ABSTRACT 
 
 
 
 
Title of Thesis: PERFORMANCE OF LINK SLAB USING 
ECC AND UHPC  
  
 Naiyi Li, Master of Science, 2019 
  
Thesis directed by: Professor Chung C. Fu 
Department of Civil and Environmental 
Engineering 
 
 
 Conventional bridge design has been challenged by durability and reliability 
issues due to expansion joints. Chloride-contaminated infiltration and debris 
accumulation in traditional expansion joints affect the bridge performance negatively. 
Link slab has emerging as an effective alternative in bridge rehabilitation and design 
by eliminating expansion joints while the bridge structure remains simply supported. 
Engineered Cementitious Composites (ECC) and Ultra-High Performance Concrete 
(UHPC) are desired material in link slab application due to their high strength and 
tensile ductility. Presented in this thesis is a research project conducted by the BEST 
center at the University of Maryland to study link slab application with UHPC and 
ECC. Two bridge models were generated for finite element analysis. In addition, a 
field test was prepared. Experiments were carried out to study material properties of 
ECC and UHPC for a preliminary assessment of link slab performance using these 
materials. Results found that ECC and UHPC are adequate for link slab for their 
strength, high tensile ductility and fine cracks development.     
 
 
  
 
 
 
 
 
 
 
PERFORMANCE OF LINK SLAB USING ECC AND UHPC 
 
 
 
by 
 
 
Naiyi Li 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Master of Science 
2019 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Dr. Chung C. Fu, Chair 
Dr. Allison C. Reilly  
Dr. Brian M. Phillips 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
© Copyright by 
Naiyi Li 
2019 
 
  
Dedication 
 I am dedicating this thesis to my family for the all supports I received. A 
special feeling of gratitude to my parents, Huang and Li whose encouragements have 
meant and continue to mean so much to me. My wife, Jingyao, has been supporting 
me throughout the process. The completion of my thesis would not have been 
possible without the support of her. 
 I also dedicate this thesis to my friends who have helped and supported me. I 
will always appreciate what they have done. 
 
 
 
 
 
 
 
 
 
 
 
ii 
 
 
Acknowledgements 
 I wish to thank my committee members who were generous with their 
expertise and precious time. A special thanks to Dr. Chung C. Fu, my committee 
chairman for his willingness and generosity to provide me an opportunity to do the 
research as a master student. Without his support and guidance, I would not be able to 
complete my master’s degree. I will be forever thankful to you. Thank you, Dr. 
Allison Reilly and Dr. Brian M. Phillips for agreeing to serve on my committee. 
  I would like to extend my sincere thanks to my peers at the BEST center. 
Many thanks to Kuang-Yuan Hou, Yifan Zhu and Xinya Liu, whom I had great 
pleasure of working with. Thanks very much for the assistance and guidance 
everyone have provided. It is sincerely appreciated. 
 I would like to acknowledge and thank the Civil and Environmental 
Engineering Department for providing me the opportunity to conduct my research 
and pursuit my goals. Special thanks go to the members of staff of the department. 
  
   
 
 
 
iii 
 
 
Table of Contents 
List of Tables ............................................................................................................... vi 
List of Equations .......................................................................................................... vi 
List of Figures ............................................................................................................. vii 
List of Abbreviations ................................................................................................. viii 
Chapter 1 Introduction .................................................................................................. 1 
1.1 Motivation and Introduction ............................................................................... 1 
1.2 Scope ................................................................................................................... 2 
1.3 Objective ............................................................................................................. 3 
Chapter 2 Literature Review ......................................................................................... 4 
2.2 Literature Review on Materials .......................................................................... 4 
2.2.1 Victor Li 2008 .............................................................................................. 4 
2.1.2 Manish A. Kewalramani et al. 2016 ............................................................ 7 
2.1.3 Oguz Gunes et al. 2012 .............................................................................. 10 
2.2. Literature Review on Link Slab ....................................................................... 13 
2.2.1 Caner and Zia 1998 .................................................................................... 13 
2.2.2 Alexander Au, Clifford Lan, Jim Au and Bala Tharmmabala 2013 .......... 16 
2.3.3 Kenneth M. Wing and Meryyn J. Kowalsky 2005 .................................... 19 
Chapter 3 Experiments ................................................................................................ 26 
3.1 Objective and overview .................................................................................... 26 
3.2 Materials and expectations ................................................................................ 26 
3.2.1 UHPC ......................................................................................................... 26 
3.2.2 ECC ............................................................................................................ 27 
3.2.3 Expectation ................................................................................................ 27 
3.3 Testing............................................................................................................... 28 
3.3.1 Sensor information ..................................................................................... 28 
3.3.2 Sensor installation ...................................................................................... 29 
3.3.3 Procedure ................................................................................................... 31 
Chapter 4 Finite Element Analysis ............................................................................. 35 
4.1 Description ........................................................................................................ 35 
4.2 Bridge Details ................................................................................................... 36 
4.3 Finite Element Model using ANSYS Workbench® .......................................... 38 
4.3.1 Overview .................................................................................................... 38 
4.3.2 Results for Modal Analysis ........................................................................ 39 
4.4 Finite Element Model using CSiBridge® .......................................................... 41 
4.4.1 Overview .................................................................................................... 41 
iv 
 
 
4.4.2 Shell Elements vs. Solid Elements............................................................. 42 
4.4.3 Results for Modal Analysis ........................................................................ 43 
4.4.4 Structural Response for Moving Truck Loads ........................................... 45 
4.6 Modal Analysis Comparison............................................................................. 48 
Chapter 5 Field Test .................................................................................................... 49 
5.1 Description ........................................................................................................ 49 
5.1.1 Strain Distribution ...................................................................................... 49 
5.1.2 Sensor System Configuration .................................................................... 50 
5.2 Preparation ........................................................................................................ 50 
5.3 Equipment ......................................................................................................... 52 
5.4 Procedure .......................................................................................................... 54 
Chapter 6 Results ........................................................................................................ 55 
6.1 Results for ECC and UHPC .............................................................................. 55 
6.1.1 Data Processing .......................................................................................... 55 
6.1.2 Maximum compressive strength ................................................................ 56 
6.1.3 Maximum tensile strain .............................................................................. 58 
6.1.4 Stress vs. Strain Curve ............................................................................... 60 
6.2 Results on Sensor Performance ........................................................................ 67 
6.2.1 Sensor Performance Criteria ...................................................................... 67 
6.2.2 Sensor Survival Rates ................................................................................ 67 
6.2.3 Sensor Failure Due to Lost Connection ..................................................... 69 
6.2.4 Sensor Failure when reaching a certain level of strain .............................. 69 
6.2.5 Complete Sensor Failure ............................................................................ 70 
6.2.6 Possible Causes for Sensor Disturbance and Failures ............................... 71 
6.2.7 Recommendation on Sensor Application ................................................... 72 
6.3 Fine Crack Development .................................................................................. 74 
Chapter 7 Discussion .................................................................................................. 77 
7.1 Lab Test ............................................................................................................ 77 
7.2 Sensor Protection .............................................................................................. 78 
7.3 Evaluation of Sensor Performance.................................................................... 79 
Chapter 8 Conclusion and Future Work ..................................................................... 80 
8.1 Conclusion ........................................................................................................ 80 
8.2 Future Work ...................................................................................................... 82 
Appendix: Bridge Thermal Analysis .......................................................................... 84 
Bibliography ............................................................................................................. 101 
 
v 
 
 
List of Tables 
Table 2.1: Typical ECC mix design (Li, 2008) ............................................................ 5 
Table 3.1: Sensor distributions ................................................................................... 32 
Table 3.2: Updated ECC mixture................................................................................ 33 
Table 4.1: Modal frequencies by Ansys Workbench® ................................................ 39 
Table 4.2: Modal frequencies by CSiBridge®............................................................. 43 
Table 4.3: Modal analysis comparison ....................................................................... 48 
Table 6.1: Maximum compressive strength ................................................................ 56 
Table 6.2: Senor failure and survival rates ................................................................. 68 
Table 6.3: Strain level of lost compatibility................................................................ 73 
 
 
 
 
 
List of Equations 
Equation 2.1 ................................................................................................................ 15 
Equation 2.2 ................................................................................................................ 17 
Equation 2.3 ................................................................................................................ 17 
Equation 2.4 ................................................................................................................ 17 
Equation 2.5 ................................................................................................................ 23 
Equation 2.6 ................................................................................................................ 23 
Equation 2.7 ................................................................................................................ 23 
Equation 2.8 ................................................................................................................ 24 
Equation 2.9 ................................................................................................................ 24 
Equation 2.10 .............................................................................................................. 25 
Equation 2.11 .............................................................................................................. 25 
Equation 6.1 ................................................................................................................ 65 
Equation 6.2 ................................................................................................................ 66 
Equation 6.3 ................................................................................................................ 66 
 
vi 
 
 
List of Figures 
Figure 2.1: “Metal-like” behavior of ECC (Li, 2008) .................................................. 7 
Figure 2.2: Tensile strength reduction of PVA fibers (Magalhães et al. 2013) ............ 8 
Figure 2.3: ECC link slab in a bridge in Michigan, USA (Magalhães et al. 2013) ...... 9 
Figure 2.4: UHPC compared with normal concrete (Gunes & Ulm et al. 2012) ........ 11 
Figure 2.5: Typical jointless bridge configuration (Caner & Zia, 1998) .................... 15 
Figure 2.6: Debonded link slab system (Alexander Au, et al 2013) ........................... 16 
Figure 2.7: Link slab crack pattern (Alexander Au, et al 2013) ................................. 18 
Figure 2.8: NCDOT link slab rehabilitation design (Wing & Kowalsky, 2005) ........ 21 
Figure 3.1: Strain Gauge SenSpotTM Sensor ............................................................... 29 
Figure 3.2: Sensor installation on a bridge girder ....................................................... 29 
Figure 3.3: Strain gauge installation on a metal plate ................................................. 31 
Figure 3.4: Three-point bending test apparatus (ASTM C78/C78M-18) ................... 33 
Figure 3.5: Link slab specimen with strain gauge ...................................................... 34 
Figure 4.1: Plan view of bridge CEX952001.............................................................. 37 
Figure 4.3: Bridge model geometry in Ansys Workbench® ....................................... 38 
Figure 4.5: Tet10, Hex20 and Wed15 elements in Ansys Workbench® ..................... 40 
Figure 4.6: Total deformation in dynamic analysis .................................................... 40 
Figure 4.7: 1st modal shape, f = 2.53 Hz .................................................................... 40 
Figure 4.8: 2nd modal shape, f = 2.72 Hz ................................................................... 41 
Figure 4.9: 3rd modal shape, f = 3.58 Hz ................................................................... 41 
Figure 4.10: CSiBridge® model using shell elements ................................................. 42 
Figure 4.11: 1st mode shape, f = 2.46 Hz ................................................................... 43 
Figure 4.12: 2nd mode shape, f = 2.65 Hz .................................................................. 44 
Figure 4.12: 3rd mode shape, f = 3.66 Hz .................................................................. 44 
Figure 4.13: HS20-44 vehicle load per AASHTO specifications ............................... 45 
Figure 4.14: Moving truck loads visualization ........................................................... 46 
Figure 4.15: Maximum and minimum vertical shear envelop .................................... 46 
Figure 4.16: Maximum moment envelop.................................................................... 47 
Figure 4.17: Maximum vertical deflection ................................................................. 48 
Figure 5.1: Strain distribution of link slab .................................................................. 49 
Figure 5.2: Plan view of sensor locations ................................................................... 51 
Figure 5.3: Elevation view of sensor location on UHPC link slab ............................. 51 
Figure 5.4: Elevation view of sensor location on ECC link slab ................................ 52 
Figure 5.5: Sensor system with a steel plate ............................................................... 53 
Figure 5.6: Solar powered DAQ ................................................................................. 53 
vii 
 
 
Figure 5.7: Network of data collection ....................................................................... 54 
Figure 6.1: ECC compressive strength ....................................................................... 58 
Figure 6.2: Maximum concrete tensile strain ............................................................. 59 
Figure 6.3: Maximum steel tensile strain .................................................................... 60 
Figure 6.4: Cyclic loading pattern of specimen No. 14 (UHPC) ................................ 61 
Figure 6.5: Stresses of specimen 14 (UHPC) ............................................................. 61 
Figure 6.6: Strains of specimen No. 14 (UHPC) ........................................................ 62 
Figure 6.7: Cyclic applied loads for specimen No.7 (ECC) ....................................... 63 
Figure 6.8: Stresses on specimen No. 7 (ECC) ........................................................... 63 
Figure 6.9: Strain in first 3 loading cycles (ECC) ...................................................... 64 
Figure 6.10: Strain in 4th and 5th loading cycles (ECC) ............................................ 64 
Figure 6.11: Stress-strain curve for the 2nd loading cycle ......................................... 65 
Figure 6.12: Stress-strain curve for the 3rd loading cycle .......................................... 66 
Figure 6.13: Stress-strain curve for the 4th loading cycle .......................................... 66 
Figure 6.15: Temporary loss of connection in sensors ............................................... 69 
Figure 6.16: Temporary loss of compatibility ............................................................ 70 
Figure 6.17: Compatibility between sensors recovered .............................................. 70 
Figure 6.19: Point of lost compatibility ...................................................................... 72 
Figure 6.20: Fine cracks on an ECC specimen. .......................................................... 75 
Figure 6.21: Fracture plane formed by fine cracks on a UHPC specimen ................. 75 
Figure 6.22: Fracture plane formed by multiple fine cracks (ECC) ........................... 76 
Figure 7.1: Thin slab showing ECC tensile ductility .................................................. 77 
Figure 7.2: Overall sensor survival rate ...................................................................... 79 
Figure 7.3: Survival rate by configuration .................................................................. 79 
 
List of Abbreviations 
SD: Structurally deficient ............................................................................................. 1 
MDTA: Maryland Transportation Authority ................................................................ 2 
BEST: Bridge Engineering Software and Technology ................................................. 2 
ECC: Engineered Cementitious Composites ................................................................ 2 
UHPC: Ultra-High Performance Concrete ................................................................... 2 
MTO: Ministry of Transportation of Ontario ............................................................. 16 
DLS: Debonded link slab system ................................................................................ 19 
 
viii 
 
 
Chapter 1 Introduction 
1.1 Motivation and Introduction 
 Bridges serve an essential role in the infrastructure system to create links 
between two points. Demands on improving bridge performance and reliability keep 
growing as the population and the size of communities increase. Unlike regular roads, 
there are fewer substitutes in bridges in terms of transportation alternatives. Hence, a 
failure in a bridge could cause massive loss for the community it serves. In fact, the 
2017 ASCE Infrastructure Report Card graded the overall condition of bridges as C+ 
in the United States. According to the report, approximately 40% of the bridges in the 
United States are at least 50 years old and more bridges are approaching their design 
life. Worse, 9.1% of the bridges in the nation are rated as structurally deficient (SD), 
while it was approximated that 188 million trips are on these bridges every day. 
Therefore, rehabilitation and innovation in bridge engineering are urgent and the 
current estimated cost for bridge rehabilitation across the country is $123 billion.     
 In bridge engineering, it is common to design bridges as simply-supported 
structures by connecting each span with expansion joints. Yet, the use of expansion 
joints allows penetration of chloride-contaminated water and debris accumulation that 
affect the joints significantly over time, which led to high cost in bridge maintenance 
and rehabilitation. This type of problem is more common in older bridges as 
corrosion has been taking place for an extended period of time. In recent years, link 
slab has emerged to become an advantageous approach in problem solving avoiding 
1 
 
 
complicated negative moment connection design. Application of link slab eliminates 
traditional expansion joints by creating a jointless bridge while keeping the spans 
simply supported. By connecting the adjacent concrete slabs with a link slab, 
damages associated with water penetration, corrosion and debris accumulation can be 
significantly reduced and alleviated to make bridges more sustainable.  
 In this paper, a research project sponsored by the Maryland Transportation 
Authority (MDTA) was conducted by the Bridge Engineering Software and 
Technology (BEST) Center at the University of Maryland to investigate link slab 
application using two types of materials: Engineered Cementitious Composites (ECC) 
and Ultra-High Performance Concrete (UHPC). Both ECC and UHPC are fiber-
reinforced concrete materials and they offer high strength and tensile ductility, along 
with ability to develop fine cracks. The material properties of ECC and UHPC are 
suitable for link slab design as the high strength and tensile ductility ensure the 
durability and reliability of the structural member. In addition, fine cracks are more 
efficient compared to expansion joints because a very limited amount of water would 
be able to penetrate through the link slab so the supporting girders and other 
substructures can be better protected. 
1.2 Scope 
 The project will study material properties of ECC and UHPC materials in a 
concrete testing facility. 14 specimens are to be casted using ECC and UHPC and will 
be subjected to three-point bending test following ASTM C78/C78M-18. Sensor 
2 
 
 
performance will be evaluated for recommendations in future application. In addition, 
two finite element models are to be generated to serve as the baseline of bridge 
performance in which only the super-structure is modeled. This research project also 
serves as a pilot project for the future field test scheduled to be performed on a typical 
overpass bridge in Maryland Transportation Authority (MDTA) highway system. 
1.3 Objective 
 The goal of this project is to obtain a better understanding of Engineered 
Cementitious Composited (ECC) and Ultra-High Performance Concrete (UHPC) in 
terms of their application on link slab. The high compressive and tensile strength of 
the two fiber-reinforced materials are to be verified. Also, the high tensile ductility of 
ECC and UHPC will be examined as this is critical in link slab performance. 
Meanwhile, structural response of ECC and UHPC need to be monitored against 
cyclic loadings. Structural members on bridges are constantly subjected to repeated 
loads due to traffic, hence, it is important for ECC and UHPC to accommodate this 
effect by providing structural response that is independent to the amount of cycles 
that the link slab has gone through over its life span. Furthermore, the effects on ECC 
and UHPC in link slab applications will be studied by analyzing the test results. In 
addition to material properties, sensor performance is also investigated in order to 
study senor properties and limit states. Therefore, recommendations can be proposed 
for future testing and long-term monitoring. A plan for future field test on an actual 
bridge is also to be carried out.   
3 
 
 
Chapter 2 Literature Review 
2.2 Literature Review on Materials 
2.2.1 Victor Li 2008 
 Dr. Li at the University of Michigan, Ann Arbor published an article 
documented recent studies on engineered cementitious composites in 2008. The study 
on fiber reinforced concrete dated back to the 1960’s by Romauldi and co-workers 
(e.g. Romauldi and Batson, 1963: Romauldi and Mandel, 1964). But it was not until 
the 1980’s when the interest in this topic became prevailed. In fact, techniques on the 
engineered cementitious composites keep developing over the years and there were 
applications of the ECC material on real structure in Japan, Europe and the US. By 
definition, ECC is defined as a group of materials whose tensile strength and ductility 
can be modified to meet certain requirements (Li, 2008). In addition, ECC usually 
brings high tensile strength and fine cracking patterns. Typical fiber used in ECC 
includes PVA, polyethylene and polypropylene fibers.  
 The most essential characteristics of ECC is the high tensile ductility that 
offers a metal-like behavior as the material approaches the inelastic region. This 
behavior is similar to that of a yield point on a metallic material. Meanwhile, the first 
microcrack will appear on the specimen. Behavior of ECC beyond this point can be 
classified as strain-hardening if the applied load keeps increasing. The material 
reaches its failure state when the fine cracks form a fracture plane. Then, ECC shows 
similar characteristics as normal fiber-reinforced concrete by showing a strain-
4 
 
 
softening behavior. The high tensile ductility of ECC is extremely valuable in 
improving the overall structural performance by providing a larger capacity in load, 
deformation and energy absorption. Consequently, ECC helps to improve structural 
safety. A typical mix design of ECC is shown in Table 2.1. 
Table 2.1: Typical ECC mix design (Li, 2008) 
 
 Despite its high tensile strength and ductility, ECC is similar to normal high 
strength concrete in compression. Typical compressive strength of ECC varies from 
30Mpa to 90Mpa (4351psi to 13052psi). The elastic modulus ranges from 20-25GPa. 
Strain capacity of ECC is 0.45%-0.65%, which is slightly higher than normal 
concrete.  
 Tensile ductility of ECC can be understood by studying its behavior under 
flexural condition. The material develops microcracking when subjected to bending 
and allows the specimen to experience a deformation with large curvature. This 
scenario makes the ECC material similar to a metal what can be bent with large 
deformation without failure. As a result, ECC is able to offer a range of 10-15MPa in 
flexural strength. Studies had shown that this behavior is instinct to ECC, regardless 
of the geometry of the specimen. Besides, ECC is advantageous over normal concrete 
materials on fatigue response (Suthiwarapirak et al, 2002).  
 Durability of ECC was also examined to achieve adequate serviceability on 
structures. Due to its high tensile ductility, ECC is expected to be used in situations 
where large deformation is present. A series of studies was carried out to investigate 
5 
 
 
its durability under various environment including freeze-thaw and hot-wet cycles, 
chloride immersion, deicing salt exposure and alkali-silicate reaction resistance (Li, 
2005). Results supported that ECC is able to pass durability requirements by 
developing microcracks along the specimens, this is an important aspect in the 
application of link slab on bridges.  
 It was summarized that the most unique benefit of ECC is the capability of a 
high tensile ductility which is several hundred times great than normal concrete 
materials. Meanwhile, ECC is able to provide high compressive strength similar to 
high strength concrete. ECC behaves similarly to a metal under bending, where the 
material undergoes deformation with large curvature while maintaining its 
functionality without fracture. The metal-like behavior can be seen in Figure 2.2. This 
property does not rely on increasing fiber content. Thus, it makes ECC more 
economical in mass production and construction projects. In addition, large 
deformation capability of ECC creates load sharing relationship between the material 
and steel rebars, making the rebars in ECC members more efficient. Besides, ECC 
tends to develop fine cracks along the member. The crack width is generally small 
enough to protect the reinforcing bars or any structural members in the substructure. 
This is a critical aspect in link slab application because one of the goals is to alleviate 
corrosion in substructure caused by chloride-contaminated water.     
 
6 
 
 
 
Figure 2.1: “Metal-like” behavior of ECC (Li, 2008) 
 
2.1.2 Manish A. Kewalramani et al. 2016 
The Abu Dhabi University had conducted a study on engineered cementitious 
composites (ECC) in recent years to provide insights on development and current 
application of the material. 
 The recommended maximum temperature is 50 degree Celsius to achieve 
service condition of ECC, below which more than 95% of the material strength can 
be maintained for over 100 years. A recent study (Magalhães et al. 2013) discovered 
that PVA fibers, which is one of the common reinforcing fibers used in ECC, showed 
7 
 
 
a massive reduction in tensile strength when the temperature increases from 90 degree 
Celsius to 250 degree Celsius. The result is presented in Figure 2.3. The figure 
indicates that the tensile strength of PVA fibers dropped 83% compared to samples 
that remained in normal service temperature as the temperature increased from 90 
degree Celsius to 250 degree Celsius.  
 
Figure 2.2: Tensile strength reduction of PVA fibers (Magalhães et al. 2013) 
 
 Another advantage of ECC is the effectiveness in self-healing ability in wet-
dry cycles (Yang et al, 2009). In addition, resonant frequency (RF) can be used to 
measure the healing process by quantifying the recovery of the material’s mechanical 
properties. Experimental results supported that the intrinsic autogenous healing of 
ECC allows the material to automatically repair itself from cracks. However, proper 
healing process demands desired temperature condition because high temperature 
could led to crack formation during the self-repair process. 
8 
 
 
 ECC has become more frequently used in structural applications in the recent 
decades on building, transportation, bridges and more. The high tensile strength and 
high tensile ductility make the material advantageous over normal concrete in various 
aspects. Specifically, structural rehabilitation projects utilizes ECCs to achieve 
improvements over previous repair methods. Link slab, for example, is a great 
example where ECC has been implementing on bridges to replacing expansion joints, 
which tend to raise concern over water-related corrosion and debris accumulation that 
impact the serviceability of the bridge. The high tensile ductility prevents ECC from 
fracture under reparative service loadings on bridges and it is easier to be repair 
compared to conventional expansion joints. Figure 2.4 presents an example of ECC 
link slab on a bridge structure. 
 
 
Figure 2.3: ECC link slab in a bridge in Michigan, USA (Magalhães et al. 2013) 
 
 
9 
 
 
2.1.3 Oguz Gunes et al. 2012 
 A research conducted by the Cankaya University, Atilim University and the 
Massachusetts Institute of Technology was dedicated to study material modeling of 
UHPC material and investigate design approach of bridge using UHPC. UHPC stands 
for ultra-high-performance concrete and represents a new group of materials being 
developed to solve problems including durability, sustainability, load capacity, 
economy and environment impact of bridge structures.  
 UHPC has been considered as a desired solution for current challenges in 
bridge rehabilitation and design. It is a fiber-reinforced concrete material that consist 
of Portland cement, silica fume, mineral fillers, fine silica sand, superplasticizer, 
water and steel fibers. A typical UHPC material is able to provide compressive 
strength up to 200 MPa (29 ksi) and a ductile tensile strength ranges from 10-15 MPa 
(1.5-2.2 ksi). Members made of UHPC are capable of sustain flexural and tensile 
loads and dissipate the energy even when the initial cracking take places. UHPC is 
significantly more ductile than normal concrete so members made of UHPC do not 
require passive reinforcement. Combining with its high strength which allows smaller 
section sizes, the cost of construction can be reduced. In addition, UHPC allows 
structural members to have long spans, satisfying serviceability and environmental 
standards. At last, UHPC has a low porosity and permeability, which improves the 
member’s resistance to water-related corrosions. Figure 2.4 shows a comparison of 
UHPC and normal concrete. 
10 
 
 
 
Figure 2.4: UHPC compared with normal concrete (Gunes & Ulm et al. 2012) 
  
 UHPC had been used in a number of bridge construction projects, with the 
first application being the Bourg l`es Valence bypass in Dr ˆome in France (2002). 
The Federal Highway Administration (FHWA) had done researches on UHPC and 
concluded that the material had shown great flexural and shear capacity even with the 
absence of passive reinforcement and shear stirrups. To achieve this, UHPC relies on 
the optimized mixture between the high-strength concrete and reinforcing fibers. 
When this condition is meet, stress on concrete can be transferred to the high-strength 
fibers, resulting in high tensile strength and ductile behavior.  
 By far, despite numerous advantages of UHPC, a number of topics need to be 
further studied before this material can be used in more conventional projects in the 
industry. Although UHPC is able to reduce the cost and labor by providing a high 
11 
 
 
strength, longer span and reduced section size, the cost for production of this material 
is high compared to that of a normal concrete. Due to the fact that UHPC is a 
relatively new concept being introduced to the industry, there is a lack of knowledge 
dealing with production and handling process, as well as codes and specifications to 
adept the material to conventional projects. Consequently, structures utilizing UHPC 
are mostly pilot projects that still rely on normal configuration of bridges, where the 
full potential of UHPC has not yet been fulfilled. While research done by the Federal 
Highway Administration (FHWA) indicated that a modified geometry is much more 
efficient in utilizing the material properties of UHPC. 
 The article concluded that UHPC is promising in further development of 
bridge structures. The high strength and ductile behavior of UHPC opens more 
alternatives for innovated and optimized shapes. Elimination or reduction in passive 
reinforcements also helps making the bridge lighter and easier to be built. Flexibility 
of the material allows the potential of UHPC to be mixed with other advanced 
composite materials, such as fiber reinforced polymers (FRP), to further innovate 
building materials for bridge construction. Overall, UPHC is a class of cementitious 
concrete materials with great potential, which still requires more effort to be unveiled 
and fully utilized.   
 
  
 
12 
 
 
2.2. Literature Review on Link Slab 
2.2.1 Caner and Zia 1998 
 In 1998 Dr. Caner and Dr. Zia (Caner and Zia, 1998) conducted a test 
program in effort of studying behavior of link slab and offering a proposed design 
method for link slab. The research was motivated by improving bridge performance 
and reduce maintenance cost due to chloride-containment water infiltration and derris 
accumulation in bridge expansion joints.  
 The study identified the bridge deck joints as a critical problem in bridge 
maintenance and has been troubling engineers for decades. Hence, the idea of a 
jointless deck was proposed. The article pointed out that although fine cracks would 
still be developed on the link slabs after replacement and water could penetrate, it was 
still a desired condition compared to that of a jointed deck (Caner and Zia, 1998). An 
effective way to construct a jointless bridge is to make the slab decks continuous, 
meanwhile, keeping the supporting girders as simple-spans. This avoid excessive 
deck reinforcement. Link slab is defined as the portion of materials connecting the 
two adjacent steel girders. In fact, simple-span jointless bridge had already been used 
in many applications and two examples can be seen in Figure 2.5.  
 The test was performed on a steel bridge and a concrete bridge. Results and 
conclusion yield that the strains in both the link slab and the supporting girders were 
independent from different support (bearing) conditions, for example, roller or pin. 
And this result was only valid within the elastic region. Due to negligible stiffness of 
the link slab compared to the steel girders, the continuity provided by the link slab 
13 
 
 
could be omitted, leaving the girders remain as simple-span. This was verified by 
comparing the theoretical and test results. Experimental results indicated that the link 
slab tend to fail in bending instead of tension, where the top portion failed in cracking 
and the bottom face failed in crushing. Furthermore, this research suggested that it is 
reasonable to design girders independently as a simple-span configuration due to the 
fact that link slabs introduce negligible continuity to the bridge. Hence, designing a 
jointless bridge with link slab was feasible (Caner and Zia, 1998). 
 Cancer and Zia also proposed a simple design method for jointless bridge 
deck using deboned link slab (Caner and Zia, 1998): Ignore the effect of link slab due 
to its negligible flexural stiffness compared the supporting girders. Thus, design each 
span separately as simply-supported structures. 
 Create a 5% debonded zone between the link slab and the girders to further reduce 
the stiffness of the link slab. 
 Consider the girders are simply-supported and calculate the maximum end 
rotations due to service loads. Transfer the rotations to link slabs and determine the 
corresponding moments Ma. Calculate the reinforcement needed to resist moment Ma 
using gross section property of the link slab. Use conservative working stress for the 
link slab, for instance, 40% of the yield strength of the reinforcing bars. 
Limit crack width on link slab with the crack control specifications of AASHTO. The 
maximum crack width is defined as 0.013 inches on the link slab. The crack control 
criteria is expressed in Equation 2.1. 
 
14 
 
 
1
𝑍 ≤ 𝑓𝑠(𝑑𝑐𝐴)3                                                              (2.1) 
Where 
𝑘𝑖𝑝𝑠
 𝑍 ≤ 143  
𝑖𝑛
 𝑓𝑠 = 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑘𝑠𝑖 
 𝑑𝑐 = 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑐𝑜𝑣𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑓𝑟𝑜𝑚 𝑒𝑥𝑡𝑟𝑒𝑚𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑖𝑏𝑒𝑟 𝑡𝑜  
                       𝑐𝑒𝑛𝑡𝑟𝑖𝑜𝑑 𝑜𝑓 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑙𝑒𝑣𝑒𝑙 𝑖𝑛 𝑖𝑛. 
 𝐴 = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑟𝑒𝑎 𝑝𝑒𝑟 𝑏𝑎𝑟 𝑖𝑛 𝑠𝑞 𝑖𝑛. 
 
Figure 2.5: Typical jointless bridge configuration (Caner & Zia, 1998) 
15 
 
 
2.2.2 Alexander Au, Clifford Lan, Jim Au and Bala Tharmmabala 
2013 
The Ministry of Transportation of Ontario (MTO) conducted a research 
project on rehabilitation of multiple bridge decks with a debonded link slab system. 
To objective of this study was to acquire a better understanding on bridge 
rehabilitation using link slab. Also to assess the long-term reliability of this method, 
the MTO managed to accomplish this goal performed experiments with scale model 
to study the structural behavior of the link slab system and investigated a bridge 
rehabilitated using the debonded link slab system (Alexander Au, Clifford Lan, Jim 
Au and Bala Tharmmabala, 2013). A typical link slab configuration is illustrated in 
Figure 2.6. 
 
Figure 2.6: Debonded link slab system (Alexander Au, et al 2013) 
16 
 
 
 The MTO had revised the original design approach proposed by Dr. Caner 
and Dr. Zia (Caner and Zia, 1998). In the past, the design bending moment M caused 
by girder end rotations imposed on link slabs, were calculated in Equation 2.2: 
2𝐸𝐼
𝐸 = 𝜃                                                                   (2.2) 
𝐿𝑑
Where 
𝑘𝑁
𝐸 = 𝑌𝑜𝑢𝑛𝑔′𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 ( ) 
𝑚2
𝐼 = 𝑠𝑒𝑐𝑜𝑛𝑑 𝑚𝑜𝑚𝑒𝑛𝑡 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑖𝑛𝑘 𝑠𝑙𝑎𝑏 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑢𝑛𝑖𝑡𝑠 (𝑚4) 
𝐿𝑑 = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑜𝑛𝑑𝑒𝑑 𝑠𝑙𝑎𝑏 𝑙𝑒𝑛𝑔𝑡ℎ (𝑚) 
𝜃 = 𝑔𝑖𝑟𝑑𝑒𝑟 𝑒𝑛𝑑 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 (𝑟𝑎𝑑) 
However, test results reflected that Equation 2.1 did not consider compatibility of the 
link slab and the girders, which could lead to unrealistic deformation in 3-D modeling 
(Au and Lam, 2011). Hence, the revised equation was proposed in Equation 2.3: 
2𝐸𝐼
𝐸 = 𝜃𝛼𝑅                                                                   (2.3) 𝐿𝑑
Where 𝛼𝑅 is the adjustment factor to account for displacement between slab and 
girder within the debonded zone and given in Equation 2.4: 
4
𝛼𝑅 =                                                                    (2.4) 3𝑒
(1 + 𝐿 )𝑑
Where 𝑒 = distance measured from adjacent simple supports at the pier location in 
Figure 2.6. 
17 
 
 
 The MTO conducted a series of lab tests to investigate structural behavior of 
the debonded link slab system. In addition, a finite element model was developed for 
comparison. The test specimens were subjected extensive cyclic loading in order to 
simulate the repetitive traffic loads on the bridge. The results showed that the cyclic 
loading pattern did not affect the overall stiffness of the link slab system because the 
slope of the load vs deflection curve remained constant. Likewise, strain in rebars 
were also not affected by the cyclic loading in the debonded link slab system. Crack 
patterns also indicated that the link slab was capable of carrying the load transferred 
by the girder end rotations by evenly distributed fine cracks along the width of the 
specimen. The crack pattern on link slab is shown in Figure 2.7. The experiment also 
validated that the 5% debonded zone between link slab and the supporting girder was 
sufficient. 
 
Figure 2.7: Link slab crack pattern (Alexander Au, et al 2013) 
 
 Furthermore, the MTO performed a field testing on a bridge that was 
previously rehabilitated with the debonded link slab system (Au and Lam, 2008; Au 
18 
 
 
et al. 2010). The structure was loaded before the installation of link slab to serve as 
the baseline. A total of 56 sensors were instrumented to collect structural response on 
selected locations. The bridge was loaded simultaneously by two trucks with weights 
of 441 kN and 430 kN. By comparing the theoretical and field test results, 
conclusions could be summarized as follows: 
1. Although deflections and steel girder strains patterns in both approaches 
generally follow the same pattern, the predicted values by theoretical values 
were constantly greater than the records obtained in the field test. 
2.  Strains in steel girders showed the same pattern in both the theoretical model 
and field test results. 
3. Field test data supported that the debonded link slab meet the SLS 
requirement of CHBDC 2000 and 2006. Thus, the proposed design 
methodology by Caner and Zia (1998) was validated. 
4. The debonded link slab system provided minimum continuity to the bridge 
deck was successful in reducing girder end rotations, total vertical 
displacements and positive bending moments in the main span. 
5. Equation 2.3 shown above was verified. 
 
2.3.3 Kenneth M. Wing and Meryyn J. Kowalsky 2005 
The North Carolina Department of Transportation (NCDOT) carried out a 
research on bridge rehabilitation with the use of debonded link slab system (DLS). 
The west bound Plott Creek bridge on US highway 23-74 was selected to be 
19 
 
 
rehabilitated by the DLS. One of the most emphasizes of this project was to validate 
that the girders could be safely treated as simply-supported under service dead and 
live loads in the design of a debonded link slab system. A solar-powered sensor 
system was instrumented on selected locations to monitor the long-term response of 
the bridge. Meanwhile, theoretical values were calculated based on an analytical 
model. 
 Originally, the bridge had three interior expansion joints. Two of the 
expansion joints were eliminated during rehabilitation, except for the center 
expansion joint. Thus, two sets of link slab replaced the two expansion joints and one 
of which was monitored for its long-term performance. Based on design 
recommendation proposed by Caner and Zia (1998), the debonded link slab system 
was designed to accommodate a girder end rotation of 0.002 radians and the overall 
design followed the methodology by Caner and Zia (1998). The bridge configuration 
after rehabilitation is shown in Figure 2.8.  
 Sixteen thermocouples were installed to monitor temperatures on along the 
bridge. The devices were the FF-K-24 Omega thermocouples with a range of 
measurement up to 200 degree Celsius. In addition, 12 thermocouples were placed 
within the deck and four were installed on the steel girders. On each steel girder 
gauges were installed on both top and bottom.  
20 
 
 
 
Figure 2.8: NCDOT link slab rehabilitation design (Wing & Kowalsky, 2005) 
 
 Live load tests were conducted in June of 2001, on two locations with four 
levels of applied loads. One of the locations was selected to produce the maximum 
positive moment in the span adjacent to the link slab. The other location was chosen 
to create the maximum negative moment in the link slab. On the other hand, the four 
load levels covered the normal service condition of the bridge: the first load was the 
weight of an empty truck, which was 137 kN; the third load has a magnitude of 304 
kN, which represents the maximum allowable load for the specific truck without a 
permit; the second load level lied in the middle of the first and third load level, which 
in this case was 214 kN; the forth load was 424 kN and is the maximum allowable 
load allowed on this bridge. 
 Based on the proposed configuration, a computer model was created to 
calculate end rotations of the steel girders. Because of the symmetry, only half of the 
spans were included where the other half was separated by a expansion joint and was 
not monitored by sensors. Each axle was modeled as a point load and one girder line 
was modeled at a time. The abutments were modeled as fixed supports and the 
21 
 
 
expansion joints were created as rollers. The link slabs were modeled as pinned 
connections at the girder end bearings. Comparisons of the results obtained from the 
live load test and the numerical simulation showed similarity in general, indicating 
that the girder demands could be sufficiently estimated by the load distribution 
formulas. 
 Long-term monitoring was fulfilled by recording the structural response of the 
bridge over the course of a year. The data were taken every two hours and lasted for 
two minutes. Approximately 40 readings were taken on each gauge. The bridge 
experienced a variation in temperature more than 15 degree Celsius daily. While the 
temperature could vary more than 45 degree Celsius seasonally. Results reflected that 
the thermal rotations measured were always smaller than the expected values due to 
large temperature fluctuation and momentary variations in surface temperature (Wing 
and Kowalsky, 2005). 
 Overall, results reflected that the debonded link slab system helped improve 
the bridge performance. The measured girder end rotations had never reached the 
design limit of 0.002 radians and the rotations recorded during the live load test were 
all smaller. Fine cracks were discovered on the link slab with a width of 1.6 mm, 
which was significantly smaller than that of a traditional expansion joint. 
Furthermore, the width of the fine cracks remained the same during the live load test, 
which was intended to simulate service condition of the bridge. This validated the 
serviceability of the DLS. 
22 
 
 
 Furthermore, the authors also proposed a limit-state design method for link 
slab particularly on the bridge where the tests were conducted: 
1. Calculate the negative moment caused by girder end rotations and cracking 
moment of the link slabs using Equation 2.5 and 2.6. 
2𝐸𝑐𝐼𝑑𝜃
𝑀𝑎 =                                                                  (2.5) 𝐿
𝑓𝑟𝐼𝑑
𝑀𝑐𝑟 =                                                                     (2.6) 𝑦
where 
𝑀𝑎 = 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 𝑐𝑎𝑢𝑠𝑒𝑑 𝑏𝑦 𝑔𝑖𝑟𝑑𝑒𝑟 𝑒𝑛𝑑 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑠 
𝐼𝑑 = 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎 𝑜𝑓 𝑙𝑖𝑛𝑘 𝑠𝑙𝑎𝑏 
𝜃 = 𝑔𝑖𝑟𝑑𝑒𝑟 𝑒𝑛𝑑 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑠 
𝐿 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑖𝑛𝑘 𝑠𝑙𝑎𝑏 
𝑀𝑐𝑟 = 𝑙𝑖𝑛𝑘 𝑠𝑙𝑎𝑏 𝑐𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 
𝑓𝑟 = 𝑓𝑙𝑒𝑥𝑢𝑟𝑎𝑙 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑑𝑒𝑐𝑘 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 
𝐸𝑐 = 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 
2. Compute stress in steel with Equation 2.7 (Caner and Zia, 1998). 
𝑓𝑟𝑀𝑎
𝑓𝑠 = 𝜇𝜌                                  (2.7) 
6𝑀 𝜌𝛾2 {1 + − 0.333[(𝜇𝜌)2 + 2𝜇𝜌]0.5𝑐𝑟 3 }
 where 
𝑓𝑠 = 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑖𝑛𝑔 𝑠𝑡𝑒𝑒𝑙 
𝜌 = 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑖𝑜 
23 
 
 
𝐸𝑠
𝜇 = 𝑚𝑜𝑑𝑢𝑙𝑎𝑟 𝑟𝑎𝑡𝑖𝑜 𝑐𝑎𝑙𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑎𝑠  
𝐸𝑐
𝛾 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑠𝑡𝑒𝑒𝑙 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑𝑒𝑝𝑡ℎ 
3. Calculate the effective tension area of concrete in the main reinforcement by 
the Gergely-Lutz expression (McCormac, 1998) shown in Equation 2.8. 
3
𝜔 = 0.076𝛽𝑓𝑠 √𝑑𝑐𝐴                                                                   (2.8) 
where 
𝜔 = 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑐𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑤𝑖𝑑𝑡ℎ 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠 𝑜𝑓 0.003 𝑚𝑚 
 
                      𝛽 = 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 𝑎𝑥𝑖𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑒𝑥𝑡𝑟𝑒𝑚𝑒  
                             𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑖𝑏𝑒𝑟 𝑎𝑛𝑑𝑓𝑟𝑜𝑚 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑 𝑜𝑓 𝑚𝑎𝑖𝑛 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 
 
         𝑑𝑐 = 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑐𝑜𝑣𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑓𝑟𝑜𝑚 𝑒𝑥𝑡𝑟𝑒𝑚𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑖𝑏𝑒𝑟 
                  𝑡𝑜 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑 𝑜𝑓 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑙𝑒𝑣𝑒𝑙 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠 𝑜𝑓 𝑚𝑚 
 
                     𝐴 = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑎𝑖𝑛 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑖𝑛𝑔 
                             𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑟𝑠 𝑖𝑛 𝑚𝑚2 
4. Calculate required reinforcement spacing by Equation 2.9 (Caner and Zia, 
1998). 
𝐴
𝑠 =                                                                    (2.9) 
2𝑑𝑐
 
24 
 
 
5. Compute the number of bars by Equation 2.10. 
𝑏
    𝑁 =                                                                    (2.10) 
𝑠
where 
  𝑏 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑙𝑖𝑛𝑘 𝑠𝑙𝑎𝑏 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠 𝑜𝑓 𝑚𝑚. 
6. Determine the area of reinforcement by Equation 2.11. 
𝜌𝑏𝛾ℎ
                                                   𝐴𝑏 =                                                           (2.11) 𝑁
where 
 ℎ = 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑𝑒𝑝𝑡ℎ 
7. Eliminate results that are not feasible. Repeat the procedure until a satisfactory 
solution is achieved. 
In conclusion, the study found that the controlling rotations on the link slab 
were not caused by traffic loads, but thermal. Hence, the design based on the 
assumption of simply-supported spans was adequate and conservative. Besides, it was 
identified that the link slab might have developed fine cracks during casting yet the 
effects on its performance is negligible. At last, the proposed design method can be 
used to develop a design chart and apply to specific applications of link slab. 
  
 
 
25 
 
 
Chapter 3 Experiments 
3.1 Objective and overview 
To gain a better understanding on material properties of UHPC and ECC, a 
series of lab tests were conducted. The goal of the experiment was to obtain a hands-
on experience on mix design; test material properties and compare the results with 
literatures; investigate sensor reliability, installation alternatives and propose 
recommended sensor designs for future experiment and bridge structural 
health/performance monitoring.  
A total of 43 sensors were used on 14 specimens. The sensors are purchased 
from Resensys LLCTM, a company specializes in wireless structural health 
monitoring. Strain gauges used in the lab tests are also intended to be install on a 
bridge in future field tests. The experiment was intended to simulate the service 
loading pattern of link slab by applying cyclic loadings to the specimen. Experimental 
results and photos of each tested specimen were stored for result analysis in chapter 6.   
 
3.2 Materials and expectations 
3.2.1 UHPC 
UHPC stands for ultra-high-performance concrete. UHPC is a cementitious 
concrete material that offers a minimum compressive strength of 120 MPa, or 17000 
pounds per square inch, and a maximum compressive strength of 200 MPa, or 29000 
pounds per square inch (psi). Fibers serve as reinforcement in material in order to 
26 
 
 
satisfy specific requirements of strength, durability, ductility and toughness 
depending on applications. Convectional fibers including PVA, Glass or high carbon 
steel. UHPC materials can provide much better ductile behavior compared to normal 
concrete. 3 out of the 14 specimens were casted as UHPC material. 
3.2.2 ECC 
Engineered Cementitious Composites, also known as ECC, represent a group 
of ultra-ductile fiber reinforced concrete (Li, 2011). Usage of ECC materials are not 
limited in laboratory. They are also used in large-scale on-site construction projects 
(Kong et al, 2003; Lepech and Li, 2007). Characteristics of ECC material includes 
high tensile strength and ductility. Another typical application of the material is 
structural repair. In addition, ECC material offers environmental benefit with negative 
carbon footprint. The material provides much higher resistance against weather by 
developing fine cracks. 11 out of the 14 specimens were made as ECC materials. 
3.2.3 Expectation 
Expectations of experimental results were made based on material properties 
discussed in previous sections. First, a high tensile strength was expected for both 
materials. The high tensile strength is one of the most essential benefits offer by 
UHPC and ECC for reduction in reinforcement and member size. Another critical 
property is the high tensile ductility of the material. Hence, it was expected that the 
material would display a “yield point” similar to that of a steel and experienced 
“metal-like” deformation with large curvature. Also, tendency of fine crack 
development allows the material to protect the rebars and substructure from chloride-
27 
 
 
contaminated water infiltration and debris accumulations. So that fine cracks were 
expected to be observed along the width of the specimen. And a fracture plane 
formed by multiple fine cracks is also expected to appear when the specimen failed. 
3.3 Testing 
3.3.1 Sensor information 
Sensors used in this experiment were the Strain Gauge SenSpotTM Sensor. 
Each sensor consist of a strain gauge that serves as a strain sensing element; a cable 
and a wireless transmitter delivering data to monitoring programs. The Strain Gauge 
SenSpotTM Sensor is shown in Figure 3.4 and 3.5. This product had been used in 
industry for real-time and long-term structural health monitoring. The sensor allows 
data to be taken wirelessly and has several features making it suitable for this test 
because the same type of sensors is planned to be install on a bridge in future field 
test. First, the Strain Gauge SenSpotTM Sensor is designed to be durable, with a 
minimum battery life for 10 years and the sensor needs no or minimum maintenance. 
The size of the sensor is small with dimensions of 2in. x 2in. x 1in. and weighs only 
50oz, communicating at IEEE 802.15.4, 2.4GHz. The small size, combing with the 
self-adhesive or flange mount, allows the sensor to be easily installed on test 
locations. The working temperature of the sensor is -40 to 150 degree Fahrenheit ( -
40 to 60 degree Celsius) and this range covers the temperature variation of both the 
experiment and field test.  
28 
 
 
 
Figure 3.1: Strain Gauge SenSpotTM Sensor 
 
 
 
Figure 3.2: Sensor installation on a bridge girder 
 
3.3.2 Sensor installation 
The sensors were designed to be placed on specimen made of ECC and UHPC 
to study their behavior under cyclic loading. Whereas, one of the challenges in this 
experiment is to simulate actual working condition in the lab test for the sensors as if 
they were working on structural members in a real bridge. Hence, modification was 
made during sensor installation in order to simulate field condition of the sensors. 
There were two types of sensor systems designed. Originally, the sensor is designed 
29 
 
 
to be directly install on a structural member by self-adhesive or flange mount. This 
was chosen to be the first approach of sensor placement, which translated into directly 
installation of sensors on the surface of the concrete specimen. Another option was to 
mount the strain gauge of a small piece of steel plate, forming a sensor system. Then 
this sensor system was installed on the surface of the concrete specimen in the same 
manner as the first alternative. The only difference was the steel plate being the 
intermediate material between the strain gauge and the concrete. Ideally, the two 
types of sensors should return similar results when placed within the same region. If 
not, relationship between them can be studied.  
 However, this method of installation could raise concerns over accuracy of 
data acquisition by introducing potential sources of uncertainties. Unlike field 
condition, where the sensor is installed directly on a structural member, the strain 
gauges here were install on a metal plate. Technically, the strain gauges were 
measuring strains on the metal plate, instead of the concrete specimen. Thus, it was 
assumed that the metal plate remains compatible with the ECC and UHPC specimen. 
In addition, it was also assumed that the bonding between the metal plate and the 
strain gauge remain strong enough for the sensor to capture any displacement. To 
eliminate discrepancy, calibration was performed during data analysis for each sensor 
because the metal plate might develop strains before the test began. For instance, if 
the data showed 150µε at time 0, the entire data set would be deducted by 150µε. 
 
30 
 
 
 
Figure 3.3: Strain gauge installation on a metal plate 
 
3.3.3 Procedure 
Fourteen link slab specimens were casted in the NRMCA’s International 
Center for Concrete Research. When ready, all specimens were tested by three-point 
bending test and the procedure followed ASTM C78/C78M-18. Schematic of the 
testing apparatus is shown in Figure 3.4. During mixing, ECC materials were 
modified for the purpose of the testing. The updated mixture is presented in Table 
3.2. There were 43 strain gauges on 14 specimens. To simulate field condition, the 
strain gauges were installed on a small metal plate prior to mixing. The sensor 
distribution is summarized in Table 3.1. Note that “bdi” and “hbm” are two types of 
sensors that were also tested here. With the sensor system established, some of the 
sensors were buried during pouring of the concrete specimen and others were 
installed on surface of the specimens. A picture of the finished product is presented in 
31 
 
 
Figure 3.5. Each specimen was loaded until failure. In order to simulate service 
condition on bridge for the link slabs, loads were applied cyclically, where on average 
each specimen had 5 loading cycles until it reached its failure point. During testing, 
data of applied loads and corresponding stresses were recorded continuously. 
However, the data was discretized at a one-second interval for data processing. 
Strains of the specimens were also monitored throughout the testing, where the 
readings were taken every 0.2 seconds on average. Similarly, strain data were 
converted into the same time interval of the stress data in data analysis.  
Table 3.1: Sensor distributions 
Test No. Material No. of Sensors Sensor Locations 
1 UHPC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
2 UHPC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
3 ECC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
4 ECC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
5 ECC 1 Embedded Bottom Steel 
6 ECC 1 Embedded Bottom Steel 
7 ECC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
8 ECC 2 Top Concrete, Top Steel 
9 ECC 3 Bottom bdi, Bottom hbm, Bottom Concrete 
10 ECC 2 Bottom bdi, Bottom Concrete 
11 ECC 4 Bottom bdi, Bottom Steel, Bottom Concrete, Bottom hbm 
12 ECC 2 Bottom Concrete, Embedded Bottom Steel 
13 ECC 4 Bottom Concrete, Bottom bdi, Bottom hbm, Embed Steel 
14 UHPC 4 Top Concrete, Bottom Concrete, Top Steel, Bottom Steel 
 
Note that the 3 UHPC specimens were casted strictly based on specifications 
from the manufacture. On the contrary, there were more flexibility when designing 
the ECC specimens. Hence, the ECC specimens provide an opportunity to explore 
different mix design by trail and errors. As a result, ECC became the focus in material 
32 
 
 
testing. The final mix design for ECC was shown in Table 3.2. The selected design 
was chosen based on the similarity to the mix design (Li, 2008) recommended in 
Section 3.1 in order to achieve the desired high tensile strength and ductility. 
 
Table 3.2: Updated ECC mixture 
Material By weight  
Cement 1 
Fly ash (Class F) 1.2 
Silica Sand (20-30 or finer) 0.8 
Water 0.53 
HRWR (Types A&F) 0.013 
PVA Fiber 2% (by volume) 
 
 
 
 
Figure 3.4: Three-point bending test apparatus (ASTM C78/C78M-18) 
 
 
33 
 
 
 
Figure 3.5: Link slab specimen with strain gauge 
 
 
 It is worth pointing out that the SenSpotTM sensor is generally applied on steel 
members as shown in Figure 3.2. Hence, practicality of the sensor on concrete 
material remains unclear. Experiments in this section would not only carry out results 
on material properties of ECC and UHPC, but also provide insights on performance 
of the SenSpotTM sensor on concrete materials. This is of great value as the tests 
offered potential on expanding the use of this type of sensor on materials other than 
steel. 
 Practicality of the SenSpotTM sensor in this project is secured by the 
characteristics of ECC and UHPC. In fact, both ECC and UHPC tend to develop fine 
cracks that are hairline in width, so that disturbance due to crack development is not 
significant. Nevertheless, discrepancies were found in data analysis, reflecting that 
the sensors were only reliable within a certain range of measurement. This subject 
will be discussed in chapter 6.       
 
 
34 
 
 
Chapter 4 Finite Element Analysis 
4.1 Description 
Numerical analysis was done to simulate the bridge behavior under service 
condition. The goal of numerical simulations is to obtain a preliminary assessment of 
structural performance of the bridge under service condition. In this section, 2 models 
were generated based on finite element methods. Computer programs Ansys 
Workbench® and CSiBridge® were utilized to create finite element models and the 
results were compared. The purpose of this section is to create a baseline for future 
installation on link slabs and corresponding numerical simulations. 
 In fact, models developed for numerical simulation were created as a 
prototype structure. Namely, the models were only going to include the concrete slabs 
and steel girders underneath. All other components in the substructures, such as bents 
and abutments were not directly included in the model. Also, the reinforcing rebars 
were also excluded. Instead, substructures were translated into boundary conditions 
and bearings to simulate their presence and the competence of the bridge model was 
ensured mechanically. However, some of the attributes in dynamics response, for 
instance, the mass matrix, were changed by simplifying the bridge model. Hence, 
when results from numerical simulation and field test were compared, it was 
anticipated that they might not perfectly reflect each other. Nevertheless, as long as 
the results fall into the acceptable range, it was considered reasonable for the purpose 
of this thesis.  
35 
 
 
4.2 Bridge Details 
The bridge serves as an overpass bridge on Winch Road, crossing interstate 
highway 95 in the Maryland state highway system. The structure number is 
CEX952001 and it was designed as a composite bridge with steel girders and 
concrete slabs. The length of the bridge is 215.5 feet and it is 31.17 feet wide. There 
are 4 spans and the reinforced concrete decks are 2 inches apart. The gap between the 
concrete decks are designed to be filled by expansion joints. The expansion joints are 
considered as non-structural component. Therefore, the joints were eliminated in the 
finite element analysis in later sections. The expansion joints are to be replaced by 
link slabs in the future. As previously discussed, all 4 reinforced concrete decks are 
supported by steel girders below, where the exterior girders are W36x135 and the 
interior ones are W27x94. Each girder has the same length as the concrete decking it 
supports. Unlike the gap between decks, bearings supporting the steel girders are 8 
inches apart measured from center to center. The bridge is designed as a simply 
supported bridge with constraints only on translational motions. The bridge is free on 
rotation. Specifically, bearings located at the center and two ends restrict translations 
in all x, y and z directions. While other 2 sets of bearings only prevent motions in z 
(vertical) direction. Photos of the bridge and some of its structural drawings are 
shown in Figure 4.1 to 4.2. 
36 
 
 
 
Figure 4.1: Plan view of bridge CEX952001 
 
 
 
Figure 4.2: Elevation view of bridge CEX952001 
 
 
37 
 
 
4.3 Finite Element Model using ANSYS Workbench® 
4.3.1 Overview 
According to information discussed above, a finite element model was created 
in Ansys Workbench® to simulate behavior of the bridge under service condition. 
Results of interested are the bridge responses to moving truck loads and its modal 
frequencies. The model generated by Ansys Workbench® only carried out the results 
of the first six modal frequencies and corresponding modal shapes, while the model 
created in CSiBrdige® would include both the structural response of standard moving 
truck loads and modal analysis. An overview of the model by Ansys Workbench® is 
presented in Figures 4.3 to 4.4. 
 
Figure 4.3: Bridge model geometry in Ansys Workbench® 
 
 
Figure 4.4: Boundary conditions at bearings 
38 
 
 
4.3.2 Results for Modal Analysis 
The results for the first 3 modal frequencies and corresponding modal shapes 
are shown in Table 4.1 and Figure 4.5 to 4.6. In fact, meshing elements were 
program-controlled in this Ansys Workbench® model. There were 3 primary element 
types used in this analysis: Tet10, Hex20 and Wed15 per Ansys Workbench® 
documentation. Specifically, Tet10 represents a 10-node linear tetrahedron element 
with 3 degree of freedom at each node, which is used to model irregular shapes. On 
the other hand, Hex 20 is a 20 nodes linear hexahedron that also has 3 degrees of 
freedom for each node. Hex20 is normally used for quadratic displacement behavior. 
At last, Wed15 is defined as a 15-nodes linear wedge (prism), with 3 degree of 
freedom and used for quadratic displacement behavior. Application of each element 
was controlled by Ansys Design Modeler® to specific conditions where a particular 
mesh was generated. Visualizations of the 3 primary meshing elements can be viewed 
in Figure 4.5. 
 
Table 4.1: Modal frequencies by Ansys Workbench® 
Modes Frequency (Hz) 
1 2.5307 
2 2.7159 
3 3.0581 
4 3.3124 
5 5.8249 
6 6.1092 
 
39 
 
 
 
Figure 4.5: Tet10, Hex20 and Wed15 elements in Ansys Workbench® 
 
 
 
Figure 4.6: Total deformation in dynamic analysis 
 
 
Figure 4.7: 1st modal shape, f = 2.53 Hz 
40 
 
 
 
 
Figure 4.8: 2nd modal shape, f = 2.72 Hz 
 
 
 
Figure 4.9: 3rd modal shape, f = 3.58 Hz 
 
4.4 Finite Element Model using CSiBridge® 
4.4.1 Overview 
Based on the same bridge layout, a finite element model was generated using 
CSiBridge®, which is a more production-oriented software. The bridge was modeled 
as simply-supported at bearings. The model consist of three spans with a skew angle 
of 6.4 degrees. There were three types of restraints: fixed bearings resist translational 
41 
 
 
motions in x, y and z directions; joint bearings resist translational motions in y and z 
directions; deck restraints resist translational motions in y and z directions to prevent 
the structure from moving sideways in modal analysis. 
4.4.2 Shell Elements vs. Solid Elements 
Unlike the model in Ansys Workbench®, where the bridge was modeled using 
solids, the structure was modeled using shell elements in CSiBridge®. In general, 
shells are considered as a mathematical simplification of solids. Shell elements are 
limited to objects that are thin, meaning that the thickness of the body should be 
approximately 20 times less than the span. This makes the shell elements applicable 
to this bridge model because the structure has a span of 215.5 feet, while the 
thickness only consist of the thickness of the slab and the depth of the supporting 
girders.  
Shell elements boost the computation process by allowing fewer elements 
when modeling thin objects. Additionally, shell elements make meshing easier and 
are less prone to negative Jacobian errors that could take place in extremely thin solid 
elements. An overview of the model using CSiBridge® is shown in Figure 4.10. 
 
Figure 4.10: CSiBridge® model using shell elements 
42 
 
 
4.4.3 Results for Modal Analysis 
The first six modal frequencies of the bridge model are summarized in Table 
4.2 and the first three modal shapes are presented in Figures 4.11 to 4.13. 
Table 4.2: Modal frequencies by CSiBridge® 
Modes Frequency (Hz) 
1 2.4636 
2 2.6572 
3 3.6629 
4 3.8235 
5 7.5090 
6 7.8355 
 
 
 
 
Figure 4.11: 1st mode shape, f = 2.46 Hz 
 
43 
 
 
 
Figure 4.12: 2nd mode shape, f = 2.65 Hz 
 
 
 
 
 
Figure 4.12: 3rd mode shape, f = 3.66 Hz 
 
 
44 
 
 
4.4.4 Structural Response for Moving Truck Loads 
Standard moving truck loads were applied to the bridge and the structural 
responses were simulated. The vehicle load was chosen as HSn-44 per AASHTO 
specifications, which stands for truck with a semi-trailer. The truck load consists of 
vertical applied forces from three axles of the vehicle. An example of a HSn-44 
vehicle load is shown in Figure 4.13. The model included two standard trucks moving 
at 40 MPH in opposite directions. Figure 4.14 demonstrates the moving truck 
situation. The duration of the simulation was set to 200 seconds and the applied loads 
were discretized every five seconds. In other words, the simulation lasted for 200 
seconds and each frame was shown every five seconds. To gain a better visualization 
of the structural response, magnification factor was set to 50. 
 
 
Figure 4.13: HS20-44 vehicle load per AASHTO specifications 
 
45 
 
 
 
Figure 4.14: Moving truck loads visualization 
 
 
 The maximum positive and negative vertical shear forces were plotted in 
Figure 4.15, with a maximum positive shear force is 62.5 kips and the maximum 
negative shear force is -59.4 kips. The maximum positive shear force is recorded at 
109 feet from the initial station and the maximum negative shear force occurs at 34 
feet from the initial station. The figure was plotted along the length of the bridge and 
the positive values indicate shear forces in the positive z direction; while the negative 
values represent shear forces in the negative z direction. 
 
Figure 4.15: Maximum and minimum vertical shear envelop 
46 
 
 
 Moments about the horizontal axis (x-axis) is plotted in Figure 4.16. The 
maximum positive moment is 1036.41 kip-ft and the maximum negative moment is 
46.92 kip-ft. The maximum positive moment occurs at 147 feet from initial station of 
the bridge and the maximum negative moment occurs at 184.5 feet measured from the 
initial station. 
 
Figure 4.16: Maximum moment envelop 
 
 Vertical displacements/deflections over the entire section is shown in Figure 
4.17. Since there are no displacements in the upwards direction, all the values are 
negative. The maximum displacement is 0.88 inches in the negative z direction; the 
minimum displacement is 0.0003 inches pointing downwards. The maximum 
deflection occurs at 147 feet measured from the initial station and the minimum 
deflection occurs at 185.2 feet from the initial station. 
47 
 
 
 
Figure 4.17: Maximum vertical deflection 
 
 
4.6 Modal Analysis Comparison 
 Modal frequencies from the two models were summarized in Table 4.3. It can 
be inferred that the two models generally agree with each other, with minor 
differences. Results for the first two modes were close, while the difference between 
the two models increases in higher modes and the average error was calculated as 
16.2%. The model generated by the CSiBridge® is expected to be more accurate. 
However, results in the numerical simulations need to be examined by data collected 
in the future field test for validation. 
Table 4.3: Modal analysis comparison 
Frequency by Ansys Workbench® Frequency by CSiBridge® Error 
Modes 
(Hz) (Hz) (%) 
1 2.5307 2.4636 2.7 
2 2.7159 2.6572 2.2 
3 3.0581 3.6629 19.8 
4 3.3124 3.8235 15.4 
5 5.8249 7.509 28.9 
6 6.1092 7.8355 28.3 
 
48 
 
 
Chapter 5 Field Test 
5.1 Description 
5.1.1 Strain Distribution 
 Field tests were scheduled to validate performance of link slab. Specifically, 
strain distribution and crack propagation will be closely monitored. In principle, 
design of link slab is strain-controlled. The depth of concrete and rebar placements 
are determined based on limit states in strain. Ideally, the strain distribution is 
assumed to vary linearly, similar to the strain diagram of a Whitney’s stress block. 
Hence, the maximum strain values will occur at the top and bottom location, 
representing the extreme compressive and tensile fibers. Figure 5.1 illustrates the 
strain distribution of ECC and UHPC link slab by design.  
 
Figure 5.1: Strain distribution of link slab 
49 
 
 
5.1.2 Sensor System Configuration 
 Ideally, fine cracks are expected to be formed when the link slab is subjected 
to bending moment imposed by girder end-rotations. Therefore, it is considered a 
failure if concentrative, visible, major cracks occur on the link slab. Another 
limitation during design is associated with sensor placement. The sensors need to be 
mounted on a small piece of metal plate in order to be stabilized on designated 
locations. Hence, the strain gauge will not be measuring the movement of the 
concrete link slab directly. Instead, the readings rely on compatibility between the 
link slab and the metal plate. During data analysis, feasible range of measurement and 
sensor calibration need to be done. Information on this subject will be discussed in 
Chapter 6.  
5.2 Preparation 
 Sensors are to be placed on girders in both top and bottom location to measure 
strains of the ECC and UHPC link slabs. The adjacent girders will both be 
instrumented with strain gauges symmetrically. The layout is shown in Figure 5.2 as 
an elevation view. For two adjacent girders, there will be 4 sensor systems and 2 on 
each girder. On each link slab, only one sensor will be activated for data acquisition 
and the other one will serve as a redundency in case one of the senors is damaged. 
Figure 5.3 and 5.4 are the elevation views of the sensor locations. 
50 
 
 
 
Figure 5.2: Plan view of sensor locations 
 
 
 
Figure 5.3: Elevation view of sensor location on UHPC link slab 
 
51 
 
 
 
Figure 5.4: Elevation view of sensor location on ECC link slab 
 
5.3 Equipment 
 Unlike shown in chapter 3, where there are two types of sensor systems in the 
lab tests, the field test is only going to use the sensor configuation shown in Figure 
5.5. In this set-up, a single strain gauge is mounted on a pice of steel plate and 
conncected to a transimitter with wires. The transimitter will be mounted on the 
outside surface of the bridge parapet. When the sensor system estabilished on the 
bridge, real-time data are to be collected by the data acquisition (DAQ) system 
located in a area with limited access 50 to 150 feet away from the transimitter. Data 
will be transported wirelessly. Then, the DAQ will deliver the data to a remote server 
using commercial cellular service. The long-term monitoring of the performance of 
the link slab will be conducted as discrbed above. Figure 5.6 shows a DAQ 
equipment and Figure 5.7 is a simple representation of the network for data 
collection. 
52 
 
 
 
Figure 5.5: Sensor system with a steel plate 
 
 
 
Figure 5.6: Solar powered DAQ 
53 
 
 
 
Figure 5.7: Network of data collection 
 
 
5.4 Procedure 
 The entire operation includes two parts: existing joints remove and 
construction of the link slabs. Procedures for ECC and UHPC link slabs are slightly 
different: for link slabs made of ECC, bottom sensors will be placed on the roofing 
paper above girders after removal of existing joints and decks; while for UHPC link 
slabs, existing joints will be removed completely but the deck will be partially 
removed and bottom sensors will be installed on sealing between the gap. During 
concrete pouring, the top sensors are to be placed on top of the deck and covered by 
overlay concrete. Cables of the sensor systems are fixed along the link slab and 
extended outside. When the concrete has cured, the cables will be connected to the 
transmitters to initiate the long-term monitoring process of the project. 
 
54 
 
 
Chapter 6 Results 
6.1 Results for ECC and UHPC 
6.1.1 Data Processing 
Fourteen tests were conducted in the NRMCA’s International Center for 
Concrete Research, including three UHPC specimens and 11 ECC specimens. Each 
specimen was loaded with cyclic loading until failure. During testing, fine cracks 
developed on the link slab specimen and a major crack marked the failure state of the 
specimen. It is possible to have fine cracks when the specimen was being casted, but 
it is acceptable for link slab.  
 Each test lasted approximately an hour on average, where readings for applied 
loads and stresses were taken every five seconds. On the other hand, strain data were 
recorded every 0.2 seconds on average. Hence, in order to generate the stress-strain 
curve, the strain data were discretized and converted to one data point for every five 
seconds, to match the frequency of the stress data. In addition, desyncs were noticed 
in data collection. That is, there were time lags between the stress and strain data 
because they were not necessary recorded at a same time. The stress data could be 
recorded long after the strain data because the strain gauges started to take readings as 
soon as they were installed on the specimen. In data processing, this scenario was 
adjusted by carefully shifting the two data so that both readings would start at a same 
time, where the first load was applied. Additionally, random errors in readings were 
identified and outliers were manually removed from the data sheet.  
55 
 
 
6.1.2 Maximum compressive strength 
Table 6.1 summarizes the maximum compressive strength of the specimens. 
Note that compressive strengths for the three UHPC specimens were not recorded due 
to its ultra-high compressive strength so its compressive strength is generally not a 
concern, when compared to its tensile behavior. In fact, the three UHPC specimens 
were casted strictly followed by the mix design provided by the manufacturer 
LafargeHolcimTM. Based on specifications provided by the manufacturer, the 
maximum compressive strength of the UHPC specimens is 14000psi. Unlike UHPC, 
ECC specimens were casted based on a mix design shown in table 3.1, which was 
determined by trial and error. Consequently, there was more flexibility in ECC 
because it was possible to select or modify the mix design to investigate how the 
optimal solution could be achieved. 
Table 6.1: Maximum compressive strength 
Test No. Material Compression strength (psi) 
1 UHPC N/A 
2 UHPC N/A 
3 ECC 9497 
4 ECC 9497 
5 ECC 11597.8 
6 ECC 11597.8 
7 ECC 10927.2 
8 ECC 11927.4 
9 ECC 11198.9 
10 ECC 11927.4 
11 ECC 11927.4 
12 ECC 11198.9 
13 ECC 11198.9 
14 UHPC N/A 
 
56 
 
 
 For quality control, multiple specimens were casted in a same batch and they 
were expected to have the same compressive strength. For instance, specimen No.3 
and No.4 were casted at the same time, with a compressive strength of 9497 psi. Due 
to the limited amount of sensors, eight out of the fourteen specimens were fully 
covered with sensors on concrete and steel on both top and bottom. As a result, six of 
the specimens were monitored on selective locations. In fact, both ECC and UHPC 
provide high compressive strength, so when a particular specimen could not be fully 
covered with four sensors, the tensile region was the focus and the tensile responses 
were prioritized. 
 The data reflected high compressive strength of the materials. The average 
compressive strength of ECC was 11135.97 psi. Compressive strength of UHPC was 
not taken because of reasons discussed above and the expected value of compressive 
strength is 14000psi. The compression test proved that the mix design is adequate by 
showing a high compression strength. In addition, compressive strengths of the 11 
specimens made of ECC were consistent without much fluctuation. This suggested 
that the experiment was done properly and the materials were able to fulfill their full 
functionality. Results in this section can be viewed as validation of mix design, 
equipment and experimental procedure. Figure 6.1 shows strength of the ECC 
specimens in compression. 
57 
 
 
ECC Compressive Strength
14000
11598 11598 11927 11927 11927
12000 10927 11199 11199 11199
9497 9497
10000
8000
6000
4000
2000
0
3 4 5 6 7 8 9 10 11 12 13
Test No.
Figure 6.1: ECC compressive strength 
 
6.1.3 Maximum tensile strain 
 Strain readings were taken simultaneously with the applied loads and stresses. 
In fact, strain data cannot be treated the same as the applied loads and stresses. Unlike 
data for loads and stresses, which were directly read from the testing apparatus, the 
strain data relied on the compatibility between the concrete and the strain gauge. 
During data analysis, it was identified that some of the strain gauges experienced 
failure. Failure conditions included debonded sensor, damaged sensor or wire and 
fracture of the concrete specimen. Among them, the situation when the ECC or 
UHPC specimen fractured did not affect accuracy of the result because the sensor was 
not expected to return any data beyond this point. However, the other two conditions 
introduced uncertainties and the data must be analyzed with these potential sources of 
errors acknowledged. Although sensor failures might introduce disturbance in data, 
they are valuable to be studied and offered insights on areas of improvement of the 
58 
 
 
Compressive Strength (psi)
sensor system to ensure a successful field test in the future. This subject will be 
discussed in later sections. 
 Figures 6.2 and 6.3 shows the maximum tensile strength in concrete and steel 
of the 14 specimens. Note that “steel” here does not refer to reinforcing rebars. Due to 
high tensile strength of UHPC and ECC, conventional reinforcing steels are not 
required for strength. “Steel” in this section stands for sensors that were mounted on a 
steel plate and then placed on the concrete surface for strain data recording. In test 
No. 5, 6 and 8, strain gauges were only installed on steel plates; in test No. 8, 9 and 
10, strain gauges were only installed on concrete; in test No. 4, the sensor system 
failed in steel. The results displayed a wide range of data with a minimum of 171µε 
and a maximum of 3155µε in concrete; a mimimum of 127µε and a miximum of 
725µε in steel. As mentioned above, strain data shown in this section could be 
disturbed by uncertainties resulted from the sensor systems. This will be disscussed in 
detail in later sections. 
Maximum Concrete Tensile Strain
3500 3155
3000 2617
2500
2000 1692
1500 1214
1000 721573
500 171 283 216 218 253
0
1 2 3 4 7 9 10 11 12 13 14
Test No.
 
Figure 6.2: Maximum concrete tensile strain 
59 
 
 
Microstrain (µε)
Maximum Steel Tensile Strain
800 717 725
700 596 627
600
500 435
400 353 308
263
300
175
200 127
100
0
1 2 3 5 6 7 11 12 13 14
Test No.
 
Figure 6.3: Maximum steel tensile strain 
 
6.1.4 Stress vs. Strain Curve 
Loads were applied in a cyclic pattern to the specimens. The specific number 
of cycles were not consistent among the 14 specimens, where some of the specimen 
experienced one cycle of loading while others had multiple. Overall, all the 
specimens displayed similar response so for illustration purpose, test No. 7 and No. 
14 were selected to demonstrate experimental findings. 
Figures 6.4-6.6 show the cyclic loading pattern, stresses and strains of 
specimen No. 14, which was made of UHPC. This particular specimen had undergone 
14 cycles of applied loads with increasing magnitude. It can be identified that the 
response of the UHPC link slab specimen remained not affected by the number of 
repetitive loads applied because the stress and strain diagrams both reflected 
responses that were consistent to the loading pattern. No matter how many loading 
cycles the specimen had experienced, the UHPC link slab specimen was able to react 
60 
 
 
Microstrain (µε)
to the applied forces respectively until it fractured. This finding is consistent with the 
literature reviews and is critical to ensure the serviceability and reliability of the link 
slab. 
 
Figure 6.4: Cyclic loading pattern of specimen No. 14 (UHPC) 
 
 
Figure 6.5: Stresses of specimen 14 (UHPC) 
61 
 
 
 
Figure 6.6: Strains of specimen No. 14 (UHPC) 
 
To study the “metal-like” behavior of the UHPC and ECC materials, specimen 
No. 7 was selected to illustrate the findings. Specimen No. 7 was made of ECC and 
Figures 6.7 and 6.8 represent the applied loads and stresses during the experiment. 
Likewise, Figures 6.9 and 6.10 present the strain data on the specimen and the data 
were shown in two segments, where Figure 6.9 covers strains in the first 3 loading 
cycles and Figure 6.10 shows strains in the fourth and fifth loading cycles.  
Similar to the UHPC specimen, the trend and magnitude of the stress and strain data 
consistently matched the applied loads, during which the specimen was loaded five 
times with increasing loads until failure. This is consistent with the findings in the 
UHPC specimen and matches the claims reviewed in the literature. 
62 
 
 
 
Figure 6.7: Cyclic applied loads for specimen No.7 (ECC) 
 
 
Figure 6.8: Stresses on specimen No. 7 (ECC) 
63 
 
 
 
Figure 6.9: Strain in first 3 loading cycles (ECC) 
 
 
Figure 6.10: Strain in 4th and 5th loading cycles (ECC) 
64 
 
 
 
 To illustrate the ductile behavior of the specimen, stress-strain diagrams were 
generated based on data shown above. During the first loading cycle there could be 
residual stresses presented and the last loading cycle experienced material failure. 
Thus, for accuracy, the second, third and fourth loading cycles were selected to be 
examined in this section. Moreover, the stress-strain curves were created using curve 
fitting tools in MATLAB and would only cover the linear elastic region of the 
specimen to show a clear demonstration of the material as it gradually entered the 
ductile region, where the strain kept increasing without much change in stress. 
Figures 6.10-6.12 show the results of the stress-strain curves using curve fitting. 
Equations 6.1-6.3 are the mathematical expression of the curves. All the curves were 
fitted using a second-degree polynomial model. 
 
Figure 6.11: Stress-strain curve for the 2nd loading cycle 
 
Where the curve can be described by: 
                     𝑓(𝑥) = −0.01689𝑥2 + 5.605𝑥 − 68.74                                     (6.1) 
65 
 
 
 
Figure 6.12: Stress-strain curve for the 3rd loading cycle 
 
Where the curve can be described by: 
                         𝑓(𝑥) = −0.01735𝑥2 + 7.16𝑥 − 151                                       (6.2) 
 
Figure 6.13: Stress-strain curve for the 4th loading cycle 
 
Where the curve can be described by: 
𝑓(𝑥) = −0.005165𝑥2 + 4.43𝑥 − 230.6                                       (6.3) 
66 
 
 
 According to the stress-strain curve, it is clear that the specimen gradually 
entered the ductile region as the slope started to gradually decrease.  
6.2 Results on Sensor Performance 
6.2.1 Sensor Performance Criteria 
 As discussed in previous chapters, there were two types of sensor 
configurations. One is the direct approach, meaning that the strain gauge was directly 
placed on the concrete specimen on designated locations. The other type of 
configuration is by mounting the strain gauge to a steel plate before installing them on 
the concrete specimen. Performance of the sensor systems were compared in this 
section to identify potential areas for improvements.  
 A satisfactory sensor system should have the following characteristics: 
consistency and compatibility. Consistency requires the sensor to be reliable, sending 
continuous data point. Compatibility means that sensors in the two configurations 
should provide data that share the same trend and are close to each other because the 
strain gauges were used to measure the strain within the same region over the 
concrete specimen.   
6.2.2 Sensor Survival Rates 
 Reliability and accuracy of the sensors have great impact on interpretations 
from the lab tests. As previously discussed, one of the purposes of this experiment 
was to serve as a pilot project in order to evaluate the feasibility and material 
properties. Therefore, performance of the sensors were recorded and evaluated in this 
67 
 
 
section to provide a review of the experiment and offer recommendations for future 
field tests. Table 6.2 summarizes sensor failure and survival rate for each the test. The 
average survival rate was calculated as , with a lower bound of 50% and an upper 
bound of 100%. This is acceptable since this is the first attempt in sensor system 
design and arrangement. 
 
Table 6.2: Senor failure and survival rates 
No. of Failure Survival 
Test No. of Failure Sensor Sensor Rates Rates 
No. Material Sensors Location Failures (%) (%) 
1 UHPC 4 None 0 0 100 
2 UHPC 4 None 0 0 100 
Bottom Concrete, 
3 ECC 4 Top Concrete 2 50 50 
Bottom Concrete, 
4 ECC 4 Top Concrete 2 50 50 
5 ECC 1 None 0 0 100 
Embeded Bottom 
6 ECC 1 Steel 0 0 100 
7 ECC 4 Bottom Concrete 1 25 75 
8 ECC 2 None 0 0 100 
9 ECC 3 Bottom Concrete 1 33.3 66.7 
10 ECC 2 Bottom Concrete 1 50 50 
11 ECC 4 Bottom Concrete 1 25 75 
12 ECC 2 None 0 0 100 
13 ECC 4 Embeded Steel 1 25 75 
14 UHPC 4 Bottom Concrete 1 25 75 
 
 
 
 
 
68 
 
 
6.2.3 Sensor Failure Due to Lost Connection 
 It was noticed that some of the sensors did not completely fail. Some of the 
sensors were able to recover. In other words, temporary loss of connection was 
observed in the sensor systems. Figure 6.13 shows an example of this situation. 
 
Figure 6.15: Temporary loss of connection in sensors 
 
 There were two sensors next to each other, measuring strains in the same area. 
In theory, readings from the two sensors should be identical or within an acceptable 
range. However, it is clear that some of the data were missing in the middle of the 
test. But the data recording resumed shortly after this point. The graph also shows a 
few other locations where some of the strain data were missing, making the data line 
discrete. Note that this sensor system was attached to a metal plate before it was 
installed on the concrete specimen. 
6.2.4 Sensor Failure when reaching a certain level of strain 
 Another failure situation is when the strain gauge returned readings that were 
not reasonable, indicating failures in the sensor system. However, in this case, the 
sensor could still recover after a short period of time and resume taking readings. 
Figure 6.14 and 6.15 describes the condition discussed above. In Figure 6.14, sensors 
69 
 
 
on mounted on steel plates lost compatibility with the sensors directly installed on 
concrete, sending enormous readings of strain. However, Figure 6.15 proves that the 
two sensors were able to recover compatibility shortly after. 
 
Figure 6.16: Temporary loss of compatibility 
 
 
Figure 6.17: Compatibility between sensors recovered 
 
 
6.2.5 Complete Sensor Failure 
 Sensor failure is defined as the sensor’s inability to provide any readings of 
strains. This could happen in the middle of the test or even at the start of the test. 
Figure 6.18 is an example of sensor failure. 
70 
 
 
Figure 6.18: Sensor failure from the start of the test 
 
 Based on the plot, the sensor with steel plate mounted on the top concrete 
position (shown in red line) was barely able to capture any readings throughout the 
entire test. While the one without a steel plate in the same location (shown in black 
line) had taken strain data. It is clear that not only this particular senor had lost its 
compatibility with the other sensor, but also failed to record any strain on the concrete 
specimen. 
6.2.6 Possible Causes for Sensor Disturbance and Failures 
 Failure of the sensor system could be attributed to a variety of reasons. 
However, it was identified that most of the disturbance and failures occur on sensors 
that were mounted on a steel plate, as 88.8% of the failures took place on them. While 
sensor failure on strain gauges without a metal plate was only 11.2% among all the 
failure cases. The results demand better understanding on connection of sensor with 
an intermediate material before placing it on a structural member. 
 One possible cause of disturbance is the cracks development during the 
bending test. As fine cracks started to developed and gradually formed a major 
fracture plane, it is possible that the movement would have been disruptive to the 
71 
 
 
nearby sensors, causing them to lost connection or compatibility. Another reason 
could be deflection of the specimen. Because of the high tensile ductility of the ECC 
and UHPC specimen, deflection could be large enough distorting wire connections 
within the sensor system, causing them to be temporary dysfunctional. Due to the 
scale of the concrete specimen, not major deflection was observed so that sensor 
disturbance caused by deflection should only be resulted in temporary loss of 
connection or compatibility. Besides, human errors are another potential source of 
errors. It is possible to introduce errors during the installation of the sensor systems. 
However, the effect of this cause should be minimal as all the strain gauges were 
treated properly and with great curtain. Similarly, defects in sensors could not be 
ruled out even though the possibility is minimal. 
6.2.7 Recommendation on Sensor Application 
 Despite senor disturbance and failure, the system is considered as reliable in a 
feasible range of measurement. Figure 6.19 shows a moment when the two sensors 
lost combability. Table 6.3 summarizes strain levels at which the sensor lost 
compatibility. 
 
Figure 6.19: Point of lost compatibility 
72 
 
 
 
 Table 6.3: Strain level of lost compatibility 
Divide in Divide in 
Test No. of Compression Tension 
No. Material Sensors (microstain) (microstrain) 
1 UHPC 4 821.61 143.2 
2 UHPC 4 891.41 304.3 
3 ECC 4 114.56 71.6 
4 ECC 4 934.38 Sensor failure 
5 ECC 1 N/A N/A 
6 ECC 1 N/A N/A 
7 ECC 4 338 200.48 
8 ECC 2 332.94 N/A 
9 ECC 3 N/A 819.82 
10 ECC 2 N/A N/A 
11 ECC 4 N/A 195.03 
12 ECC 2 N/A 123.51 
13 ECC 4 N/A 134 
14 UHPC 4 304.44 212.74 
  
 Based on experimental results, there exists a linear relationship between the 
two types of sensor systems: sensors directly mounted on concrete and sensors 
attached to a steel plate before they are installed on concrete. In compression, the 
maximum feasible range was recorded as 340*10-6 in ECC and 890*10-6 in UHPC; in 
tension, the feasible measurements were up to 200*10-6 in ECC and 304*10-6 in 
UHPC. When the specimen experienced a strain that exceeds the value presented 
above, the sensors will lose compatibility and cannot be calibrated. Under 
compression, strain data calibrated using respective coefficient factors were within 
the range of feasible range of measurement for both UHPC and ECC. On the 
73 
 
 
contrary, the factored tensile strain in UHPC and ECC generally exceeded the 
feasible range of measurement. In order to solve this problem, nonlinear analysis is 
needed to address the incompatibility of the sensor with steel plates in regions of high 
tensile strain. Despite the present of this discrepancy, the experiment is considered 
successful by providing details of the sensor and material properties and offering 
guidance for future improvements.  
 
6.3 Fine Crack Development 
 One of the advantages in material properties of ECC and UHPC is the ability 
to form fine cracks across the width of the specimen. Fine crack allows ECC and 
UHPC link slabs to limit the amount of water penetration, protecting the girders and 
other substructures. By developing fine cracks ECC and UHPC are also able to 
sustain deformation with large curvature and display high tensile ductility. 
 Cracks on the 14 concrete specimens were recorded by photos. Most of the 
cracks were hairline in width until multiple fine cracks formed a major fracture plane 
when the specimen was loaded to failure. Figures 6.20 to 6.22 are cracks overserved 
on the concrete specimens. For better visibility, the cracks were first painted in blue 
inks. The results are satisfactory because the specimens were able to develop fine 
cracks along the width. The width of the cracks overserved is small enough to limit 
the amount of water penetration into the concrete, therefore providing a better 
protection for the member and substructures. 
74 
 
 
 
Figure 6.20: Fine cracks on an ECC specimen. 
 
 
Figure 6.21: Fracture plane formed by fine cracks on a UHPC specimen 
 
75 
 
 
 
Figure 6.22: Fracture plane formed by multiple fine cracks (ECC) 
 
  
 Although high tensile ductility was observed in both ECC and UHPC 
materials, it was evident that specimens made of ECC were generally more ductile 
than those made of UHPC. On most of the ECC specimens, cracks were developed 
more gradually and there were a larger number of fine cracks on the specimen. On the 
other hand, UHPC materials tend to have more concentration in crack development 
where most of the fine cracks occurred in the center of the specimen, in which the 
moment was the greatest.  
76 
 
 
Chapter 7 Discussion 
7.1 Lab Test 
 Overall, experiments conducted in the are successful. The material properties 
of ECC and UHPC were studied, including compressive strength, tensile ductility and 
fine crack propagation. Nevertheless, there is room for improvement. First of all, a 
thinner geometry can be used in the production of the concrete specimens. An 
example can be seen in Figure 7.1. By reducing the depth of the specimen to be 
considerably smaller than the width of the concrete slab, this type of geometry is able 
to convey the high tensile ductility of ECC and UHPC more effectively. A thinner 
slab can be monitored in terms of its vertical deflection to describe its ductility under 
a bending test. Vertical deflections prior and after the test can be compared to indicate 
the material’s ability to resist permanent deformation in response to stress. In this 
case, a stress-strain curve that is closer to a metallic material is also expected.  
 
Figure 7.1: Thin slab showing ECC tensile ductility 
77 
 
 
7.2 Sensor Protection 
  Sensor performance are satisfactory, considering this is the first trail using the 
SenSpotTM strain gauge on concrete materials. Conventionally, this specific sensor is 
generally used on structural steel members. Uniquely, possibility of expanding the 
use of the sensor into concrete materials are explored in this project. The SenSpotTM 
strain gauge were used on both ECC and UHPC specimens in the lab test and are also 
planned to be installed on the bridge in field test for long-term monitoring. 
 One of the biggest challenges associated in the use of the SenSpotTM strain 
gauge is sensor protection. A potential source of distortion is crack developed on 
concrete, compared to steel that does not crack. Cracked concrete can led to damage 
in wires and the strain gauges, resulting in lost communication between the sensor 
and the data acquisition system. For the purpose of long-term monitoring, this is not 
ideal because consistency and continuity in data recording is essential. Another 
potential threat is the vulnerability of the sensor system when exposed to the 
environment. Despite exterior coating on the wires, a full cycle of four seasons and 
various weather conditions could potentially introduce damage to the wires and 
transmitters that are exposed to the environment. However, the devices can be 
substituted from back up storage if any failure is identified.   
 
 
 
78 
 
 
7.3 Evaluation of Sensor Performance 
 According to experimental data, the survival rate of the sensor systems in the 
lab test is 76.7%. Figure 7.2 summaries this result. For a first trail, the result is 
acceptable. Specifically, strain gauges mounted on a piece of steel plate proved to be 
significantly more reliable than those directly installed on concrete. This finding 
validates the design of the sensor system for the field test. However, an improved 
design of the sensor system is still being developed. Possible adjustment includes 
thinner and smaller metal for reduced uncertainty; and alternative options for wire 
protection.  
 
Figure 7.2: Overall sensor survival rate 
 
 
 
Figure 7.3: Survival rate by configuration 
79 
 
 
Chapter 8 Conclusion and Future Work 
8.1 Conclusion 
 It is common to design bridges as simple span structures with expansion joints 
between adjacent spans. However, chloride-contaminated water penetration and 
debris accumulation have been causing issues in bridge maintenance and 
rehabilitation. To solve this problem, link slab has emerged to become a desirable 
option in recent years. By replacing conventional expansion joints with a continuous 
concrete link slab that connect two adjacent spans, the amount of water infiltration 
and debris accumulation can be massively reduced so the supporting girders and 
substructures can be better protected. Meanwhile, application of link slab allows the 
bridge spans to remain simply-supported. Furthermore, flexural stiffness of the link 
slab is significantly smaller than that of the supporting girders so that it will introduce 
negligible amount of flexural stiffness to the system. Moreover, stiffness of the link 
slab can be further reduced by add a 5% debonded zone between the link slab and the 
girders underneath. Nevertheless, link slab will not solely solve issues of structurally 
deficient bridges. Link slab is more suitable in rehabilitation for older bridges. For 
bridges that are structurally deficient, a combination of engineered approaches is 
needed to protect the structural integrity of the bridges. 
 For link slab application, certain material properties must be satisfied: high 
strength for structural integrity; high tensile ductility to ensure serviceability and 
reliability under service traffic loads; limited crack width. To meet the above 
80 
 
 
specifications, ECC and UHPC are adopted for constructing link slabs. Both ECC and 
UHPC provide high strength and tensile ductility, with fine cracks in the longitudinal 
direction. To study performance of link slab using ECC and UHPC, two finite 
element models were generated to simulate original bridge performance; experiments 
were conducted to learn about material properties of ECC and UHPC; sensor 
performance was evaluated for recommendation to future applications. Presented in 
this section is a summary of the conclusions made based on results obtained in this 
research project: 
1. Overall, ECC specimens show high strength, with an average compressive 
strength of 11135.97 psi for the 11 ECC specimens. Strength of the three 
UHPC specimens were not directly recorded because they were mixed 
strictly based on specifications provided by the manufacturer. According to 
the manufacturer, the average compressive strength of UHPC is 14000psi. 
The high strength of ECC and UHPC ensures the link slab’s ability to meet 
specifications in bridge loading criteria. 
2. Responses and performances of the link slab specimens are independent to 
the number of cyclic loadings applied. This result reflects the reliability and 
predictivity of the link slab.  
3. Ductile performances were achieved during the three-point bending tests. A 
“yield” point was observed in the stress-strain curve, reflecting the “metal-
like” property of the ECC and UHPC material. This finding verifies the high 
tensile ductility of the material. 
81 
 
 
4. Performance of sensor systems in the lab are overall satisfactory. While 
disturbance and failure exist.  
5. Feasible range for measurement of the strain gauges is 340*10-6 in ECC and 
890*10-6 in UHPC under compression; 200*10-6 in ECC and 304*10-6 in 
UHPC under tension. Beyond this range, sensor systems will lose 
compatibility. 
6. Fine cracks developed on the ECC and UHPC specimens are hairline in 
width across the longitudinal direction on the specimens. The width of the 
fine cracks is narrow enough to efficiently protect the supporting girders and 
other substructures from damage caused by water penetration. Hence, the 
results support that link slab made of ECC and UHPC is effective on 
preventing damage due to leakage. 
  
8.2 Future Work 
 Further study needs to be done to further improve the knowledge of link slab 
in terms of application on actual bridge structures. The following list summarizes the 
proposed future work of this research project: 
1. Structural response of the bridge under standard truck loads need to be 
collected and compared with the results measured in field test. 
2. Plots of strain distribution of the link slabs need to be generated based on 
data recorded in the field test. 
82 
 
 
3. A better design is required to improve stability of the sensor system in terms 
of its performance. 
4. Nonlinear analysis is needed to calibrate sensor incompatibility when the 
readings exceed range of feasible measurement. 
5. More experiments can be performed to specifically focus on the high tensile 
ductility of ECC and UHPC. For instance, thinner specimens (one dimension 
of the specimen is considerably larger than the other, similar to a “deep 
beam”) of ECC and UHPC can be produced for a better visualization of the 
“metal-like” behavior under bending, where the material shows large tensile 
ductility. Deformation with large curvature under bending is more obvious in 
a thin member and this is going to help demonstrating the high tensile 
ductility of ECC and UHPC.  
6. Link slabs can be implemented into the finite element models to simulate 
long-term response of the bridge. 
 
 
 
 
 
83 
 
 
Appendix: Bridge Thermal Analysis 
1. THERMAL STRESSES 
 If the structural element is restrained from movement then a change in 
temperature will lead to thermal stresses. Changes in the uniform temperature 
generally only lead to thermally induced stresses in statically-indeterminate 
structures. Thermal gradients that are nonlinear over the cross section will result in 
the development of thermally-induced stresses in both statically determinate and 
indeterminate structures. These nonlinear thermal gradients will induce self-
equilibrating stresses in the bridge superstructure. 
a. Self-Equilibrating Stress 
 The nonlinear variation of temperature along the depth of the bridge will 
produce nonlinear strain. But as plane sections tend to remain plane so the final strain 
profile must be linear as per the Naiver-Bernoulli hypothesis. This will cause a strain 
difference. The difference between these strains will result in self equilibrating 
stresses. 
 
Figure 1 Strain Difference causing self-equilibrating stresses 
 
84 
 
 
 The heating and cooling of steel girder systems with composite bridge decks 
was analyzed. Due to the differences in thermal expansion coefficient and different 
exposure to radiation, convection and conduction, the heating and cooling of a 
composite girder cross-section is non-uniform. If both the deck and the girder, are 
restrained in the same place, thermal stresses will be induced due to the uneven 
heating and cooling of the structure. Accounting for these additional stresses through 
increases in material strength, flexible piles, hinged abutments, and/or bearings could 
help alleviate stresses in this local behavior. 
 
2. NCHRP REPORTS REVIEW 
a. NCHRP 20-07/106 - Thermal Movement Design Procedure for Steel and 
Concrete Bridges (2002) 
 This report was submitted by Charles w. Roeder in 2002. This report provides 
us the methods to calculate the maximum and the minimum design temperatures for 
steel and concrete bridges throughout the US. Two simplified methods (Emerson and 
Kuppa) were developed to estimate the average bridge temperature since the actual 
calculation of bridge temperature distribution is complex. The results obtained from 
these methods were compared to the limited field measurements available. This 
comparison showed that the Kuppa method provided better estimates of the extreme 
average bridge temperatures. Since we use extreme temperatures for 5 determining 
bridge design movements the Kuppa method was considered to produce design maps. 
Emerson method was conservative compared to the Kuppa method. Historic weather 
85 
 
 
data was combined with Kuppa method to create design maps for the maximum and 
minimum average bridge temperatures for steel girder bridges with concrete decks 
and concrete girder bridges with concrete decks. The design maps showed that 
composite steel bridges can be designed for smaller movements than recommended 
by procedure A in AASHTO specifications. The design maps were introduced in 
AASHTO as procedure B under uniform temperature change. Kuppa method used 
extreme events to calculate the average temperature since these extreme events 
control the thermal design. The temperature distribution within the bridge will depend 
on time and the type of bridge. They proposed a formula to calculate the average 
temperature TAvg. This method included all the properties of the bridge along with 
conduction, convection and radiation heat transfer. 
 
∑ 𝐴𝑖𝐸𝑖𝛼𝑖𝑇𝑖
𝑇𝑎𝑣𝑔 =  ∑ 𝐴𝑖𝐸𝑖𝛼𝑖
Where 
i = different segments of the bridge 
Ai = Cross sectional area of the ith segment 
Ei = Elastic Modulus of the ith segment 
αi = Coefficient of thermal expansion of the ith segment 
Ti = Temperature of the ith segment 
 
86 
 
 
 
Figure 2: Maximum average temperature of bridges by 1. Emerson 2. Kuppa 
methods 
 
 
 The comparison between average maximum temperature of bridges calculated 
by both methods show similar temperature ranges. These figures show that there are 
consistent trends for average bridge temperatures. Emerson method is consistently 
conservative in predicting extreme low temperatures. It predicts a lower minimum 
extreme temperature when compared to the Kuppa method. 
 
Table 1: Temperature variation for bridge types 
  
 The proposed design maps were verified with the measured field data in 
Minnesota. The previous AASHTO specifications provided lower values for the 
87 
 
 
temperatures. The new contour design maps were used to estimate the maximum and 
minimum temperatures and they are compared to the values of temperature ranges 
calculated from the measured field displacements. The measured temperature ranges 
were within the temperature ranges provide by the design maps. 
 
b. NCHRP Report 276, Thermal Effects in Concrete Bridge Superstructures, 
(Imbsen et al., 1985) 
 This report provides us the proposed design criterion for thermal gradients for 
concrete bridges. Several concrete precast bridges were studied in this case study 
under various thermal gradients taken from several codes around the world. The 
report is a comprehensive study of thermally induced stresses in concrete bridge 
superstructures. The stresses resulting from average temperature have an important 
effect while the stresses developed due to thermal gradients effected the bridges in 
only some cases. Previously most bridges have been designed to accommodate only 
the longitudinal movement caused by uniform temperature change. But In this report 
several bridges were evaluated under various thermal gradients taken from US and 
foreign countries. The thermal gradients used in this report were from New Zealand, 
England, Ontario and US. Although AASHTO didn’t specify a thermal gradient in 
1985, the gradient used by PTI (Post Tensioning Institute) was used on behalf of the 
US. The following concrete bridges were considered for the case studies. 
 
88 
 
 
 
Figure 3: Bridges used for case studies 
 
 
 
Figure 4: Thermal Gradients Used for the Case Studies 
 
 
 The results from stress diagrams showed that some conditions influence the 
values significantly. The following stress diagrams show the effect of bottom slab 
flare and monolithic column on bottom fiber stresses. The presence of bottom slab 
89 
 
 
flare near reduced the stress values where the thickness is maximum. The values of 
the top fiber stresses did not show any sudden change since there is no flare present. 
 
Figure 5: Bottom Fiber Stress values 1. No Bottom Slab Flare 2. Bottom Slab 
Flare 
 
  
 Effect of monolithic column on the stresses is shown in the following figure. 
The values near the supports reduced significantly. 
 
 
Figure 6: Effect of monolithic column on bottom fiber stresses 
90 
 
 
 The presence of a hunched girder also significantly varies the stress values. 
The bottom fiber stress values are maximum where the depth of the girder is least. 
 
 
Figure 7 Bottom Fiber stress values for hunched girder bridge 
 
 
 i. Proposed Thermal Gradient 
 The thermal gradient proposed by this report was derived from the New 
Zealand thermal gradient. The shape was simplified from 5th order curve to three-line 
segments. It divided the country into four zones. Each zone was provided with three 
temperatures to form the thermal gradient. 
91 
 
 
 
Figure 8 Proposed Thermal Gradient for Concrete Superstructures 
 
  
 This gradient with slight modification was taken and incorporated in the 
AASHTO specifications which is discussed in the next section. 
 
c. Australian Design Codes (AUSTROADS, 1992) 
 The thermal gradient for steel bridges was derived from the gradient which is 
used in AUSTROADS 1992. This gradient is a fifth order curve that goes up to the 
steel-concrete interface and then has a uniform temperature throughout the girder. 
The simplifications made to this gradient are the transformation of the 5th order curve 
into simple line segments which are similar to the NCHRP report 276 for concrete 
superstructure. 
92 
 
 
 
Figure 9 AUSTROADS VS AASHTO Thermal gradient for steel bridges 
 
  
 The proposed gradients from NCHRP Repot 276 for concrete bridges and 
AUSTROADS 1992for steel bridges are combined and provided in the present 
AASHTO specifications. 
 
 
3. COMPARISON OF ALL THERMAL GRADIENTS 
 The below graph shows all the thermal gradients. All the 3 gradients, 
AASHTO Steel, AASHTO Concrete and Proposed NCHRP (Report 276, 1985) 
follow the same path up to the steel and concrete interface. After the interface the 
temperature throughout the steel girder is the same whereas they vary in other 
gradients. 
93 
 
 
 
Figure 10 Comparison of thermal gradients 
 
 
4. AASHTO DESIGN CRITERION 
 AASHTO LRFD Bridge Design specifications provides us with methods to 
calculate the bridge temperatures and the thermal deformations. The thermal loads are 
divided into two categories. The first effect is due to the uniform temperature change 
and other is effects due to thermal gradient along the depth of the bridge. 
a. Uniform Temperature change 
 The temperature of the whole bridge is considered uniform across the depth 
and length. Uniform temperature change will cause expansions and contractions due 
94 
 
 
to positive and negative temperature change. The temperature at which the bridge was 
constructed is known as the setting temperature. During summer if the temperature of 
the bridge goes above the setting temperature then the bridge will expand because of 
the positive temperature difference while during winter the temperature goes below 
the setting temperature causing a negative temperature difference resulting in 
contraction. The ranges of temperature that need to be considered for several types of 
bridges and regions are specified in section AASHTO 3.12.2. There are two methods 
to calculate the thermal movements caused by uniform temperature difference. 
Procedure A: 
 This is the historic procedure used for the calculation of thermal movements 
in the bridge design. This procedure provides us with the upper (TMaxDesign) and lower 
(TMinDesign) boundaries of the temperature and the base construction temperature that 
is assumed in the design shall be used. The 11 states are not divided in the US. The 
climates are differentiated according to the number of freezing days. Freezing days 
are defined as days where the average temperature is less than the 32℉. If the total 
number of freezing days are less than 14 per year then the location comes into 
moderate climate. If the number of freezing days is greater than 14 then the climate is 
cold. This procedure can be applied to all bridges unlike procedure B. The bridges are 
divided into 3 types steel, concrete and wood. The following table provides us with 
the maximum and minimum temperatures for several types of bridges in different 
climates. 
 
95 
 
 
PROCEDURE A TEMPERATURE RANGES 
 
 
 
Procedure B: 
 This procedure was developed in 2002 based on the NCHRP report (NCHRP 
20-07/106) written by Charles Roeder. This procedure uses Contour maps to obtain 
the TMaxDesign and TMinDesign depending upon the type of the bridge and its location. 
Two methods were used to construct these design maps. Kuppa and Emerson 
methods have been used to calculate the average maximum and minimum bridge 
temperatures. It was found that the Kuppa method provided better estimates in 
average bridge temperature. Hence the Kuppa method was combined with the 
historical weather data to produce the contour design maps. These are the maps that 
we use in procedure B. This procedure can be only applied to certain type of bridges. 
It can be applied to concrete girder bridges with concrete decks and steel girder 
bridges with concrete decks. There are a total of 4 contour maps for bridges which 
will provide TMaxDesign and TMinDesign for bridges with concrete girder and concrete 
decks and steel girders with concrete decks. 
96 
 
 
 
 
Figure 11 Contour Maps for TMaxDesign and TMinDesign for Steel Girder 
Bridges with Concrete Decks 
 
  
The value closest to the contour can be taken or the value can be found out by linear 
interpolation between the two contour lines adjacent to the location of the bridge. 
Maximum temperature maps have an increment of 5℉ while the minimum 
temperature maps have an increment of 10℉. 
 
 
97 
 
 
Calculation of Design Thermal Movements: 
 After obtaining the TMaxDesign and TMinDesign from either procedure A or 
Procedure B we use them to calculate the design thermal movements using the 
following formula 
𝛥𝑇 =  𝛼 𝐿 (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  − 𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛) 
Where  
L = Span of the bridge (in.) 
α = Coefficient of thermal expansion (in./in./℉) 
 These design thermal movements are used to design bearings and expansion 
joints. The present AASHTO specification doesn’t provide any instructions for 
calculating the installation temperatures of bearings and expansion joints. NCHRP 
report recommends including the installation temperature of bearings and expansion 
joints in the design criterion for bridges. It provides us with the formula to calculate 
the installation temperature and then calculate the design thermal movements. 
Installation Temperature and Design Movements for the following: 
Elastomeric Bearing Pads: 
𝑇𝑖𝑛𝑠𝑡𝑎𝑙𝑙  =  𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛  +  0.65 ∗  (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  − 𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛) 
𝛥 =  + 𝛼 𝐿 0.65 ∗  (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  − 𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛) 
Other Bearings:  
𝑇𝐼𝑛𝑠𝑡𝑎𝑙𝑙  =  𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛  +  0.5 ∗  (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  − 𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛) 
𝛥 =  + 𝛼 𝐿 (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  − 𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛  +  20℉) 
98 
 
 
 
Expansion Joints: 
𝑇𝐼𝑛𝑠𝑡𝑎𝑙𝑙  =  (𝑇𝑀𝑎𝑥𝐴𝑖𝑟  + 𝑇𝑀𝑖𝑛𝐴𝑖𝑟) / 2 
𝛥 =  𝛼 𝐿 (𝑇𝑀𝑎𝑥𝐷𝑒𝑠𝑖𝑔𝑛  −  𝑇𝑀𝑖𝑛𝐷𝑒𝑠𝑖𝑔𝑛  +  30℉) 
 
b. Thermal Gradient 
 This gives us the variation of temperature along the depth of the bridge 
section. The country is divided into four zones depending upon the solar radiation 
with each having different values for temperature gradient. The variation of the 
temperature is given in the figure and the values of T1 and T2 are provided in the 
table. 
 The current thermal gradient is derived from the NCHRP 276 (1985) report 
and the Australian design codes (AUSTROADS, 1992). The thermal gradient for 
concrete structures was taken from the NCHRP 276 report (1985) while the thermal 
gradient for steel bridges was taken from the Australian design codes (AUSTROADS, 
1992). 
99 
 
 
 
Figure 12 Solar Radiation Zones for the United States 
 
 
 
 
 
 
 
Figure 13 Positive Vertical Temperature gradient in Concrete and 
Steel Superstructures 
 
 T o3 will be taken as 0 F unless an accurate value is determined and should not 
exceed 5oF. For negative thermal gradient we multiply the values for the positive 
gradient by a factor of -0.3 for concrete decks. 
End of Section  
100 
 
 
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