factor (rad/V), 
TCF = torque calibration factor (N-m/V), 
INP = input reading of torsional coil (V), 
RTO = response or output reading of torsional coil (V), 
J = total polar mass moment of inertia including the top platen and soil column (Kg-m2), 
fnT = resonant frequency of the system in the torsional direction. 
2.5.3 Calculation of Shear Strain 
The moduli and damping ration of soil depend upon the magnitude of the strain. 
For sinusoidal torsional excitation, the shear strain amplitude can be obtained using 
Drnevich?s approach as follows: 
 
 (2.18) 
where = shear strain; RCF = rotational calibration factor (rad/V)rms; RTO = rotational 
transducer output Vrms; d = diameter of specimen; L = length of the specimen. 
 
 
 
 
93 
 
CHAPTER 3 DETERMINATION OF OPTIMUM FIBER CONTENT 
 
 This chapter deals with the testing undertaken prior to the dynamic testing 
program. The study discussed in this chapter involves a new compaction procedure 
developed for finding the optimum fiber content (OFC) of fiber-clay mixtures. The 
purpose of this procedure is to determine the optimum fiber content that produces the 
largest maximum dry density (?d max). Samples for dynamic testing were prepared at their 
maximum dry density. The results of this study will be useful for fiber selection in terms 
of fiber type and percentage content and also will establish a procedure that can be 
followed to obtain the proper fiber-clay composite mix design. 
3.1 Current State of the Research 
Researchers have added fiber to soil and found that it improves the soil behavior. 
However, they followed the same approach that is being used in concrete. In concrete, 
fiber is added to improve its behavior as well. The amount of fiber added is usually an 
arbitrarily specified percentage to increase the strength properties of the concrete. The 
percentage usually varies with the intended use of the concrete. Soil behavior is a 
function of its density, which is not the case with concrete. Thus, the concrete approach 
will not provide a matrix with improved geotechnical properties. Therefore, it should not 
be adopted in adding fiber to soils. 
The other approach is the metallurgical approach to form desired composite 
systems, such as Metal Matrix Composites (MMC), Ceramic Matrix Composites (CMC), 
or Polymer Matrix Composites (PMC). The percentage of mixture constituents is 
obtained using the traditional rule of mixtures. In this approach, composite properties are 
 
94 
 
traditionally predicted using a micro-mechanics approach termed the rule of mixtures. 
 The Rule of mixtures is mathematical expression that describes some properties 
of the composite in terms of the properties, quantities and arrangements of its 
constituents. The rule of mixtures is widely used for different composite systems, i.e., 
MMC, CMC, and PMC. The density of a general composite can be predicted from the 
following equation: 
 
 (3.1) 
where:  ? is density of a general composite; Mclay is mass of clay; Mfiber is mass of fiber; 
V is the total volume of composite. 
The above equation can be rewritten based on volume fractions of clay (Vfclay) and fiber 
(Vffiber) as follows: 
  (3.2) 
where: ?clay is density of clay; ?fiber is density of fiber. 
The above equation can be rewritten based on volume fraction of fiber knowing that Vfclay 
+ Vffiber = 1. Thus, 
 
 
 
(3.3) 
The equation shows that the density of the composite is a function of the density of the 
clay, density of the fiber, and the volume fraction of the fiber. The following schematic 
 
95 
 
graph, Figure 3-1, shows that the density of matrix can vary based on the fiber volume 
fraction and the density of the fiber and clay. 
 
Figure 3-1: Schematic graph of density of matrix versus fiber volume fraction 
       The schematic sketch in Figure 3-1 shows that the density of the matrix 
cannot be greater than the density of the material with the larger density, in this case, 
clay. Other properties of a composite, e.g., stiffness, can also be predicted using this 
approach. 
The following assumptions have been made in the rule of mixtures: 
1- Fibers are uniformly distributed throughout the matrix. 
2- Perfect bonding between fibers and matrix. 
 
96 
 
3- Matrix is free of voids. 
4- Applied loads are either parallel or normal to the fiber direction. 
5- Fiber and matrix behave as linearly elastic materials. 
All soils including clay are composed of solids and voids as shown in the 
schematic Figure 3-2. Voids are filled with both air and water. Thus soil is a three-phase 
material. Using soils in construction or as a foundation material requires mechanical 
stabilization to rearrange its structure and thus improve its behavior. Compaction of soil 
applies mechanical energy to rearrange its particles and reduce its air voids and thereby 
improve its behavior by increasing its density, strength, and reducing its compressibility. 
 
Figure 3-2: Schematic graph of soil composition 
In the process of compaction water is added to allow soil particles to slide over 
each other more easily (a lubricant) up to a certain point; further addition of water beyond 
this point will occupy space that could be filled with soil and thus the density of the soil 
will be reduced. Therefore, geotechnical investigators perform compaction tests at 
 
97 
 
different water content levels and determine the amount of water needed that produces 
the maximum density of the soil, which is termed the optimum moisture content. 
However, it is impossible to get rid of all the air voids, thus at the end the soil will be still 
composed of solids, air and water, but at a higher density and a specified moisture 
content. 
Using the rule of mixtures is appropriate if the matrix is free of voids. The matrix 
is made up of solids and voids filled with water, air, and fiber as shown in Figure 3-3, 
which is then compacted. Compaction does not eliminate air voids. Also, different 
degrees of compaction will have different amounts of voids remaining. The existence of 
voids violates the rule of mixtures assumptions.  
 
Figure 3-3: Schematic graph of fiber reinforced soil composition 
Another assumption made in the rule of mixtures approach is that the matrix and 
fiber are assumed to behave as linearly elastic materials. Soils in general tend to behave 
as non-linear materials and clays in particular can also behave as plastic materials 
 
98 
 
depending on the clay?s plasticity index. So, in dealing with soils, testing is the only way 
to determine the characteristics and behavior. 
3.2 Density and Compaction 
For many civil engineering projects, soils are compacted to a denser state to 
enhance their engineering properties. Soil compaction consists of packing the soil 
particles together by mechanical means so that it increases the soil dry unit weight. Soils 
are made of solid particles with voids filled with air and water. Compaction only reduces 
the air fraction of the voids. In theory, the most effective compaction process should 
completely remove the air fraction. However, in practice, compaction cannot completely 
eradicate the air fraction, but only reduces it to a minimum. In the following sections, the 
compaction behavior of fiber added clayey soil is discussed. 
3.2.1 Soil and Fiber Materials 
The synthetic soil used in this study was Kaolinite obtained from Feldspar 
Corporation23. The soil was commercially obtained in a dry, powdered form (50 lbs per 
bag). The chemical components of the soil are listed in Table 3-1. The Kaolinite mineral 
is the simplest and best understood clay mineral. This clay can be considered as a 
standard clay, like Ottawa sand is used as a standard sand. Because the Kaolinite was 
received in a powdered form, the properties of the prepared specimens might vary 
depending on the uniformity of the batches; therefore, two bags were thoroughly mixed 
together in a large container and stored in a dry place. 
 
                                                 
23 Edgar, FL 32149 
 
99 
 
Table 3-1: Chemical properties of Kaolinite Soil 
Component Percentage Component Percentage Component Percentage 
SiO2 45.2 Al2O3 38.8 Fe2O3 0.3 
FeO - MgO 0.3 CaO 0.05 
Na2O 0.3 K2O 0.05 TiO2 1.4 
CO2 - SO2 - H2O 0.7 
P2O5 -     
 
 The Atterberg limits were determined following ASTM D4318 to be LL = 49, PL 
= 29, and PI = 20. The liquid limit device used in this research was equipped with a 
motor to turn the cam at 2 ? 0.1 revolutions per second. This device also has an automatic 
and adjustable counter for counting the blows. A Casagrande grooving tool was used in 
the test. The calibration of the apparatus was performed in accordance with steps 
provided in ASTM D4318. 
The most commercially available fiber sizes were used for this study. As shown in Figure 
3-4, the polypropylene fibers were 1.9 cm (0.75 in) and 1.27 cm (0.5 in) in length virgin 
homopolymer monofilament and fibrillated fibers obtained from ABC Polymer 
Industries, LLC (ABC)24 for the testing. 
                                                 
24 Helena, AL 35080 USA 
 
100 
 
 
 
Figure 3-4: Polypropylene fibers used in the experiments. a) Fibrillated fiber b) 
Monofilament fiber 
Summary of the properties of both PP fibers are presented in table 3-1. 
 
 
 
101 
 
Table 3-2: Properties of polypropylene fibers 
Properties Monofilament Fiber Fibrillated Fiber 
Specific Gravity 0.91 0.91 
Tensile Strength 552-758 MPa (80-110 ksi) 552-758 MPa (80-110 ksi) 
Denier  6 1500 
Thickness* 0.030 mm (0.0012 in) 0.48 mm (0.019 in) 
Melting Point Above 160C (320F) Above 160C (320F) 
Flash Point Above 329C (624F) Above 329C (624F) 
Autoignition Temperatures 
** 
Above 357C (675F) Above 357C (675F) 
Electrical & Thermal 
Conductivity 
Low Low 
Acid & Salt Resistance High High 
Alkali Resistance Alkali Proof Alkali Proof 
* The following formula can be used in order to measure thickness of a fiber using the 
denier and specific gravity of the fiber: 
  
** The Autoignition Temperatures or Kindling Point of a substance is the lowest 
temperature at which it will spontaneously ignite in a normal atmosphere without an 
external source of ignition, such as a flame or spark. 
3.2.2 Sample Preparation and Compaction Criteria 
The soil-water mixture for compaction was prepared by first mixing a measured 
amount of dry soil with a predetermined amount of water (about 2 kg for each test) by 
hand and then by a mechanical mixer as shown in Figure 3-5. 
 
102 
 
 
Figure 3-5: Mixing using mechanical mixer 
In the case of fiber addition, the weight of specific content of fibers was calculated based 
on the weight of air dried soil. The required amount of fiber was first mixed with the dry 
soil and then water was added. Mixing continued until a uniform mix is produced. Figure 
3-6 shows a mixture of soil and fibrillated fibers. 
 
103 
 
 
Figure 3-6: Mixture of kaolinite soil and fibrillated fibers (FC = 0.6%) 
The specimens were prepared by mixing the soil with various percentages of fiber 
content (FC), determined by weight. Table 3-3 shows the composition of the mixtures 
used in this study. 
           Table 3-3: Composition of mixtures 
Number of Mixtures By weight (%) 
1 
2 
3 
4 
5 
Soil + 0.0% Fiber 
Soil + 0.2% Fiber 
Soil + 0.4% Fiber 
Soil + 0.6% Fiber 
Soil + 0.8% for 0.5? Fiber 
 
A compaction test was performed for each mixture immediately after achieving a uniform 
and homogeneous mixture. To obtain four well-placed points on the compaction curves, a 
low water content was selected for the first test point and was gradually increased for the 
subsequent points. The water content should ideally be about 4 to 5% below the optimum 
 
104 
 
water content for the first point, and 4 to 5% above the optimum for the fourth and last 
point. For 2 kg of clayey soil, about 500 g of water was used for the first point, about 100 
g of water was added for the second point and 50 g of water was added for the third and 
fourth points to achieve totals of about 600 g, 650 g, and 700 g of added water for the 
mixture at the second, third, and fourth points. 
The soil-fiber composite was compacted in three layers, each with 25 blows in the 4 inch 
(101.6 mm) standard proctor mold following ASTM D 698 using standard effort (12,400 
ft-lbf/ft3(600 kN-m/m3)). Figure 3-7 shows a compacted soil-fiber composite being 
extruded from the standard mold. 
 
Figure 3-7: Compacted soil-fiber composite being extruded from the standard mold 
3.2.3 Compaction Data and Discussion 
Compaction tests were performed on a mixture of kaolinite soil with 
monofilament and also with fibrillated fibers at the following fiber contents: 0%, 0.2%, 
 
105 
 
0.4%, and 0.6% for 0.5 and 0.75 inch of fiber length, and 0.8% for only 0.5 inch of fiber 
length. The results are presented below for monofilament and fibrillated fibers. 
 
Figure 3-8: Compaction curves for composites of kaolinite soil and monofilament fibers 
with various fiber contents (fiber length = 0.75 in) 
 
 
 
106 
 
 
Figure 3-9: Compaction curves for composites of kaolinite soil and monofilament fibers 
with various fiber contents (fiber length = 0.5 in) 
 
Figure 3-10: Compaction curves for composites of kaolinite soil and fibrillated fibers 
with various fiber contents (fiber length = 0.75 in) 
 
 
107 
 
 
Figure 3-11: Compaction curves for composites of kaolinite soil and fibrillated fibers 
with various fiber contents (fiber length = 0.5 in) 
 
A Summary of the compaction test results is presented in Table 3-4 and Figures 3-12 
through 3-15 in the form of bar charts. 
Table 3-4: Compaction test result for various fiber contents 
 Monofilament Fiber Fibrillated Fiber 
FL 
(in) 
FC 
(%) 
MDD25 
(kN/m3) 
OMC26 (%) MDD (kN/m3) OMC (%) 
0.75 
0.0 12.18 26.0 12.18 26.0 
0.2 12.95 29.9 14.04 31.0 
0.4 12.82 30.6 13.60 32.0 
0.6 12.89 30.2 13.45 32.3 
0.50 
0.0 12.18 26.0 12.18 26.0 
0.2 12.87 30.2 13.00 30.0 
0.4 12.78 30.8 12.88 30.7 
0.6 12.71 30.9 12.75 30.9 
0.8 12.69 31.0 12.55 31.2 
                                                 
25 Maximum Dry Density 
26 Optimum Moisture Content 
 
108 
 
 
 
Figure 3-12: Change in ?d max with various fiber contents (fiber length = 0.75 in) 
 
 
Figure 3-13: Change in ?d max with various fiber contents (fiber length = 0.5 in) 
 
11
 11.5
 12
 12.5
 13
 13.5
 14
 14.5
 0 0.2 0.4 0.6
 M
 ax
 im
 u
 m
  D
 ry
  De
 n
 si
 ty
 , 
kN
 /m
 3
  
Fiber Content, % 
Monofilament
 Fibrillated
 
109 
 
 
 
Figure 3-14: Change in OMC with various fiber contents (fiber length = 0.75 in) 
 
 
Figure 3-15: Change in OMC with various fiber contents (fiber length = 0.5 in) 
 
0
 5
 10
 15
 20
 25
 30
 35
 0 0.2 0.4 0.6
 O
 p
 ti
 m
 u
 m
  M
 o
 ist
 u
 re
  C
 o
 n
 te
 n
 t,
  %
  
Fiber Content, % 
Monofilament
 Fibrillated
 
110 
 
Based on the above results, it can be seen that the addition of fibers affected both 
the ?d max and OMC. The ?d max of soil increased with the inclusion of fiber. It shows the 
fiber inclusion can more effectively eradicate the air fraction of the voids and can 
increase the dry density of the soil. The maximum value for ?d max for both type of fibers 
and lengths were at 0.2% fiber content. The value of ?d max increased approximately 6% 
and 15%, respectively, for mixtures with monofilament and fibrillated fibers of 0.75 inch 
length compared to the soil without fibers. The value of ?d max also increased 
approximately 5.5% and 7%, respectively, for mixtures with monofilament and fibrillated 
fibers of 0.5 inch length compared to soils without fiber. The largest increase in the value 
of ?d max was determined for the mixture with fibrillated fiber of 0.75 inch length. The 
results of maximum dry density for mixtures of 0.2% fiber and clay are shown in Figure 
3-16. An increase in the value of OMC was also observed when comparing to soil with 
no fiber content. The lowest values for OMC of the soil-fiber composites were for the 
fiber inclusion of 0.2%.  
 
Figure 3-16: Change in MDD with various fiber lengths and types  
 
111 
 
3.2.4 Conclusion 
It can be concluded that the changes in ?d max are mainly due to the displacement 
and rearrangement of soil particles caused by the inclusion of fibers. With the inclusion 
of fiber in general, fibers will fill the voids in the soil and therefore the soil specimen 
density becomes higher. At the optimum fiber content (OFC = 0.2%), fibers have 
effectively filled in the pore voids of the soil. As the amount of fiber exceeds the 
optimum value, the extra fibers will be placed in between soil particles and will not allow 
the soil particles to come close to each other and thus result in the reduction in the ?d max 
value. To obtain the maximum benefit of adding fiber, the optimum fiber could be 
determined from compaction tests.  
Soil behavior is a function of its density. By performing compaction tests on soils 
with different percentages of fiber it is shown that there is an optimum percentage of 
fiber that produces the maximum density of soil and determines the optimal water content 
needed for that percentage of fiber. Such percentages will produce the maximum benefit 
of the fiber. It is expected that the optimum percentage of fiber will be different for 
different types of fibers and for different types of soil, as well as for different degrees of 
compaction. Thus geotechnical engineers need to perform compaction tests if different 
fibers or soils are used and the percentage of fiber will likely be different for different 
situations (Amir-Faryar & Aggour, 2012a).  
The proper selection of the fiber content for each mixture is also important. It is 
suggested that fiber contents be selected with small intervals, at least 0.2%. As an 
example, in our study, the optimum fiber content could have been missed if fiber contents 
of 0, 0.5%, and 1% had been selected (0.5% intervals). Hence, the fiber contents of 0, 
 
112 
 
0.5%, and 1% could not provide the trend necessary to determine the optimum fiber 
content for the used fiber-reinforced composite. Furthermore, fiber content should be 
increased until a reduction in the value of the maximum dry density is observed for each 
particular clay type. The reduction will take place when all the soil voids are filled in 
with fibers and additional fibers are placed in between soil particles rather than in the 
voids. 
 
  
 
113 
 
CHAPTER 4 DYNAMIC TESTING PROGRAM AND RESULTS 
4.1 Introduction 
The research presented in this chapter has been performed for five main purposes: 
(1) to investigate the effect of fiber inclusion on the dynamic properties of clay; (2) to 
study the effect of the fiber content on the dynamic properties of the composite; (3) to 
investigate the effect of the type of fibers on the dynamic properties of clay; (4) to 
determine an analytical relationship between shear modulus and shear strain and also 
between material damping and shear strain of the composite; (5) to develop a general 
formula correlating material damping to the shear strain of soil. The developed formula is 
applied to all soil types, clayey, sandy, and fiber-reinforced soil composites. 
Formulas play a central role in predicting variables across various fields of study. 
Mathematical modeling of empirical data contains a general discussion about the 
experimental data obtained and its integration with data obtained from various 
experimental works in the field. A curve fitting model function correlating shear modulus 
with shear strain for soils is proposed in this chapter. Analytical relationships are then 
developed for clay and also fibrillated fiber-clay composites at fiber contents of 0.2% and 
0.4%. 
There are several mathematical models, formulas, and methods available to 
predict the material damping of soil. The majority of the available models and methods 
are lengthy and do not describe the damping system accurately. Some of them are limited 
to training data (the data used to develop that particular formula) or developed using a 
specific type of soil experiment in a particular condition that does not apply to a different 
 
114 
 
soil when the conditions are dissimilar. The available formulas are not universal, meaning 
if developed for sandy soils; it may not be able to be used for clays or vice versa. 
Therefore, developing a general formula that can correlate damping ratio to shear strain 
was needed. A general universal mathematical model was developed and evaluated using 
verification data (data that was not used to set the model?s parameter) to determine if the 
developed mathematical model can describe a soil damping system accurately. The 
obtained ?General Material Damping Formula for Soils? was evaluated against different 
soil types; i.e., sandy, clayey soils as well as fiber-clay composites. 
4.2 Testing Apparatus 
The Drnevich resonant column apparatus, a relatively nondestructive testing 
equipment, was used for this research. The resonant column testing apparatus employs a 
chamber having a lower and a top active platen confining a column of soil in between and 
with means to provide water and compressed air into the chamber for subjecting the 
column of soil to conditions representative of in-situ soil. A magnetic plate supporting 
torsional and longitudinal accelerometers, in association with fixed coils connected with 
an electrical circuit, provides for torsional vibration of the soil column. A centrally placed 
coil on the torsional magnet plate provides for torsional vibration of the soil column and a 
length measuring transducer (LVDT) in the upper platen serves to give constant readings 
of the length changes of the soil column. 
The excitation system of the resonant column device is an electromagnetic system 
comprising of a permanent magnet and coil, which can move in the gap between the 
north and south poles of the permanent magnet. For the torsional mode, the assembly 
comprises four rectangular coils and horseshoe-shaped magnets. The coils are connected 
 
115 
 
to the brackets and the magnets are connected to the top active platen. Equal gaps should 
be maintained between the magnets and the coils to minimize the development of any 
bending forces. The torsional coils allow movements (1.3 cm) in the vertical direction to 
accommodate the change in length during the consolidation process of clay. By 
generating an AC current of controlled frequency through the coils a magnetic field 
would be generated that in turn develops torsional forces on the top of the soil column. 
During each testing routine, the wave oscillator signals are amplified by the 
power amplifier and then inputted to the drive coils after passing through the power 
resistor in the control box. The pick-up system comprises of a piezoelectric meter 
(Columbia Model 200-1-H) placed in the active-end platen. The transducer is mounted at 
a distance of 0.0316 meters from the axes of rotation. The digital multimeter and 
oscilloscope are used to record the responses. A digital multimeter gives readings of 
sample acceleration in terms of rms; which in turn can be converted to define the shear 
strain. The oscilloscope monitors the frequency response of the sample. 
Sinusoidal excitation is used to study the dynamic properties, usually shear 
modulus and shear damping ratio, of soil in resonant column devices. In the tests, soils 
specimens vibrate torsionally under a sinusoidal excitation, and the shear modulus and 
damping ratio are measured from the resonant frequency and response, which are 
obtained by adjusting the frequency of the sinusoidal signal generator to a situation in 
which a vertical ellipse is observed.  
 
116 
 
4.3 Low-Amplitude Moduli of Fiber Reinforced Clay 
Low-amplitude moduli, or the maximum moduli of soils, are important to 
practical engineering, for example, low-amplitude moduli of soils are used in evaluating 
wave velocities, strength, etc. of soil. Currently, many methods are used to evaluate the 
low-amplitude moduli of soil in the field and laboratory as stated in chapter 1. In the 
Resonant Column Test, a confining pressure of 5 psi (34.5 kPa), corresponding to 
approximately six feet of soil in an in situ condition, was applied to the specimen.  
4.4 Sample Preparation 
The specimens were prepared by mixing kaolinite with various percentages of 
fiber content (FC) and percentages of mixtures by weight, per Amir-Faryar and Aggour?s 
established compaction procedure (Amir-Faryar and Aggour, 2012a) as explained in 
Chapter 3. The soil-water mixture for compaction was prepared by first mixing a 
measured amount of dry soil (about 2 kg in each test) with a predetermined amount of 
water by hand and then by a mechanical mixer. In the case of fiber addition, the weight of 
the specific fiber contents was calculated based on the weight of the air dried soil. The 
required amount of fiber was first mixed with the dry soil, and then water was gradually 
added. Mixing continued until a uniform mix was produced. Compaction tests were 
performed on a mixture of kaolinite soil with fiber immediately after achieving a uniform 
and homogeneous mixture. Mixtures of monofilament fiber and kaolinite soil and also 
fibrillated fiber and kaolinite were made at their maximum dry densities and optimum 
moisture contents. Resonant Column tests were performed on composites with different 
fiber contents. An undisturbed sample from the fiber-clay composite at fiber contents of 
 
117 
 
0.2%, 0.4%, and 0.6% were carefully obtained using a hollow brass cylinder shown in 
Figure 4-1. 
 
Figure 4-1: Hollow brass cylinder with clay sample inside 
The inside and outside of the hollow cylinder was lubed using 3M Silicone Lubricant. 
The hollow cylinder was pushed into the already-compacted-clay in the standard mold, 
using a Tinius Olson Compressor. Then, the clayey soil was taken out of the standard 
mold using a standard mold extruder as shown in Figure 4-2. 
 
118 
 
 
Figure 4-2: Hollow brass cylinder pushed into the compacted soil 
The brass cylinder with soil inside was recovered as shown in Figure 4-1. Then, 
the soil specimen was gently taken out of the brass hollow cylinder using a filled cylinder 
shown in Figure 4-3, and a Tinius Olson Compressor. The diameter of the filled cylinder 
is slightly smaller than the diameter of the brass hollow cylinder. 
 
119 
 
 
Figure 4-3: Filled cylinder 
Caution should be undertaken when the specimen is taken out of the hollow 
cylinder in order to obtain a specimen with the least amount of disturbance. Shear wave 
velocity and maximum shear modulus measurements in the field and laboratory are very 
sensitive to sample disturbance effects. Therefore, field values may be 20 % to 100 % 
higher than lab values. Specimens of approximately 35 mm diameter and 82 mm length 
were prepared. 
The dynamic test should not be started until the resonant column apparatus and all its 
attached devices are assured to be properly working. Hence, each time a soil specimen 
was made it was kept inside a lidded jar to maintain its moisture content and minimize 
the loss of moisture. The specimen is shown inside a lidded jar in Figure 4-4. 
 
120 
 
 
Figure 4-4: Soil specimen held inside a lidded jar 
When the testing was about to start, a thin membrane was wrapped around the 
specimen then placed inside the resonant column apparatus. Two O-rings were used to 
block water from seeping into the specimen as shown in Figure 4-5. 
 
121 
 
 
Figure 4-5: Membrane wrapped around soil specimen. Two o?rings can be seen in the 
picture 
  Specimens for all different mixtures were placed under 34.5 kPa (5 psi) pressure 
for 1020 minutes in order to have the primary consolidation completed prior to starting 
the dynamic testing. It is indicated that under uniform confining pressure primary 
consolidation of clay can be completed after approximately 1000 minutes of pressure 
application (Afifi & Richart, 1973). Some researchers have indicated that the completion 
of the primary consolidation can take place at approximately 100 to 200 minutes after 
which secondary consolidation begins (Kokusho, et al., 1982). After placement of the 
specimen under confining pressure for 1020 minutes (17 hours), no longitudinal strain 
 
122 
 
was recorded. Therefore, 1020 minutes appeared to be sufficient for our testing. The 
dynamic testing was also performed under 34.5 kPa confining pressure. 
4.5 Dynamic Testing Procedure 
After the weight, diameter, and length of the specimen was determined, the 
specimen was inserted in the rubber membrane and set up on the bottom platen of the 
resonant column and the top platen attached when the magnet platen was lowered and 
placed on the top of the specimen. Two rubber O-rings were used close to each end of the 
specimen to protect the specimen from being soaked by the confining media. Then, the 
torsional drive coil system and LVDT were assembled. Vacuum grease was used prior to 
placing the pressure chamber in order to seal the chamber. The pressure chamber was 
filled with water to the top porous stone to ensure a uniform confining pressure around 
the specimen. After allowing the water turbulence to settle, the initial reading of the 
LVDT was recorded. Then, the specimen was placed under the confining pressure as 
described in Section 4.4. After the confining period, the sample was torsionally excited 
with sinusoidal waves. The resonance condition of the system at each strain amplitude 
was established by adjusting the frequency of the excitation until a Lissajous figure was 
observed as shown in Figure 4-6. A Lissajous figure is a vertical ellipse that corresponds 
to a 90 degree phase angle between the acceleration response and the excitation. 
 
123 
 
 
Figure 4-6: Observed Lissajous figure on oscilloscope 
The resonant frequency of the system was measured with a digital frequency counter and 
the excitation and response accelerations were measured by a digital multimeter in 
millivolt (rms). 
The dynamic testing was performed on clay with 0%, 0.2%, 0.4%, and 0.6% fiber 
contents with an initial frequency and voltage amplitude of 15 Hz and 50 mV, 
 
124 
 
respectively. The frequency was gradually increased to reach up to the sample?s resonant 
frequency while the voltage amplitude remained constant. The test was repeated for each 
sample with 100, 200, and 300 mV voltage amplitudes to obtain data for different shear 
strains. The test was performed on clay mixtures with fibrillated fibers as well as 
monofilament. 
4.5 Dynamic Testing Results for Fibrillated Fiber Reinforced Clay 
The resonant column tests were conducted on clay as well as mixtures of clay and 
0.75 inch fibrillated fiber with different fiber contents in order to study the effect of fiber 
inclusion as well as fiber content on the dynamic properties of clay.  As for fiber lengths, 
a 0.75 inch length was selected over a 0.5 inch length because it was shown in Chapter 3 
that the composites made with 0.75 inch fiber provided denser mixtures, as shown in 
Table 3-3. The results of the dynamic testing are discussed in the following sections. 
4.5.1 Effect of Fibrillated Fiber Inclusion and Fiber Content on Shear Modulus of 
Clay 
It was observed that the addition of fibrillated fibers affected the shear modulus of 
clay. The results indicated that the inclusion of fibrillated fiber increased the maximum 
shear modulus of the clay. Figure 4-7 shows the maximum shear modulus versus fiber 
content of the composite.  
 
125 
 
 
Figure 4-7: Maximum shear modulus versus fiber content graph (fibrillated fiber) 
From Figure 4-7, it can be seen that the inclusion of fiber can increase the value of the 
maximum shear modulus as much as 17.5%. It can also be seen that the maximum value 
for the maximum shear modulus (Gmax) is when the fiber content of the composite is 
equal to 0.2%. It also corresponds to the optimum fiber content value of the mixture 
obtained in Chapter 3. The value of the maximum shear modulus was increased when the 
fiber content increased until it reached up to 0.2%, then, by increasing the fiber content 
the value of the maximum shear modulus started to decrease. 
The rate of degradation of the shear modulus is normally done by dividing the 
shear modulus by the maximum shear modulus at different shear strains. It is called the 
Normalized Shear Modulus (G/Gmax). The curve of normalized shear modulus versus 
shear strain can provide valuable information about the soil as to how gradually the soil 
can lose its shear modulus value when the shear strain increases. In general, soils that 
lose their maximum shear modulus value faster due to larger strains are less stiff than the 
 
126 
 
ones that lose their maximum shear modulus slower. Figure 4-8 shows graphs of 
normalized shear modulus versus shear strain of clay and fiber reinforced composites 
with 0.2%, 0.4%, and 0.6% fibrillated fiber.  
 
Figure 4-8: Normalized shear modulus versus shear strain graph for different fiber 
contents (Fibrillated fiber) 
The results of Figure 4-8 generally indicated that fibrillated fiber, if used as 
reinforcement, could improve the shear modulus, which is an indication of torsional 
stiffness of the clay. Fiber reinforced composites showed that they had larger normalized 
shear modulus at the same shear strain. It was also shown that the composite with 0.2% 
fibrillated fiber lost its maximum shear modulus value slower than the other composites 
and the clay. 
4.5.2 Effect of Fibrillated Fiber Inclusion and Fiber Content on Damping Ratio of 
Clay 
It was also seen that the addition of fibers affected the damping ratio of the clay. 
The results indicated that the inclusion of fibrillated fiber increased the material damping 
 
127 
 
of the clayey soil. Figure 4-9 shows the minimum damping ratio (Dmin) versus fiber 
content of the composite.  
 
Figure 4-9: Minimum damping ratio versus fiber content graph (fibrillated fiber) 
From Figure 4-9, it can be seen that the inclusion of fiber can increase the value of the 
damping ratio of the clay. It was observed that the increase in the value of material 
damping of the soil would be greater in composites with larger fiber content values. 
Figure 4-10 shows the graphs of damping ratio versus shear strain of clay and fiber 
reinforced composites with 0.2%, 0.4%, and 0.6% fibrillated fiber. It was observed that 
the value of the damping ratio of the clayey soil as well as fiber reinforced composites 
increased when the shear strain increased. 
 
128 
 
 
Figure 4-10: Damping versus shear strain graph for different fiber contents (fibrillated 
fiber) 
4.6 Dynamic Testing Results for Monofilament Fiber Reinforced Clay 
In order to further study the effect of fiber type, the length of the fiber was kept 
constant at 0.75 inch and mixtures with assigned fiber compositions, i.e., 0.2%, 0.4%, and 
0.6% of monofilament type were made for testing. 
4.6.1 Effect of Monofilament Fiber Inclusion and Fiber Content on Shear Modulus 
of Clay 
The addition of monofilament fibers also affected the shear modulus of the clay. 
The results indicated that the inclusion of monofilament fiber increased the maximum 
shear modulus of the clay. Figure 4-11 shows the maximum shear modulus versus fiber 
content of the composite.  
 
 
129 
 
 
Figure 4-11: Maximum shear modulus versus fiber content graph (monofilament fiber) 
From Figure 4-11, it can be seen that the inclusion of monofilament fiber can increase the 
value of the maximum shear modulus as much as 14.7%. It can also be seen that the 
maximum value for the maximum shear modulus (Gmax) is when the fiber content of the 
composite is equal to 0.2%. It also corresponds to the optimum fiber content value of the 
composite. The value of the maximum shear modulus was increased when the fiber 
content increased until it reached up to 0.2% fiber, then by increasing the fiber content 
the value of the maximum shear modulus started to decrease. 
Figure 4-12 shows the graphs of normalized shear modulus versus shear strain of clay 
and fiber reinforced composites with 0.2%, 0.4%, and 0.6% monofilament fiber. 
 
130 
 
 
Figure 4-12: Normalized shear modulus versus shear strain graph for different fiber 
contents (monofilament fiber) 
The results of Figure 4-12 generally indicated that monofilament fiber, if used as 
reinforcement, could improve the torsional stiffness of the clay. Fiber reinforced 
composites showed that they had a larger normalized shear modulus at the same shear 
strain. It was also shown that the composite with 0.2% monofilament fiber lost its 
maximum shear modulus value slower than the other composites and clay (Amir-Faryar 
& Aggour, 2012b). 
4.6.1 Effect of Monofilament Fiber Inclusion and Fiber Content on Damping Ratio 
of Clay 
The addition of monofilament fibers affected the damping ratio of the clay. The 
results indicated that the inclusion of monofilament fiber increased the material damping 
of the clayey soil. Figure 4-13 shows the minimum damping ratio (Dmin) versus fiber 
content of the composite.  
 
131 
 
 
Figure 4-13: Minimum damping ratio versus fiber content graph (monofilament fiber) 
From Figure 4-13, it can be seen that the inclusion of fiber can increase the value of the 
damping ratio of the clay. It was also observed that the increase in the value of material 
damping of the soil would be greater in composites with larger fiber content values. 
Figure 4-14 shows the graphs of damping ratio versus shear strain of clay and fiber 
reinforced composites with 0.2%, 0.4%, and 0.6% fibrillated fiber. It was observed that 
the value of the damping ratio of the clayey soil as well as fiber reinforced composites 
increased when the shear strain increased (Amir-Faryar & Aggour, 2012b). 
 
132 
 
 
Figure 4-14: Damping versus shear strain graph for different fiber contents 
(monofilament fiber) 
It should be noted that the shear strain axis plotted is not in a logarithmic scale so as to 
emphasize the changes in both the shear modulus and damping ratio in the low shear 
strain range tested for the clay and the fiber reinforced clay. 
4.7 Effect of Fiber Types on the Dynamic Properties of Clay 
The results show that the inclusion of both types of fiber at optimum fiber content 
can improve the shear modulus of clay. It was observed that the inclusion of fiber can 
increase the maximum shear modulus of clay as much as 17.5% and 14.7% for fibrillated 
and monofilament fibers, respectively. The maximum shear modulus of the fiber 
reinforced clay is greater in the case of using fibrillated fiber as fiber reinforcement. This 
observation could be due to the fact that a mixture made with fibrillated fiber is denser 
than that made with monofilament fiber at the same fiber content. A conclusion can also 
be drawn by comparing fiber deniers. A fiber?s denier is 1500 and 6 in case of fibrillated 
and monofilament fibers, respectively. It means that 9000 meters of fibrillated fiber is 
 
133 
 
250 times heavier than 9000 meters of monofilament fiber, based on the denier definition. 
That could be a reason for producing a denser composite when mixed with soil. 
In addition, the inclusion of fiber increased the material damping ratio of the clay. 
The increase in the material damping ratio was 29.7% and 26.4% for fibrillated and 
monofilament fibers, respectively. The experiments showed that the inclusion of 
fibrillated fiber can improve the dynamic properties of clay slightly more than 
monofilament fiber.  In order to better understand the damping results and why damping 
results in these two types of fiber were slightly different, we need to understand the 
fundamentals of damping in composites. The damping in composites is controlled by the 
matrix (clay) properties, the fiber properties, the interaction between fibers and the 
matrix. The matrix properties remained constant for composites made up of 
monofilament and fibrillated fibers when the dynamic testing was conducted. Hence, the 
effect of matrix properties and its contribution to the total material damping in each 
composite was the same. Since both fiber types, monofilament and fibrillated fibers, are 
made up of polypropylene fibers, the effect of fiber material on the total composite 
damping can also be similar. The fiber length and orientation for both types of 
composites were also kept constant. Therefore, the fiber properties could be eliminated as 
a cause in damping result differences between these two types of composites. The fiber-
 matrix interface or interphase region is an area where energy can be converted into heat is 
the most probable cause of obtaining slightly different material dampings. Different fiber-
 matrix adhesion and molecular motion within the interphase can be the reason for the 
slight difference in the material damping of these two types of composites. 
 
134 
 
4.8 Comparison of the Dynamic Response of Clay with Published Data 
The results obtained from the dynamic testing of clay for this study were 
compared with the results of Vucetic and Dorby?s (1991) general curves for clay at a 
similar plasticity index. Vucetic and Dorby?s general curves for clay are used extensively 
to predict the dynamic properties of clay at different shear strains. The comparison shows 
that the normalized shear modulus and damping ratio obtained in this study agree with 
the Vucetic and Dorby?s results. Figures 4-15 and 4-16, respectively, show normalized 
shear modulus versus shear strain and damping ratio versus shear strain developed from 
this study data and also Vucetic and Dorby?s data. 
 
Figure 4-15: Normalized shear modulus versus shear strain comparison graph  
 
 
135 
 
 
Figure 4-16: Damping versus shear strain comparison graph 
4.9 Repeatability 
Three samples of kaolinite were mixed and prepared with fibrillated fiber at 
optimum fiber content. The normalized shear moduli at low shear strains were 
determined. The mean and standard deviation (SD) of the samples are 0.99275 and 
0.001at the shear strain of 0.00388 %, respectively. The mean and standard deviation of 
the samples for shear modulus are 51.71 MPa and 0.6 at the shear strain of 0.00388 %. 
All three samples fall within the 95 % mean confidence level (Varde, et al., 1996). The 
damping ratios at low shear strains were determined. The mean and standard deviation of 
the samples are 2.74 % and 0.02 at the shear strain of 0.00388 %, respectively. All three 
samples fall within the 95 % mean and ?4 SD confidence levels. Normalized shear 
modulus and damping ratio versus shear strain curves of all the three series of samples 
are shown in Figures 4-17 and 4-18. 
 
136 
 
 
Figure 4-17: Normalized shear modulus versus shear strain series of data 
 
Figure 4-18: Damping ratio versus shear strain series of data 
Figure 4-19 shows the damping data and also the confidence levels. 
 
137 
 
 
Figure 4-19: Modeling of damping ratio as function of shear strain 
The results show that the obtained data are within the acceptable confidence level 
expected in soil preparation variability. 
4.10 Mathematical Modeling of Empirical Data 
A formula with four coefficients was proposed to be used as the function for the 
curve-fitting. Non-linear curve-fitting was performed to determine an analytical 
relationship between the shear modulus and shear strain of clay and fiber-clay composite 
using the proposed function. The measured and predicted values provided a good 
agreement for clay and fiber reinforced clay. 
For damping ratio, there have been several equations and methods that they have 
been developed for a specific type of soil, and thus for other types of soils, do not provide 
a suitable agreement between experimental data and predicted data. Some of the methods 
are very lengthy and time-consuming and the ultimate predicted data is not accurate. 
Therefore, a general formula was developed for the damping ratio that can correlate soil 
 
138 
 
and composite?s material damping to shear strain. The obtained formula is universal and 
can be used for any type of soil; i.e., clay, sand or even a fiber-clay composite. It is of 
paramount importance to form an effective strategy to determine coefficients of the 
formula. Hence, non-linear curve fitting using the least square error method following a 
procedure explained in Section 4.10.1 was utilized.  
A function can be either linear or non-linear in the coefficients. The word ?linear? 
in linear curve-fitting (regression) does not mean that the function is a straight line, but 
that the partial derivatives with respect to each coefficient are not a function of other 
coefficients. There are many published computer programs and commercial software 
packages that perform non-linear regression analysis. Out of which, Mathcad, Matlab, 
and Microsoft Excel Add-in Solver are the most popular applications to use for a non-
 linear least square method. 
4.10.1 Non-linear Least Square Method 
Least Square analysis is used to fit a set of ?m? observations with a model that is 
non-linear in n unknown parameters (m>n). A set of ?m? data points (x1,y1), (x2,y2), ?, 
(xm,ym) and a model function y = f (x,b) where x is an independent variable and ?b? is 
unknown parameters, b = (b1, b2, ?, bn), with m>n. The objective is to obtain ?b? 
parameters such that the model best fits the given data in the least squares sense, that is 
the sum of residual squares as shown in Equation 4.1. The difference between the actual 
data point and the point predicted by the model function is called residual (error). 
 
139 
 
 
 
(4.1)  
where, ri = residuals, S = sum of residual squares. 
To obtain the best fit the sum of residual squares (S) should be minimized, where the 
residuals are given by equation 4.2. 
 
 
 
(4.2)  
The minimum value of S occurs when the gradient is equal to zero. Since the model 
contains n parameters there will be n gradient equations as equation 4.3. 
 
 
 
(4.3)  
In a non-linear system, the derivatives  are functions of both the independent 
variables and the parameters. Therefore, these gradient equations do not have a closed 
solution. Instead, initial values must be chosen for the parameters, then, the parameters 
are refined iteratively to obtain optimized solutions. The optimization process can be 
done by published software packages. For instance, Mathcad has a function called 
?genfit? that can be used to find the best-fit coefficients. Matlab software also has a 
similar function called ?fmins?, which provides the same results as Mathcad function. 
There is also an add-in software package to a Microsoft Excel program that provides the 
same results as commercial software packages such as Mathcad and Matlab. The Solver 
 
140 
 
code is not written by Microsoft, but instead is a product of Frontline Systems, Inc. 
(www.frontsys.com) (Billo, 2001). The Solver add-in was used as an optimization tool 
for this research. 
 The Solver is an optimization package that attains a maximum, minimum, or 
specified value of a target cell by varying the values in one or several cells. It can achieve 
these tasks by means of an iterative process, beginning with trial values of the parameters 
(coefficients). The value of each parameter is changed by a suitable increment, the new 
value of the function is obtained and the change in the value of the function is used to 
calculate improved values for each of the parameters. The process is repeated until the 
desired result is achieved. The Solver uses the above mentioned gradient method to find 
the optimum set of parameters. Since the Solver operates by a search routine, it will 
obtain a solution most efficiently if the initial provided estimates are close to the final 
values. On the contrary, it may not be able to obtain a solution if the initial estimates are 
far from the final values (Billo, 2001). To ensure that the Solver has obtained a global 
minimum rather than a local minimum, a different set of initial estimate values was used 
to obtain a solution. 
To obtain an equation covering a wide strain range with data points in a wide 
strain range using a function model, all district point data were used for the optimization. 
In addition, to obtain an equation covering a wide strain range with data obtained in a 
small strain range using a function model, an iterative method was established using the 
data points for a small range and also one arbitrary data point selected in a larger strain 
part of the curve, i.e., (a,b), where a is a dependent parameter (normalized shear modulus 
or damping ratio), b is shear strain in a larger strain part of the curve.  The non-linear 
 
141 
 
curve fitting was performed and the coefficient of regression using experimental data 
points and point (a,b) was obtained.  While the value of ?b? remained constant, the value 
of ?a? changed to improve the coefficient of regression. This iterative process was 
continued until no improvement in the coefficient of regression was observed. A 
schematic sketch showing the curve fitting approach is shown in Figure 4-20. This 
procedure can provide a suitable result if a correct model is used for the data set. For 
normalized shear modulus versus shear strain amplitude, a model function, Equation 4.4, 
was proposed in Section 4.10.2 and used for curve-fitting. For the damping ratio versus 
shear strain amplitude a general equation developed in Section 4-10.3 of this manuscript 
was used. 
 
 Figure 4-20: Schematic sketch showing the curve fitting approach 
After developing the equations, the predicted values from the developed equation and 
measured values were compared. The values were generally within ? 5%. 
 
142 
 
4.10.2 Normalized Shear Modulus Equations 
A formula with four coefficients was proposed to be used as the function for the 
curve-fitting. Non-linear curve-fitting was performed to determine an analytical 
relationship between the shear modulus and shear strain of clay and fibrillated fiber-clay 
composite using the proposed function. The proposed function is a modification of 
Borden?s equation (Borden, et al., 1996). The measured and predicted values were 
compared to examine the accuracy of the proposed model for clay and fiber reinforced 
clay. 
A curve fitting model function for soils are proposed in this section. The function 
correlates the normalized shear modulus G/Gmax with an increase in shear strain 
amplitude (?). The suggested function is presented in Equation 4.4. 
  (4.4) 
where, constants a, b, c, and d represent the decay rate of G/Gmax with an increase in 
shear strain amplitude (?). The equations developed for clay and fiber-reinforced clay at 
optimum fiber content and 0.4% fiber content are presented in Equations 4.5, 4.6, and 
4.7, respectively. 
Clay  
FC = 0.0% 
R2=0.99 
 
 (4.5) 
 
 
143 
 
Fibrillated 
Fiber- Clay 
Composite at 
FC = 0.2% 
R2=0.99 
 
 (4.6) 
Fibrillated 
Fiber- Clay 
Composite at 
FC = 0.4% 
R2=0.99 
 
 (4.7) 
Figure 4-21 shows a graph of shear modulus versus shear strain of clay and fiber-clay 
composites using Equations 4.5 to 4.7. 
 
Figure 4-21: Graph of shear modulus versus shear strain for clay and fiber-reinforced 
clay (FC = 0.2% & 0.4%) 
 
144 
 
A graph of measured versus predicted was presented in Figures 4-22, 4-23, and 4-24 to 
show how accurate the obtained values are using the developed Equations 4.5, 4.6 and 
4.7. 
 
Figure 4-22: Graph of measured G/Gmax versus predicted G/Gmax for clay (FC = 0.0%) 
 
145 
 
 
Figure 4-23: Graph of measured G/Gmax versus predicted G/Gmax for fiber-reinforced 
clay (FC = 0.2%) 
 
Figure 4-24: Graph of measured G/Gmax versus predicted G/Gmax for fiber-reinforced 
clay (FC = 0.4%) 
 
146 
 
Figures 4.22 through 4.24 show that the obtained data are well-fitted into the formula 
developed to predict shear modulus values for clay and fiber-clay composites. 
4.10.3 General Material Damping Formula for Soils 
There are several available functions, formulas, and methods to predict the 
material damping of soil. A majority of the available models and methods cannot 
describe the damping system accurately. Some of them are limited to training data (the 
data used to develop that particular formula) or developed using a specific type of soil 
experiment in a particular condition that does not apply to a different soil or similar soil 
with dissimilar conditions. Therefore, a general universal mathematical model was 
proposed and evaluated using our experimental data and verification data (data that was 
not used to set the model?s parameter) to determine if the developed mathematical model 
can describe a soil damping system accurately. The obtained ?Damping General Formula 
for Soils? was evaluated against different soil types; i.e. sandy, clayey soils as well as 
fiber-clay composites. 
After prudently studying material damping ratio versus shear strain curves for 
cohesive and cohesionless soils and performing extensive non-linear curve fitting using 
different mathematical functions, it was realized that curves represent damping versus 
shear strain are similar to power equations ( ) with a more gentle slope inclination 
at larger shear strains. Therefore, some modification to power equations was made to take 
the gentle slope inclination into consideration. A curve fitting model function that 
correlates the damping ratio (D) with an increase in shear strain amplitude (?) is proposed 
as below: 
 
147 
 
  (4.8) 
where, constants a, b, c, d, and e represent the increasing of D with an increase in shear 
strain amplitude (?). The equation is valid when the shear strain is in the range of 
 . The damping ratio in a strain smaller than 0.001% can be assumed 
to be constant and similar to a damping ratio corresponding to 0.001% shear strain. The 
damping equations developed for clay and fiber-reinforced clay at optimum fiber content 
are presented in equations 4.9, and 4.10, respectively. 
Clay  
FC = 0.0% 
R2=0.99 
 
 
 
(4.9) 
Fibrillated 
Fiber- Clay 
Composite at 
FC = 0.2% 
R2=0.99 
 
 
 
(4.10) 
Figure 4-25 shows a graph of shear modulus versus shear strain of clay and fiber-clay 
composites using equations 4.9 and 4.10. 
 
148 
 
 
Figure 4-25: Graph of damping ratio versus shear strain for clay and fiber-reinforced clay 
(FC = 0.2%) 
A graph of measured versus predicted is presented in Figures 4-26 and 4-27 to show how 
accurate the obtained values are using the developed equations 4.9 and 4.10. 
 
149 
 
 
Figure 4-26: Graph of measured damping ratio versus predicted damping ratio for clay 
(FC = 0.0%) 
 
Figure 4-27: Graph of measured damping ratio versus predicted damping ratio for fiber-
 reinforced clay (FC = 0.2%) 
 
150 
 
Figures 4.26 and 4.27 show that the obtained data are well-fitted to the formula 
developed to predict damping ratio values for clay and fibrillated fiber-clay composite. 
4.11 Damping Formula Evaluation Using Verification Data 
In order to validate the accuracy of the proposed damping formula, Seed and 
Idriss 1991?s data for sand as well as Vucetic and Dorby 1991?s data for clay was used as 
verification data. Non-linear regression was performed on the data and the coefficient of 
regression was obtained to confirm the accuracy of the fit. Seed and Idriss 1991 has three 
sets of data called Upper Limit, Mean Limit, and Lower Limit. The data are presented in 
Table 4.1. Normalized shear modulus and damping versus shear strain curves were drawn 
in Figures 4.28 and 4.29, respectively. 
 
 
 
 
151 
 
 
 
Table 4-1: Upper, mean, and lower limits data, after Seed and Idriss, 1991 
Upper Limit Data 
Strain G/Gmax Damping 
0.0001 1 0.24 
0.0003 1 0.42 
0.001 0.99 0.8 
0.003 0.96 1.4 
0.01 0.85 2.8 
0.03 0.64 5.1 
0.1 0.37 9.8 
0.3 0.18 15.5 
1 0.08 21 
3 0.05 25 
10 0.035 28 
 
Lower Limit Data 
Strain G/Gmax Damping 
0.0001 1 0.75 
0.0003 0.98 1.1 
0.001 0.93 3 
0.003 0.84 5.5 
0.01 0.64 9.5 
0.03 0.43 15 
0.1 0.23 21.2 
0.3 0.12 25.4 
1 0.04 28 
3 0.03 28.8 
10 0.025 29 
Mean Limit Data 
Strain G/Gmax Damping 
0.0001 1 0.48 
0.0003 0.99 0.8 
0.001 0.96 1.5 
0.003 0.9 3.2 
0.01 0.76 5.7 
0.03 0.57 9.5 
0.1 0.3 15.2 
0.3 0.15 20.5 
1 0.06 24.6 
3 0.04 27 
10 0.03 28.5 
 
 
 
 
 
 
152 
 
 
 
Figure 4-28: Graph of normalized shear modulus versus shear strain for sand, after Seed 
and Idriss 1991 
 
Figure 4-29: Graph of damping ratio versus shear strain for sand, after Seed and Idriss 
1991 
The damping equations developed for sand are presented in equations 4.11 through 4.13. 
 
153 
 
Sand ? 
Lower Limit 
R2 = 0.9899 
 
 
(4.11) 
Sand ? Mean 
Limit 
R2 = 0.9940 
 
 
(4.12) 
Sand ?Upper 
Limit 
R2 = 0.9957 
 
 
 
(4.13) 
A graph of measured versus predicted is presented in Figures 4-30 through 4-32 to show 
how well the verification values for sands fit into the general damping equation. 
Equations 4.11 through 4.13 were used to determine the predicted values for the damping 
ratio of sand. 
 
Figure 4-30: Graph of measured damping ratio versus predicted damping ratio for lower 
limit sand, after Seed and Idriss, 1991 
 
154 
 
 
Figure 4-31: Graph of measured damping ratio versus predicted damping ratio for mean 
limit sand, after Seed and Idriss, 1991 
 
Figure 4-32: Graph of measured damping ratio versus predicted damping ratio for upper 
limit sand, after Seed and Idriss, 1991 
 
155 
 
Figures 4.30 through 4.32 plus developed equations that have high coefficients of 
regression show that the data for sand are well-fitted to the formulas developed to predict 
damping ratio values. 
 The other verification data that was used to evaluate the accuracy of the general 
damping formula is Vucetic and Dorby (1991) data for clay. The damping equations 
determined using Vucetic and Dorby 1991?s data is presented in Equation 4.14. 
Clay 
R2 = 0.9985 
 
 
(4.14) 
A graph of measured versus predicted is presented in Figures 4-33. 
 
Figure 4-33: Graph of measured damping ratio versus predicted damping ratio for clay, 
after Vucetic and Dorby 1991 
 
156 
 
4.12 Conclusions 
This research shows that the addition of fiber to clay has improves its dynamic 
properties. It increases the shear modulus as well as its damping. The main conclusion of 
this study is that the inclusion of fiber at optimum fiber content as a ground improvement 
technique can improve the dynamic properties of soft and weak clayey soils at low shear 
strains. This increase in the value of dynamic properties of clay can be mainly due to the 
rearrangement of soil particles caused by the addition of fibers. Since the soil at its 
optimum fiber content becomes fiber-saturated, meaning that all soil voids are mostly 
filled with fiber, it produced a stiffer composite while benefiting from the material 
damping properties of the polypropylene materials. It is important to note that the fact 
that both the shear modulus and damping increased provides a double benefit for the 
dynamic response of a site by increasing the stiffness of the site and reducing its 
amplitude of vibration. 
If the foundation of a building is planned to be placed on a soft clayey soil and the 
building foundation is planned to be subjected to a limited amount of vibration, the 
density of soft clayey soil and its stiffness can be improved using fiber as reinforcement 
while increasing the clay?s damping ratio. The fiber modification will reduce the 
vulnerability of the building foundation to seismic loads. 
The other use of the fiber reinforced clay could be when a machine foundation is 
to be designed. The inclusion of fiber in clayey soil can limit and attenuate the vibration 
and could be a desirable method to limit the amplitude of vibration of the machine 
foundation system. It is recommended to first obtain the optimum fiber content for the 
 
157 
 
composite and select the fiber type based on the extent to which the vibration is desired to 
be controlled. 
A general damping equation as well as a shear modulus equation was developed 
correlating the dynamic properties of soil material to shear strain. The proposed equations 
can predict dynamic soil behaviors for all types of soils.  
 
158 
 
CHAPTER 5 EFFECT OF FIBER REINFORCEMENT OF CLAY ON 
SEISMIC SITE RESPONSE  
In recent years, earthquakes such as the Haiti 2010, Alaska (USA) 2011, Tohoku 
(Japan) 2011, Talca (Chile) 2012, and the most recent Ahar (Iran) 2012 have caused 
considerable damage to buildings and infrastructure. One of the causes of heavy damages 
due to earthquake motions is the role of soft clay in amplifying bedrock ground motions. 
Modifying the soil conditions of a site in order to mitigate the earthquake damage can be 
one of the methods of enhancing site conditions and its effects on seismic site response. 
In the previous chapter the results of fiber inclusion on dynamic properties of 
clayey soil, normalized shear modulus and damping ratio, were presented. This chapter 
presents the results of a study on the clay?s seismic site response and the effect of fiber 
inclusion on the site response. DEEPSOIL software was used to perform one dimensional 
wave propagation analysis. Equivalent-linear material property characterization was 
employed in the analysis. Two different material types, clay and fibrillated fiber 
reinforced clay, were used for different soil columns.  
The research presented in this chapter was performed to: (1) investigate the effect 
of the modification of clay using fibrillated fiber reinforcements on the site response; (2) 
study the effect of depth to bedrock on the site response of the fiber reinforced site; (3) 
further investigate the effect of the thickness of soil reinforced layer; (4) study the effect 
of different earthquake motions on the site response. 
 
159 
 
5.1 Seismic Response of Horizontally Layered Soil 
There are several methods for evaluating the effect of soil conditions on the site?s 
response during an earthquake. Most of these methods assume that the main response of a 
soil layer is caused by the upward spread and propagation of shear waves (S Waves) from 
the underlying bedrock formation. Figure 5.1 shows a schematic figure of the upward 
propagation of a shear wave from bedrock.  
 
Figure 5-1: Schematic figure showing the upward propagation of a shear wave from 
bedrock 
Analytical methods based on this assumption of incorporating a linear estimate of the 
nonlinear soil behavior, have been shown to provide results in reasonable agreement with 
field data.  
5.1.1 Seismic Site Response Evaluation Procedure 
The analytical procedure performed in this chapter involves the following steps: 
 
160 
 
a) Determine the characteristics of the motions likely to propagate from a bedrock 
formation underlying the site.  
b) Determine the dynamic properties of the soil layers. 
c) Compute the response of the soil layers to the bedrock motions at the ground 
surface. 
The maximum acceleration, predominant period, and effective duration are the most 
essential parameters of an earthquake motion. These parameters should be considered 
when an earthquake motion is selected as a design motion for the site response analysis. 
The predominant period (Tp) is a period at which the maximum spectral acceleration 
takes place in an acceleration response spectrum obtained for 5% viscous damping. The 
maximum response acceleration is the maximum response of a single degree of freedom 
(SDOF) system to a particular input motion. It is a function of the natural period and 
damping ratio of the SDOF system. The dynamic properties of the soil deposits also play 
an important role in the site response analysis. A dynamic testing procedure can provide 
accurate input for the analysis. A one-dimensional method of analysis can be used if the 
soil formations are largely horizontal. Computer programs developed for performing such 
analysis are usually based on either the solution to the wave equation or a lumped mass 
simulation. Finite element analysis can be used if more irregular soil layers are dealt with. 
For our study, one dimensional analysis has been selected because of the fact that it is 
commonly used in engineering practice and also for the purpose of comparison of the 
values of unreinforced clay and fiber reinforced clay, it provides acceptable results. 
 
161 
 
5.1.2 Equivalent Linear Approach 
The equivalent linear method was based on the work of Idriss and Seed (Idriss & 
Seed, 1968); (Seed & Idriss, 1970).  Seed and Idriss works are also employed in the 
extensively used program SHAKE (Schnabel, Lysmer, & Seed, 1972) and its later 
version SHAKE91 (Idriss & Sun, 1992). The option of equivalent linear in the 
DEEPSOIL software assumes that the layers are horizontal and are infinite in the 
horizontal direction. The non-linear dynamic soil moduli and damping as a function of 
shear strain are entered into the program as discrete points. Then, the actual nonlinear 
hysteresis stress-strain behavior of cyclically loaded soils is estimated by the equivalent 
linear soil dynamic properties. The equivalent linear shear modulus (G) is taken as a 
secant shear modulus, and the equivalent linear damping ratio is taken as the damping 
ratio that generates the same energy loss in a single cycle in the developed hysteresis 
loop. These equivalent linear dynamic properties are strain dependent. In the equivalent 
linear approximation, it is common to determine the strain level in terms of an effective 
shear strain. The shear strain has been found to be in a range between 50% and 70% of 
the maximum shear strain (Kramer, 1996). For our analysis, the effective shear strain was 
taken as 65% of the peak strain. An iterative procedure is required because of the fact that 
the values of the computed strain level depend on the values of the equivalent linear 
dynamic properties. The use of an iterative procedure makes certain that the properties 
used in the analysis are representative properties in all layers. It also ensures that the 
computed response is not specifically sensitive to the effective shear strain. 
 
162 
 
5.1.3 Analysis using DEEPSOIL Software Program 
DEEPSOIL is a one-dimensional site response program application that can 
perform the frequency domain analysis method (linear, equivalent linear) as well as the 
time domain non-linear wave propagation analysis method (Hashash, et al., 2011). 
DEEPSOIL software was initially developed as a Matlab program in 1998 and later 
reprogrammed as a C based executable software to improve computational capabilities 
(Hashash, et al., 2011). The program can calculate the response for a design motion given 
anywhere in the soil profile. Hence, acceleration obtained from the lower soil layers can 
be obtained and used to generate new rock motions which, in sequence, can be used as a 
design motion for upper soil layers. Figure 5-1 shows a schematic sketch of the procedure 
for computing the ground response at point B from a design motion propagated from 
bedrock formation (point A). 
The version 5 of the software has five graphical interfaces (windows) to input 
data. The interfaces are designed to obtain data for initialization, analysis type selection, 
define soil profile and model properties, motion and output control, and output. Figure 
5.2 shows the input soil properties interface of the software.  
 
163 
 
 
Figure 5-2: Input graphical interface of DEEPSOIL software 
After the soil and the model properties are defined in the software, the shear 
strength is calculated from the normalized shear modulus curves. At each point on the 
curve, shear stress can be calculated using: 
 
 (5.1) 
where,  is shear stress at given points;  is the shear velocity in a given layer;  is the 
mass density of the soil;  is the shear modulus at given points;  is the maximum 
shear modulus; and  is shear strain at given points. 
The software provides the strength of the soil profile, shear strength versus depth, 
normalized shear strength ( ), and the friction angle versus depth. By 
using the maximum value for shear stress, the software can calculate the friction angle 
using Equation 5.2. 
 
164 
 
  (5.2) 
where,  is the friction angle;  is maximum shear stress;  is effective vertical 
stress at the mid-depth of the layer. 
In the frequency domain analysis, there are three most commonly used methods to 
estimate response spectra of single degree of freedom (SDOF) systems, the frequency 
domain solution, Newmark ? method, and Duhamel integral solutions. A brief 
description is provided for each method. The dynamic equilibrium equation of motion is 
expressed as (Newmark, 1959); (Chopra, 1995): 
  (5.3) 
where m, c, and k are the mass, viscous damping and stiffness of a SDOF system, 
respectively. , , and  are the nodal relative accelerations, relative velocities and 
relative displacements, respectively.  is the exciting acceleration applied at the base of 
SDOF. 
 In the frequency-domain solution method, a modification is performed on the 
Fourier Amplitude Spectra (FAS) by a transfer function. The transfer function is defined 
as: 
 
 (5.4) 
where is the natural frequency of the oscillator obtained from , and D is 
the damping ratio obtained from  . In order to move between the frequency-
 domain and the time domain, fast fourier transforms (FFT) are used. The frequency-
 
165 
 
domain is used where the oscillator transfer function is applied and the time-domain is 
where the peak oscillator response is approximated. The frequency-domain is only exact 
in the frequency range of the bedrock motion. 
 The Duhamel integral solution is another method to compute the response of 
linear SDOF systems. It linearly interpolates the excitation function ( ) and solves 
the dynamic equilibrium equation of motion meeting the following conditions: 
a) Free-vibration due to initial displacement and velocity 
b) A response step force ( )  with zero initial conditions 
c) Response of the ramp force 
?
  
The solution in terms of velocities and displacements can be solved by: 
  (5.5) 
  (5.6) 
where: 
 
 (5.7) 
 
 (5.8) 
   
   
   
 
166 
 
 
 (5.9) 
 
 (5.10) 
 
 (5.11) 
 
 (5.12) 
  (5.13) 
  (5.14) 
The third method in calculating the response spectra is the Newmark ? method. In 
the Newmark ? method, the nodal relative velocity and displacement can be 
obtained at any time  by using: 
  (5.15) 
  (5.16) 
where,   is the time step, and  and  are parameters assuming the acceleration 
variation. 
The drawback of using Newmark ? method is that the method under-predicts the high 
frequency responses (Chopra, 1995), (Mugan & Hulbe, 2001). The frequency-domain 
solution method was used in the analyses. 
 
 
167 
 
In order to be consistent when analysis is performed for each layer and to 
compare the results, the layers were broken down into sublayers of 5 ft thicknesses. For 
instance, if the total column of soil was 60 feet, the total thickness was divided into 12 
sublayers, each with the thickness of 5 feet. Following this procedure, the comparisons 
will be performed when software analyses are conducted for the same points in the soil 
profile. 
5.2 Design Earthquake Parameters 
When performing soil behavior assessments under earthquake motion, it is 
essential to know the magnitude of the earthquake and to define the ground motion in 
expressions that can be used for engineering analysis. Design earthquake waves were 
traditionally described in terms of the peak acceleration, but modern techniques 
nowadays use the response spectrum or time histories of motion. The most reliable 
approach for achieving this is to perform the analysis based on data obtained at the site. A 
second option is to find another site similar in seismic and geologic setting where ground 
motion was measured during a design level magnitude earthquake. However, the chance 
of finding such a site that measurements at a design level magnitude had been done is 
very slim. Therefore, estimates of ground motions based on correlations and geologic and 
seismologic evidence for the specific site are essential (Department of Defense 
Handbook, 1997). 
5.2.1 Earthquake Motions 
Earthquakes are one of the most costly natural hazards posing a significant risk to 
people living in earthquake zones. Earthquakes are the result of a sudden release of 
energy in the Earth?s crust that forms seismic waves. Two different earthquake motions, 
 
168 
 
the Parkfield and the Imperial Valley, were used in the analysis. The Imperial Valley 
earthquake was a magnitude 6.5 and happened in Imperial Valley on the Mexico-
 California border on October 15, 1979 at 4:54 pm local time. The main earthquake 
injured 91 people and caused structure damages estimated at 30 million dollars. The 
shock destroyed two houses and 11 commercial buildings and damaged 1,565 houses and 
440 commercial buildings in the Imperial Valley. Older buildings were severely 
damaged. The Imperial Valley earthquake was the result of a rupture along the Imperial 
fault, with the epicenter 4 kilometers north of the International Border (Stover & 
Coffman, 1993). 
Moderate-sized earthquakes of magnitude 6 have occurred on the town of 
Parkfield section of the San Andreas Fault at fairly regular intervals ? in 1857, 1881, 
1901, 1922, 1934, and 1966. The last earthquake in the year 1966 motion has been used 
in this study. The most recent earthquake happened in the Parkfield area on September 
28, 2004. A summary of the earthquake motions used in the analysis is listed below. 
Table 5-1: Earthquake motions data used in the analysis (Hashash, et al., 2011) 
Motion 
Name 
Date of 
Event 
Magnitude 
Hypocentral 
Distance to 
Fault 
Rupture 
(km) 
Geomatrix 
USGS Site 
Class 
PGA (g) 
Imperial 
Valley 
10/15/1979 6.5 26.5 B 0.169 
Parkfield 06/28/1966 6.1 9.9 B 0.357 
 
 In the analysis, these two motions are considered to be two extreme conditions. 
Parkfield is the one with large peak ground acceleration (PGA) of 0.357 g but the 
earthquake duration is very short (less than 30 seconds). On the contrary, Imperial Valley 
 
169 
 
has not as large a PGA as Parkfield had but its duration is very long (slightly greater than 
60 seconds). Acceleration versus time graphs for these two motions are shown in Figure 
5.3. 
  
Figure 5-3: Graph of Imperial Valley motion and Parkfield acceleration versus time are 
shown on the left and right, respectively. 
5.3 Factors Affecting Ground Shake 
Factors that affect strong ground shake comprise: 
a) Wave types ? S and P waves that travel through the earth and surface waves. 
b) Earthquake magnitude 
c) Depth to bedrock (distance from epicenter) 
d) Soil deposit conditions (site conditions) 
e) Fault type, depth, and recurrence interval  
As part of this research, the effect of two different motion types, depth to bedrock, and 
soil conditions using clay and fiber modified clay was studied. 
 
170 
 
5.4 Materials Used in the Analysis 
To study the effect of fiber inclusion on the site response of a clayey soil column, 
two different material types, clay and fibrillated fiber modified clay, were used for 
different soil column analyses. In the previous chapters, fibrillated fiber had shown that it 
can provide a denser mixture than monofilament fiber if mixed with clay at optimum 
fiber content. Hence, the experimental data for 0.75 inch fibrillated fiber was used for the 
analysis. In addition, the experimental data for kaolinite soil tested at optimum moisture 
content was used in the analysis to allow a comparison with fiber modified clay. In the 
experimental stage of the research, the mass density and maximum shear modulus (Gmax) 
for each soil/composite type were determined. By knowing the mass density and 
maximum shear modulus of each soil layer, unit weight and shear wave velocity can be 
calculated, respectively. The values of unit weight and shear wave velocity defined in the 
software are listed in Table 5.2. 
Table 5-2: Properties of materials 
Soil/Composite 
Layer 
Unit Weight 
(lb/ft3) 
Shear Wave 
Velocity 
(ft/s) 
Clay 108.8 519.98 
Fiber-Soil 
Composite 
114.32 549.88 
5.5 Dynamic Properties of Clay and Fiber Modified Clay Used in the Analysis 
The program models the non-linear dynamic soil modulus and damping as a 
function of shear strain. The equations developed in Chapter 4 for soil modulus and 
damping ratio of clay were used to plot soil modulus and damping ratio curves. The 
Equations 4.5 and 4.6 were used to model shear modulus versus shear strain curve and 
Equations 4.9 and 4.10 were used to model damping ratio versus shear strain curves. 
 
171 
 
Then 10 discrete points on each curve were input to the software. The software can 
simulate the curves by entering the discrete points. Please note that a better curve can be 
plotted if the discrete points cover a large range of shear strain. The curves of shear 
modulus and damping ratio as functions of shear strain are shown in Figures 5-4 and 5-5, 
respectively. 
 
Figure 5-4: Normalized shear modulus versus shear strain for clay and fiber-clay 
composite with FC = 0.2% 
 
172 
 
 
Figure 5-5: Damping ratio versus shear strain for clay and fiber-clay composite with FC = 
0.2% 
5.6 Effect of Fiber Reinforcement on Dynamic Response of a Clayey Site 
Clay and fiber reinforced material properties were assigned to a soil column of 60 
feet and were separately studied. Firstly, for case 1, one column of soil was studied using 
clay material. Then for case 2, 10 feet off the top of soil column was replaced with fiber 
modified clay using properties presented in Section 5.4 of this manuscript, as shown in 
Figure 5-6. 
 
173 
 
 
Figure 5-6: Site profile sketch - soil column = 60 ft 
5.6.1 Seismic Site Response of 60 feet Column of Soil 
After performing equivalent linear analysis applying two different earthquake 
motions, Imperial Valley and Parkfield, at the bedrock for a 60 foot column of clayey soil 
in case 1, the graphs of acceleration versus time, amplitude ratio versus frequency, and 
response spectra versus period were developed for the ground surface for all-clay (case 1) 
and fiber modified condition (case 2). The graphs are shown in Figure 5-7 to 5-9 for all-
 clay condition. 
 Clayey 
Layer 
Fiber Modified 
Layer 
Bedrock 
Formation 
50? 
10? 
Case 1 Case 2 
60? 
Ground 
Surface 
 
174 
 
 
Figure 5-7: Acceleration versus time graph for all-clay condition, 60 ft column of soil, 
Imperial Valley motion (case 1) 
 
Figure 5-8: Amplitude ratio versus frequency graph for all-clay condition, 60 ft column 
of soil, Imperial Valley motion (case 1) 
 
175 
 
 
Figure 5-9: Response spectra versus period graph for all-clay condition, 60 ft column of 
soil, Imperial Valley motion (case 1) 
The site response graphs were also determined when Parkfield motion was 
applied. The graphs are shown in Figures 5-10 to 5-12 in all-clay condition (case 1). 
 
Figure 5-10: Acceleration versus time graph for all-clay condition, 60 ft column of soil, 
Parkfield motion (case 1) 
 
176 
 
 
Figure 5-11: Amplitude ratio versus frequency graph for all-clay condition, 60 ft column 
of soil, Parkfield motion (case 1) 
 
Figure 5-12: Response spectra versus period graph for all-clay condition, 60 ft column of 
soil, Parkfield motion (case 1) 
 
 
 
177 
 
The analysis was performed on the 60 foot column of clay in the condition where the top 
10 feet of the column was fiber modified (case 2). Then, the soil column was analyzed 
under the application of the Imperial Valley and Parkfield motions separately at the 
bedrock. The ground surface site response graphs are shown in Figures 5-13 to 5-15 for 
Imperial Valley and in Figures 5-16 to 5-18 for Parkfield motions. 
 
Figure 5-13: Acceleration versus time graph, 60 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft (case 2) 
 
Figure 5-14: Amplitude ratio versus frequency graph, 60 ft column of soil, Imperial 
Valley motion, thickness of fiber modified layer is 10 ft (case 2) 
 
178 
 
 
Figure 5-15: Response spectra versus period graph, 60 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft (case 2) 
 
Figure 5-16: Acceleration versus time graph, 60 ft column of soil, Parkfield motion, 
thickness of fiber modified layer is 10 ft (case 2) 
 
 
179 
 
 
Figure 5-17: Amplitude ratio versus frequency graph, 60 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft (case 2) 
 
 
Figure 5-18: Response spectra versus period graph, 60 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft (case 2) 
 
 
180 
 
5.6.2 Analysis for 60 feet Column of Soil 
The comparison of the results between all-clay condition (case 1) and fiber 
modified clay condition (case 2) indicated that the inclusion of fiber in the top 10 feet of 
the clayey site improved the dynamic response of the clayey site on the ground surface. 
Figures 5-19 to 5-21 compare the site response of the all-clay and fiber modified 
conditions when Imperial Valley motion was applied. 
 
Figure 5-19: Maximum PGA comparison graph, 60 ft column of soil, Imperial Valley 
motion 
 
Figure 5-20: Amplitude ratio comparison graph, 60 ft column of soil, Imperial Valley 
motion 
 
181 
 
 
 
Figure 5-21: Maximum PSA comparison graph, 60 ft column of soil, Imperial Valley 
motion 
Figures 5-22 to 5-24 compare the site response of the all-clay and fiber modified 
conditions when Parkfield motion applied. 
 
Figure 5-22: Maximum PGA comparison graph, 60 ft column of soil, Parkfield motion 
 
182 
 
 
Figure 5-23: Amplitude ratio comparison graph, 60 ft column of soil, Parkfield motion 
 
 
Figure 5-24: Maximum PSA comparison graph, 60 ft column of soil, Parkfield motion 
The summary of the analyses and percentage changes between fiber modified and all-clay 
conditions are shown in Table 5-3. 
 
183 
 
Table 5-3: The results of site response analyses for all-clay and fiber modified conditions 
(60 ft column) 
Motion Site Response Type 
All-Clay 
Condition 
(Case 1) 
Fiber 
Modified 
Condition 
(Case 2) 
Percentage 
Change 
(%) 
Imperial 
Valley 
Peak Ground Acceleration (PGA) 0.2990232 0.2909593 -2.70 
Amplitude Ratio 4.89354389 4.8811289 -0.25 
Maximum PSA 1.3133 1.2968 -1.26 
Parkfield 
Peak Ground Acceleration (PGA) 0.34479423 0.33499685 -2.84 
Amplitude Ratio 5.15131805 5.12702791 -0.47 
Maximum PSA 1.14008 1.37634 -2.39 
 
The site response analyses show an improvement of the site condition when the top 10 
feet of the clayey site is fiber modified and being subjected to two different earthquake 
motions. 
5.7 Effect of Depth to Bedrock on Seismic Response of Clayey Sites 
Clay and fiber reinforced material properties were assigned to a soil column of 20 
feet and were similarly studied. First for case 1, a column of soil was studied using all 
clay material properties. Then for case 2, 10 feet off the top of the clay column was 
replaced with fiber modified clay using properties presented in Section 5.4 of this 
manuscript as shown in Figure 5-25.  
The results were then compared with the 60 foot column to investigate the effect of depth 
to bedrock in seismic site response of clayey sites. 
 
 
184 
 
 
Figure 5-25: Site profile sketch- soil column = 20 ft 
5.7.1 Seismic Site Response of 20 feet Column of Soil 
After performing equivalent linear analysis applying two different earthquake 
motions, Imperial Valley and Parkfield, at the bedrock for 20 feet column of clayey soil, 
the graphs of acceleration versus time, amplitude ratio versus frequency, and response 
spectra versus period were generated for the ground surface for all-clay and fiber 
modified conditions. The graphs are shown in Figures 5-26 to 5-28 for the all-clay 
condition for the Imperial Valley motion and Figures 5-29 to 5-31 for the all-clay 
condition for the Parkfield motion. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Clayey 
Layer 
Fiber 
Modified 
Layer 
Bedrock 
Formation 
10? 
10? 
Case 1 Case 2 
20? 
Ground 
Surface 
 
185 
 
 
Figure 5-26: Acceleration versus time graph for all-clay condition, 20 ft column of soil, 
Imperial Valley motion 
 
Figure 5-27: Amplitude ratio versus frequency graph for all-clay condition, 20 ft column 
of soil, Imperial Valley motion 
 
186 
 
 
Figure 5-28: Response spectra versus period graph for all-clay condition, 20 ft column of 
soil, Imperial Valley motion 
 
 
Figure 5-29: Acceleration versus time graph for all-clay condition, 20 ft column of soil, 
Parkfield motion 
 
 
187 
 
 
Figure 5-30: Amplitude ratio versus frequency graph for all-clay condition, 20 ft column 
of soil, Parkfield motion 
 
Figure 5-31: Response spectra versus frequency graph for all-clay condition, 20 ft 
column of soil, Parkfield motion 
 
 
 
188 
 
The analysis was then performed on the 20 foot column of clay where the top 10 feet of 
the column was fiber modified. The column was analyzed applying Imperial Valley and 
Parkfield motions separately at the bedrock. The ground surface site response graphs are 
shown in Figures 5-32 to 5-34 for Imperial Valley and in Figures 5-35 to 5-37 for 
Parkfield motions. 
 
Figure 5-32: Acceleration versus time graph, 20 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft 
 
Figure 5-33: Amplitude ratio versus frequency graph, 20 ft column of soil, Imperial 
Valley motion, thickness of fiber modified layer is 10 ft 
 
189 
 
 
Figure 5-34: Response spectra versus period graph, 20 ft column of soil, Imperial Valley 
motion, thickness of fiber modified layer is 10 ft 
 
Figure 5-35: Acceleration versus time graph, 20 ft column of soil, Parkfield motion, 
thickness of fiber modified layer is 10 ft 
 
190 
 
 
Figure 5-36: Amplitude ratio versus frequency graph, 20 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft 
 
Figure 5-37: Response spectra versus period graph, 20 ft column of soil, Parkfield 
motion, thickness of fiber modified layer is 10 ft 
5.7.2 Analysis for 20 feet Column of Soil 
The comparison of the results between all-clay condition and fiber modified clay 
condition indicated that the inclusion of fiber in the top 10 feet of the clayey site 
 
191 
 
improved the dynamic response of the clayey site on the ground surface. Figures 5-38 to 
5-40 compares the site response of the all-clay and fiber modified conditions in the case 
of the Imperial Valley motion. 
 
Figure 5-38: Maximum PGA comparison graph, 20 ft column of soil, Imperial Valley 
motion 
 
Figure 5-39: Amplitude ratio comparison graph, 20 ft column of soil, Imperial Valley 
motion 
 
 
192 
 
 
Figure 5-40: Maximum PSA comparison graph, 20 ft column of soil, Imperial Valley motion 
Figures 5-41 to 5-43 compares the site response of the all-clay and fiber modified 
conditions in the case of the Parkfield motion. 
 
Figure 5-41: Maximum PGA comparison graph, 20 ft column of soil, Parkfield motion 
 
 
193 
 
 
Figure 5-42: Amplitude Ratio comparison graph, 20 ft column of soil, Parkfield motion 
 
Figure 5-43: Maximum PSA comparison graph, 20 ft column of soil, Parkfield motion 
The summary of the analyses and percentage changes between fiber modified and all-clay 
conditions are shown in Table 5-4. 
 
194 
 
Table 5-4: The results of site response analyses for 20 ft soil column 
Motion Site Response Type 
All-Clay 
Condition 
Fiber 
Modified 
Condition 
Percentage 
Change 
(%) 
Imperial 
Valley 
Peak Ground Acceleration (PGA) 0.4058655 0.359121541 -11.52 
Amplitude Ratio 5.90347087 5.57596176 -5.55 
Maximum PSA 2.26456 2.13058 -5.92 
Parkfield 
Peak Ground Acceleration (PGA) 0.73319242 0.7058454 -3.73 
Amplitude Ratio 4.78843299 4.47991985 -6.44 
Maximum PSA 2.77943 2.66402 -4.15 
 
The site response analyses of 20 feet clayey soil column show an improvement of the 
seismic response of the site when the top 10 feet of the clayey site is fiber modified. 
 The comparison between the percentage changes in 60 and 20 foot soil columns 
indicates that if the same amount of fiber improvement is performed (10 feet) on clayey 
sites, the site that has a shallower bedrock formation can experience a larger reduction in 
seismic site response values. 
5.8 Effect of Thickness of Fiber Improvement on Seismic Site Response of 
Clayey Sites 
The 20 feet clayey site was used for site response analysis using two different 
motions. The fiber improvement increment was chosen as 5 feet and the direction of the 
improvement was chosen from the ground surface downward. Therefore, five cases of, 0 
(all-clay condition), 5, 10, 15, and 20 (all fiber modified condition) feet of soil 
improvement were analyzed to compare the effect of thickness of fiber improvement on 
the seismic site response of a clayey site. Figure 5-44 shows the five cases used in the 
analyses. 
 
195 
 
 
Figure 5-44: Site profile sketch, soil column = 20 ft (fiber improvement increment is 5 
feet) 
Site response analysis was performed separately using two different earthquake 
motions, Imperial Valley and Parkfield, at the bedrock for all five cases. The graphs of 
acceleration versus time, amplitude ratio versus frequency, and response spectra versus 
period were developed for every case. For the all-clay condition (case 1), the graphs are 
shown in Section 5.7.1, Figures 5-26 to 5-28 for the Imperial Valley motion and in 
Figures 5-29 to 5-31 for the Parkfield motion. For the case of 5 feet of fiber improvement 
(case 2), the graphs are shown in Figures 5-45 to 5-47 for the Imperial Valley motion and 
in Figures 5-48 to 5-50 for the Parkfield motion. For the case of 10 feet of fiber 
improvement (case 3), the graphs are shown in Section 5.7.1, Figures 5-32 to 5-34 for the 
Imperial Valley motion and in Figures 5-35 to 5-37 for the Parkfield motion. For the case 
of 15 feet of fiber improvement (case 4), the graphs are shown in Figures 5-51 to 5-53 for 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
Clayey 
Layer 
Fiber Modified 
Layer 
Bedrock 
Formation 
5? 
5? 
Case 
1 
Case 
2 
Case 
3 
Case 
4 Ground 
Surface 
5? 
5? 
Case 
5 
 
196 
 
the Imperial Valley motion and in Figures 5-54 to 5-56 for the Parkfield motion. For the 
case of 20 feet of fiber improvement (case 5, all fiber modified), the graphs are shown 
Figures 5-57 to 5-59 for the Imperial valley motion and in Figures 5-60 to 5-62 for the 
Parkfield motion. 
 
Figure 5-45: Acceleration versus time graph for case 2 (5 feet of fiber improvement), 20 
ft column of soil, Imperial Valley motion 
 
Figure 5-46: Amplitude ratio versus frequency graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion 
 
197 
 
 
Figure 5-47: Response spectra versus period graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion 
 
Figure 5-48: Acceleration versus time graph for case 2 (5 feet of fiber improvement), 20 
ft column of soil, Parkfield motion 
 
198 
 
 
Figure 5-49: Amplitude ratio versus frequency graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion 
 
Figure 5-50: Response spectra versus Period graph for case 2 (5 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion 
 
199 
 
 
Figure 5-51: Acceleration versus time graph for case 4 (15 feet of fiber improvement), 20 
ft column of soil, Imperial Valley motion 
 
Figure 5-52: Amplitude ratio versus frequency graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion 
 
 
200 
 
 
Figure 5-53: Response spectra versus period graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Imperial Valley motion 
 
 
Figure 5-54: Acceleration versus time graph for case 4 (15 feet of fiber improvement), 20 
ft column of soil, Parkfield motion 
 
201 
 
 
Figure 5-55: Amplitude ratio versus frequency graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion 
 
 
Figure 5-56: Response spectra versus period graph for case 4 (15 feet of fiber 
improvement), 20 ft column of soil, Parkfield motion 
 
 
202 
 
 
Figure 5-57: Acceleration versus time graph for case 5 (all fiber modified), 20 ft column 
of soil, Imperial Valley motion 
 
 
Figure 5-58: Amplitude ratio versus frequency graph for case 5 (all fiber modified), 20 ft 
column of soil, Imperial Valley motion 
 
 
203 
 
 
Figure 5-59: Response spectra versus period graph for case 5 (all fiber modified), 20 ft 
column of soil, Imperial Valley motion 
 
Figure 5-60: Acceleration versus time graph for case 5 (all fiber modified), 20 ft column 
of soil, Parkfield motion 
 
204 
 
 
Figure 5-61: Amplitude ratio versus frequency graph for case 5 (all fiber modified), 20 ft 
column of soil, Parkfield motion 
 
Figure 5-62: Response spectra versus period graph for case 5 (all fiber modified), 20 ft 
column of soil, Parkfield motion 
Figures 5-63 to 5-65 show the seismic site response for all cases at the ground surface 
when Imperial Valley motion was used as applied motion to the bedrock formation. 
 
205 
 
 
Figure 5-63: Peak ground acceleration change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Imperial Valley motion 
 
Figure 5-64: Amplitude ratio change versus thickness of soil improvement graph for all 
cases, 20 ft column of soil, Imperial Valley motion 
 
206 
 
 
Figure 5-65: Maximum response spectra change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Imperial Valley motion 
Figures 5-66 to 5-68 show the seismic site response for all cases at the ground surface 
when Parkfield motion was used as applied motion to the bedrock formation. 
 
Figure 5-66: Peak ground acceleration change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Parkfield motion 
 
207 
 
 
Figure 5-67: Amplitude ratio change versus thickness of soil improvement graph for all 
cases, 20 ft column of soil, Parkfield motion 
 
Figure 5-68: Maximum response spectra change versus thickness of soil improvement 
graph for all cases, 20 ft column of soil, Parkfield motion 
The results of the site response analysis for a 20 feet column of soil are shown in Table 5-
 5. 
 
 
208 
 
Table 5-5: The results of site response analyses to investigate the effect of thickness of 
soil improvement 
Motion 
Site Response 
Type 
Case Number 
Percent 
Change 
(%) 
1 2 3 4 5 
Thickness of Soil Improvement (ft) 
0 5 10 15 20 
Imperial 
Valley 
Peak Ground 
Acceleration 
0.4058655 0.3834526 0.359121541 
0.32914980
 7 
0.32483029 -19.97 
Amplitude 
Ratio 
5.90347087 5.82078669 5.57596176 5.20701808 5.047959928 -14.49 
Maximum PSA 2.26456 2.15909 2.13058 
2.05574665
 9 
1.90566 -15.85 
Parkfield 
Peak Ground 
Acceleration 
0.73319242 0.72672892 0.7058454 0.65998579 0.65251719 -11.00 
Amplitude 
Ratio 
4.78843299 4.7064245 4.47991985 4.30324353 4.194953124 -12.39 
Maximum PSA 2.77943 2.705904909 2.66402 2.29255 1.79147 -35.54 
 
The results indicated that by increasing the thickness of fiber reinforcement in a clayey 
site, the seismic site response of the clayey site is improved. The amount of the response 
reductions is more pronounced when a larger depth of site soil is fiber reinforced. 
5.9 Effect of Fiber Improvement on Natural Period of Clayey Site 
Determining the natural frequency (fn) and natural period (Tn) of a site is one of 
the main steps in predicting the potential effects of earthquakes on a structure erected at 
the site. The assumption in calculating fn and Tn is that the main responses in a soil 
deposit are caused by the upward propagation of a shear wave from the underlying 
bedrock formation.  
The equation of motion describes the behavior of a soil column in terms of its 
dynamic motion as a function of time. 
 
 (5.17) 
where, G is soil shear modulus,  is the mass density of soil, u is the displacement, t is 
the time, and z is the distance. 
 
209 
 
 
For calculating fn and Tn, the solution for an equation of motion for elastic soils, 
equation 5.17, was used in the first mode (  , where  is the circular 
frequency, G is the soil shear modulus,  is the mass density of soil, and H is the soil 
column thickness). The first mode solution can be rephrased to calculate for fn and Tn as 
 and  . Hence,  is equal to . Since structural engineers consider  in 
their analysis, the data are presented in two forms of and . 
When the soil columns contain different soil sublayers with different shear wave 
velocities, the weighted average of the shear wave velocity of the sublayers with respect 
of each layer thickness should be used for the calculation of fn and Tn as presented in 
Equation 5.18. 
  (5.18) 
where, Hi is the thickness of any sublayer and vsi is the shear wave velocity of the 
sublayer. 
The natural frequency and natural period were calculated for the 20 foot and 60 
foot column of soils and the results were compared with the 10 foot fiber modified 
condition. The results are shown in Figures 5-69 and 5-70. 
 
210 
 
 
Figure 5-69: Natural period versus depth to bedrock for 20 ft and 60 ft columns of 
soil. Blue bar: fiber modified condition (thickness of improvement = 10 ft), red bar: all-
 clay condition  
 
Figure 5-70: Natural frequency versus depth to bedrock for 20 ft and 60 ft columns of 
soil. Blue bar: fiber modified condition (thickness of improvement = 10 ft), red bar: all-
 clay condition 
The natural period and frequency changes are shown in Figures 5-71 and 5-72. 
 
211 
 
 
Figure 5-71: Natural period change versus depth to bedrock for 20 ft and 60 ft columns of 
soil 
 
Figure 5-72: Natural frequency change versus depth to bedrock for 20 ft and 60 ft 
columns of soil 
The summary of the results and percentage changes between fiber modified and all-clay 
conditions is shown in Table 5-6. 
 
212 
 
Table 5-6: The results of natural frequency and natural period for all-clay and fiber 
modified conditions 
Depth to 
Bedrock 
Thickness 
of Fiber 
Modified 
Layer 
Natural 
Frequency 
Natural 
Period, s 
Percentage 
Change, % 
20 0 6.499 0.1539  - 
20 10 6.680 0.1497 2.7 
60 0 2.166 0.46168 - 
60 10 2.186 0.45745 0.9 
 
The presented results show that, in the case of 10 feet of fiber improvement, the natural 
frequency of the site will increase 2.7 % and 0.9 % for sites with depth to bedrock of 20 
and 60 feet, respectively. It can also be resulted in 2.7 % and 0.9 % reductions in the 
natural period of the site. 
In addition, Equation 5-18 was used to determine the natural period and natural 
frequency of vibration for a 20 foot column of soil with 0, 5, 10, 15, and 20 feet 
thicknesses of fiber improvement. The results are shown in Figures 5-73 and 5-74. 
 
Figure 5-73: Site natural frequency versus thickness of fiber reinforced layer for 20 ft 
soil column 
 
213 
 
 
Figure 5-74: Natural period versus thickness of fiber reinforced layer for 20 ft soil 
column 
The results of natural frequency and natural period change due to fiber improvement are 
shown in Figures 5-75 and 5-76. 
 
Figure 5-75: Site natural frequency change versus thickness of fiber reinforced layer 
for 20 ft soil column 
 
 
214 
 
 
Figure 5-76: Natural period change versus thickness of fiber reinforced layer for 20 ft 
soil column 
Summary of the results are shown in Table 5-7. 
Table 5-7: The results of site response analyses for all-clay and fiber modified conditions 
Thickness of 
Fiber 
Modified Layer 
Natural 
Frequency 
Natural 
Period, s 
Percentage 
Change, % 
0 6.499 0.1539  - 
5 6.589 0.1518 1.38 
10 6.681 0.1497 2.80 
15 6.776 0.1476 4.26 
20 6.873 0.1455 5.75 
 
The results showed that larger thickness of fiber improvement further increased the 
natural frequency and further reduced the natural period of the site. The results indicate 
that the natural frequency of the site increases 1.38 %, 2.80%, 4.26%, and 5.75% in cases 
where 5, 10, 15, and 20 feet of the site were fiber modified, respectively. 
 
215 
 
5.10 Conclusions 
Seismic site response analyses were performed using DEEPSOIL software for 
several cases in order to investigate the effect of fiber improvement on seismic ground 
response. The results showed that the addition of fiber with clay can reduce the ground 
response when earthquake motions applied. The magnitude of seismic response changes 
due to fiber modification of the clayey site mainly depends upon the thickness of soil 
modified layer, depth to bedrock, and also earthquake motion types and properties. 
It was also shown that the inclusion of fiber can increase the natural frequency of 
clayey sites and also reduce the natural period of the clayey sites. Hence, the fiber 
improvement of clayey sites can benefit the construction considering the natural period of 
the planned building. Given that fiber reinforcement is able to change the natural 
frequency of a site, the thickness of fiber improvement can be specifically designed for 
each building to achieve the required seismic designs. 
 
 
 
 
 
 
 
216 
 
CHAPTER 6 SUMMARY, CONCLUSIONS, AND 
RECOMMENDATIONS FOR FURTHER RESEARCH 
6.1 Summary 
In this study, the effect of fiber modification of clayey soil was investigated. 
Different commercially available polypropylene fiber types and sizes were used. Since 
the inclusion of fiber with soil is a relatively new method for the improvement of soft 
soils, a detailed study was performed to determine the optimum fiber content for both 
types of fibers, monofilament and fibrillated, as a reinforcement of kaolinite clay. A new 
procedure, independent of the current state of research that is applied to concrete or using 
a metallurgical approach, was developed that can be applied to a composite consisting of 
fiber and soil. 
Furthermore, a series of low strain dynamic tests was performed using both types 
of PP fibers mixed with kaolinite clay to form composites. The effect of fiber inclusion in 
clay on its dynamic properties was investigated using sinusoidal torsional waves. Plots of 
normalized shear modulus and damping ratio versus shear strain were generated. In 
addition, curve fitting model functions correlating shear modulus and material damping 
ratio with shear strain for soils and fiber-clay composites were proposed. The accuracy of 
the models was examined using available verification data for sand and clay. 
The advantage of using fiber as a modification technique was analytically 
demonstrated using DEEPSOIL software to show if the fiber inclusion could mitigate 
earthquake damages by determining the seismic site response of both clayey sites and 
fiber-modified clayey sites. Two extreme earthquake motions, the Imperial Valley and 
 
217 
 
the Parkfield earthquakes, were used in the analysis. The site responses results were 
compared between the two sites? conditions. Also, the effect of depth of the soil layer to 
bedrock on the site response of the fiber reinforced site and the effect of the thickness of 
soil reinforced layers were also investigated. 
6.2 Conclusions 
To obtain the maximum benefit of the use of the fiber, the laboratory compaction 
testing procedure can be adopted to obtain the optimum fiber content. For static or 
dynamic geotechnical use of any fiber-clay composites, it should be undertaken at the 
optimum fiber content that produces the proper composite mix design. 
Dynamic testing shows that the addition of fiber to clay improves its dynamic 
properties. It increases the shear modulus as well as its damping.  The main conclusion of 
this study is that the inclusion of fiber at optimum fiber content as a ground improvement 
technique will improve the dynamic properties of soft and weak clayey soils. This 
increase in the value of the dynamic properties of clay can be mainly due to the 
rearrangement of soil particles caused by the addition of fibers. Since the soil at its 
optimum fiber content becomes fiber-saturated, meaning that all soil voids are mostly 
filled with fiber, it produces a stiffer composite meanwhile benefiting from the material 
damping properties of the polypropylene materials. It is important to note that the fact 
that both the shear modulus and damping increase provide a double benefit for the 
dynamic response of a site by increasing the stiffness of the site and reducing its 
amplitude of vibration. 
 
218 
 
The obtained damping results were slightly different for the composites made up 
of different PP fiber types, fibrillated and monofilament fibers. Since the fiber-matrix 
interface (interphase region) is an area where energy can be converted into heat, it is 
expected to be the main reason for obtaining slightly different material dampings. 
Different fiber-matrix adhesion and molecular motion within the interphase can be the 
reason for the slight differences in the material damping of these two types of PP fiber-
 clay composites. 
The developed general model functions for shear modulus and damping ratio at 
different shear strain levels can be adopted as universal models for sand, clay, and 
composites. The developed general model functions used the conducted experimental 
data as well as available data from others to determine the shear modulus and damping 
ratio as a function of shear strain for the kaolinite clay, and for the fibrillated fiber-clay 
composites at the optimum fiber content. 
Based on the seismic site response analyses performed, it was shown that the 
addition of fiber to clay can reduce the seismic ground response of the clayey site 
subjected to earthquake loading. The results showed that modifying the soil conditions of 
a site using fiber reinforcement in order to mitigate earthquake damage can be one of the 
methods of improving the site conditions and thus improve the seismic site response. It 
was shown that by fiber reinforcing the clayey site the natural frequency of the site can be 
changed. The depth of the fiber improved clayey layer can be specifically designed for 
each building to achieve the required seismic designs. 
 
219 
 
6.3 Recommendations 
6.3.1 Recommendations for Further Research 
The following are recommendations for further research: 
1- The effect of plasticity index on optimum fiber content of fiber-clay composites 
needs to be studied. The study should be performed using cohesive soil with 
different PI values. Mixtures with different clay fractions can also be examined 
for their effect on optimum fiber content. 
2- The effect of fiber inclusion on large strain dynamic properties of clay needs to be 
studied using a Cyclic Triaxial test or Cyclic Torsional Shear test. 
3- The optimum depth of the fiber improvement can be examined considering 
seismic properties of different motions, dynamic properties of existing and fiber 
improved sites, depth to bedrock or earthquake source, etc. 
4- The dynamic effect of fiber inclusion can be examined when the matrix of the 
composite is non-cohesive (sandy). The use of fiber reinforcement with a sandy 
soil susceptible to liquefaction (loose sand/poorly graded sand) may reduce the 
possibility of liquefaction while improving the soil dynamic properties. 
5- A cost benefit analysis should be undertaken to compare the cost of using fiber as 
reinforcement for soils with other methods of soil modifications; such as, cement 
or lime treatments.  
6.3.2 Recommendations for Modifying the Equipment 
1- When using the Drnevich resonant column apparatus in the torsional mode, the 
values of resonant frequency of the materials are shown to be highly dependent on 
 
220 
 
the distance between the coils and magnet. In other words, if the distance between 
coils and magnet are changed, the value that is obtained can vary. Apparatus 
calibration is done in a way that coils are set in a certain distance from the magnet 
using an aluminum rod. The operator has to change this setup when the 
calibration rod is replaced with the top platen. This action would change all the 
previous data obtained from the calibration process. It is proposed to modify the 
coils and magnet placement so that the calibration aluminum rod can be replaced 
by a top platen without changing the coil-magnet set up. 
2- The Drnevich apparatus configuration can be modified by changing the location 
where the air pipe enters the chamber. In the current apparatus configuration, the 
compressed air can influence the resonant frequency of the specimen placed for 
testing. In order to eliminate this influence, the coil and magnet system and air 
pressured chamber can be placed in different sections/chambers to eliminate the 
effect of the air pressure on the coil and magnet system. 
 
 
 
 
 
221 
 
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