ABSTRACT Title of Dissertation: Design of Rigid Overlays for Airfield Pavements Raymond Sydney Rollings, Jr., Doctor of Philosophy, 1987 Dissertation directed by: Matthew W. Witczak, Professor, Civil Engineering Existing rigid overlay pavement design methods are empirical and use a specified level of cracking as the defined failure condition. The existing empirical designs are based on tests run thirty years ago, and current analytical models provide greatly improved abilities to examine the overlay pavement structure. Emphasis by many agencies on life cycle cost analysis and more sophisticated maintenance and rehabilitation strategies require methods of predicting pavement performance rather than simply developing safe designs. A layered elastic analytical model was selected to evaluate stresses from applied loads in the pavement structure. Pavement performance was measured in terms of a Structural Condition Index which related the type, degree, and severity of pavement cracking and spalling on a scale of 0 to 100. Models were developed to represent the effect of cracking in base slabs under the overlay, to account for fatigue damage of previous traffic on the base pavement, and to account for the effects of substandard load transfer at slab joints. The predicted performance of overlays and pavements using this analysis was checked against the results of full-scale accelerated traffic tests conducted by the Corps of Engineers and against current overlay design methods and was found to provide reasonable agreement. This methodology using the layered elastic analytical model and analysis of fatigue and cracking in the base slab provides a method of predicting pavement and overlay deterioration in terms of a Structural Condition Index. DESIGN OF RIGID OVERLAYS FOR AIRFIELD PAVEMENTS by Raymond Sydney Rollings, Jr . ... Dissertation Submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy Advisory Committee: Professor M. Witczak Professor C. Schwartz Professor M. Aggour Professor D. Vanney Professor D. Barker 1987 vo [. \ C • I PREFACE This study was conducted by Raymond S. Rollings, Jr., U.S. Army Engineer Waterways Experiment Station· (WES), under the direction of Pro- fessor Matthew W. Witczak, University of Maryland. Funding for this project was provided by the Federal Aviation Administration under Inter- Agency Agreement No. DTFAOl-81-Y-10523 "Update Overlay Thickness Criteria" with the WES. ii DEDICATION This is dedicated to my parents for their support and encouragement. iii ACKNOWLEDGEMENT The assistance of Mr. E. J. Alford, Mr. P. S. McCaffrey, Jr. and· Mr. D. D. Mathews of the Engineering Investigations, Testing, and Vali- dation Group, Pavement Systems Division (PSD), Waterways Experiment Sta- tion (WES), in conducting the slab tests described in Part V of the report is gratefully acknowledged. Mr. D. Pittman of the Engineering Analysis Group, PSD, performed the computer stress calculations in Table C2 that were used for the layered elastic and Westergaard stress comparisons. Ms. Shirley Heath, formerly of the Engineering Analysis Group, PSD, and presently with Explosive Effects Division, Structures Laboratory, WES, performed the joint deflection to load transfer con- versions described in Part VI. Mr. Starr Kohn, formerly with the Engi- neering Investigation, Testing and Validation Group, PSD, presently with Soils and Materials Engineering, Inc., performed the stress analysis for Lockbourne test sections R through T in Appendix A. The assistance and contributions of all of these individuals to this report are greatly appreciated. The assistance of Ms. Sammie Haney and Ms. Rhonda Herrington of the PSD in numerous administrative tasks associated with the preparation of this report is gratefully acknowledged, Drafting by the WES Engineering, Graphics, and Cartographic Section and typing by Systems Research and Development Corporation is also gratefully acknowledged. The encouragement and advice of numerous colleagues, particularly Dr. Walter Barker, Ms. Marian Poindexter, and Ms. Phyllis Davis, were of great assistance. iv The encouragement, assistance, and critical review by Profes- sor M. W. Witczak in particular were invaluable in carrying out and completing this study. v TABLE OF CONTENTS PART I: INTRODUCTION BACKGROUND • • PART II: Current Airfield Rigid Pavement Design Current Rigid Overlay Design Methods PART III: BASIS FOR IMPROVED OVERLAY DESIGN PROCEDURE PART Performance Criteria Analytical Model Previous Traffic Damage • Methodology IV: PERFORMANCE MODEL FOR RIGID PAVEMENTS Test Section Data .•. Test Section Performance Model Evaluation Summary • . . . • . • . PART V: EFFECTIVE MODULUS FOR CRACKED SLABS Existing Models Slab Tests Cracked Slab Model PART VI: LOAD TRANSFER Measured Load Transfer Modifications for Layered Elastic Theory PART VII: PROPOSED DESIGN PROCEDURE Methodology • . • . . Example Calculations Summary • • • . • PART VIII: ANALYSIS OF CORPS OF ENGINEERS OVERLAY TEST DATA Test Section Data Unbonded Overlays Partially Bonded Overlays Fully Bonded Overlays • . Overlays Without Load Transfer PART IX: EVALUATION AND COMPARISON OF OVERLAY DESIGN PROCEDURES Design Methods Evaluation Comparisons . . Effect of Previous Traffic PART X: CONCLUSIONS AND RECOMMENDATIONS Conclusions . . . . . . . . . • Recommendations for Future Research . vi Page 1 4 4 26 40 40 48 56 58 60 60 69 80 92 94 95 102 125 129 129 135 140 140 155 167 170 170 173 190 195 196 200 200 202 220 225 232 232 234 TABLE OF CONTENTS (Continued) APPENDIX A: CORPS OF ENGINEERS RIGID PAVEMENT TEST SECTION DATA . . . . . . . 236 APPENDIX B: SLAB TEST DATA • . . . . . . . . . 253 APPENDIX C: WESTERGAARD AND LAYERED ELASTIC STRESS CALCULATIONS . . . . . . . 289 APPENDIX D: CORPS OF ENGINEERS RIGID OVERLAY TEST SECTION DATA • . 297 REFERENCES . . . . . . . . 313 BIBLIOGRAPHY . . . . 319 vii LIST OF TABLES No. Page 1 Reduction in Pavement Thickness for High-Strength 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17· 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 A1 A2 A3 Foundations . . • . • . Condition Factor Values • Descriptive Rating of the PCI • PCI Distress Types PCI Rigid Pavement Distress Types Used with the SCI Example SCI Values Meeting the Corps of Engineers Initial Failure Definition • . • . • . • . • • • • . • Available Rigid Pavement Field Test Data . . . . Example SCI Calculation for Keyed Longitudinal Joint Test Section Item 2-C5 • . . . • . • • • • • c0 and CE Values for Test Sections . • . • • • • . Predictea Performance of Unfailed Test Items ••. Failed Pavements at U-Tapao Airfield • • . • Sample Calculations for Determining SCI and E-Ratio from Nominal Slab Fragment Size •.. Predicted Initial Modulus Values Before Cracking Summary of SCI Calculations for Test Slabs . . . Predicted Modulus Values from Slab 1 by Matching Deflection Basins . • • . • • . . • • • • • • • • Effective Concrete Modulus Using Center Deflections Load Transfer for Different Joint Types Typical Modulus of Elasticity Values Base Slab Stresses and Performance Factors Stress and Performance Factors for Overlay Example Overlay Damage Calculation Test Section A 2.7-60. Summary of the Corps of Engineers Overlay Tests Comparison of Predicted and Observed Performance of Unhanded Overlay Test Items • • • . • . • • . Effect of Including Base Slab Cracking on Prediction of Overlay Deterioration • . • • • • . • Performance of Test Items with Substandard Load Transfer . . • . • • • . . • • • Comparison of Overlay Design Methods Design Parameters for the Overlay • • • • Design Parameters for the Base Pavement Aircraft Characteristics . • . • Distribution of Design Parameters Unhanded Overlay Results . • .. Partially Bonded Overlay Results Comparison Between Unhanded and Partially Bonded Overlay Designs . • . . • • • • Comparison of Overlay Design Procedure Results , • , • Material Properties for Lockbourne No, 1 Test Sections Performance of Lockbourne No. 1 Test Sections ... , Material Properties for Lockbourne No. 2 Test Section and Modification • • • . • , . . . . . . . . • A4 Performance for Lockbourne No. 2 Test Section and Modification viii 25 27 42 43 47 49 61 67 75 87 89 100 112 119 121 126 133 144 159 163 165 171 184 185 198 201 204 206 207 208 213 217 218 222 237 239 243 244 LIST OF TABLES (Continued) No. AS Material Properties for Sharonville Heavy Load and Multiple Wheel Heavy Gear Load Tests • • . • . . . • . 246 A6 Performance for Sharonville Heavy Load and Multiple Wheel Heavy Gear Load Tests • • • • • • • • • • • • . • • • • 247 A7 Material Properties for Keyed Longitudinal Joint Study and Soil Stabilization Pavement Study • . • • • . • • • 248 A8 Performance for Keyed Longitudinal Joint Study and Soil Stabilization Pavement Study . . • • • 249 A9 Calculated Stresses and Design Factors . . • . 251 B1 Falling Weight Results, Slab 1, Position 100 •• 269 B2 Falling Weight Results, Slab 1, Position 100.5 •.•••• 270 B3 Falling Weight Results, Slab 1, Position 200 271 B4 Falling Weight Results, Slab 1, Position 300 • 273 BS Falling Weight Results, Slab 2, Position 100 • 274 B6 Falling Weight Results, Slab 2, Position 200 .••.• 275 B7 Falling Weight Results, Slab 2, Position 300 . 276 B8 Falling Weight Results, Slab 3, Position 100 • 277 B9 Falling Weight Results, Slab 3, Position 200 278 B10 Falling Weight Results, Slab 3, Position 300 • 279 Bl1 Falling Weight Results, Slab 4, Position 100 • 280 B12 Falling Weight Results, Slab 4, Position 200 • 281 Bl3 Falling Weight Results, Slab 4, Position 300 • 282 B14 Falling Weight Results, Slab 5, Position 100 • 283 B15 Falling Weight Results, Slab 5, Position 200 284 B16 Falling Weight Results, Slab 5, Position 300 285 B17 Falling Weight Results, Slab 6, Position 100 286 B18 Falling Weight Results, Slab 6, Position 200 . 287 B19 Falling Weight Results, Slab 6, Position 300 • 288 C1 Stresses Calculated From Corps of Engineers Test Sections • 290 C2 Calculated Westergaard and Layered Elastic Stresses for Different Aircraft and Subgrade Conditions 293 D1 Overlay Material Properties . • • • • • • . • • • • • 298 D2 Observed Field Deterioration Data • . • • . • • . . . 299 D3 Base Slab Stress Calculations for Unbonded Overlays • 300 D4 Overlay Stress Calculations for Unbonded Overlays . . 301 D5 Calculated Composite Unbonded Overlay Deterioration 305 D6 Base Slab Stress Calculations for Partially Bonded Overlays . . . . . . . . . . . . . . . . . . . . 307 D7 Overlay Stress Calculations for Partially Bonded Overlays 308 DB Calculated Composite Partially Bonded Overlay Deterioration • • • • • • • • • • • • • • • • . • • . • 311 ix No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 LIST OF FIGURES Representative Concrete Fatigue Curves Fatigue Curves for Pavement Design Corps of Engineers Overlay Test Data Results Base, Overlay, and Equivalent Slabs •••. Overlay Equations for Different Definitions of Equivalent Slab . . • • • . . . • • . • . • • • Conceptual Deterioration of a Pavement and Overlay Sample SCI-Coverage Relationships . . . . Sample SCI-Logarithm Coverages Relation • • Proposed Performance Model Relation Between DF and c0 • • • • • • • . • • Relation Between DF and CF •••••• Relationship Between c0 and CE and the Criterion of Parker et al. ~1979) SCI-CN Relationship • • • • • • . • • • Predicted Performance of U-Tapao Airbase Pavements Relationship between Corps of Engineers Visual C Factor and SCI • • • . • • • • . • . • . AASHTO Relation Between Visual C Factor and E-Ratio Relationship BetweenNominal S~ab Fragment and E-Ratio • • • • • • . . • • • . • . · . Existing Relationship Between SCI and E-Ratio . • Deflection Basin Analysis Model • • . • • • • . Position of Falling Weight Tests for Slabs 1 and 2 Position of Falling Weight Tests for Slabs 3 and 4 Position of Falling Weight Tests for Slabs 5 and 6 Deflection Basins for Slab 1, Position 100 Deflection Basins for Slab 1, Position 200 Deflection Basins for Slab 1, Position 300 SCI and E-Ratio Model • • • • • • • . • • • Relation Between Joint Efficiency and Edge Stress Deteriorat·ion of Load Transfer with Traffic for a Keyed Construction Joint • • • • . . . • . .• Relation Between Westergaard and Layered Elastic Calculated Stresses • • . • • • . . • • • • , • Multiplier for Layered Elastic Stresses to Account for Load Transfer • • • . • • • . • • Steps in the Proposed Design Procedure Model of Lockbourne No. 1, Item A 2.7-60 Equivalent Traffic and Base Slab Support for I tern A 2 .7-60 . . • . • . • . • . , • • • . • Traffic Intervals for Item A 2.7-60 Analysis Construction of the Deterioration of the Overlay for Item A 2. 7-60 . . • • • . • . . . . Overlay Deterioration of Item A 2.7-60 Performance of Item 23 Performance of Item 24 Performance of Item 25 Performance of Item 26 Performance of Item 27 X . . . Page 16 20 30 33 38 57 70 71 73 77 79 82 84 90 . 96 98 99 101 . 107 . 108 • 109 110 122 • 123 • 124 127 131 • 134 136 • 138 141 156 160 • 161 166 168 176 177 • 178 179 180 No. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Bl B2 B3 B4 B5 B6 B7 B8 B9 BlO Bll Bl2 Bl3 B14 Bl5 B16 B17 Bl8 B19 B20 B21 B22 B23 B24 B25 B26 B27 LIST OF FIGURES (Continued) Performance of Item 28 Performance of Item 69 Effect of Cracked Modulus on Predicted Performance of Item 25 . . . • . Revised E-Ratio-SCI Relationship Performance of Item D 2.7-66 Performance of Item E 2.7-66M •. Performance of Item F 2.7-80 Comparison of Proposed Procedure and Corps of Engineers Overlay Design Equation for Unhanded Overlays Effect of Concrete Modulus Ratio in Unhanded Overlays • • • . . . . • • • • . • . . . • Comparison of Unbonded and Partially Bonded Page 181 182 187 188 . 192 193 194 214 • • 215 Overlay Designs . . . . . . . . . . . . . . . . . . 219 Comparison of Proposed Method, Corps of Engineers, and Federal Aviation Administration Design Results Effect of Fatigue and Initial Base Slab Cracking on the Predicted Performance of the Case 5 Overlay Comparison of the Corps of Engineers and the Proposed Design Method Overlay Performance for Case 5 Effect of Fatigue and Initial Base Slab Cracking on Overlay Relationships . . . . • • • • • . • • • • Crane and Headache Ball Used to Crack Slabs • • • • Dynatest Falling Weight Deflectometer, Model 8000 Initial Condition, Slab 1 • . . • Initial Condition, Slab 2 . . . . Initial Cracking·for Slabs 1 and 2 Initial Cracking, Slab 1, SCI = 80 Initial Cracking, Slab 2, SCI = 80 Second Cracking for Slabs 1 and 2 . Second Cracking, Slab 1, SCI = 58 • Second Cracking, Slab 2, SCI = 80 at Position 100 .• Third Cracking Phase for Slabs 1 and 2 Third Cracking, Slab 1, SCI = 23 Third Cracking, Slab 2, SCI = 39 Fourth Cracking, Slab 1, SCI= 0 Slab 1 Next Morning • . • • • . . Fourth Cracking, Slab 2, SCI = 23 Initial Condition, Slab 3 • • Initial Condition, Slab 4 ..... First Cracking, Slab 3, SCI = 39 Second Cracking, Slab 3, SCI = 23 • First Cracking, Slab 4, SCI 58 First Cracking, Slab 4, SCI 23 Initial Condition, Slab 5 . Initial Condition, Slab 6 • First Cracking, Slabs 5 and 6, SCI = 39 and 55 Second Cracking, Slabs 5 and 6, SCI = 23 Third Cracking, Slabs 5 and 6, SCI = 0 xi 224 226 • 228 230 . 254 • • 254 255 . 255 256 257 257 • 258 • 259 259 • 260 261 • 261 262 • 262 263 • 263 • 264 264 • 265 265 266 266 • 267 267 268 268 PART I: INTRODUCTION Design of rigid concrete overlays to upgrade existing concrete base pavements for airfields today use the same techniques that were developed by the U.S. Army Corps of Engineers (CE) over 30 years ago. Although current methods of concrete pavement design have developed into a blend of theory, laboratory investigation, field testing, and modifications based on observed field behavior, overlay design conti- nues to be purely empirical and is based on a limited number of tests conducted during the 1940's and 1950's. Today the need for rehabili- tation of existing pavement facilities is more important than ever before, and continued reliance on an empirical design approach for such a basic rehabilitation technique as pavement overlays needs to be reevaluated. Analysis of in-service pavements has found that the current methods of concrete pavement design have proven adequate in the past for selecting new airfield pavement thickness (Kohn 1985, Hutchinson and Vedros 1977). However, similar analysis of in-service overlays comparing their performance to a design method has not been done. A review of the existing CE overlay design method by a group of con- sultants to the Waterways Experiment Station (WES), summarized by Chou (1983), identified a number of problems with the current overlay design approach. Inconsistent failure definitions and inadequate empirical equations are major limitations of the design method. Future requirements for life cycle cost analysis and improved methods for pavement rehabilitation will need an improved mechanistic analysis approach. A review of concrete overlays by Hutchinson (1982) also 1 suggested replacing the current empirical approach with a new theoret- ical design procedure. Pavement design procedures may either develop a safe design which will not fail under future traffic, or they may attempt to pre- diet future pavement performance. The current concrete pavement and overlay design methods use the safe design approach wherein thick- nesses of pavement are selected for some specified design traffic to keep the surface pavement above a predefined failure level in terms of slab cracking. The current approaches have been found to be generally adequate for structural design of new concrete pavements but have been strongly questioned for overlay design. In recent years numerous government agencies have placed new emphasis on life cycle cost analyses, growing pavement rehabilitation requirements, and effective pavement management. This change in emphasis requires design methods capable of predicting pavement per- formance, and previous safe design approaches are no longer totally satisfactory. Witczak (1976) noted, 11However, this approach (safe design approach), while sound for other engineering designs, leads to excessive costs and, fur- thermore, provides little, if any, ability to predict dete- rioration and, hence, performance with time. In the author's opinion, this latter concept (design predicting performance) is absolutely mandatory if pavement design is to ever achieve a 'higher step' in rational design concepts. As a result, the overall interaction of initial fracture prediction, rate of crack propagation, subsequent distress-to-performance relation- ships, and a failure level based upon functional concepts is considered necessary in order to truly define a procedure that can predict future pavement performance." The need for an improved overlay design method has been noted by a number of investigators including Hutchinson (1982) and the WES con- sultants (Chou 1983). Furthermore, this improved method should use a 2 mechanistic approach and be capable of predicting pavement performance rather than simply providing a safe design. The ability to predict performance then allows a realistic appraisal of alternate strategies of rehabilitation and maintenance of pavements. The objective of this study is to develop a mechanistically based design procedure for rigid concrete overlays of an existing concrete base pavement that will pre- dict deterioration of the pavement as a function of applied traffic. 3 PART II: BACKGROUND Current Airfield Rigid Pavement Design At present, thickness designs for concrete airfield pavement are generally done by a fatigue analysis. Tensile stresses in the bottom of the slab from a selected design aircraft are calculated and then related to passes of the design aircraft through a fatigue relation- ship. The most widely used concrete airfield design procedures in the United States were developed originally by the US Army Corps of Engi- neers (CE) (Sale and Hutchinson 1959) and the Portland Cement Associa- tion (PCA) (Packard 1973). The CE approach is used by the US Army, the US Air Force, and the Federal Aviation Administration (FAA). The PCA approach is used by the US Navy and a number of commercial design- ers. These two approaches differ primarily in the analytical models and fatigue relationships used, but each individual agency also modi- fies these basic approaches to reflect its specific needs and experi- ences. Descriptions of these individual agency design preocedures are presented by Yoder and Witczak (1975). In order to implement any design approach, the aircraft traffic on the pavement must be analyzed; the real pavement structure and air- craft loads must be idealized so that tensile stresses may be calcu- lated by an analytical model; these stresses must be compared to some fatigue criterion to determine the number of cycles of load the pave- ment can withstand; and finally the field performance of pavements designed with these idealizations must be evaluated to make adjust- ments in the design approach. The following sections present in more 4 detail some of the specific idealizations and assumptions used in cur- rent airfield design approaches. Aircraft traffic Aircraft do not traverse the same point on a pavement with each pass of the aircraft. Studies of aircraft traffic at airfields (Brown and Thompson 1973, HoSang 1975) developed the concept of using a nor- mal distribution to develop a pass to coverage ratio that represents the variable pattern of aircraft traffic. Brown and Thompson's (1973) observations found that 75 percent of the traffic on a channelized traffic area such as a primary taxiway or runway was concentrated within a 70-in. wander width. For less channelized traffic areas such as runway interiors or parking aprons a representative wander width was 140 in. For an aircraft gear with a single wheel the pass to coverage ratio is the inverse of the maximum probability of the wheel passing over a point within the traffic lane or where P/C = Pass to coverage ratio c X cr X w t Maximum ordinate of the normally distributed curve of the applied traffic Maximum ordinate of the standard normal distribution curve, tabulated values found in references such as Harr (1977) Standard deviation of the applied traffic distribution = Width of the tire 5 However, if the gear contains a second wheel the distribution of each wheel must be added together to determine a composite distribu- tion and the previous equation becomes where c XC maximum ordinate of the composite distribution found by summing the individual wheel distribution curves For instance, a 70-in. wander width which is defined to include 75 percent of the total traffic has a standard deviation of 30.43 in. The maximum ordinate from the standard normal distribution for a single wheel is 0.399. Therefore c = = X 0.399 30.43 = 0.0131 The B-727 has two 13.5-in. wide tires spaced 34-in. apart. When the distribution curves of these two tires are added together the maximum ordinate, C , of the composite curve is 0.0228, and the pass-to- xc coverage ratio becomes p c 1 c w XC t 3.25 1 0.0228 X 13.5 6 The maximum tensile stress normally is underneath the tire of the B-727. Consequently the number of coverages on a concrete pave- ment is the maximum number of stress repetitions to which the concrete is subjected. Certain twin-tandem gears such as the B-747 develop only a single maximum stress between the forward and trailing wheels. These trailing wheels are not counted in determining a pass-to- coverage ratio for rigid pavements as they are for flexible pavements. Brown and Thompson (1973) identify these aircraft and tabulate pass- to-coverage ratios for 70- and 140-in. wander widths for a variety of current civil and military aircraft. The actual traffic at an airfield will almost always consist of a mix of different sizes of aircraft with varying gear configurations. Not only does the pattern of traffic cause difficulty in formulating the problem, but the mix of aircraft with each aircraft type causing a different stress level must be considered in the analysis. Further- more, aircraft of the same type operate at varying loads, sometimes at only 70-80 percent of the maximum gross load. Landing aircraft are often thought to impart an impact load on the pavement, but this is unsubstantiated. Tests conducted by the CE during World War II found that a dynamic load could only be measured during intentionally hard landings that often resulted in mechanical damage to the aircraft (US Army Engineer Rigid Pavement Laboratory 1943). Later more extensive tests were conducted jointly by the FAA and the CE (Ledbetter 1976). These tests found that concrete pave- ments tended to show relatively flat pressure and deflection responses to a wide variety of aircraft operations. The responses were a 7 maximum for the stationary aircraft loads and decreased somewhat for taxiing, landing, rotation, etc. Flexible pavements showed much sharper and more pronounced peak measurements for the static loads compared to other aircraft operations than did the concrete pavement. The actual traffic at an airfield is a complex combination of varying aircraft types, gear configurations, and loads following diverse patterns of traffic at varying speeds. To reduce this situ- ation to manageable proportions, airfields are usually designed only for departing aircraft on the assumptio? that the lighter landing air- craft have little effect. For simplicity aircraft are assumed to operate at maximum load in the absence of more detailed information. Agencies such as the CE or FAA include in their published design pro- cedures (Department of the Army 1979, Federal Aviation Administration 1978) methods to convert a mix of aircraft into equivalent passes of the single, most severe aircraft loading in the mix. Analytical models The first analytical models for theoretical analysis of concrete pavements were developed by Westergaard (1926, 1948). These models characterized the pavement as a thin elastic plate supported on a bed of independent springs. Three stress solutions were developed: a load in the interior of a slab infinite in horizontal directions, a load adjacent to an edge of a slab infinite in the other three hori- zontal directions, and a load on a corner of a slab infinite in the other two horizontal directions. These solutions are expressed as 8 a e where Interior Loading (j = i 3P(l+v) (a/£,)2 64 h 2 . Edge Loading 3 (l+v) P = 1T (3+v) h2 (_ Eh3 ~ + 1. 84 - 4v + 1-v + 1.18 (1+2 v) (a/£.)] \100ka~ 3 2 Corner Loading a = 3P [ 1 - (a 1 )0 • 6 ] c h2 R, cr 1 tensile stress for interior loading cr = tensile stress for edge loading e cr tensile stress for corner loading c a = radius of circular load P total applied load v Poisson's ratio h slab thickness ~ radius of relative stiffness [ E h3 ] 1/4 12(1-})k E modulus of elasticity k = modulus of subgrade reaction distance to point of action of resultant along corner angle bisector /2a y Euler's constant = 0.5722 ..... . 9 Ioannides, Thompson, and Barenberg (1985a) present a detailed description of the origins and various forms of these equations including other load shapes (elliptical, semicircle, and square), simplified forms, and the inclusion of a "special theory" adjustment for cases where the radius of the loaded area is less than 1.724 times the pavement thickness. A number of modifications have been proposed for the corner load by other investigators and these modifications are discussed by Ioannides, Thompson and Barenberg (l985a). They con- sidered the above forms of the equations for interior and edge loading to be the most correct and complete. Based on comparisons with finite element analysis they concluded that the ratio of the smallest slab dimension to the radius of relative stiffness must be at least 3.5, 5.0 and 4.0 to meet the infinite or semi-infinite Westergaard assump- tions for the interior, edge, and corner loading cases. The concrete pavement slab in these models is characterized with the elastic material properties of a modulus of elasticity and a Pois- son's ratio while the supporting layers of base course and subgrade materials are represented by a spring constant, k , termed modulus of subgrade reaction with units of pounds per square inch per inch (lb/in. 2/in.). Westergaard (1948) referred to this spring constant k as "an empirical makeshift, which however has been found in the past to give usable results." Terzaghi (1955) extensively discussed the applications and limitations of the plate load tests used to determine the value of k. The idealization of all the supporting layers as linear springs is generally the major objection to the Westergaard model. Major drawbacks to this idealization include the difficulty of determining a k value during design since this 10 determination requires an in situ field test and the poor idealization by a single number for the real layered base course and subgrade structure. If one or more of these layers is stabilized, representing the structure with only a spring constant is particularly poor. Pickett and Ray (1951) developed solutions to the Westergaard equations in terms of influence charts that simplified the required calculations. Computerized solutions were also presented later for the interior load problem (Packard, no date) and for the edge load problem (Kreger 1967). A regression equation to calculate the Wester- gaard free edge stress was developed by Witczak, Uzan, and Johnson (1983) and later modified slightly at the US Army Engineers Waterways Experiment Station (WES). This equation is in the form: where a e regression constants dependent on individual air- craft gear and tire properties (tabulated values published by Rollings (1985)) P gear load, lb The limitations in the Westergaard model's representation of the materials under the concrete slab led to interest in using the layered elastic analytical model to calculate stresses. The widespread use of nondestructive pavement testing equipment that analyze pavement prop- erties by comparing field measured deflection basins with those 11 calculated by the layered elastic theory has also contributed greatly to the interest in layered elastic solutions for pavement evaluation and design. The CE and the FAA recently developed an airfield rigid pavement layered elastic design procedure (Parker et al. 1979) that is accepted by the CE as an alternative to the Westergaard-based design procedures. The layered elastic model idealizes the pavement structure as a sequence of continuous, horizontally uniform, homogeneous, isotropic layers each characterized by a modulus of elasticity and a Poisson's ratio. The interface between the layers can be full slip, no slip, or some specified intermediate level of slip. The formulation of the problem of a circular load on a layered elastic system is usually expressed with one or more stress functions for each layer. For instance the vertical displacement, can be expressed as where u z cr zz Laplace operator v ' zz ~ Stress function in r, 6, and z and stress, crzz' in a layer The stress function, ~. can be transformed with the Hankel transform by 1 2 where T (~) n J (m,r) 0 m T (~) n 00 f 0 r ~ J (m,r) dr 0 Hankel transform of ~ Bessel function of the first kind and of zero order Hankel transform parameter Neglecting body forces, equilibrium and compatibility are met if 4 0 The general solution to this equation in the Hankel transform of the stress function becomes T (~) n . The four constants, A, B, C, and D, are evaluated for each layer from the layer boundary conditions. The stress function is found by inverting the transformed solution by the Hankel inversion theorem: 00 f m T (~) J (m,r) dm n n 0 Displacements, stresses, and strains in the layer can then be found from the stress function. Complete derivations of generalized forms of the layered elastic model have been presented by Schiffman (1962), Peutz and Kempen (1968), Jong, Peutz, and Korswagen (1973), and Cauwelaert, Lequeux, 13 and Delaunois (1986). The integrals in the layered elastic model can- not be solved analytically and must be evaluated numerically. Some solutions are available for specific numbers of layers and assumptions of material properties (e.g., Burmister 1943 or Jones 1962); however, computers are the only practical method of solving the general layered elastic model. Several computer programs are available, and they differ primarily in the numerical methods used to evaluate the integrals. The limitations of the Westergaard and layered elastic models have led to interest in numerical methods using discretization such as finite element or finite difference methods. Of these approaches, finite element analysis has generated the most interest, but the Westergaard models remain the most widely used for calculating stresses in published design procedures and in practice for airfield pavements. The PCA (Packard 1973) and the US Navy (Department of the Navy 1973) use the Westergaard interior load model while the CE (Department of the Army 1979), the US Air Force, and the FAA (1978) use the Westergaard edge load model. Fatigue relationships Airfield rigid pavement thickness design is normally based on a fatigue analysis of the concrete. The fatigue strength of plain con- crete is that proportion of the static strength that can withstand a specified number of load cycles. It is usually considered to be the same in compression, tension, and flexure. In general, the modulus of elasticity decreases and strains increase with increasing load repetitions. 14 If concrete is subjected to fluctuating levels of stress, the ratio of the minimum stress level to the maximum stress level affects the fatigue strength. This is illustrated by the stress-fatigue life curves in Figure 1 (American Concrete Institute 1981) for plain con- crete beams tested in flexure. The ratio of maximum applied stress to concrete flexural strength that supports a given number of cycles of load increases dramatically if the ratio of the minimum stress to the maximum stress applied to the test beam increases from 0.15 to 0.75. There is considerable scatter in fatigue test results for concrete, so it is common to show the probability of sample failure as presented in Figure 1 for the minimum-maximum stress ratio of 0.15. Tepfers (1979) and Tepfers and Kutti (1979) have proposed a concrete fatigue relation to include this effect of the minimum-maximum stress ratio as where a max f s A N a max f 1 - S (1-A) log N maximum applied stress compressive or tensile strength of concrete a coefficient with proposed value of 0.0685 stress ratio a . ja m~n max number of load cycles to produce failure An in-service pavement exists under fluctuating stress condi- tions. Temperature and moisture gradients in the pavement slab change with time and result in varying stress conditions in the slab upon l 5 I f- t:J z w a: f- Ul ...J <( a: :::> >< w ...J lL ~ X <( ~ 1.0 0.8 0.6 0.4 0.2 0 0 -- -- -- --- -- -- - -- --- -- -- SMIN =MINIMUM STRESS SMAX =MAXIMUM STRESS P =PROBABILITY OF FAILURE 10 -- --- s __!:!!!:!_ = 0. 1 5 SMAX 103 104 CYCLES TO FAILURE, N - P~B.ow .......____ /Q --p~ --- so% --- -- ----p"'"Sa -% --- -- Fig. 1. Representative Concrete Fatigue Curves (American Concrete Institute 1981) periodic load induced stresses. Domenichini and Marchionna (1981) studied the effects of temperature variation for the concrete pavement in the American Association of State Highway Officials (AASHO) road test. Their data show that the stress ratio of minimum temperature stress to the sum of the temperature and load stresses for AASHO road test slabs 6.5 to 9.5 in. thick varied from 0.16 to 0.60 depending on the time of day and season of the year. The analysis by Domenichini and Marchionna (1981) only considered the daytime condition of the surface of the slab to be warmer than the bottom and neglected other potential stresses such as those caused by a moisture gradient. Nevertheless, their work clearly shows that the stress ratio that exists in pavements is not a constant. The fluctuating stress ratio in pavements implies that there is not a unique concrete fatigue relationship for concrete pavements. The effect of varying magnitudes of loading is usually handled by Miner's hypothesis (Miner 1945) which states that failure occurs when the summation of ni/Ni equals 1, where ni is the number of cycles applied at a particular stress level and N. ~ is the number of cycles that would cause failure at the same stress level. The effect of varying magnitudes of cyclic loading has not been adequately inves- tigated, and Miner's hypothesis does not always give conservative results. Initial loads near 90 percent of the ultimate static strength reduce fatigue life, whereas initial loads below 50 to 55 percent increase fatigue life (Witczak 1976). Consequently, Miner's hypothesis would appear to be unsafe for high loads and con- servative for low loads (Kesler 1970). 17 Pavements are subject to varying frequencies of loading and have rest periods of varying length between loadings. Laboratory tests have found that these factors can have significant effect on the fati- gue performance of concrete. If the applied cyclic stress is less than 0.75 of the ultimate strength, frequencies of loading in the range of 70 to 900 cycles per minute do not have much effect on fati- gue performance. However, at higher stress levels frequency has sig- nificant effect on fatigue performance of concrete (American Concrete Institute 1981). Also periodic rest periods between loadings appear to significantly improve fatigue life (Kesler 1970). There are two basic approaches to developing a concrete fatigue relationship for use in pavement design. The first is to use a con- servative interpretation of laboratory beam tests at a low minimum to maximum stress ratio. The PCA (1984) fatigue relationship is probably the most widely used relation of this type. The second approach is to use full-scale accelerated traffic tests of concrete pavements to develop "field" fatigue relationships. The CE has conducted large- scale accelerated traffic tests using aircraft size loads and gear assemblies, and the AASHO road test provided similar information for truck-sized axle loads. Full-scale tests have the advantages of testing actual slab and joint systems, testing the concrete under actual multiaxial stress conditions, and including, to some extent, temperature and moisture stresses. As illustrated in the previous discussion a number of factors such as stress ratios, rest periods, relative load magnitude, and load frequency can affect the fatigue performance of concrete. Field tests include some of these effects, 18 but they have the disadvantages of high cost and difficulty in defin- ing applied stress levels. Figure 2 shows a comparison of several concrete fatigue rela- tionships used or proposed for use in the design of concrete pave- ments. The ordinate of this figure is plotted as the design factor which is the concrete flexural strength divided by the applied stress. This factor is used by the CE for pavement fatigue analysis and will be used for the remainder of this report rather than its inverse which is commonly used by the PCA (1984) and the American Concrete Insti- tute (ACI) (1981). The PCA relation can be seen to be a very conser- vative interpretation when compared to the ACI (1981) curves for 5 and 50 percent probability of failure at a minimum to maximum stress ratio of 0.15. The other curves in Figure 2 are based on field tests and are different from these laboratory developed curves. The problem of defining the applied stress level in field tests is illustrated in Figure 2 by the two CE relationships. Both CE fati- gue relationships are based on the same field tests, but one relation uses the layered elastic analytical model to calculate the stresses under the test load while the other uses the Westergaard edge load model. Each model calculates a different numerical value for the stress with the layered elastic calculated stress always being lower. Consequently, the resulting fatigue relation for each analytical model is different. The same effect is seen for the AASHO road test results in Figure 2 where Treybig et al. (1977) used the layered elastic model and Vesic and Saxena (1969) used the Westergaard edge load analytical model. The actual stresses in the slabs in the field are actually variable depending on the placement of the load, rate of loading, load 19 ;j ~ II II J il q "' "' w a: f- ~ I f- (:> z w a: f- "' o:· 0 f- u 1\..) iii UJ 0 2.0 1.5 1.0 1.000 10.000 100.000 COVERAGES OR LOAO CYCLES 1.000.000 Fig. 2. Fatigue Curves for Pavement Design 10.000.000 transfer of joints, temperature conditions, moisture gradient, etc. Consequently, the stresses calculated from the analytical models are nominal stresses reflecting the relative effect of imposed traffic loads rather than actual stresses. The fatigue relationships based on field tests must define some condition of failure for the test sections. The CE tests defined failure as occurring when one half or more of the trafficked slabs have one or more structural cracks. Vesic and Saxena (1969) defined failure as a Pavement Serviceability Index (PSI) of 2.5. As a compar- ison, the CE failure criteria would represent a PSI of 3.0 to 3.3. The relationship developed by Treybig et al. (1977) defined failure as the development of class 3 cracking in an AASHO road test section. A class 3 crack is a ''crack opened or spalled at the surface to a width of 1/4 in. or more over a distance equal to at least one-half of the crack length'' (Scrivner 1962). Fatigue relationships based on field tests will vary depending on the analytical model used to calculate stresses and on the defined failure level, but the shape of relationships based on the AASHO road tests are very different from other fatigue relationships. The ACI and both CE curves in Figure 2 are straight lines on a semilogarithmic plot whereas the AASHO relationships are sharply curved. This differ- ence is probably due to extensive pumping that developed at the AASHO road test. Consequently, AASHO road test relationships actually include the damage from both concrete fatigue and the pumping. Pump- ing is a severe problem in highway pavements but less so in airfields. 21 Design methods The most common airfield pavement design procedures are the PCA and CE design methods or some modification of these. The basic steps in the design are to convert the actual pattern of aircraft traffic to cycles of stress or coverages, calculate the load-induced stresses using an analytical model, and then determine the number of coverages of this load that could be sustained by the pavement using one of the fatigue relationships. The PCA uses a Westergaard interior load analytical model for its stress calculations neglecting the effects of higher stresses at the joints. The higher stresses at the joints and the other addi- tional environmental stresses are accounted for indirectly by use of a factor of safety of 1.5 to 2.0 with concrete flexural strength and the conservative interpretation of laboratory fatigue test results pre- viously shown in Figure 2. The CE design method using the Westergaard edge load model with 25 percent load transfer is widely used and has been adopted by the US Army, the US Air Force, and the FAA. This design method does not use any factor of safety directly. The assumptions on loads are con- servative, and the use of field test developed fatigue relations include some thermal and moisture related stress in the performance criteria. The CE construction specifications require that 80 percent of the quality control flexural tests fall above the specified design flexural strength. The practical effect of this requirement is that the contractor usually produces a concrete that is well above the design flexural strength. The CE now uses the Westergaard or layered elastic fatigue relationships in Figure 2. However, earlier CE and 22 the current FAA design methods used fatigue relationship defined in terms of percent standard thickness. The concepts are similar and have little effect on the results. The background of the percent standard thickness fatigue relationships are described by Rollings (1981) and Parker et al. (1979). Soon after the first version of the CE design method was pro- duced in World War II, a long-term pavement performance monitoring program began that produced modifications to the design procedure to reflect field performance of pavements. One of the early observations was that the ends of concrete runways were failing before the runway interior. This observation in conjunction with the study of traffic at military air~ields led to the definition of four types of pavement at military airfields. Type A areas are runway ends and primary taxi- ways that are subject to highly channelized, slow moving aircraft and are designed for 70-in. wander widths and full aircraft loads. Type B areas are parking and similar areas where traffic is more widely dis- tributed. These areas are designed for full aircraft load and 140-in. wander widths. Type C areas are runway interiors and are designed for 75 percent of the aircraft load and 140-in. wander widths. Type D areas are seldom trafficked areas like the outside edges of the runway and are designed for reduced weight, a limited number of aircraft passes, and 140-in. wander widths. Traffic at commercial airfields is more complex in mix and pat- tern than military airfields, so the FAA adopts a different approach. Full design thickness is used for areas subject to departing aircraft. Areas such as high speed turnoffs that are used primarily by arriving aircraft may be reduced 10 percent from the full design thickness. 23 Seldom trafficked areas analogous to the military Type D areas can be reduced 30 percent in thickness. The CE pavement performance monitoring program and test sections found that the Westergaard model did not adequately reflect the effect of subgrade strength on observed pavement performance. The modulus of subgrade reaction, k , appears in Westergaard stress calculations as a fourth root in the denominator of the radius of relative stiffness, ~ , for the edge and interior load stress calculations. Taking the natural logarithm of the radius of relative stiffness in several of the equations further reduces the effect of k . Consequently, the subgrade support as measured by the k value has a relatively small effect on the calculated stresses. Pavements on high- and low- strength subgrades were observed to crack approximately as predicted by the CE criteria, but at this point their performance diverged. Pavements on low~strength subgrades rapidly deteriorated with addi- tional cracking, faulting, and spalling whereas the pavements on high strength subgrades deteriorated at a much slower rate. Consequently, the CE reduces the required pavement thickness on high-strength sub- grades as shown in Table 1 to take advantage of this improved post- cracking behavior. The FAA, however, does not use this reduction for high-strength subgrade in their design. The existing design methods are essentially fatigue analyses that are modified by agency and organization experience. A number of idealizations are used to reduce the real field problems of aircraft operating on pavements so that these analyses can be done. Much of each method is based on past experience; therefore modifications, changes, and substitutions in the design procedures cannot be done 24 Table 1 Reduction in Pavement Thickness for High-Strength Foundations Sub grade Modulus, k Reduction in (lb/in. 2/in.) Thickness (%) 200 0.0 300 4.6 400 10.6 500 19.2 :25 blindly. To obtain reliable results with any of these design methods, the complete method must be used as the agency specifies. Current Rigid Overlay Design Methods CE design method The most widely used overlay design methods are the empirical relations developed by the CE. The required overlay thickness is determined by the overlay equation: where h 0 h e thickness of overlay = required thickness for a new pavement to support the design traffic planned for the overlay hb = original thickness of existing pavement to be overlaid n = a power dependent on the bond condition between base pavement and overlay 1.0 fully bonded overlay 1.4 partially bonded overlay 2.0 unbonded overlay C condition factor for existing base pavement values summarized in Table 2 An overlay is considered to be unbonded if there is a separation layer of asphalt concrete or other material between the overlay and base slab so that no bond can develop. If the overlay is cast directly on the base slab, it is considered a partially bonded overlay. If the 26 Table 2 Condition Factor Values C Factor Base Pavement Condition 1.0 Existing pavement is in good structural condition with little or no structural cracking. 0.75 0.35 Existing pavement has some initial structural cracking but little pro- gressive distress such as spalling and multiple cracks. Existing pavement is badly cracked and may show multiple cracking, shattered slabs, spalling, and faulting. 27 surface is well prepared by cold milling or similar techniques and a bonding grout is used between the overlay and the base slab, the over- lay is considered to be fully bonded. If the flexural strength of the overlay and the base pavement are substantially different, this difference may be included by replacing hb in the original equation with where h eo x h heb b hb original thickness of pavement to be overlaid h eo required thickness for a new pavment to support the over- lay design traffic determined with the overlay concrete flexural strength = required thickness for a new pavement to support the overlay design traffic determined with the existing base pavement concrete flexural strength This adjustment is used by the CE but not by the FAA. The origin of the concept relating an overlay slab and a base slab to an equivalent slab by a summation of the thicknesses raised to a power is unclear. Older (1924) used a square relation (n=2 and C=l in the CE overlay equation) to evaluate a monolithic structure of bricks bonded to a concrete base slab for the Bates road test, and this reference to equation 1 is the earliest that has been found. Arms, Aaron, and Palmer (1958) suggested that this relation with n equal to 2 came into general use for overlay design with the recog- nition that it was not technically accurate. The ACI Committee 325 on con·crete pavements states that "for many years" concrete overlays have 28 been designed on the "assumption" that the strength of a base and * overlay slab is equal to that of a single slab with a thickness equal to the square root of the sum of the squares of the base and overlay slab thicknesses (American Concrete Institute 1967). During the 1940's and 1950's the CE conducted a series of accel- erated traffic tests of overlay test items. Many of these tests were never adequately documented. but summaries of the results were pub- lished by Hutchinson and Wathen (1962) and Mellinger (1963). The Engineering Design Manual 1110-45-303 (Department of the Army 1958) from this period stated that: "The results of the traffic testing at Lockbourne No. 1 and No. 2 and Sharonville No. 2 indicated that the above relation- ship (n=2 and C=l in equation 1) was approximately correct when a leveling course, cushion course, or bond-breaking course was placed between the two slabs, and that the relationship was too conservative when the overlay was placed directly on the base slab without purposely destroying the bond between the slabs." As shown in Figure 3,* the CE accelerated traffic testing suggested that the power in the overlay design equation should be 1.4 instead of 2.0 when partial bond was allowed between the overlay and the base slab. Fully bonded overlays (n 1 and C = 1) should behave monolith- ically with the base pavement. However, problems of constructing ade- quate joints in the overlay capable of load transfer have not been solved, and fully bonded overlays are now considered most appropriate in airfield work for solving surface problems such as scaling or smoothness rather than for pavement structural upgrade (Hutchinson 1982). This figure was provided by M. Ronald Hutchinson (CE, retired, pre- viously at the Ohio River Division Laboratories and Chief of the PSD at the WES) from his personal files. 29 100 =11 +11 o e 80 z 60 .::: u. 0 1- z w (.) a: w a.. h 1.4 = h 1.4 (/) 40 <( N o 0 .::: 20 hN REQUIRED THICKNESS OF NEW PAVEMENT h0 OVERLAYTHICKNESS he EXISTING PAVEMENT THICKNESS 0 0 20 40 60 80 100 h6 AS PERCENT OF hN Fig. 3. Corps of engineers Overlay Test Data Results 30 The CE overlay design equations are widely used, but their deri- vation and basis are poorly documented and incomplete. Other design methods Problems with the CE developed empirical overlay design equa- . tions have led to examinations of other approaches to overlay design. Martin (1973) used the results of the AASHO road test to establish allowable maximum deflections and propose a design procedure based on measured deflections. The use of allowable deflections has generally been applied to flexible overlays over a rigid pavement rather than to rigid overlays. The weakness of the Westergaard models for evaluating layered overlay systems led other investigations to examine approaches using stronger analytical models. The layered elastic model does a better job of modeling the multiple layers of the overlay geometry than any of the Westergaard models. Several investigators used the layered elastic model or a hybrid finite element model to calculate tensile stresses which were related to performance through one of the fatigue relationships discussed earlier. Smith et al. (1986) and Hutchinson (1982) provide summaries of current overlay design practice and describe the characteristics of some of the proposed design procedures using stronger analytical models. Tayabji and Okamoto (1985) developed a design procedure for bonded and unhanded overlays using a finite element plate element model to represent the concrete slabs and a spring foundation to represent the underlying layers. No attempt was made to evaluate partially bonded overlays. Several approaches to overlay desig·n summarized by Smith et al. (1986) and Hutchinson (1982) have been studied to try to improve upon 31 the CE equation. Most of these have been oriented toward highways rather than airfields. Major problems encountered in these investi- gations have included problems in evaluating the condition of the base pavement, establishing design performance criteria, and adequately modeling slab joints and interface conditions. Basic overlay relationships Simple beam theory can be used to derive equations for unbonded overlays and an equivalent slab that are in a form similar to the CE overlay design equation given earlier, An overlay slab and a base slab can be considered to be structurally equal to an equivalent slab such as shown in Figure 4. If a thin slice of unit width, b , from this equivalent slab is subjected to a moment, M , the curvature of e the beam is where pe = radius of curvature M = moment e E modulus of elasticity e I = moment of inertia e = M e E I e e If the overlay and base slab are subject to an equivalent moment such that Me = M1 + M2 , compatibility requires the radius of curvature of the base and the overlay slabs to be equal so that 1 p 32 EQUIVALENT SLAB - OVERLAY .-:: SLAB (E 1) ----FRICTIONLESS ) INTERFACE <'II BASE M2 .-:: SLAB (E 2) Fig. 4. Base, Overlay, and Equivalent Slabs 33 ---------------~-"--------·- There are three potential ways of defining an equivalent slab: a. The equivalent slab must have the same rigidity as the over- lay and base slab, i.e., Eeie = E1I 1 + E2I 2 . b. The tensile stress in the equivalent slab, cr , must be equal to the tensile stress in the base slab, cr 2 , I.e., cre cr 2 • c. The tensile stress in the equivalent slab must be equal to the tensile stress in the overlay, cr 1 , i.e., cre cr 1 . Substituting the formula for the moment of inertia of a rec- tangular cross section (bh3/12) into the requirement that the equiva- lent slab's moment of inertia must equal the sum of the moment of inertia of the base and the overlay results in the relation: Now if an equivalent slab and the base slab thickness are known and all modulus values are equal, then the required overlay thickness to meet this definition would be This relation is analogous to the current unbonded overlay equation except the power relation is a cube rather than a square. Although this approach provides a system of equal rigidity, it does not provide any information on stresses. In a simple, linearly elastic beam the extreme fiber stress may be determined as -----·--~------ ·-·- ~-~~~ ~-~~--~--- ---· -- ---- -- cr 34 He I where o extreme fiber stress M applied moment c centroidal distance h/2 I moment of inertia The stress in the equivalent slab and the base slab can be represented as M (h /2) 6 Me e e 0 = = "7 e I e e M2 (h2/2) 02 12 Noting that the radius of relative stiffness of the overlay and the base slab must be equal and that the equivalent moment is equal to the sum of M1 and M2 leads to 1 "1\El 1 M2E2 pl Il P2 12 Ml IlE1 --M r 2E2 2 M I1El M2 M.., ( E1hi ) --M + 1 + --e I 2E2 2 .. 3 E2h2 35 Expressing M2 in terms of Me followed by substituting into the expression for stress in the base slab leads to M3 E2 (h2/2) 6 M 3 e E2h2 02 3 El 12 3 3 Elhl E2h2 + Elhl 1 + --3- E2h2 Requiring that oe and o2 must be equal in the second definition of an equivalent slab and setting the expressions for each equal to one another will simplify to If the equivalent slab and the base slab are known, the required over- lay thickness to keep the stresses in the base slab and equivalent slab equal becomes A similar analysis with the requirement that the equivalent slab stress and overlay slab stress, o1 , are equal results for the third case in the relation 36 i' II Since h1 appears on both sides of this equation, it can solved most easily by an iterative solution process. Figure 5 shows each of the equations for the three definitions of equivalent slab (equal rigidity, overlay slab stress equals equiva- lent slab stress, and base slab stress equals equivalent slab stress) plotted together if the overlay and base slab moduli of elasticity are equal. Also shown is the CE unbonded overlay equation. Each axis has been normalized by he. and they are expressed in terms of h1/he and h2/he. The CE equation, the overlay stress equation, and the base slab all intersect when 0.707 Each value of h2 /he has two solutions in the base stress equation. As the thickness of the base slab term h 2/he increases toward 1172, relatively thick overlays are required to maintain the stress in the base equal to the stress in the equivalent slab without increasing the stress in the overlay above the value for the equivalent slab. If the lower value of h1/he is selected for any given h2/he value, the over- lay stress equation shows that the stress in the overlay exceeds that of the equivalent slab. When the h 2/he value exceeds 1172, the over- lay stress equation controls. The CE equation keeps stresses in the 37 0.9 0.8 0.7 0.6 Q) ~ 0.5 .s:: 0.4 0.3 0.2 0.1 0 0 CORPS OF ENGINEERS UN BONDED EOUA TION --- _., ., ,.,. 0.1 0.2 0.3 0.4 // \ I I I I I I I I I I I I ///~BASE STRESS / 0.6 0.7 0.8 0.9 1.0 Fig. 5. Overlay Equation for Different Definitions of Equivalent Slab 38 overlay or the base higher than the equivalent slab in all cases except the point h1/he = h2/he = 1//2. The equal rigidity equation keeps the stresses in both the overlay and the base slab below that of the equivalent slab for all values. Simple beam theory can derive forms of overlay design equations similar to the CE overlay design equation depending on how the equiva- lent slab is defined. The definitions of equivalent slab on the basis of stress show there are different regions where stress in the overlay and stress in the base slab control. Which stress control depends on the ratio of base slab thickness to equivalent slab thickness. 39 PART III: BASIS FOR I~~ROVED OVERLAY DESIGN PROCEDURE An improved rigid pavement overlay design procedure will require development of a method of measuring performance of the concrete pave- ment to replace the current defined failure level approach. An ana- lytical model will be needed to calculate stresses, strains, deflec- tions or some combination of design parameters to replace the current empirical overlay relationships. This analytical model will have to be able to represent two layers of concrete with various possible interface conditions as well as model the underlying base and subgrade materials. The existing base pavement to be overlaid may have suf- fered some deterioration from past traffic, and a method of measuring or accounting for this damage is needed. A complete methodology for an improved overlay design procedure must address each of these concepts. Performance Criteria Current prescriptive definitions of pavement failure in specific terms such as percentage of cracked slabs are not adequate to monitor or predict pavement performance. A pavement is either failed or not failed by such definitions. There is no way to express how well or poorly a pavement is performing, how fast it is deteriorating, etc. Once the defined state of failure is reached the pavement is still functional, but there is no way to express this postfailure perfor- mance. Defining pavement performance by a specified failure condition will not meet the objective of this study. 40 The AASHO road test introduced the concept of Present Servicea- bility Index (PSI) to express the condition of a pavement numerically. A PSI of 5.0 represents a perfect pavement while a 0.0 rating would be an unusable pavement. This concept was originally developed by Carey and Irick (1960) and is a measurable function of roughness, cracking, patching etc. Longitudinal roughness is the primary controlling fac- tor that affects the PSI value. The PSI is an improvement over the previous defined failure levels, but it is oriented toward highway uses and is not directly applicable to airfields. The US Army Construction Engineering Research Laboratory devel- oped a system of rating airfield pavement for the US Air Force (Shahin, Dar.ter, and Kahn 1976). This system is known as the Pavement Condition Index (PCI) and has been adopted by the US Air Force, the US Navy, and the FAA (Shahin, Darter, and Kahn 1977b, FAA 1980, Department of the Navy 1985). Further work has extended this system as a rating and management tool for roads and streets for munici- palities, army posts, and similar organizations. The PCI varies from 0 to 100. Qualitative pavement ratings and corresponding PCI ranges are shown in Table 3. The PCI is a simple, reproducible method of obtaining a numerical rating of a pavement that would equal the subjective rating of a panel of experienced pavement engineers. The PCI recognizes the 31 types of distress listed in Table 4. Deduct values are assigned depending on the type of distress, its severity, and the amount or density of the distress in the pavement. The PCI is described by the equation: 41 PCI Table 3 Descriptive Rating of the PCI Rating DescriEtive Rating 86-100 Excellent 71-85 Very good 56-70 Good 41-55 Fair 26-40 Poor 11-25 Very poor 0-10 Failed 42 Pavement Type Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Rigid Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Flexible Distress Number 1 2 3 4 5 6 7 8 9 10 ll 12 l3 14 15 1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15 16 Table 4 PCI Distress Types Name Blowup Corner break Longitudinal/transverse/diagonal cracking Durability cracking Joint seal damage Small patch Patching/utility cut defect Pop outs Pumping Scaling Settlement Shattered slab Shrinkage cracks Spalling along joints Spalling corner Alligator cracking Bleeding Block cracking Corrugation Depression Jet blast erosion Joint reflective cracking Longitudinal and transverse cracking Oil spillage Patching and utility cut Polished aggregate Raveling, weathering Rutting Shoving of flexible pavement by PCC slabs Slippage cracking Swell * PCC = portland cement concrete. 43 Number of Recognized Severity Levels 3 3 3 3 3 3 3 1 1 3 3 3 1 3 3 3 1 3 3 3 1 3 3 1 3 1 1 3 3 1 3 where where PCI m n 100- a L L f(T., S., D .. ) l. J l.J i=1 j=1 a = an adjustment factor depending on the number of distress types with deduct values in excess of 5 points (this factor was necessary to match the original engineer panel's ratings) m total number of distress types n = total number of severity levels for each distress type f(Ti, Sj, Dij) =deduct value for distress type, T. , at severity level, S. , existing at d~nsity D .. J l.J The PCI may conceptually also be considered as follows: PCI 100 - D - D - D - D - D S E M C 0 n5 = structural deduct due to distress types, severities, and densities associated with loads (e.g., distress No. Rl2 shattered slab) environmental deduct due to distresses associated with environmental effects (e.g., distress No. Fl2 raveling, weathering) materials deduct due to distress associated with materials used in construction (e.g., distress No. R8 popouts) construction deduct due to distress associated with construction procedures (e.g., distress No. F2 bleeding) operations deduct due to distress associated with opera- tions and maintenance of the pavement (e.g., distress No. R7 patching/utility cuts) 44 In many cases, the distress types identified in Table 4 may be caused by different factors. For example, distress No. R3 longitudinal/ transverse/diagonal cracking may be caused by structural loads, or it may be caused by environmentally induced thermal stresses. Distress No. RlO scaling may be due to poor construction procedures or to cer- tain siliceous aggregates undergoing an alkali-aggregate reaction. Many of the distress types used in the PCI are caused by factors that are not reflected in analytical models (durability cracking dis- tress type No. R4 in concrete, for example). This kind of damage in pavements has usually been controlled by construction and material specifications that control how pavements are constructed and what materials are allowed to be used in the pavement. The PCI system as it currently exists includes distress types that cannot be evaluated with current analytical models, and so some modification to the PCI is needed. A Structural Condition Index (SCI) from the PCI can be defined as: m n SCI 100- a 2: 2: i=l j=l with variables as defined previously, but T. l. is now limited to only those distress types associated with structural deterioration caused by loads. It also follows that PCI = SCI - all other deducts 45 Thickness design of concrete pavement for fatigue is based on the load-induced tensile stresses in the slab. Available analytical models are capable of calculating the magnitudes of these stresses by usi~g various idealizations of the pavement structure. There are some other load-caused distresses in pavements which, however, are not directly related to the tensile stress in the slab. The most impor- tant of these is pumping which is a function of soil type, availabil- ity of moisture, and load magnitude and frequency. Pumping forms voids under the pavement resulting in loss of support and accelerated deterioration. These other load-related problems such as pumping are not considered directly in pavement thickness design. Instead protec- tion, such as requiring pumping resistant base courses or stabi- lization, is specified. Pumping is usually a highway rather than an airfield problem and is a special topic in itself. The SCI for this study is limited to considering only those distress types associated with load-induced tensile stresses that result in fatigue damage to pavements. Table 5 shows the PCI distress types that have been selected to be used with rigid pavements to determine the SCI value. Distress No. 13, shrinkage cracking, is included in the SCI because this dis- tress type would include a tight, load-related crack that does not extend across the entire width or length of the slab as well as the conventional shrinkage cracking due to improper curing procedures. With further traffic this crack, if caused by loads, will propagate across the slab into a type 3 longitudinal/transverse/diagonal crack of low severity with a higher deduct value. For the SCI value, this Number 2 3 12 13 14 15 Table 5 PCI Rigid Pavement Distress Types Used with the SCI Name Corner break Longitudinal/transverse/diagonal cracking Shattered slab Shrinkage cracks* (cracking partial width of the slab) Spalling along joints Spalling corner Associated Severity Levels 3 3 3 1 3 3 * Used only to describe a load induced crack that extends only part way across a slab. In the SCI it does not include conventional shrinkage cracks due to curing problems. 47 distress will be counted only when it is caused by load and not if it is due to improper concrete curing practice, The SCI allows a much more precise and reproducible rating of a pavement's condition than previous methods. Table 6 shows six exam- ples of the range of SCI values that could be obtained by pavements all meeting the traditional Corps of Engineers (CE) initial crack failure criterion. The results in Table 6 illustrate the greater precision possible using the SCI to describe pavement performance compared to the prescribed failure definitions such as the CE initial crack criterion. Analytical Model Westergaard models As discuss~d in Part II the Westergaard free edge load or the Westergaard interior load models form the basis of most current air- field design methods. The major limitation of either of these models is the characterization of all material below the slab as a spring with a nonvariable spring constant. The inability of this kind of model to consider the layered structure of an overlay slab resting on a base slab led to the original development of the current empirical overlay design equations. To avoid the empirical approach, either the base slab must be included with the underlying materials as part of the spring system supporting the overlay slab or the base slab and the overlay slab must be added together to form an equivalent slab. Neither approach was considered satisfactory for this study, 48 Table 6 Exam12le SCI Values Meet in~ the Cor12s of En~ineers Initial Failure Definition Example No. Densitl• % Severitl TyJ2e SCI 1 so 1 No. 3 1/T/D cracking* 80 2 so M No. 3 L/T/D cracking 55 3 25 L No. 3 1/T/D cracking 61 zs· M No. 3 L/T/D cracking 4 15 L No. 3 1/T/D cracking 45 20 M No. 3 L/T/D cracking 15 H No. 3 L/T/D cracking 5 25 1 No. 3 L/T/D cracking 70 25 L No. 12 shattered slab 6 15 1 No. 3 L/T/D cracking 55 15 M No. 3 1/T/D cracking 10 L No. 12 shattered slab 10 M No. 12 shattered slab * PCI Rigid Pavement Type No. 3 with 1/T/D (longitudinal/transverse/ diagonal) cracking. 49 $ ~ ~ ! I I lll II il Finite element models Finite element analysis is a powerful numerical method that is capable of solving engineering problems with complex material proper- ties and geometry. In this method the continuum to be analyzed is represented as a collection of finite elements connected only at their nodes; a displacement function is assumed over the region of the ele- ment; an element stiffness matrix is determined reflecting the assumed displacement function, geometry of the element, and material proper- ties; a global stiffness matrix is assembled for the continuum from the individual element stiffness matrices; unknown nodal displacements are determined from the global stiffness matrix and load vector; and finally element stresses and strains are calculated from the nodal displacement. Obviously this technique must be computerized. A variety of finite element computer programs are available that offer a broad selection of element types, displacement functions, material models, and special functions such as friction or slip sur- faces. As the programs become more sophisticated and generalized, their cost for input preparation, computer support, and output analy- sis and their demand for accurate material characterization increase dramatically. Also finite element solutions for a problem can seldom be performed in a single step but must include sensitivity studies to determine factors such as an adequate finite element mesh or appropri- ate number of loading steps for some material models. The most generalized finite element solutions available are the three-dimensional codes that allow complex modeling of material varia- tion and structural geometry in all planes, but their application is prohibitively expensive for routine pavement design and analysis. 50 H II !I II II II Some work has been done with prismatic solid elements for analysis of pavements, but these have also been too expensive for general pavement work. The plane strain, plane stress, and axisymmetric finite element programs use idealizations that seldom, if ever, are applicable to rigid pavement problems. A group of hybrid finite element codes have been developed that are simpler and more economical than the three- dimensional and solid prismatic solutions. These codes appear to have more immediate potential for pavement design and analysis than those mentioned previously. These hybrid codes typically use a four-node thin plate finite element to represent the rigid concrete pavement surface and either a spring or layered elastic representation of the remaining pavement structure (Huang and Wang 1973, Chou and Huang 1981, Huang 1985, Ioan- nides et al. 1985b, Majidzadeh et al. 1985). Overlays and stabilized layers are analyzed by transforming the surface slab and the base slab or stabilized layer into an equivalent thickness of plain concrete assuming either no bond or complete bond between the layers. Indi- vidual slabs are analyzed as an assemblage of the four-node thin plate finite elements, and load transfer between slabs can be included in the analysis by such methods as assigning joint deflection efficien- cies, treating dowel bars as beam elements, or using springs to model load transfer across the joint. Layered elastic model Layered elastic analytical models idealize the pavement system as a sequence of homogeneous, elastic, horizontally uniform layers subject to circular uniform loads. The formulation of the solution to stresses, strains, and deflections to this problem was originally set 51 ~' forth by Burmister (1943). The solution requires the integration of Bessel functions which, except for two- or three-layer systems, is done numerically. A variety of computer programs have been developed to solve the layered elastic problem, and they differ primarily in the methods and accuracy of these numerical procedures. Crawford and Katona (1975) and Parker et al. (1979) provide some comparisons and evaluations of several of these commonly available programs. The bond between layers may be treated as unhanded (friction- less), fully bonded (full friction), or intermediate between the two. The fully bonded case requires that the horizontal displacements on either side of the boundary between layers be equal. For the unbonded case, the interface is considered a principal plane and shear stresses at the interface are set equal to zero. These two cases are the most common idealizations for pavement analysis. Usually, the interface between a rigid pavement and the underlying layer is considered unbonded or frictionless, and almost all other pavement interfaces are considered fully bonded. The generally recognized existence of partially bonded rigid overlays makes it desirable to treat cases intermediate between fully bonded and unbonded. One approach, originally proposed by Westergaard (1926), assumes that the shear stress of a layer above an interface is a function of the difference between the horizontal displacement of the layer above the interface and the horizontal displacement of the layer below the interface. This approximation does not meet the elas- ticity compatibility equations and has led to another intermediate friction solution based on making the horizontal displacement of the layer above an interface a function of the horizontal displacement of 52 the layer below the interface (Cauwelaert, Lequeux, and Delaunois 1986). The BISAR layered elastic program uses the Westergaard approxi- mation for intermediate bond conditions at interfaces. Cauwelaert, Lequex, and Delaunois (1986) have developed an initial version of a layered elastic program, FLIP, which solves the intermediate bond condition as noted above. Initial checks of this program indicate that it matches the fully bonded and unbonded deflections of BISAR, and it is currently undergoing further study and testing at the US Army Engineer Waterways Experiment Station. A wide variety of other programs such as CHEVRON, CHEVIT, ELSYM5, CIRCLY, or CRANLAY are available to solve either the fully bonded or unbonded interface cases. Parker et al. (1979) recommended the BISAR layered elastic program for use with rigid pavements because of problems encountered with erratic deflection basins with some other programs when the ratio of the concrete modulus to the subgrade modulus was very large. There was little difference in calculated concrete pavement tensile stress between the programs, however. The FLIP program may eventually offer an alternate intermediate bond interface model. Model selection Most of the analytical models discussed above use linearly elas- tic material properties. Much more powerful material models are available for use with some finite element techniques, but they have not found much application in pavement work. To date, the input data required for these models and the increased effort involved in this type of modeling have not produced results that can be analyzed effectively. More research is required in this area before these 53 types of models will become usable. The Westergaard models and the hybrid finite element models that use the spring subgrade describe all material below the pavement surface with a single value spring con- stant. Representing each of these lower layers separately with lin- early elastic material properties as with the layered elastic model or some of the finite element models offers the advantage of modeling the effects of different layers of material with varying stiffness within the pavement structure. The Westergaard edge-loaded model, the hybrid finite element codes, and the three-dimensional finite element codes offer the best geometric models of actual pavement slabs and can directly include the effect of slab joints in the analysis. The inability of the layered elastic model to include the effect of joints in the pavement is a major limitation of its usefulness in analysis of concrete pavements. However, the layered elastic model offers an excellent representation of the layered overlay structure with variable interface conditions between layers. The joint limitation can be overcome by the use of empirical correlations and adjustment factors. The layered elastic model and some of the more complex finite element models include methods of accounting for different levels of bond or friction between layers. The hybrid finite element programs handle no bond and complete bond by transforming the surface and base slab into an equivalent slab but are unable to examine intermediate levels of bonding. A similar approach of transforming to an equiva- lent slab could be used with the Westergaard models. The existence of the partially bonded overlay concept suggests that the effect of 54 various levels of friction and bonding between the overlay and base slab is important in developing an effective overlay analysis technique. Input time, computer support, and overall cost of analysis of· the different models varies. The Westergaard and layered elastic models are readily solved on current levels of microcomputers. Rapidly increasing capacity of these machines suggests that some of the simpler finite element programs will soon be available on micro- computer. At the present time, finite element analysis at sufficient detail to be usable for pavements requires the support of a mainframe computer. Cost of analysis is lowest for the Westergaard solutions followed in increasing order of cost by layered elastic, hybrid finite element with spring subgrade, axisymmetric finite element, hybrid finite element with layered elastic subgrade, prismatic solid, and three-dimensional finite element programs. The layered elastic model solved with the BISAR computer program will be used for this program. Selection of this model is based on the following: a. Reasonable modeling accuracy. This model can represent the layered structure and variable interface condition that exist in an overlay with appropriate material models. The inability to model joints and effects of nonstandard load transfer is a major disadvantage of this approach. b. Costs and computer support. This model has reasonable input, computer, and analysis costs. It can be supported on current generations of microcomputers. c. Compatible with other systems. Layered elastic models are currently being used at the WES and in other agencies for flexible and rigid pavement design and analysis and are widely used for evaluation of nondestructive pavement tests. 55 Previous Traffic Damage Figure 6 illustrates some of the interactions between the base slab and an overlay slab. A base slab subjected to traffic from t 0 to t 1 will undergo some deterioration. If nothing is done, con- tinued traffic would allow the pavement to deteriorate as shown by the dashed line. If, however, the slab is overlaid at t 1 , the stresses in the base slab are reduced. As traffic is applied to the overlay slab the base slab will continue to deteriorate as shown by the solid line but at a reduced rate from before. At traffic t 1 the base slab is capable of providing a certain amount of support to the new overlay slab. Since the base slab has undergone some deterioration from t 0 to t 1 , it will not provide the same support as a brand new slab. For this amount of support the traffic on the overlay will develop a certain stress level which will result in deterioration of the overlay slab. However, at traffic t 2 the base slab has deteriorated further; its support value has decreased; the stress in the overlay, therefore, has increased; and the deterioration of the overlay slab is faster than would be pre- dieted from the conditions at Similarly, at base slab deterioration has continued with the same result of accelerating deterioration in the overlay. Any predictive performance model for the overlay slab must recognize and account for the acceleration of the deterioration of the overlay slab as the base slab deteriorates with continuously decreasing support to the overlay. 56 OJ <:( .....J (f) >- <:( ...J a: u.J > 0 co <:( .....J (f) UJ (/) <:( CXl z 0 t: 0 z 0 u f- z w :2 w > ---....... /DETER/ORA T/ON .......... IF SUPPORT IS ' ... , CONSTANT .... ... , '',, <( a.. ACTUAL DETERIORATION ', >- <( ....J a: w > 0 ~ en en w a: f- en 'o ,_o~ r------------------------------- a: w <( ----oe--1 C..>UJ ~iE~ V>o. r-z zo w- :;;:1:= wo >Z <(0 a..u TRAFFIC ' SLAB DETER/ORATION AFTER OVERLAY Fig. 6. Conceptual Deterioration of a Pavement and Overlay 57 Methodology The objective of this research study is to develop a mechanistic method of designing concrete overlays for rigid pavements that will pre- diet the performance of the overlay. The layered elastic model has been selected as the analytical basis for this study. The SCI has been defined as the measure of performance of the pavement. Prediction of performance of an overlay will require three steps: a. Determine pavement properties. A layered elastic analysis requires that each material be described by a modulus of elasticity and a Poisson's ratio. Modulus values can be determined for in-place materials by standard nondestructive testing, destructive sampling and testing. or construction data. If nondestructive testing techniques are not used, modulus values for soil and aggregates are usually estimated by correlations with standard pavement tests such as modulus of subgrade reaction or California Bearing Ratio (CBR), but they can also be determined from laboratory tests such as the resilient modulus test. The concrete modulus for the proposed overlay can be estimated from local historical con- struction data, or it can be determined before construction as part of the mixture proportioning studies. Layered elastic calculations are relatively insensitive to Poisson's ratio, and these values are usually taken as 0.15 to 0.20 for concrete and 0.3 to 0.5 for aggregates and soils. The interface conditions between each layer must also be selected. The interface between concrete and soil or aggre- gate is commonly modeled as frictionless and most other soil or aggregate interfaces are modeled as fully bonded. The appropriate bond condition between the concrete overlay and base pavement needs to be determined. b. Base slab analysis. The condition of the base slab to be overlaid must be determined. The effect of previous traffic before overlay on the base slab's remaining fatigue life must be evaluated. Its support provided to the overlay slab must be quantified in terms usable with the layered elastic model. Similarly, if the existing base slab load transfer is substandard, this must be expressed in some manner usable with the layered elastic model. c. Overlay slab analysis. As the base slab deteriorates, its supporting value to the overlay slab must be determined. This effect will be accounted for by dividing the traffic into intervals, determining the reduction in support value 58 provided by the base slab during that interval of traffic, calculating the stress in the overlay for this changed sup- port condition, and then calculating the loss in the SCI of the overlay during that traffic interval. In order to carry out this type of analysis, a model will be needed to describe the deterioration of a concrete pavement in terms of the SCI as load repetitions are applied. Substandard load transfer between slabs in the base pavement must be expressed in terms usable with the layered elastic model. A method of quantifying the change in support provided by the base slab as it deteriorates is also needed. Once these models are available this concept of analysis can be checked against available overlay test section data and compared to current design methods. 59 PART IV: PERFORtUillCE MODEL FOR RIGID PAVEMENTS The most extensive historic controlled trafficking data using full-scale aircraft loads are the Corps of Engineers (CE) accelerated trafficking tests conducted at Lockbourne AFB, Sharonville, and the US Army Engineer Waterways Experiment Station (WES). These were the only tests conducted with full aircraft size loads and include tests with weights up to the current B-747 and C-5 aircraft. Sixty-seven test sections were built and tested during this test program that originally started in World War II. These tests used full-size con- crete slabs for testing and applied traffic with full-size aircraft gear and gear loads. A summary of all these tests is given by Parker et al. (1979). Test Section Data The new rigid pavement performance models developed for this research study are based on a reevaluation of the accelerated traffic tests conducted by the CE. The analysis of these test sections used the original test reports and supplemented this information with photographs, work logs, minutes of meetings, and any related corre- spondence that could be located in the files at WES. Table 7 lists 67 test sections that were part of this test program. These data are divided into three classes, I, II, and III as shown. The class III data were not. used in the analysis for the following reasons: lack of information needed for the analysis, no deterioration under traffic,. failure conditions such as severe pumping that are not included in the 60 Table 7 Available Rigid Pavement Field Test Data Item DesiBnation Parker et al.* Original Test Series (1979) Test Quality Remarks l. Lockbourne A-1 A2.60 II Poor data spread No. 1 A-2 A1. 60 II Poor data spread B-1 B2.66L II One slab B-2 Bl. 66L II Unusual failure C-1 C2.66L I C-2 Cl. 668 I D-1 D2.66 I D-2 Dl.66 I E-1 E2.66M III No deterioration E-2 E1.66M I F-1 F2.80 III No deterioration F-2 Fl. SO III Unusable data spread K-3 K2.100 III Unusual failure K-2 K1.100 III Unusual failure N-2 N1.86 I N-3 N2.86 II Poor data spread 0-2 01.106 I 0-3 02.106 I P-2 Pl.812 III Unusable data spread (Continued) * Parker et al. (1979) summary of test information used a shortened designation for test items in Lockbourne Test No. 1 and No. 2. (Sheet 1 of 4) 61 Test Series 1. Lockbourne No. 1 (Continued) 2. Lockbourne No. 2 Table 7 (Continued) Item Designation Parker et al. * (1979) P-3 Q-2 . Q-3 R-2 R-3 S-2 S-3 T-2 T-3 Original Test P2.812 Q1.102 Q2 .102 Rl.612 R2.612 Sl. 66 82.66 Tl.60 T2.60 U-2 Ul.60 U-3 U2.60 A-Rec A-Rec E-1 * E-2 * E-3 * E-4 * E-5 * E-6 * Quality III III I III III III III III III II III III III III III III III II (Continued) Remarks Unusable data spread Unusable data spre~d R-2 through T-3 had unusually rapid failure. These sec- tions have been deleted in past studies Poor data spread Unusable data spread Insufficient data Bad load transfer condition Poor data Bad load transfer condition Bad load transfer condition Bad load transfer condition Poor data spread * Specific original slab designations for these test items are shown in Appendix A. (Sheet 2 of 4) 62 Table 7 (Continued) Item Desi8nation Parker et al. * Original Test Series (1979) Test Qualitz: Remarks 2. Lockbourne No. 2 E-7 * III No deterioration (Continued) M-1 * I M-2 * II Poor data spread M-3 * III No deterioration 3. Lockbourne No. 3 III Insufficient data 4. Sharon- ville 57 III No detailed data ever Channelized published on Sharon- 58 III ville Channelized Test Sections 59 Ill 60 III 61 III 62 III 5. Sharonville Heavy Load 71 III No failure 72 III Poor data, unusual deterioration 73 II Unusual deterioration 6. Multiple Wheel 1-CS I Wheel Heavy Gear Load 2-CS III Severe pumping (MWHGL) 3-CS III Severe pumping 4-CS II Slight pumping (Continued) * Specific original slab designations for these test items are shown in Appendix A. (Sheet 3 of 4) 63 Table 7 (Concluded) Item Desis;nation Parker et al.* Original Test Series (1979) Test Qualit;y Remarks 6. Multiple 2-DT I Wheel Heavy Gear 3-DT I Load (MWHGL) (Continued) 7. Keyed l-C5 II Slight pumping Longitudi- nal Joint 2-CS I Study (KLJS) 3-CS II Possible damage from instrumentation traffic 4-C5 III Pumping 4-DT I 8. Soil Stabi- 3-200 I lization Pavement 3-240 III Damaged by static test Study (SSPS) 4-200 I 4-240 II Possible damage by adja- cent traffic (Sheet 4 of 4) 64 SCI, test slabs that had no load transfer or peculiar joint construe- tion no longer in use, and the quality or spread of the data inadequ- ate to determine performance (e.g., at one point SCI= 100, many repetitions later SCI= 0 with no information between these points). Lockbourne No. 1, test sections R-2, R-3, S-2, S-3, T-2, and T-3 are also included as class III data. These sections failed inexplicably. With high design factors they reached shattered conditions in as little as 1.5 coverages. These test sections have been excluded in past analyses of these data because of their peculiar behavior and have been excluded from this analysis also. The remaining data are divided into two classes, I and II. The class I data are the best quality.data. Class II data include tests that may have had slight pumping that could have influenced test results, data that had a poor spread in values so that it was difficult to interpret, or tests that had a large amount of unusual distress such as extensive joint spall- ing without any cracking. Most test section reports include a crack map taken at either specific traffic intervals or the traffic coverage level at which a crack formed is indicated on the map itself. This map is-usually sup- plemented with written descriptions and photographs in the report. Additional information in the form of photographs, work logs, and briefing papers are also available for some test sections. The PCI procedures as published by the Federal Aviation Adminis- tration (FAA) were used to develop the test section SCI, except only the five distress types listed in Table 5 were used. Each of these distress types has a description and photographs that describe its severity level. Charts provide a deduct value for each distress type 65 1 d ! depending on its severity level and density. These deduct values are summed and then adjusted if more than one distress type exists. The damage.descriptions and deduct curves used to compute the SCI can be found in the FAA publication describing the PCI (Federal Aviation Administration 1980). Table 8 shows an example SCI calculation for one test section. Judging the severity level of a distress from the available records was often very difficult. It was particularly difficult to separate low- and medium-severity type 3 longitudinal/transverse/ diagonal cracking. This separation is based on spalling along the joint, crack width, or formation of a second crack. During traffick- ing, observers are watching for cracks and generally note when the first crack occurs. This crack is undoubtedly a tight, low-severity crack. However, the working of this crack which leads to widening and spalling may not be recorded, and photographs may not be available or show adequate detail. The transition between low- and medium-severity cracks then cannot be clearly identified in the tests. Therefore, all cracks were assumed to be low-severity cracks unless information was available to indicate otherwise. Applying this rule a slab would be assigned a low-severity crack rating when the initial crack forms. It is raised to a medium severity level when a second crack forms and divides the slab into three pieces. When additional cracks divide the slab into four or five pieces, the rating becomes a low-severity shat- tered slab. This ratio is raised to medium severity when the slab is further subdivided into six pieces. As multiple cracks occur, they usually begin to work and almost invariably spalling is noted in the report text, marked on the crack map, or is visible in photographs. 66 Table 8 ExamEle SCI Calculations for Kezed Longitudinal Joint Test Section Item 2-CS Traffic Distress Summed Adjusted Coverage No. DescriEtion Severity Densitz (%) Deduct Deduct Deduct SCI 0 100 144 3 L/T/D cracking* Low 25 15 15 15 85 344 3 L/T/D cracking Low SCJ 20 20 20 80 ~ 504 3 L/T/D cracking Low 25 15 -...] 12 Shattered slab Med 25 43 58 50 so 688 3 L/T/D cracking Low 25 15 12 Shattered slab Med 25 43 103 87 13 1696 3 L/T/D cracking Med 25 32 12 Shattered slab Med 25 42 High so 77 151 100+ 0 * L/T/D cracking longitudinal/transverse/diagonal cracking. Cons~quently, it is usually possible to appropriately class a shat- tered slab's severity level on the basis of the severity of the cracks in addition to its number of pieces. The SCI is a function of the- density or amount of distress that. occurs in a test section. Commonly, a test section consisted of four slabs, but some had only two slabs. On an actual pavement the large number of slabs would be expected to deteriorate gradually, providing a smooth curve. Test section data will tend to be rougher because of the limited number of slabs that lead to large, abrupt changes in the density measurement associated with distresses. Another problem existed with the Lockbourne No. 1 tests. These sections were built during World War II, and joint design was one of the test variables. A test section was typically 20 by 40 ft and separated from the test section before and after it by transition slabs. Each test section was divided into four 10- by 20-ft slabs by contraction joints. One longitudinal edge joint was a keyed joint with an adjacent test section. The other longitudinal edge was free. One transverse joint at the end of the test section was a doweled expansion joint while the other end had a free expansion joint with no provisions for load transfer. Since the layered elastic model was used for stress calculations, and it cannot accurately account for varying load transfer levels, only slabs that represent current con- struction methods with reasonable joint load transfer were used to develop the performance models. In the Lockbourne No. l tests, only the two slabs adjacent to the doweled construction joint can be used for calculation of the SCI. Some of the Lockbourne test items also applied traffic to within 2 ft of the free edge longitudinal joint. 68 For these sections only the single slab adjacent to the doweled expan- sion joint and the keyed longitudinal joint could be used in the analysis. Appendix A presents the detailed summary of the analysis of the CE test sections. The thickness and material properties for each item are tabulated for each test series. These data were taken from the original CE test reports listed in the bibliography and references or from the test summary by Parker et al. (1979). Next the calculated SCI value for the test items in each test series are tabulated with the calculated c0 and CF values, the specific slabs analyzed for the test item, and the size of the load. The SCI values are shown for each coverage level for which there was a map of cracking, photo- graphs, or written description that allowed the SCI to be calculated. The final table in Appendix A presents the stresses and design factors calculated for each test item. Test Section Performance Proposed deterioration model Test section deterioration data show a great deal of scatter as can be seen by the examples in Figure 7. Fatigue analysis in Part II used the logarithm of stress cycles or coverages, and when this is used for the abscissa of the test section deterioration plots, the scatter of the data is greatly reduced. Figure 8 shows the test items from Figure 7 replotted with SCI as a function of the logarithm of coverages. The relation for each test item is essentially linear with the logarithm of coverages. 69 u U) 100 sa 60 40 20 0 0 100 200 Fig. 7. 300 400 500 600 700 BOO TRAFFIC COVERAGES LEGEND 0 LOCKBOURNE NO.2 ITEM M-1 c. MWHGL ITEM 1-CS 0 KLJS ITEM 2--CS e LOCKBOURNE NO.1 ITEM 0-2 • LOCKBOURNE NO. 1 ITEM C-2 Sample SCI-Coverage Relationships u rn 100 80 60 40 20 0 5 10 100 TRAFFIC COVERAGES LEGEND 0 LOCKBOURNE NO.2 ITEM M-1 t::. MWHGL ITEM 1-C5 0 KLJS ITEM 2-C5 e LOCKBOURNE NO.1 ITEM 0-2 • LOCKBOURNE NO. 1 ITEM C-2 1,000 Fig. 8. Sample SCI-Logarithm Coverages Relationships 71 10,000 Rigid pavements and the CE test items generally go through a period with little or no deterioration, and then, as suggested in Fig- ure 8, they deteriorate in a linear form as a function of the loga- rithm of coverages. This allows the definition of the proposed rigid pavement performance model shown in Figure 9. A rigid pavement suf- fers no structural fatigue related deterioration until the point iden- tified as c0 in Figure 9 is reached. During this period the SCI is 100. From c0 to CF where the SCI is zero, the pavement deterior- ates linearly as a function of the logarithm of coverages. c0 repre- sents the onset of structural deterioration, and CF is essentially complete or absolute failure with an SCI of zero. Some test sections (e.g. MWHGL Item l-CS in Figure 8) show a gradual upper curve into the linear deterioration behavior rather than the abrupt deterioration in the proposed model. This is probably true of actual pavements also. As noted earlier the test section data have relatively few slabs, so the damage density values used to calculate the SCI for test items show sudden large increases as slabs begins to deteriorate. In actual pavements this increase in damage density would be progressive resulting probably in a smooth curve. The major deterioration occurs along the line defined by c0 and CF , and the minor deterioration that may occur along the upper curve line in Fig- ure 9 does not significantly affect the usefulness of the proposed model. The structural fatigue deterioration of a rigid pavement can be uniquely described by the two parameters, c0 and CF . The pavement undergoes no deterioration until c0 is reached and thereafter deteriorates linearly as a function of the logarithm of coverages 72 u '-1 "' w 100 ~--------------------------------------~------, 80 60 40 20 0 ACTUAL BEHA V/0:;> OF SOME SECTIONS Co LOG TRAFFIC COVERAGES MODEL BEHA V!OR Fig. 9. Proposed Performance Model until CF is reached. If these two parameters can be predicted for a rigid pavement, then the SCI at any given coverage level can also be predicted. Determination of Model Parameters The c0 and CF values were calculated for each CE test item by fitting a least squares regression straight line to the SCI and coverage data of each item. The c0 value was found by setting SCI equal to 100, and CF value was found by setting the SCI equal to zero. Table 9 summarizes the results of this analysis for each test item rated as having type I or II quality data. Not all the SCI- coverage data points were used in the analysis as indicated in Table 9. Excluded data points fell into three groups. When the SCI was equal to 100, the data point was on the horizontal portion of the model in Figure 9 and had not reached c0 yet. Generally, this kind of point was excluded from the analysis. When a data point had an SCI of zero, it has a similar problem since it can be past CF and on the horizontal portion of the model in Figure 9. Also as noted in Fig- ure 9, some test items have a slightly curved upper portion from the SCI of 100 horizontal line to the straight line deterioration line. These points have SCI values of 80 to 100 at coverage levels before c0 is reached. This type of point was excluded from the data points used to determine c0 and CF • The correlation coefficient values in Table 9 indicate that the data used to determine c0 and CF were reasonably linear as idealized by the model in Figure 9. Figure 10 shows three relationships developed for c0 as a func- tion of the design factor (DF). The design factor is the concrete flexural strength divided by the layered elastic calculated stress. 74 Table 9 C 0 and C F Values for Test Sections Number Correlation of Data Coefficient co CF 2 Test Section gualit~ Points r l. Lockbourne No. 1 A-1 II 225 10,084 2 A-2 II 13 59 2 B-1 II 59 522 3 0.88 B-2 II 3 96 4(3)* 0.99 C-1 I 48 636 4 0.93 C-2 I 13 92 3 0.99 D-1 I 289 3, 776 3 0.96 D-2 I 6 104 3 0.95 E-2 I 50 212 3 0.95 N-2 I 105 284 4(3) * 0.99 N-3 II 6 32 2 0-2 I 347 1,606 4 0.97 0-3 I 41 155 4(3)* 0.99 Q-3 I 36 209 4 0.92 U-2 II 123 488 3(2)* 2. Lockbourne No. 2 E-6 II 1,342 13,083 2 M-1 I 93 353 9 0.87 M-2 II 1,693 6' 774 3(2)* 3. Sharonville Heavy Load 73 II 668 7,054 4 0.83 4. Multiple Wheel Heavy Gear Load Test (MWHGL) l-CS I 150 936 5(4)* 0.93 4-CS II 165 258 2 2-DT I 128 476 4 (3) * 0.99 3-DT I 177 960 5(4)* 0.95 5. Keyed Longitu- dinal Joint Study (KLJS) 1-CS II 16 683 4 0.91 2-CS I 292 783 4(3)* 0.97 (Continued) * Number in parentheses is number of points actually used to deter- mine c0 and CF . 75 Table 9 (Concluded) Number Correlation of Data Coefficient co CF 2 Test Section Qualitz Points r 5. Keyed Longitu- dinal Joint Study (KLJS) (Continued) 3-C5 II 11 395 4 0.94 4-DT I 228 1,094 4 0.95 6. Soil Stabili- zation Pavement Study (SSPS) 3-200 I 937 4,258 5(4)* 0.93 4-200 I 1,179 5,934 3 0.95 4-240 II 22 377 4 0.99 76 2.0 1.8 1.6 u. 0 ci 0 1- 0 <{ 1.4 u. z 2 U) "-.1 w "-.1 0 1.2 1.0 / • • • CLASS.IIDF=0.78+0.31LOGC0 ° h • ,2~o;JOn~31~ ~~ • o/ • • / o/ / /{ 0 0 0 / y 00 / ~ / h LEGEND 0 CLASSIDATA 0 CLASSDa DATA e CLASSll DATA //? . / / CLASS I!a OF= 0.52 + 0.39 LOG C0 /0 / 0 10 0 100 r 2 =0.819 n=21 • COVERAGES TO ONSET OF DETERIORATION, C0 Fig. 10~ Relation Between DF and c 0 1,000 10,000 The c0 values for each test item are from Table 9. The design fac- tors for each test item were calculated using stresses from layered elastic theory and are tabulated in Appendix A. The first relation was developed for the class I test sections identified in Table 7. The second relation identified as class IIa includes four data points that were listed as class II because of poor data spread that made calculation of c0 uncertain. These points gave results in line with the class I data. The third relation identified as class II includes all class I and class II data. All but one of the class II data, exclusive of the four points shown as IIa, have positive residuals for any of the relationships. These positive residuals suggest that a systematic error may exist. In this case, the poor data spread in most of these test items has resulted in underestimating c0 . The one section that has a negative residual is item 4-CS of the MWHGL test that was classified as class II data because slight pumping occurred during the test. Including the four class IIa data points changes the slope of the relationship between DF and c0 significantly. The addition of these four data points appears reasonable relative to the class I data. The class IIa relationship slope of 0.39 is also similar in magnitude to the 0.35 developed earlier by Parker et al. (1979) for conventional initial failure design with layered elastic models. Overall, the class Ila relationship appears to be the best relation available for the quality and quantity of data available, and it is recommended for predicting the c0 value. Figure 11 shows three relations developed for CF for the data divisions as before. The residuals for the class II data do not show 78 2.0 1.8 1.6 u. 0 cr:' 0 I- (.) <( 1.4 u. z 2 (I) w 0 1.2 1.0 0.8 10 • CLASS! DF = 0.02 + 0.47 LOG CF • 6 • 0 0 CLASS II DF = 0.30 + 0.39 LOG CF CLASS Ilii OF= 0.24 + 0.39 LOG CF n = 21 r2 = 0. 755 n = 31 0 • 0 0 oe 100 1,000 COVERAGES TO COMPLETE FAILURE, CF Fig. ll. Relation Between DF and CF LEGEND 0 CLASSIDATA 6 CLASSila DATA e CLASSTIDATA 10,000 100,000 the pattern of being all positive that they did for c0 The class II and IIa relations are parallel lines while the class I line once again has an appreciably larger slope. There does not appear to be any reason to exclude any of the data points in Figure 11, so the relation for all of the class II data is the most appropriate for use. In this analysis, it has been assumed that c0 and CF are functions only of the design factor. As previously noted this assump- tion may not be completely true. Postcracking behavior of slabs may also be a function of the subgrade support. The CE recognized this effect by the high-strength subgrade thickness reduction used with the traditional CE design method discussed in Part II. However, attempts to use subgrade strength with the design factor to obtain better c0 and CF relationships were unsuccessful because the test sections were almost universally built on low-strength subgrades. Therefore, insufficient data exist to examine the effect of high-strength sub- grade influence on postcracking behavior of the pavements. Also, the use of an elastic modulus value with a layered elastic analytical model may simply reflect the contributions of the subgrade better than the Westergaard model with the subgrade spring constant. As discussed in Part II, the Westergaard stress calculation is not very sensitive to the modulus of subgrade reaction. Model Evaluation Comparison with other criteria The relations developed for the two parameters c0 and CF allow the prediction of a pavement's SCI value for any specific 80 L traffic coverage if the design factor is known. The design factor is calculated from the concrete flexural strength and layered elastic stresses. These relations for c0 and CF are in effect fatigue relations, and they follow the same linear form as other concrete fat- igue relations discussed in Part .II. These relations for c0 and CF are based on tests with relatively small magnitudes of traffic. How- ever, their extrapolation to larger coverage levels is supported by the linear concrete fatigue relations found in beam fatigue tests described in Part II. The current CE fatigue relationship for Westergaard edge load model calculated stresses and the fatigue relationship developed by Parker et al. (1979) for layered elastic model calculated stresses use the same form as the c0 and CF relations. Design factor is expressed as a linear function of the logarithm of coverages. The relationships for c0 and CF and Parker et al. (1979) relationship use the same analytical model to calculate stresses for determining the design factor. Parker et al. (1979) used the CE definition of rigid pavement failure to determine their relationship. As noted in Table 6, the CE definition of failure could have SCI values that rea- sonably range from 55 to 80 depending on the amount and severity of cracking in the test slabs. As shown in Figure 12, the relationships for c0 and CF bracket the Parker et al. (1979) relationship within the ranges of traffic used in the CE test sections. Since the c0 and CF relationships are for an SCI of 100 and 0 and the Parker et al. (1979) is for some range of SCI values between these extremes, the relative positions of the three relations are consistent. 81 2.1 2.0 1.8 u. 0 c£ 0 f- 1.6 u <( u.. co z c..? N U5 w 1.4 0 1.2 1.0 100 1,000 10.000 100,000 COVERAGES Fig. 12. Relationship Between C0 and CF and the Criterion of Parker et al. (1979) Rate of deterioration The relationships for c0 and CF have the same form as other concrete fatigue relationships and appear consistent with other con- crete pavement criteria. However, the logarithmic form of the c0 and eF relationships indicates that once deterioration begins the rate of deterioration decreases with increasing coverages. The deterioration of a test section can also be examined using a normalized coverage factor, eN , defined as where e is the coverage leve-l at which a specific SCI is calcu- lated. The relation between CN factor and SCI in Figure 13 is a measure of the rate of structural deterioration at a given coverage level. Normalizing the traffic coverage data using the calculate c 0 and CF values effectively collapses the data. By definition, when C is equal to c0 the normalized factor CN should be zero, and when C is equal to CF , eN should be 1. The relation in Figure 13 passes through these points. Negative CN values with SCI values less than 100 are due to the initial curved deterioration some test sections showed as was seen in Figure 9. The decrease in the rate of deterioration is not consistent with some of the results reported from the field performance of pavements. Shahin, Darter, and Kohn (1977a) found that Air Force airfield pave- ments up to 35 years old showed a slightly convex relationship between PCI and the pavement age in years. This is an increase in the rate of deterioration with age and implies that if the annual traffic rate is 83 110 100 0 90 0 0 80 70 60 SCI= 100.0- 181.6 CN + 81.6 C~ 00 u 50 "' .p- 0 40 30 20 0 0 0 0 10 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 c- c0 eN = c,- Co Fig. 13. SCI - CN Relationship approximately constant then the rate of pavement deterioration increases with coverage level as opposed to decreasing with coverage level as implied by Figure 13. This discrepancy is due to several factors. First, the PCI includes all forms of distress and not just the structural deducts used by the SCI. Some of the distress, particularly those associated with durability or maintenance, will become more pronounced with age regardless of loading. The assumption of constant equivalent annual traffic is probably erroneous also. Although the Air Force has not seen the same increase in traffic volume that has occurred in civil aviation, aircraft have become progressively larger and heavier with increasing structural loading of the pavement. The addition of the other PCI deducts not included in the SCI and increasing aircraft loading will tend to accelerate the rate of deterioration of in- service pavements. As a pavement begins to structurally deteriorate, its ability to carry load through bending decreases. When carried to the extreme the pavement is cracked into small blocks that are pushed into the sub- grade with negligible bending. Consequently, in badly deteriorated pavements further progression of deterioration will depend less on fatigue tensile related cracking than it will on spalling and fault- ing. Also, deteriorated pavement will allow water to penetrate to the subgrade thereby weakening it and reducing the pavement support. The c0 and CF relationships are based on accelerated traffic tests that, although they include field effects such as temperature or mois- ture warping or nonuniform subgrade support, generally do not last 85 long enough to provide information on water penetration and subgrade weakening that may occur over years as a pavement deteriorates. The rate of deterioration of the SCI predicted by the c0 and CF relationships is reasonable for the data and limitations upon which the relations are based. An in-service pavement will have addi- tional deterioration besides that predicted by the SCI loss from the c0 and CF relations. Unfailed test sections Four test items in Table 7 had SCI values of 100 at the end of traffic testing. Table 10 shows the predicted performance of each of these sections along with the coverage level at the end of traffick- ing. Only one test section exceeded its predicted c0 value where deterioration would have been expected to start. The other three test sections stopped traffic before reaching their c0 values and, as predicted by the model, showed no deterioration. U-Tapao Airbase During the Vietnam War, three pavement features failed under B-52 traffic at U-Tapao Airbase, Thailand. It is generally very dif- ficult to assess field performance of in-service pavements because the actual number of aircraft using the feature and their actual weights are seldom known. However, since these were bomber aircraft on combat missions, departing aircraft were probably at or near their maximum weights. Also, the military operations were concentrated in a rela- tively short period of 1967-1972. These pavement features were sub- ject to predominately B-52 traffic which is such a severe aircraft when fully loaded that traffic by unloaded B-52 aircraft or other types of aircraft is insignificant. The failed U-Tapao features offer 86 Table 10 Predicted Performance of Unfailed Test Item Predicted Performance Unfailed Test Series Test Item co CF Coveras;es l. Lockbourne No. l E2.66M 252 1,024 556 F2.80 2,708 11, 253 550 2. Lockbourne No. 2 E-7 74,791 325,068 2,2204 3. Sharonville Heavy Load 71 7.142xl0 6 32.653xl0 6 9,680 87 the opportunity to check the proposed performance models against in- service pavement performance. Pavement condition surveys by Lambiotte and Chapman (1969) and Lambiotte (1972) provide the basis for this analysis. Properties drawn from these reports are shown in Table 11. The SCI values were estimated from the condition survey reports. The c0 and CF values were calculated using the performance models presented earlier in this section. About 14 percent of Hardstand Taxiway 2 (the south end) failed and was rebuilt after only 74 coverages. The remainder con- tinued to be used with the estimated SCI deteriorating from 88 to 76 over the next few years. Access Taxiway 2 failed after 1,230 cover- ages and was rebuilt. No condition information was available other than the pavement failed. Access Taxiway 1 failed after 9,820 cover- ages and was abandoned. At this point, it had an estimated SCI of 36. Figure 14 shows the performance of the three U-Tapao pavement features predicted by the c0 and CF values from Table 4. Also shown are estimates of the SCI values for Hardstand Taxiway 1 and Access Taxiway 1. The predicted performance curves reflect the relative performance of the actual pavements, i.e,. Access Taxiway 1 significantly outperformed Access Taxiway 2, which in turn outper- formed Hardstand Taxiway 1. The best traffic and condition data were available for Access Taxiway 1, and its SCI of 36 when it was replaced with an adjacent bypass taxiway agrees well with the predicted performance. Access Taxiway 2 failed sooner than would be predicted. The rapid failure of one end of Hardstand Taxiway 1 at 74 coverages is probably not repre- sentative. The fact that one end failed rapidly and the remaining 88 Table ll Failed Pavements at U-Tapao Air base Ra Subgrade Predicted Behavior k E Coverages (lb/ (lb/ (lb/ Pavement "At h . 2) 2 . 2) scrb co CF Feature (in.) ln. in. /in.) 1n. Failure" Hardstand TW l 16 580 300 39,400 76-88 538 1486 c Access TW 1 16 645 400 57,000 36 5285 19427 9820 Access TW 2 16 615 350 48,000 "Failed" 1731 6309 1230 a b c Concrete flexural strength. SCI was estimated by percentage of cracked slabs and joint spalls reported. One half of each damage type was assumed to be of low severity, and one half was assumed to be of medium severity. Five hundred feet on south end failed and was rebuilt in 1967 shortly after opening, approxi- mately 74 coverages. The remaining approximately 3,000 feet remained in use without repair, and some condition survey data were reported for 1968, 1969 and 1971 inspections. 100 ' \ h • C) ' \ C) ' 1:> • • I'll '1:> (") LEGEND ~ '(") (") \ ~ '(") m 80 'm (f) OBSERVED PERFORMANCE \I .;:::: ~ 'lfl (f) \~ I'll ~ \(f) ..... • HARDSTAND TAXIWAY 1 ...... 1:> \~ tJ ._ -,.:. • ACCESS TAXIWAY 1 ~ '.1:> ~ \~ '-,.:. -.;; ,- 1> PREDICTED PERFORMANCE \~ f\.) ,~ -<. ACCESS TAXIWAY 1 60 .~ \-'. \IV ACCESS TAXIWAY 2 u \~ ' HARDSTAND TAXIWAY ' (/) \~ ' ' \0 1> ' 0 40 \-<. ' ' \ ' ' \ ' \ \ ' \ 20 \ \ \ \ 0 100 1,000 10,000 100,000 COVERAGES Fig. 14. Predicted Performance of U-Tapao Airbase Pavements 86 percent of the feature continued to perform leads to the suspicion that moisture or subgrade conditions in this area were worse than reported or that construction problems may have resulted in low- strength concrete. Although pavement condition d~ta for the rest of the feature were reported to allow estimates of the SCI in 1968, 1969, and 1971, there are no reliable traffic data. If the 74 coverages that caused failure after "several months" are considered as typical for a third of a year, then there were about 250,500, and 1,000 cover- ages as is plotted in Figure 14. If it is considered as typical for two months, then the coverage levels would be about 500, 1,000, and 1,500. The rapid failure of the south end of Hardstand Taxiway 1 no doubt caused considerable concern, and evaluation of the structural capacity of the pavement recognized that this pavement was not capable of sustained B-52 traffic (Lambiotte and Chapman 1969). In all like- lihood traffic on this feature was reduced as much as possible, and all the constant rate of accumulation traffic estimates are erroneous. Lambiotte and Chapman (1969) note that on Hardstand Taxiway 1: "Traffic intensity, however, is far lighter than on either of the access Taxiways (1 and 2) or other primary facilities. Thus the prognosis for this pavement section is that it (deteriora- tion) will probably occur more gradually than other pavement failures experienced to date on the station." Overall, the performance models did an excellent job predict- ing the performance of Access Taxiway 1, overestimated the performance of Access Taxiway 2, and in light of the uncertainties concerning traffic levels made a reasonable estimate of the performance u£ Hard- stand Taxiway 1. The relative predicted performance of each feature was consistent with the relative actual pavement performance. 91 Summary Concrete pavement fatigue deterioration can be described by a model using the two performance factors, c0 and CF . Until traffic coverages reach c0 , there is no significant structural deterioration and the pavement SCI is 100. Between the coverage levels of c0 and CF , the pavement SCI value decreases linearly with the logarithm of coverages until an SCI value of zero is reached at CF . Conceptu- ally, c0 is the onset of deterioration, and CF is complete fail- ure. The two performance factors, c0 and CF , may be determined from the following relationships: where DF 0.5234 + 0.3920 Log C0 DF 0.2967 + 0.3881 Log CF DF design factor concrete flexural strength + layered elastic calculated stress The relations for c0 and CF are essentially layered elastic based field fatigue curves from accelerated traffic field tests. They account for fatigue damage due to applied loads and indirectly include factors such as temperature and moisture induced stresses and nonuni- form subgrade support because they are based on full-scale field tests. Actual in-service pavements will show additional deterioration due to factors not related to fatigue loading. Some of these other factors include durability problems such as D-cracking, deterioration 92 due to maintenance problems such as failed joint sealant, or environ- mental effects such as subgrade weakening due to moisture infiltration through cracked pavements .or improperly sealed joints. The c0 and CF relations are developed from full-scale field tests, and the data show appreciable scatter. However, this variabil- ity is common in fatigue testing in both the laboratory and field. The relationships presented for c0 and CF appears to be the most appropriate for the available data. They are consistent with other criteria and follow the same form as other fatigue relationships. When these relations were used with unfailed test items and the U- Tapao AB in-service pavements, they gave reasonably good agreement between actual and predicted pavement performance. The pavement performance model based on c0 and CF parameters predicts the SCI of a specific pavement system for any coverage level. This is a major departure from conventional pavement design criteria that use a specific failure condition as their basis. The model with the c0 and CF factors has no specified failure level; but if the final predicted SCI value is between 55 and 80 at the end of the design traffic, then the design will be consistent with the current CE failure criterion. 93 PART V: EFFECTIVE MODULUS FOR CRACKED SLABS When a plain concrete pavement slab cracks, its ability to transmit load through bending is reduced. Generally such a crack in a pavement is unable to transmit moment, although aggregate interlock across the crack can transmit shear. This shear transfer across the crack decreases with further application of load repetitions or open- ing of the crack. The progressive cracking and decreasing load carrying capacity of a slab must be modeled for overlay design. The performance rela- tions for concrete pavements developed in the previous section require that the supporting layers be characterized by a thickness, a·modulus of elasticity, a Poisson's ratio, and an interface condition. When a concrete base slab is overlaid, the base slab can continue to crack and deteriorate under traffic loads, and the support provided to the overlay is decreased as the base slab deteriorates. Consequently, the support provided to an overlay slab by the base pavement is a variable and not a constant. Within the limitations of the layered elastic model there are two potential ways to represent this decreasing support. The base slab thickness used in the stress calculations can be replaced with a decreased or effective thickness, or the base slab concrete modulus of elasticity can be reduced. Of these two approaches, use of a reduced effective modulus of elasticity for the cracked concrete was selected as the preferable approach for this study. Thickness is almost the only pavement parameter that can physically be measured with con- fidence. The concepts of linear elasticity and the concrete modulus 94 of elasticity used for analysis are artificial constraints placed on a real, nonlinear system to make it analyzable. Therefore, it was felt that the thickness should not be varied and that an effective modulus of elasticity was a more reasonable adjustment. Existing Models A design study for an overlay at Diego Garcia by Lyon Asso- ciates, Inc. (1982) used 200 falling weight deflectometer tests on cracked slabs to develop a correlation between the Corps of Engi- neers (CE) visual condition or C factor in Table 2 and the effective modulus of cracked slabs. This relation was expressed as where E r c E 67.8 C + 22.9 r ratio of the effective modulus of the cracked slab to the modulus of the uncracked slabs as a percent CE visual condition factor from Table 2 One of the criticisms of the CE C factor has been that it is sub- jective and poorly defined. Figure 15 shows a range of possible SCI values for the available definitions of the C factor. An approximate relation within this band is shown in Figure 15 and is described by C -0.076 + 1.073 (SCI) 95 0.8 a: 0 1- u ...J :::> 0 0 :?: ro ... ..) 103 Closely spaced cracks 100 0 * L/T/0 Cracking longitudinal/transverse/diagonal cracking. 119 L l Determining cracked concrete modulus A concrete modulus was calculated for each stage of cracking, as described earlier, by matching the falling weight deflection basin as closely as possible. Table 15 shows the results of these calculations for slab 1 at positions 100, 200, and 300 at each stage of cracking. For the calculations for slab 1, the subgrade modulus of elasticity was set equal to 10,000 lb/in. 2 for all positions. Results for the initial tests 100, 200, and 300 appear reasonable. However, once cracking starts (tests 101, 201, etc.) calculated concrete modulus values decrease rapidly, and the error in matching the basin increases dramatically. Figures 23 through 25 show the measured and calculated basins at each position and degree of cracking on slab 1. From these figures, it is apparent that layered elastic theory can do a reason- able job of matching the deflection basin of an intact slab. Once cracking begins, differences between the measured and predicted basins become more pronounced. Since the cracked slab deflection basin could not be matched acceptably by layered elastic theory, the effective modulus of con- crete was defined to be that modulus which would give the same deflec- tion under the center of the loaded plate using layered elastic theory as was measured in the falling weight test. The representative posi- tions, initial concrete modulus, and subgrade modulus for uncracked concrete slabs were selected earlier. For each test at subsequent levels of cracking, the measured field center deflection from the falling weight test was matched by varying the concrete modulus and holding the subgrade modulus the same as for the initial uncracked condition. The BISAR layered elastic computer code was used for all 120 Table 15 Predicted Concrete Modulus from Slab 1 by Matching Deflection Basins Predicted Position Cone. Modulus (Esi) a Absolute Error b Arithmetic Error c a b c d 100 2,266,000 3. 1 101 545,000 11.2 102 50,000 31.4 103 50,500 30.3 104 10,200 35.2 200 1,870,000 5.5 201 467,000 10.7 202 153,000 22.1 203 312,000 11. 7 204 10,000 25.9 300 1,504,000 2.0 301 783,000 25.0 302 500,000 17.3 303 215,000 24 .·7 304Rd 20,136 29.5 Subgrade modulus for all runs set at E = 10,000 psi. Arithmetic Error = sum of the percent error. -2.6 9.9 31.4 30.0 35.2 -4.3 10.7 22.1 11.6 18.2 2.0 -5.4 11.3 24.3 29.5 Absolute error = sum of the absolute values of percent error. Percent error= (measured deflection- calculated deflection)/ (measured deflection) Retested next day, original test overranged sensors for lowest load. 121 z 0 ,.. u w •.J.. w 0 20 40 60 20 40 60 p t 0 I I I I I I I I DISTANCE FROM CENTER OF LOADING PLATE. IN. 12 y ..... I I I 24 36 48 CRACK CRACK o------ . ...... 4 ...... • 0 4 60 TEST 100 P ~ 22.437 LB e MEASURED 0 PREDICTED TEST 101 P ~ 22.373 LB MEASURED 101 PREDICTED 101 7~ MEASURED 101.5 p 101.5 = 22,294 TEST 102 p102 13.125 LB p102.5 ~ 13.538 TEST 103 P103 = 13.093 LB p 103.5 = 13.840 TEST 104 P10d 7.850 LB p1045. 7.611 Fig. 23. Deflection Basins for Slab l, Position 100 122 z '? 0 X z" 0 i= u UJ __J u.. w 0 20 40 60 20 40 60 20 40 DISTANCE FROM CENTER OF LOADING PLATE, IN. 12 24 36 48 60 72 ,., .,.., .;::r---- TEST 200 P = 23.470 LB • MEASURED 0 CALCULATED TEST 201 P = 22,039 LS ...o-u-_:-:-=-=-.:....--o....._-_-_--_- _ ... ~-<::>------ ...... 60 . CJ'.,. .. ., .... "'"' TEST 202 P = 21.610 LB 20 40 TEST 203 60 P "'21 ,356 L8 20 40 TEST 204 60 P ": 21.595 LS Fig. 24. Deflection Basins for Slab 1, Position 200 123 p t 0 20 40 60 20 40 60 z '7 20 0 X 40 z· 0 f= 60 u UJ ..J u. w 0 20 40 60 20 40 so 80 100 Fig. 25. l DISTANCE FROM CENTER OF LANDING PLATE, IN. 12 24 36 48 6C TEST 300 P = 21.992 LB e MEASURED 72 0 CALCULATED TEST 301 P = 22.055 LS TEST 302 P = 21.881 Lo TEST 303 P = 21 .8~9 LS NEXT DAY RET!:ST PJ04R 8 1:0 LS • MEASURED 0 C"-LCUL"-TED Deflection Basins for Slab 1, Position JOO 124 calculations. Table 16 summarizes the calculations of effective con- crete modulus for each level of cracking of each slab. Cracked Slab Model Figure 26 shows the data in Table 16 plotted with the original estimated relationships of the E-ratio and SCI from Figure 18. The best fit second order polynomial least squares regression for these data is described by the equation: ? E-ratio 0.0198 + 0.0064 (SCI) + (0.00575 X SCI)~ n 24 2 0.95 r Std. error of regression 0.083 At the SCI value of 100, the predicted E-ratio is 0.99. The coeffici- ents of the above equation were adjusted slightly so that at the SCI of 100, the predicted E-ratio is 1.00. The form of this final recom- mended equation is plotted in Figure 26 as E-ratio ? 0.02 + 0.0064 (SCI) + (0.00584 x SCI)- This equation appears to be a reasonable relationship. It is in agreement with trends suggested by existing relationships in Fig- ure 26. It also appears to do a reasonable job of agreeing with the data developed in the WES slab tests. At the SCI value of zero the predicted E-ratio is 0.02. For a common concrete modulus of 125 Table 16 Effective Concrete Modulus Using Center Deflections Slab Test Position Concrete Modulus (lb/in. 2) E-Ratio a SCI 1 300 1,620,000 b 1.000 100 301 1,180,000 0.728 80 302 985,000 0.608 58 303 258,000 0.159 23 304 24,250 0.015 0 2 100A 2,758,000 b 1.000 100 100 1,950,000 o .. 707 80 102 1,724,000 0.625 80 103 466,000 0.169 39 104 306,000 0.111 ..,~ .::...) 3 100 5,862,000 b 1.000 100 101 2,650,000 0.452 39 102 1,110,000 0.189 23 300 5,884,000 b 1.000 100 4 301 4,350,000 0.739 58 302 1,210,000 0.206 ...,~ .:...) 5 100 3,959,000 b 1.000 100 101 950,000 0.240 39 102 496,000 0.125 23 103 135 '000 0.034 0 6 100B 4,632,000b 1.000 100 101 2,000,000 0.432 55 102 995,000 0.215 23 103 313,000 0.068 0 a E-Ratio = effective E of concrete slab/initial E of concrete slab. b Taken from Table 13. 126 1.0 EXISTING RELATIONS SHADED AREA IS SUGGESTED AASHTO RELATION ---- DIEGO GARCIA 0.8 RELATION --- REL<\TION BASED ... OrJ NOMINAL FRAGMENT SIZE 1- u --' <1 • SLAB 4 N a: 0 u SLAB 5 '-.J w 0 • SLAB 6 1- 0.4 -' (.) z w (.) w u.. u.. w 1- z 0 ...., 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 40 SAWAN AND DARTER (1979) PERCENT MAX EDGE STRESS (f::.u) (6u)2 99.oo- 2.21 "'EQ - 43.so 62 LEGEND 6u- DEFLECTION UNLOADED SIDE OF JOINT 62- DEFLECTION LOADED SIDE OF JOINT 0 POINTS FROM CHOU 11983) so 60 70 80 PERCENT MAXIMUM EDGE STRESS 0 90 100 Fig. 27. Relation Between Joint Efficiency and Edge Stress 131 differences of up to approximately 8 percent in the estimate of per- cent maximum edge stress for a given joint efficiency. Table 17 shows the results of the analyses of the deflection and strain data reported by Grau (1979), Ahlvin et al. (1971) and Ohio River Division Laboratory (1946, 1950, and 1959b). Doweled joints and contraction joints with aggregate interlock achieved high mean values of load transfer that exceeded the common 25 percent assumption while the keyed joint mean load transfer barely met this assumption. The "free" joint that was used at the Lockbourne tests consisted of a piece of redwood board the full depth of the slab which as can be seen provided highly variable and low levels of load transfer. This joint is not ·a standard joint, and deterioration in test items that used this joint usually started around these joints. For this reason the earlier analyses did not include test item slabs with this joint. A joint, particularly if overloaded, will deteriorate with increasing traffic repetitions. Figure 28 shows that the initially high load transfer of 45.2 percent of a keyed joint deteriorated under C-5A traffic to levels of 15.4 and 11.1 percent. Reductions in load transfer with traffic repetitions have also been reported for other types of joints (Barenberg and Smith 1979). This loss of load transfer with traffic is of particular impor- tance for overlay analysis. The base pavement is often being overlaid because of structural damage from past traffic. Consequently, an integral part of any overlay design must be the assessment of the existing load transfer at the joints in the base pavement. If these joints are not achieving at least the 25 percent load transfer commonly assumed for standa_rd joints, then adjustments to the proposed 132 Table 17 Load Transfer for Different Joint Types Number of Load Transfer Coefficient of Type of Joint Data Points Range Mean Variation (%) Doweled Construction Joint 195 0.0-50.0 30.6 38.0 Doweled Expansion Joint 15 15.4-42.6 30.5 24.4 Contraction Joint with 46 15.6-50.0 37.2 19.2 Aggregate Interlock Keyed Joint 61 5.6-49.0 25.4 41.4 Leekbourne "Free" Joint 8 5.8-24.5 15.5 40.9 133 ....__ 50 40 ... 30 a: w u_ U) 2 <{ a: .... a <{ a -' 20 10 0 0 • _e_ ...._ _LT~ 45.2% • n; 5 • • • • • • • LT; 15.4% e # e ______ --&; __ _ n; 14 • 1000 COVERAGES OF C·SA THAFFIC • LT= 11.4% ¥ : • I e n=20 -.-·-- -~ • 2000 Fig. 28. Deterioration of Load Transfer with Traffic for a Keyed Construction Joint (Hased on Data Reported by Ahlvin et al. (1971)) design method must be made. These adjustments can be made by develop- ing a factor to increase the stresses calculated by the layered elas- tic model if substandard load transfer is found in the joints of the base pavement. Modifications for Layered Elastic Theory Parker et al. (1979) observed that the relation between stresses for rigid pavement test sections calculated using the Westergaard edge loaded model and the layered elastic model was approximately linear. To obtain additional information on the relation between Westergaard and layered elastic stresses, both stresses were calculated for an additional 60 cases to supplement the 60 test sections analyzed by Parker et al (1979). These additional cases included F-4, B-707, B-727, B-747, and C-141 aircraft with modulus of subgrade reactions from 50 to 400 lb/in. 2/in. and thicknesses of 6 to 40 in. These cal- culations along with the Parker et al. (1979) stress calculations are tabulated in Appendix C. Several different least square regression relations were tried for these 120 total cases. As can be seen in Figure 29, a simple power relationship did better than the linear relationship suggested by Parker et al. (1979). The scatter of the data is larger at high levels of stress. However, in the range of stresses encountered in normal design the scatter is much less. This power relationship can also be considered as 135 1600 • 1400 ~ "' z 1200 ~ m _J vi U) 1000 w a: f- (/) ..... u w i= a-- (/) < 800 _J w 0 w 600 a: w >- <{ ' • _J 400 • 200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 WESTERGAARD STRESS, LB/IN 2 l'ig. 29. Helat.ion Between Westergaard and Layered Elastic Calculated Stresses where 0.64(S o ) 0 · 972 w crLE stress from layered elastic analytical model cr stress from Westergaard edge loaded analytical model w B the proportion of the Westergaard stress used in design to account for load transfer, i.e., 1.0- a a = load transfer to adjacent slab y equivalent proportion of layered elastic stress to account for load transfer in the Westergaard stress It is apparent that y is simply B raised to the 0.972 power. All the models and relationships developed for use with the proposed design procedures are based on joints meeting the common 25 percent load transfer assumption. Normalizing the relation between Y and S for the standard 25 percent load transfer results in a multiplier, X , ior the layered elastic stress as shown in Figure 30. The equation for the multiplier, X , is where a = load transfer X (1-a) 0. 972 0.7561 This multiplier accounts for load transfer different from that used to develop the models and relations in the proposed design procedure. The average joint load transfer of a base pavement can be found using Figure 27 from the ratio of the deflection on the unloaded and loaded side of a joint. If this load transfer meets or exceeds 137 a: w ..J a. f: ..J :J :::!: (/) (/) 1.4 1.2 ~ 1.0 f- en u f: (/) ..:: ..J w 0 w ~ 0.8 >- ..:: ..J x· 0.6 0 10 ( 1 _ ex ) 0.972 X= 0.7561 20 30 ex, JOINT LOAD TRANSFER(%) 40 Fig. 30. Multiplier for Layered Elastic Stresses to Account for Load Transfer 138 50 25 percent, then no adjustment in stresses should be made. If the load transfer is lower than this value, the layered elastic calculated stresses in the base slab should be increased by multiplying them by the appropriate X from Figure 30. 139 DESIGN OF RIGID OVERLAYS FOR AIRFIELD PAVEMENTS by Raymond Sydney ~pllings, Jr. Dissertation Submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment Advisory of the requirements for the degree of Committee: Professor M. Professor c. Professor M. Professor D. Professor D. Doctor of Philosophy Witczak Schwartz Aggour Vanney Barker 1987 vo /. 2- c, I -----=~----~~ .. PART VII: PROPOSED DESIGN PROCEDURE Methodology The improved design concept outlined in Part III required models to describe the deterioration of the pavement, to describe cracking in the base slab, and to account for substandard load transfer. These models were developed in Parts IV through VI, and a proposed design procedure using these models with the design concept from Part III will be developed in this part. This proposed design procedure uses the layered elastic analytical model to calculate load induced tensile stress in the base pavement and overlay. These stresses are used to predict deteriqration of the base and overlay in terms of a Structural Condition Index (SCI) varying from 0 to 100. Effects of fatigue dam- age to the base pavement prior to placing the overlay, progressive cracking in the base pavement, and substandard load transfer at the pavement joints are included in the analysis. The steps in the pro- posed design procedure are shown in Figure 31 and will be discussed ~nd illustrated with a design example in the following sections. Material properties Each layer in the pavement must be described by a modulus of elasticity and a Poisson's ratio. A very effective method of esti- mating the modulus of elasticity for the existing base pavement and underlying layers is to calculate the modulus values from the deflec- tion basin of a falling weight as was done for the six slabs in Part V and as is described by Bush (1980). The modulus value for the overlay concrete could be determined in the laboratory as part of the mixture 140 DETERMINE BASE PAVEMENT AND OVERLAY MATERIAL PROPERTIES ~ DETERMINE BASE PAVEMENT FATIGUE AND STRUCTURAL CONDITIONS t SELECT TRIAL OVERLAY THICKNESS + CALCULATE C0 AND CF FOR BASE PAVEMENT ~ DIVIDE TRAFFIC INTO INTERVALS FOR ANALYSIS l CALCULATE OVERLAY C0 AND CF FOR EACH TRAFFIC INTERVAL + DETERMINE COMPOSITE OVERLAY DETERIORATION ~ NO DOES PERFORMANCE MEET DESIGN REQUIREMENTS + YES l END _I Fig. 31. Steps in the Proposed Design Procedure 141 proportioning studies; or it could be conservatively estimated as 4,000,000 lb/in. 2 as is currently done for the Corps of Engineers (CE) and Federal Aviation Administration (FAA) pavement design curves. Another option would be to estimate it from typical laboratory or non- destructive test values from recently completed local projects that used concrete mixture proportions similar to that anticipated for the overlay. Poisson's ratio is seldom measured for pavement analysis. Instead it is commonly estimated to be 0.15 to 0.20 for concrete, 0.30 for granular materials, and 0.40 to 0.50 for cohesive soil materials. If falling weight deflectometer or similar nondestructive tests are not used to determine modulus values, laboratory tests can be run on samples taken from the base pavement and underlying layers to deter- mine modulus values. This is relatively simple for the concrete in the base pavement or for samples of stabilized material. On the other hand, laboratory resilient modulus tests on undisturbed or representa- tive recompacted soil samples are expensive and often difficult to interpret properly. Modulus values for soils are often estimated from correlations with existing tests. For example, the California Bearing Ratio (CBR) is often used to estimate modulus values if no more detailed informa~ tion is available. An approximate relation suggested by Dorman and Klomp (1964) is E 1500 x CBR 142 where E modulus of elasticity in lb/in. 2 CBR the California Bearing Ratio in percent Parker et al. (1979) have suggested the following relationship Log E 1.415 + 1.284 log k where E =modulus of elasticity in lb/in. 2 k modulus of subgrade reaction in lb/in. 2/in. If no other data are available, the modulus values could be estimated from the soil classification, but this is obviously the least accurate approach. Table 18 shows some typical modulus of elasticity values. The values vary widely and reflect variations due to temperature, state of stress, load frequency and duration, age and composition of materials, and strain level. Selection of modulus values for design is a critical step. More detailed information on determining modulus values for paving materials to be used with layered elastic analysis can be found in Parker et al. (1979), Barker and Brabston (1975), and Green (1978). A problem arises if the modulus of subgrade reaction, k , is used to estimate the elastic modulus values for a granular base over a subgrade. A 30-in. diam plate is used to determine a composite k on the surface of the base that, unless the base is exceptionally thick, includes the influence of both the base and subgrade. This is the k that would be used in conventional design. For the proposed design 143 ' 1 Table 18 Typical Modulus of Elasticity Values Material Typical ranges (lb/in. 2) Portland Cement Concrete 3.5 - 6.0 x 106 Asphalt Concrete 100,000 - 1,000,000 (highly temperature dependent) Highly Plastic Clay or Silt (CH, MH)* 2,000 - 8,000 Clays and Silts of low plasticity, 5,000 - 20,000 Silty Clays (CL, ML)* Sands, Sandy Clays, Clayey Sands 15,000 - 40,000 (SP, SW, SM, SC)* Natural Gravels (GP, GW, GM, GC)* 15,000 - 50,000 Crushed Well-Graded Stone (GM, GW)* 30,000 - 100,000 Stabilized Base Course Materials 200,000 - 1,000,000 * Unified Soil Classification Symbols 144 procedure it would be appropriate to conduct plate load tests (or CBR tests) on the subgrade as well as on the surface of the base course to get better estimates of modulus values. If a relatively thin granular base on the order of 4-6 in. thick rests on a clay subgrade, the com- posite k may give a reasonable estimate of the modulus of elastic- ity. Such thin layers in a pavement may not actually act indepen- dently and are ~ery difficult to compact if they are on a resilient subgrade. Consequently, these thin bases may not obtain very high modulus values. If, on the other hand, the base is relatively thick, any modulus value estimated from the composite k will not adequately reflect the lower modulus of the subgrade. Each structural layer in_ the pavement must have its modulus value evaluated. Tests with the falling weight deflectometer or similar device are the best method of characterizing the pavement properties under these conditions. Flexural strength has a major impact on concrete pavement per- formance. Consequently, the best possible estimate of flexural strength is needed. The flexural strength of the overlay concrete should be determined as part of the mixture proportioning studies. The flexural strength of the base pavement may be determined from historical data, flexural beams cut from the base pavement, or approx- imate correlations between flexural strength and tests run on cores taken from the base pavement. Flexural strength is often estimated by the relation ff K If' 1 c 145 where f' c 2 flexural strength in lb/in. a constant varying from 8 to 10 compressive strength in lb/in. 2 Also Hammitt (1974) has suggested the relationships where f' c f + 2123 ff c = 10.02 n 189 tests 2 o. 77 r ff = 210 + 1.017 n 199 tests 2 0.73 r compressive strength, lb/in. 2 2 flexural strength, lb/in. f st splitting tensile strength, lb/in. 2 There is no unique correlation between flexural strength and compressive or splitting tensile strengths. The actual relationship varies depend- ing on the aggregates and mixture proportions used in the concrete. Even though cores are far easier to obtain from an existing pavement than are beams, the estimate of flexural strength from compressive or splitting tensile tests on the cores may not be very reliable. The interface conditions between layers must also be described. In general all pavement interfaces except those with concrete have been treated as fully bonded in most layered elastic analyses of pavements. 146 The interface between concrete and other materials is usually treated as frictionless. Obviously, the interface for a fully bonded overlay with special surface preparation and bonding grouts should be treated as fully bonded, whereas the unbonded overlay interface with a dis- tinct bond breaking course would be more appropriately treated as frictionless. The partially bonded overlay is more of a problem, and an appropriate friction factor will be developed in Part VIII from the CE overlay test section data. The condition of the base pavement at the time of overlay often determines the bonding condition used for the overlay. Any crack or joint in the base pavement will reflect through the overlay soon after placement unless there is a positive bond breaker between the overlay and base pavements. Therefore, joints in the overlay are matched with the base pavement joints for fully bonded or partially bonded over- lays. Also, their use is usually limited to overlay of pavements that are in sound structural condition. Fully bonded overlays are used only on uncracked pavements or pavements with cracked slabs that are replaced prior to placement of the overlay. Partially bonded overlays are sometimes placed on pavements with some minor load related crack- ing. The pavement SCI should be 70 or better if a partially bonded overlay is to be used. However, slabs showing multiple cracks or spalling or raveling cracks should be replaced prior to placement of the overlay. The bond breaking course used with unhanded overlays is gener- ally thin and will not normally need to be modeled in the layered elastic analytical model. Typical examples of bond breakers include polyethylene, heavy applications of curing compound, building paper, 147 applications of sprayed bitumen and sand or gravel, or thin asphalt concrete layers. Sometimes thicker bond breaker layers of asphalt concrete, roller compacted concrete, or econocrete may be used as leveling courses or to make major grade changes. If these layers are one inch or more in thickness, it will probably be necessary to include them in the layered elastic model. Base pavement conditions Previous traffic on the base pavement has consumed some of its fatigue capacity. If it has begun to structurally deteriorate from this traffic, an SCI can be determined from the PCI procedures in Fed- eral Aviation Administration (1980), Department of the Navy (1985), or Shahin, Darter, and Kahn (1976) using the specific distress types listed in Table 5. The ratio between the effective modulus of elas- ticity and the initial undamaged modulus of elasticity can be deter- mined for any SCI from the relationship developed in Part V: E 0.02 + 0.064 x SCI + (0.00584 x SCI) 2 r Since the initial concrete modulus was determined in the previ- ous step, the effective concrete modulus to use in the layered elastic model can be determined. The initial modulus of elasticity should be determined from intact concrete. For example, falling weight deflect- ometer tests should be run at the center of intact slabs. Certain durability related distress problems such as severe D-cracking or crazing due to alkali aggregate reaction affect the concrete modulus of elasticity, and this may need to be included in the analysis. If the falling weight is used to determine the initial modulus of the 148 concrete from an intact slab that is undergoing alkali aggregate reac- tion, the alkali aggregate reaction damage is already included in the initial modulus estimate. No adjustment would then be needed. How- ever, if the initial modulus was determined from historical construc- tion records or estimated, then it would be appropriate to include the PCI deducts for crazing due to alkali aggregate reaction in calculating the SCI. However, minor crazing due to plastic shrinkage cracking from improper curing has little or no effect on the concrete modulus and should not be considered in any adjustment to modulus values. Each case needs to analyzed individually. If the pavement to be overlaid has an SCI of 100, the amount and type of past traffic on the base pavement must be determined. Records of this type are often poor, but the best possible estimate of this must be made so that fatigue damage to the base pavement can be cal- culated later. A mix of aircraft types can be converted into equiva- lent passes of a single selected type of aircraft using one of the published methods (Federal Aviation Administration 1978, Department of the Army 1979). The effective load transfer at the joints of the base pavement needs to be determined. This may be done by determining the ratio of the deflections on the loaded to the unloaded side of a joint and using the relationship in Figure 27 to estimate load transfer. If the effective load transfer is below 25 percent, then a stress multiplier from Figure 30 needs to be selected. This multiplier will be used in a later step to adjust the calculated stresses in the base. Presum- ably, no adjustment will normally be needed for the overlay since con- ventional joint construction would be used. Load transfer is a 149 variable rather than a constant, and it also often decreases with increasing traffic repetition. Consequently, consistent substandard load transfer measurement in the base pavement might conservatively be treated as no load transfer to recognize the potential for future deterioration. Trial thickness This design method is an iterative process. A trial thickness of overlay is selected, and its condition in terms of SCI at the end of the design traffic is predicted. If this SCI is unacceptably low, then a thicker overlay is tried. If, on the other hand, the initial trial overlay thickness is capable of supporting much more traffic than necessary, a thinner overlay can be tried. The models used in this proposed design procedure only represent the deterioration of a concrete pavement due to cyclic fatigue damage caused by repetitive loading. Other causes of pavement deterioration such as pumping or D-cracking must be guarded against by other means. Base pavement performance The base pavement performance factors, c0 and CF , before overlay must be calculated for the traffic load applied before the overlay is placed. Next, these factors must be recalculated for the base after the overlay is placed using the traffic load to be applied after overlay. These factors are determined from the following equations: DF 0.5234 + 0.3920 log c0 DF = 0.2967 + 0.3881 log CF 150 where DF = design factor = flexural strength ~ calculated stress c0 .= coverage level at which SCI begins to decrease from 100 C = coverage level at which SCI becomes 0 F If the base pavement has not begun to deteriorate before over- lay, the fatigue damage, d , from this previous traffic can be cal- culated as where d c d = fatigue damage coverage of traffic applied before overlay base performance factor, c0 , calculated for traffic load applied before overlay The equivalent amount of traffic that this represents after overlay is determined by where the equivalent amount of traffic after overlay that would do the same fatigue damage to the base pavement as was done by the traffic before the overlay was placed base performance factor, c0 , after overlay calculated using trial overlay thickness and the overlay traffic load 151 If the joint load transfer has been found to be substandard, the appropriate stress multiplier, X, selected earlier should be used to increase the calculated stresses used to determine the base c0 and CF factors. Traffic intervals The design traffic to be applied to the overlay is divided into intervals so that the stresses from the varying base slab support dur- ing each interval can be determined. The first interval of traffic is up to the base c0 value calculated after overlay, and the last interval is all traffic past CF • If some equivalent traffic has been applied before overlay, these traffic coverages must be sub- tracted from c0 and CF since this damage has already occurred. During the initial traffic interval the full uncracked concrete modulus is used for the base slab to calculate the stresses in the overlay. During the last interval the SCI is 0 and the appropriate reduced base concrete modulus is used to calculate the stresses in the overlay. Between c0 and CF the traffic is divided into intermediate intervals for analysis. This study used four intermediate intervals and used the appropriate reduced modulus for SCI values of 80, 60, 40, and 20 for the intervals. The intervals of traffic were from co to the coverage level at which the SCI was 70, from this last point to the coverage level at which the SCI was 50, from this la'st point to the coverage level at which the SCI was 30, and from this last point to CF If there ha~ been fatigue damage, these traffic intervals have to be reduced by the equivalent traffic. If the base pavement has 152 begun to deteriorate before the overlay is placed, the base SCI value at the time of overlay determines the initial support conditions. If applied traffic before the overlay is placed exceeds the C 0 b value (possibly due to limits of the model, poor traffic estimates, or inaccurate material or load parameters), the equivalent traffic can be set equal to c0 after overlay. Doing so is equivalent to assuming that the base pavement will begin to deteriorate with the first cover- age of traffic on the overlay. Overlay performance for each traffic interval During each interval of traffic the damage suffered by the over- lay during that interval is assumed to be controlled by the perfor- mance factors, c0 and CF , calculated for the overlay stresses for that interval. Each interval of traffic results in a decrease in the modulus of the concrete in the base pavement. This causes higher ten- sile stresses in the overlay with a corresponding decrease in the overlay performance factors, c0 and CF . Once these overlay per- formance factors are calculated for the stresses in each interval of traffic, the fatigue damage during an interval of traffic can be determined by where d. ~ c. ~ c . 0~ d. ~ c. ~ c . 0~ overlay fatigue damage during the ith interval of traffic coverages of traffic during the ith interval the overlay c0 performance factor calculated using the appropriate base pavement modulus of elasticity for the ith traffic interval 153 Composite overlay deterioration The damage suffered by the overlay during each interval of traf- fie must be combined to determine a composite overlay deterioration. The first step is to determine the coverage level at which overlay deterioration begins. This coverage level is essentially the overlay composite, c0 . During the first interval of traffic (i.e., the traffic up to the point where the base slab begins to deteriorate and support to the overlay decreases), the fatigue damage, d. , during l the first interval can be calculated as noted before. Because of this fatigue damage the c0 for the next interval needs to be adjusted as follows: where C* o,i+l d. 1 c . l o,1+ C* o,i+l (l - d.) c l o,i+l c0 factor for interval i+l adjusted for fatigue damage from the preceding interval. fatigue damage from the preceding traffic interval c0 factor calculated from the stress for traffic interval i+l. This process is continued until traffic applied during an inter- val exceeds the adjusted c0 value. When traffic reaches this adjusted c0 value the overlay is assumed to begin to deteriorate. The loss in SCI over the remaining traffic interval is assumed to be the same as the loss in SCI for the same amount of traffic past c0 on the original unadjusted c0 - CF line of the traffic interval. The loss in SCI for the next interval of traffic will be the same as 154 the loss along that interval's c0 - CF line. This is continued until the SCI is zero. The discussion up to this point assumed that the base cracked under the overlay traffic. Under some conditions of load, overlay geometry, and material properties the base will not crack before the overlay does. For this case, the composite overlay performance is simply the unadjusted c0 - CF relationship for the first interval of traffic. Design requirements The composite overlay deterioration curve tells how much struc- tural deterioration is expected for a given overlay thickness at any traffic level. If the rate of deterioration results in an unaccept- able SCI at the end of the design traffic, then a thicker overlay needs to be tried. If it has more capacity than needed, a thinner overlay can be tried. Example Calculations The overlay design procedure will be illustrated by analyzing overlay test item A 2.7-60 from the Lockbourne No. l tests. Material properties Figure 32 shows the model of item A 2.7-60. Material properties were reported by the Ohio River Division Laboratories original test report of construction (1946) and are also summarized by Parker et al. (1979). Concrete modulus of elasticity was determined in the labora- tory from field cast cylinders. Concrete flexural strength was deter- mined from field cast beams, and Poisson's ratio was estimated as 155 P = 20 KIP WHEEL, l CONTACT AREA • 387 /N.2 'i~-~-~Q:/~~-'!-1 ~BASE SLAB :;t?a.<;>¢9tJP ··,# E = 3.8 X 106 LB/IN. 2 j;;-.oo.-oo. ·:·.«p -.;~a· ... :.;;PO-o~>' V = 0 15 ·;W"· .·.ao·. ~ • ~---:-:..:._~.:___: R = 740 LB!IN. 2 -----------~ /CLAY SUBGRADE -~~~~=-~/ E = 16,000 LB/1N.2 v = 0.4 ~===~==~ /RIGID BOUNDARY _-_-_-_--_-: f E = 1 x 106 LB/IN.2 ~~ V=0.5 BEFORE OVERLAY ------- :._-_-_-_-_:-_-_ v = 0.4 ~=-=-=-==-=-=~/RIGID BOUNDARY ~~ E = 1 x 10~ LB//N.2 v=0.5 AFTER OVERLAY Fig. 32. Model of Lockbourne No. 1, Item A 2.7-60 0.15. The modulus of elasticity of the clay subgrade was estimated using the relation developed by Parker et al. (1979) from the modulus of subgrade reaction. The modulus of subgrade reaction was determined from field plate load tests. The Poisson's ratio for the clay sub- grade was estimated. The inclusion of the rigid boundary at a depth of 20 ft follows the recommendation of Parker et al. (1979). The bond between the overlay and base pavement was treated as unbonded. The 3/4-in.-thick sand asphalt bond breaker was not modeled directly. If the bond breaker was much thicker, it would probably be necessary to include the bond breaker in the model. This bond breaker must be stable under loading. The cutback asphalt actually used in the sand asphalt bond breaker did not cure and pumped up through cracks and joints. This unstable material led to premature failure of the overlay, illustrating that pavement failure can arise from factors other than the fatigue damage considered in this study. Base pavement condition Prior to the overlay placement the base slab was subjected to 520 coverages of a 20,000-lb wheel load. At the end of this traffic the base pavement had an SCI of 100. All joints for this example meet the basic 25 percent load transfer. Trial thickness The trial thickness for this example calculation is the actual 7-in. thickness of the overlay. Base pavement performance A 20,000-lb wheel trafficked the base pavement before the. over- lay, and a 60,000-lb wheel trafficked the overlay afterwards. The calculated stresses under these loads and the equivalent c0 and CF 157 factors are shown in Table 19. The fatigue damage from the 20,000-lb wheel load traffic slab can be calculated by c d co (20 kip) 520 2117 The equivalent traffic is d C0(60 kip) 0, 2456 X 2779 0.2456 682 coverages The 520 coverages of 20,000-lb wheel before the overlay caused the same damage as 682 coverages of 60,000-lb wheel would cause to the base pavement after the overlay was in place. Traffic intervals Figure 33 illustrates the effect of the traffic prior to the overlay placement and the decrease in the support provided by the base slab after it begins to deteriorate. The traffic on the overlay is divided into six intervals as shown in Figure 34. During each inter- val of traffic on the overlay the SCI of the base is assumed to be con- stant, and the modulus of elasticity of the base during the interval is assumed to be equal to the value corresponding to a constant SCI value. The SCI values for this analysis are 100 for interval 0, 80 for interval 1, 60 for interval 2, 40 for interval 3, 20 for interval 4, and 0 for interval 5. The dividing point between intervals 1, 2, 3, and 4 are points a, b, and c in Figure 34 which correspond to the cov- erage level where the base SCI is 70, 50, and 30. Notice that the equivalent traffic has already been applied to the base. 158 Table 19 Base Slab Stresses and Performance Factors 1. Calculated Stresses for Base Slab 2. (1) ( 2) 2 Before overlay (20-kip wheel) 405 lb/in. After overlay (60-kip wheel) 395 lb/in. 2 Performance Factors c0 and CF for Base Slab (1) co before overlay (20-kip wheel) 2,117 (2) co after overlay (60-kip wheel) 2, 779 (3) CF before overlay (20-kip wheel) 8,779 (4) CF after overlay (60-kip wheel) 11' 552 159 ,_. Q"\ 0 I i I I. I I _J 10,870 0 0.020 77,554 584 97 388 163 This analysis is continued for each interval of traffic until the point where cracking or onset of deterioration, c0 , of the over- lay is reached. Table 21 shows these calculations for test item A 2.7-60. At the end of the interval of traffic number 1 (3,579 coverages) in Table 21, the damage factor, d. , shows that ~ 37.3 percent of the overlay's capacity before the onset of deterio- ration has been used. The adjusted c0 value for the next interval is 1,400 coverages and the applied traffic is 1,405 coverages, so the overlay cracks after 1,400 coverages in this interval (4,979 total coverages). From this point to the end of the interval (4,984 cover- ages) the deterioration or loss in SCI will be the same as on the unadjusted c0 - CF line for the interval. For this specific example, there are only 5 more coverages in the interval, thus resulting in the loss of only a fraction of the point in the SCI. This can be ignored. During all following intervals the deterioration will be the same as the interval's original c0 - CF line during their respective traffic levels until SCI value of zero is reached. This is illustrated in Figure 35. Once cracking is predicted to start in the overlay, the loss of SCI in this example over the 1,868 cover- ages of interval 3 will be the same as the loss of SCI for the first 1,868 coverages past c0 for interval 3. This brings the SCI of the overlay to 27 at the end of interval 3 or at 6,852 total coverages. Between 6,852 and 10,870 coverages the loss of SCI will be determined from the c0 - CF relation for interval 4. As shown in Figure 35, 164 Table 21 ExamEle Overlay Damage Calculation Test Section A 2.7-60 Overlay Applied Overlay Damage Adjusted Traffic c. COi f. co, Interval Traffic ~ ~ i+l 0 0-2097 2,097 ll '254 0. 186 ll '254 1 2,097-3,579 1,482 4,881 0.373 3,973 2 3,579-4,984 1,405 2,233 Overlay Cracks 1,400 3 4,984-6,852 1,868 1,030 4 6,852-10,870 4,018 452 5 10870+ 97 165 100 80 60 u ...... en 0' 0' 40 20 0 100 1868 1868 COVERAGES cov \ \ \ \ \ \ \" \o, '" ,-.- \~ \;, \-j. \0 ,::_ \z ,~ \~ ):> r 0 < ITI :JJ r- )> -<. cov COVERAGES 0 ITI -1 "' :JJ 0 :JJ )> -1 0 < Fig. 35. Construction of the Deterioration of the Overlay for Item A 2. 7-.60 .I I 100,000 • -·· ··~- • *---:~ .. ---- -~- ·-- _,__...-- the SCI goes from 27 to zero after 582 coverages in interval 4. Therefore, the composite overlay will reach the SCI value of 0 after another 582 coverages or 7,427 coverages total. Design requirements The composite overlay deterioration is shown in Figure 36. The overlay begins to structurally deteriorate after 4,979 coverages and reaches an SCI value of zero after 7,427 coverages. If the overlay must carry more traffic than this, another thicker trial overlay thickness must be selected and the procedure must be repeated. Figure 36 also shows the deterioration that would be predicted if cracking in the base slab was neglected. This is simply the behav- ior described by the c0 and CF performance factors for interval 0 in Table 21. Including the effect of progressive deterioration of the base slab greatly reduces the predicted performance of the overlay. Summary The proposed overlay design procedure is analytically more powerful than the existing empirical design procedures. It is able to include the effects of varying material properties in the overlay struc- ture; it accounts for past traffic and the condition of the base pave- ment at the time of overlay; it includes the effects of progressive cracking in the base under overlay traffic; and it predicts deteriora- tion of the pavement in terms of SCI. The proposed overlay design pro- cedure will be used in the following sections to analyze the CE 167 '.I 0 C/) 100 r----- H !'" ...... li rn co V> _. U) II !\-) 0 Co ,~;>. a 40 - '-1 a a a TEST ITEM 27 LEGEND 20 I- • PREDICTED OVERLAY DETERIORATION /::; BASE CRACKS E5 = 4.700 .. BASE CRACKS E5 = 12,800 .j_ 0 I I I I _L I I ilL I 1 tJ 10 100 1,000 10,000 COVERAGES Fig. 41. Performance of Item 27 () "' 100 80 ,.... 60 1- 40 1- ITEM 28 LEGEND 20 1- e PREDICTED OVERLAY DETERIORATION ~ BASE CRACKS E5 ~ 3,800 A BASE CRACKS E5 ~ 12,800 0 <::: rn :JJ r- ):. -< rn "' II w b:l 0 0 -r TEST 0 ITEM <::: FAILED rn :l:J r-):. _._ -< rn "' i\j b:l 0 a 0 L-----~IL_ __ L_I_J __ L_~IL~I~JL_ __ ~~----IL--L-JI-J-a~~IJ_J ______ L_, __ ~,--~,--L-'L-'~'~1 10 100 1,000 10,000 COVERAGES Fig. 42. Performance of Item 28 u Cll 100 80 - 60 f- 40 1- 0. ..... TEST ITEM FAILED (MELLINGER 1963) u...... n -.. .,. -- \ -- \ ---......... \ --- Q TEST ITEM 69 LEGEND ........ __ _ .... .... -... .._..... \ 'q\ ~ '~ ' ,6 ~ • PREDICTED OVERLAY DETERIORATION ~ 0 OBSERVED TEST ITEM DETERIORATION 20 f- 0 OBSERVED TEST ITEM DETERIORATION IGNORING EARLY CRACKING ' ' b 0 100 A BASE CRACKS, AVERAGE FLEXURAL STRENGTHS A BASE CRACKS, LOW FLEXURAL STRENGTH I I I 1,000 COVERAGES Fig. 43. Performance of Item 69 I I I I I 10,000 100,000 I .I I j, I "I I of the SCI, Mellinger's failure level and the SCI computed from the minutes of the board of consultants meeting are in good agreement as seen in Figure 42. Table 23 shows the predicted coverage levels at which the SCI reached 70 for each test item. Except for items 27 and 69, the predicted performance is in reasonable agreement with the observed performance. The traffic on items 23, 24, and 26 would not be predicted to have caused deterioration in the base pavement, and no reduction was made in the base pavement modulus value in calculating the deteriora- tion of the overlay. As seen in Figures 37, 38, and 40, the predicted deterioration in these items agreed well with the observed performance for the higher subgrade modulus values. Thus, the performance models developed in Part IV are considered adequate for predicting the perfor- mance of an unbonded overlay using layered elastic theory. The use of a reduced cracked base slab modulus at different lev- els of'traffic for items 25, 27, 28, and 69 was less successful. Pre- dictions of performance for items 25 and 28 gave reasonable agreement with the observed behavior, but the traffic predicted to cause deteri- oration in items 27 and 69 was higher than observed in the test items. The inclusion of the reduced cracked slab modulus in the analysis greatly reduces the traffic required to cause deterioration in an over- lay. This effect can be seen in Table 24 where failure to include the reduced modulus for cracked base slab in the analysis results in greatly overpredicting the overlay traffic until deterioration starts. In the extreme example of item 28 with the higher subgrade modulus, the traffic until deterioration starts is three orders of magnitude above 183 Iii 11: Test Item 23 24 25 26 27 28 69 Table 23 Comparison of Predicted and Observed Performance of Unbonded Overlay Test Items Predicted Failure Coverage Level 14,700a-39,500b 19,000a-71,500b 8,200a-45,000b 435a-1,380b 700a-3,100b 145a-640b 6 ,-500c-24,000d Observed Failure at 22,000 unfailede at 22,000 unfailede 18,500e 1,200e 250e 230e 2,400f-4,000e a Coverage at which SCI is 70 in Figures 37 through 42 for lower subgrade E value. b Coverage at which SCI is 70 in Figures 37 through 42 for higher subgrade E value. c Coverage level at which SCI is 70 in Figure 43 for low concrete flexural strength values. d Coverage level at which SCI is 70 in Figure 43 for average concrete flexural strength values. e Failure level reported by Mellinger (1963). f Coverage at which SCI is 70 based on cracking and spalling as reported by Ohio River Division Laboratories (1959a). 184 Table 24 Effect of Including Base Slab Cracking on Predictions of Overlal Deterioration Sub grade Predicted Onset of Deterioration, co Reported Item Modulus With Base Cracking Without Base Crackin~ Failure 25 Lower 7,523 28,596 18,500 25 Higher 40,426 92,751 18,500 27 Lower 609 1,186 250 27 Higher 2,556 3,701 250 28 Lower 134 81,694 230 28 Higher 615 253,128 230 69 Average* 23,076 3,326,121 4,000 69 Lower* 6,297 812,257 4,000 * For item 69 average flexural strength and lower flexural strength were variables rather than subgrade elastic modulus. 185 the reported failure of the test item. The effect of including the cracked slab in the analysis is shown graphically in Figure 44 for item 25. The importance and validity of including a reduced modulus to represent cracking of the base slab at different intervals of traffic is strongly supported by the results of the analysis of items 25, 27, 28, and 69. However, the mixed success of the predictions is indica- tive that the cracked slab model developed in Part V requires further research. The three data points iri Figure 26 that lie above the sug- gested AASHTO relation pull the original equation for the E-ratio developed in Part V upward. Figure 45 shows a revised E-ratio equa- tion which, neglecting these three points, shows substantial agreement with the remaining data and the suggested AASHTO relation and which predicts a more rapid reduction in the cracked slab modulus as the SCI decreases. This revised equation was used to predict the overlay deteriora- tion of item 25 and 69. It reduced the onset of deterioration for item 25 with the higher modulus subgrade from 40,426 coverages to 38,872 coverages. For item 69, it reduced the onset of deterio- ration using the low flexural strength values from 6,297 coverages to 5,857 coverages. These changes do not appreciably improve the agree- ment with the reported failures of 18,500 and 4,000 coverages. The use of a reduced modulus for cracking in the base slab greatly accel- erates the predicted onset of cracking in the overlay, but it is not very sensitive to the precise form of the equation. Consequently, the original equation for predicting the E-ratio should remain as devel- oped in Part V using all of the data points. 186 100 ITEM 25 LEGEND 0 E5 = 4,900 LB/IN.2 -z._ 0 BO • E5 = 12,800 LB/IN. 2 -\ -z._ ~ () (J TEST \ r- c. c: ITEM Cl tl FAILED -z._ 60 ;::: G t-' C) CD (J '-I \) C3 )J )J U'J ~ )> \) (J "' "'-40 ~ -;::: (I) G) (/) 20 IT\ rn (/) (/) r- r- ~ )> OJ OJ 0 1,000 10,000 100,000 1,000,000 COVERAGES Fig. 44. Effect of Cracked Modulus on Predicted Performance of Item 25 1- u ! u - 25 4 10 20 35 50 50 4 10 20 35 50 Table 27 Design Parameters for the Overlay F-4C E-concrete (x 106 lb/in. 2) 4.0 4.5 5.0 1 2 Aircraft B-727 E-concrete (x 106 lb/in. 2) 4.0 4.5 5.0 4 5 6 7 (Continued) C-141B E-concrete (x 106lb/in. 2) 4.0 4.5 5.0 9 10 11 B-747 E-concrete (x 106lb/in. 2) 4.0 4.5 5.0 N 0 V1 Design Coverages (x 103) 75 100 250 E-Soil (x 103 (lb/in. 2) 4 10 20 35 50 4 10 20 35 50 4 10 20 35 50 F-4C E-concrete (x 106 lb/in. 2) 4.0 4.5 5.0 3A Table 27 (Concluded) B-727 E-concrete (x 106 lb/in. 2) 4.0 4.5 5.0 8A Aircraft C-141B E-concrete (x 1061b/in. 2) 4.0 4.5 5.0 12 B-747 E-concrete (x 106lb/in. 2) 4.0 4.5 5.0 13 14 Table 28 Design Parameters for the Base Pavement Base Pavement Base Pavement Base Pavement E = 4 X 106lb/in. 2 E = 4.5 X l06lb/in. 2 E 5.0 X 106lb/in. 2 Case Thickness of Base Pavement hbase/hequivalent No. 0.25* 0.40 0.50 0.60 0.75 0.25* 0.40 0.50 0.60 0.75 0.25* 0.40 0.50 0.60 0.75 -- -- 1 X 2 X 3A X 4 X N 0 5 X 0" 6 X 7 X 8A X 9 X 10 X 11 X 12 X 13 X 14 X * No base pavement allowed to go below 4 in. regardless of this ratio. Table 29 Aircraft Characteristics Aircraft F-4C B-727 C-141 B Main Gear Type Single Twin Twin-Tandem Spacing (in., 38.2 32.5 X 48 width x length) Wheel Load (lb) 25,000 44,000 40,800 Tire Contact Area (in. 2) 100 238 208 Contact Pressure (lb/in. 2) 250 185 196 Equivalent radius (in.) 5.64 8. 70 8.14 207 B-747 Twin-Tandem 44 X 58 47,000 219 215 8.35 \Ill 1 1~1 Ill Iii 1111 !ill "I ,,, I ill ill !Ill Ill '" IIi 111 Iii ill Ill Table 30 Distribution of Desi~n Parameters Percent Number of in Total Desi~n Parameters Value Sample Cases 1. Aircraft F-4C 3 21 B-727 5 36 C-141 4 29 B-747 2 14 2. Design Coverage Levels 10,000 3 21 [fit !91 25,000 2 14 [II Iii 50,000 4 29 ill Ill 75,000 Ill 3 21 I' Jll 100,000 II 1 7 ill 250,000 1 7 Soil Modulus (lb/in. 2) II 3. 4,000 2 14 IU li 10,000 4 29 II 20,000 2 14 :11 II 35,000 4 29 50,000 2 14 4. Concrete Modulus ~or 6 4 4.0x10 29 Overlay (lb/in. ) 6 7 4.5x10 50 5.0x10 6 3 21 5. Concrete Modulus for 2 6 3 4.0x10 21 Base Pavement (lb/in. ) 6 36 4.5x10 5 5.0x10 6 6 43 6. Thickness of Base Pavement 0.25 4 29 (~ase/hequivalent) 0.40 2 14 0.50 1 7 0.60 3 21 0.75 4 29 208 The modulus of elasticity of concrete and the modulus of rupture or flexural strength are not independent so flexural strength was not used as a variable in Tables 27 and 28. However, there is no single, specific relation between concrete modulus of elasticity and flexural strength because it varies depending on the aggregate and mix proper- tions used in the concrete. The modulus of elasticity for concrete is commonly estimated as where E c f' c E c 57,000 If' c modulus of elasticity of concrete, lb/in. 2 compressive strength of concrete, lb/in. 2 Also, flexural strength is commonly estimated from the compressive strength as where R K If' 1 c R = flexur21 strength or modulus of rupture of concrete in lb/in. K1 = a constant varying from 8 to 10 A variety of different modulus of elasticity and corresponding flexural strength values can be calculated from these relations. For this anal- ysis intermediate values in the possible range of calculated values were used. Concrete with a modulus of 4 million lb/in. 2 was estimated 209 have a flexural strength of 600 lb/in. 2 , and concrete modulus of elas- ticity values of 4.5 and 5 million lb/in. 2 were estimated to have flexural strength values of 700 and 800 lb/in. 2 , respectively. Pois- son's ratio for all concrete was assumed to be 0.15. The Poisson's ratio for soil was assumed to vary depending on its modulus of elasticity. Soil modulus of elasticity values of 4,000 and 10,000 lb/in. 2 were considered representative of cohesive soils, and a Poisson's ratio of 0.4 was used for these soils. Modulus of elasticity values of 35,000 and 50,000 lb/in. 2 were representative of good quality cohesionless materials, and a Poisson's ratio of 0.3 was used with these. The soil with a modulus of elasticity of 20,000 lb/ in. 2 was considered to be an intermediate soil such as a sandy clay, silty sand, or silty gravel. A Poisson's ratio of 0.35 was used for this soil. For any case in Tables 27 and 28, the design factor required so that the onset of deterioration, c0 , will be reached at the design coverage level can be determined from the following equation developed in Part IV by substituting the case's required design coverage level DF Flexural strength = 4 Calculated stress 0 · 523 + 0 · 3920 Log C 0 The equivalent slab is defined to have the same concrete properties as the overlay concrete for the specific case to be overlayed. For that case's flexural strength an allowable stress level can be determined from the required design factor. 210 ~I ill t.l ill Next, an iterative series of layered elastic calculations deter- mined what thickness of equivalent pavement is needed to match this allowable stress level for a specific case's loading, overlay concrete properties, and subgrade properties. In all calculations an artifi- cial stiff layer with a modulus of one million and a Poisson's ratio of 0.5 was placed at a depth of 20 ft as recommended by Parker et al. (1979). Once the equivalent slab thickness is determined, the thickness of the base pavement is set since each case's base thickness in Table 28 is defined as a proportion of the equivalent slab thickness. As mentioned before no base slab was allowed to be less than 4-in. regardless of the proportion shown in Table 28. Once the equivalent slab and base slab thicknesses are determined, the CE overlay thick- ness can be determined from the power equation. The required overlay thickness by the proposed design method using the layered elastic analytical model follows the same analysis technique as was outlined in Part VII. A series of trial overlay thicknesses is analyzed for a case's specific loading, base thickness, and material properties until an overlay thickness is found that reaches c0 at the specific case's design coverage level. If the base pavement does not reach its c0 deterioration value within the case's design coverage level, the overlay thickness is determined simply from the c0 value calculated from overlay stresses with full support from the base slab. If, however, the base slab reaches its ·C0 before the design coverage level, the traffic is divided into intervals and dete- rioration of the overlay in each interval is calculated with the reduced base support as was done in Part VII. Trial overlay 211 ,,!I '"' Next, an iterative series of layered elastic calculations deter- mined what thickness of equivalent pavement is needed to match this allowable stress level for a specific case's loading, overlay concrete properties, and subgrade properties. In all calculations an artifi- cial stiff layer with a modulus of one million and a Poisson's ratio of 0.5 was placed at a depth of 20 ft as recommended by Parker et al. (1979). Once the equivalent slab thickness is determined, the thickness of the base pavement is set since each case's base thickness in Table 28 is defined as a proportion of the equivalent slab thickness. As mentioned before no base slab was allowed to be less than 4-in. regardless of the proportion shown in Table 28. Once the equivalent slab and base slab thicknesses are determined, the CE overlay thick- ness can be determined from the power equation. The required overlay thickness by the proposed design method using the layered elastic analytical model follows the same analysis technique as was outlined in Part VII. A series of trial overlay thicknesses is analyzed for a case's specific loading, base thickness, and material properties until an overlay thickness is found that reaches c0 at the specific case's design coverage level. If the base pavement does not reach its c0 deterioration value within the case's design coverage level, the overlay thickness is determined simply from the c0 value calculated from overlay stresses with full support from the base slab. If, however, the base slab reaches its ·c0 before the design coverage level, the traffic is divided into intervals and dete- rioration of the overlay in each interval is calculated with the reduced base support as was done in Part VII. Trial overlay 211 ill ill II II thicknesses are analyzed until the c0 in the overlay including the reduced support of the base pavement is reached at the design coverage level. Unbonded overlay Table 31 shows the results of these calculations for unbonded overlays for the 14 cases in Tables 27 and 28. Invariably, the required overlay thicknesses by the proposed design method are smaller than those calculated by the CE power equation. Figure 49 shows the thicknesses calculated using the proposed design approach with the CE unhanded design equation. The CE equation serves as an effective upper bound for the proposed design method solutions. As was seen in Figure 5, there are distinct separate regions where stress in the overlay controls and where stress in the base controls. These regions are apparent in Figure 49 and also in Figure 50 where the ratio of base modulus of elasticity to overlay modulus of elasticity is included in the fig~re. This ratio reflects a difference in flexural strength as well as modulus values. In the region where cracking in the base occurs under the design traffic, the modulus ratio in Fig- ure 50 also shows a trend that increasing modulus ratio, hence increasing base modulus and flexural strength relative to the over- lay's values, results in a decrease in overlay thickness. This trend is not true of the cases where the base did not crack. In Figure 5, it was seen that the equal rigidity definition of an equivalent slab resulted in an upper bound solution when compared to those definitions of an equivalent slab using stress in the overlay or base as the criteria for defining the eq~ivalent slab. Similarly 2U ill Iii ill IIi ill ill Table 31 Unbonded Overlay Results Equivalent Slab Overlay Base Slab Sub!;lrade h E hb Eb E CE eq h 0 s h (lb/in. 2) 0 (lb/in. 2) (lb/in. 2) (lb/in. 2) 0 Case Aircraft (in.) (in.) (in.) F-4 8.5 7.3 5.0x10 6 4.0 5.0x10 6 35,000 7.5 2 F-4 10.6 9.5 4.5x10 6 4.0 4.0x10 6 10,000 9.8 3 F-4 10.0 4.9 4.5x10 6 7.5 5.0x10 6 35,000 6.6 4 B-727 16.0 14.2 4.5x10 6 4.0 4.5x10 6 10,000 15.5 N 5 B-727 14.2 6.4 4.0x10 6 10.7 4.5x10 6 50,000 9.3 ,__. w S.Ox106 5.0x10 6 6 B-727 14.4 7.9 10.8 20,000 9.5 B-727 13.7 9.8 4.5xt0 6 8.2 4.0x10 6 50,000 11.0 8 B-727 17.5 10.9 4.5x10 6 10.5 4.5x10 6 10,000 14.0 9 C-141 19.0 6.5 4.0x10 6 14.2 4.5x106 10,000 12.6 10 C-141 21.5 14.0 4.5x10 6 8.6 5.0x10 6 4,000 19. 7 11 C-141 14.2 12.6 4.5x10 6 4.0 4.5x10 6 35,000 13.6 12 C-141 22.3 12.1 5 .Oxl0 6 11.2 5.0x10 6 4,000 19.3 13 B-747 16.2 14.5 4. Oxl0 6 4.0 5.0x10 6 35,000 15.7 14 B-747 19.6 11.5 4.0x10 6 11.8 4.0x10 6 20,000 15.6 Table 31 Unbonded Overlaz: Results Equivalent Slab Overlal Base Slab Sub grade CE h h E hb Eb E h eq 0 s (lb/in. 2) 0 2 (lb/ in. 2) (lb/in. 2) 0 Case Aircraft (in.) (lb/in. ) (in.) (in.) 1 F-4 8.5 7.3 5.0x10 6 4.0 5.0x10 6 35,000 7.5 2 F-4 10.6 9.5 4.5x10 6 4.0 4.0x10 6 10,000 9.8 3 F-4 10.0 4.9 4.5x10 6 7.5 5.0x10 6 35,000 6.6 4 B-727 16.0 14.2 4.5x10 6 4.0 4.5x10 6 10,000 15.5 N B-727 6.4 6 10.7 6 50,000 9.3 ,_. 5 14.2 4.0x10 4.5xl0 v..> 6 6 6 B-727 14.4 7.9 5.0x10 10.8 5.0x10 20,000 9.5 7 B-727 13.7 9.8 4.5xl0 6 8.2 4.0x10 6 50,000 11.0 8 B-727 17.5 10.9 4.5x10 6 10.5 4.5x10 6 10,000 14.0 9 C-141 19.0 6.5 4.0x10 6 14.2 4.5x10 6 10,000 12.6 10 C-141 21.5 14.0 4.5xl0 6 8.6 5.0x10 6 4,000 19.7 11 C-141 14.2 12.6 4.5x10 6 4.0 4.5x10 6 35,000 13.6 12 C-141 22.3 12.1 5.0xl0 6 11.2 5.0x10 6 4,000 19.3 13 B-747 16.2 14.5 4.0x10 6 4.0 5.0x10 6 35,000 15.7 14 B-747 19.6 ll.5 4.0x10 6 11.8 4.0xl0 6 20,000 15.6 - ---------- ----------- .J::. 1- z w ...J <( :::: ::::l 0 w -.J::. >- <( ...J a: w > 0 1.0 0.8 0.6 0.4 LEGEND 0 F -4 0.2 6 B -727 0 c- 141 (> B- 747 NOTE: COLORED SYMBOLS INDICATE BASE SLABCRACKEDBEFOREOVERLAYCRACKEQ 0 0 0.2 0.4 0.6 BASE hi EQUIVALENT h 0.8 Fig. 49. Comparison of Proposed Procedure and Corps of Engineers Overlay Design Equation for Unbonded Overlays 214 1.0 ill ill til ill til Ill ill I'll ~u ill til II II II II II II II 1.0 0.8 J: 1- z 0.6 w ...J <( ::: ::::> 0 w -J: > <( ...J 0.4 a: w > 0 0.2 0 0 h 0 =heq-hb LEGEND 0 F-4 Cl B -727 0 c -141 0 6-747 NOTE: COLORED SYMBOLS INDICATE BASE t::. 0.86 .. 0.86 .1.00 SLAB CRACKED BEFORE OVERLAY CRACKED. NUMBER BY SYMBOLS ARE Ebasa1E0 verlav -0.2 0.4 0.6 BASE h/EOU IV ALENT h 0.8 Fig. 50. Effect of Concrete Modulus Ratio on Unbonded Overlays 215 1.0 II II the CE equation in Figures 49 and 50 serves as an upper bound for the solutions from the proposed design method. Partially bonded overlays The analysis was repeated for seven of the cases in Table 31 for partially bonded overlays. Variation of the partially bonded inter- face K condition between 660 and 750 for four cases, as suggested by the analysis in Part VIII, resulted in negligible changes in required overlay thickness. Changes varied from 0 to 0.2 in. Consequently, a K of 750 appeared to be appropriate for representing the partially bonded overlay conditions. Results of the overlay design for par- tially bonded conditions are shown in Table 32. Unlike the unbonded condition, the CE partially bonded equation is not an upper bound for the proposed design approach solutions. Table 33 shows a comparison of the CE and the proposed design overlay requirements for both the bonded and partially bonded cases. Including the increased friction of partially bonded overlays in the analysis results in a decrease in required overlay thickness using the proposed design approach. However, this decrease is relatively small, 1 to 7 percent for these cases. The CE partially bonded equation reduces the required overlay thickness from 8 to 32 percent. Figure 51 shows the unbonded and partially bonded overlay thick- nesses calculated using the proposed layered elastic based approach, the CE test section data from Figure 3, and Fhe CE design equations. The CE partially bonded equation with the 1.4 power serves as a visual "best fit" relation for all data regardless of bond condition while the unbonded equation with the 2.0 power serves as an upper bound. The effect of increased friction between the overlay and the base is 216 Table 32 Partiall;r Bonded Overlai': Results Equivalent Slab Overlay Base Slab Sub grade CE h E hb Eb E eq h 0 s h (lb/in. 2) 0 2 2 2 0 Case Aircraft (in.) (lb/in. ) (in.) (lb/ in. ) (lb/in. ) (in.) l F-4 8.5 7.2 5.0x10 6 4.0 5.0x10 6 35,000 6.3 2 F-4 10.6 9.3 4.5x10 6 4.0 4.0x10 6 10,000 8.6 3 B-727 16.0 13.9 4.5x10 6 4.0 4.5x10 6 10,000 14.3 4 B-727 N 14.2 6.0 4.0x10 6 10.7 4.5x10 6 50,000 6.4 ,__. 5 B-727 14.4 7.8 6 10.8 6 20,000 6.5 -.....! 5.0x10 5.0x10 6 B-727 13.7 9.1 4.5x10 6 8,2 4.0x10 6 50,000 8.5 12 C-141 22.3 11.7 5.0x10 6 11.2 S.OxlO 6 4,000 15.8 Table 33 ComEarison Between Unhanded and Partial!~ Bonded Overla~ Designs Percent Difference Bet,veen Unhanded Partialll Bonded Unbonded and hb/h CE h (in.) LE h (in.) CE h LE h (in.) Partially Bonded Case Aircraft eq 0 0 0 0 LE CE 1 F-4 0.47 7.5 7.3 6.3 7.2 1.3 16.01 2 F-4 0.38 9.8 9.5 8.6 9.3 2. 1 12.2 4 B-727 0.25 15.5 14.2 14.3 13.9 2.1 7.7 5 B-727 0.75 9.3 6.4 6.4 6.0 6.2 31.2 N 6 B-727 0.75 9.5 7.9 6.5 7.8 1.3 31.6 ...... CXl 7 B-727 0.60 11.0 9.8 8.5 9.1 7.1 22.7 12 C-141 0.50 19.3 12.1 15.8 11.7 3.3 18.1 Note: CE Corps of Engineers design. LE Proposed design method using layered elastic analytical model. Percent Difference = (h - h ) /h unbonded partial bond unhanded 1.0 o.a .r:: 1- z 0.6 w ..J 0 w :2 .;.. 0 0.2 0.0 0.0 h 1.4 = h 1.4 eq 0 LEGEND • ORIGINAL CE TEST SECTIONS 6 UNBONDED CALCULATED POINTS • PARTIALLY BONDED CALCULATED POINTS 0.2 0.4 0.6 BASE h/EOUIVALENT h 0.8 Fig. 51. Comparison of Unbonded and Partially Bonded Overlay Designs 219 llfil I ICI "' 11:1, '~· I, 1.0 beneficial; however, this effect appears to be relatively small com- pared to other effects such as relative modulus values, strength, and loading conditions. The layered elastic model is much more powerful than the power equation for evaluating these effects; however the Corps of Engineers unbonded overlay equation is an effective, simple, design method but conservative. The use of the partially bonded over- lay equation is not conservative; it does not adequately reflect the interaction of the various design parameters; and consequently, its continued use appears questionable. Comparisons The CE and the FAA airfield design methods have a common basis, but as discussed in Part II they differ in a variety of details such as definitions of traffic areas, thickness reduction for high-strength subgrades, and use of design factors versus percent standard thickness fatigue relationships. The Waterways Experiment Station computer pro- grams RAD611 and R611FAA were used to develop designs for the 14 cases in Tables 27 and 28. These programs were developed specifically to be usable on IBM-compatible microcomputers, and these programs are pres- ently undergoing evaluation in CE Division and District offices and FAA Regional offices. The program RAD611 is an interactive program designed to follow the new Army and Air Force airfield rigid pavement design manual scheduled for printing and distribution in the fall of 1987. Similarly, R611FAA follows the existing FAA design guidance except that the adjustment for differing flexural strength in the base and the overlay discussed in Part II is included in the computer 220 program, although it is not in the published advisory circular (Fed- eral Aviation Administration 1978). The proposed design approach using the layered elastic model attempts to predict performance of a pavement in terms of the SCI. Some design performance level must be selected to use with this approach to compare its required pavement thickness with the thick- nesses determined for the CE and FAA approaches. The performance level used for this comparison will be, as before, the onset of dete- rioration, c0 Table 34 shows the results for equivalent slab, unbonded, and partially bonded overlays determined by the proposed layered elastic based approach, the CE RAD611 program, and the FAA R611FAA program for the 14 cases in Tables 27 and 28. The subgrade modulus of elasticity values in these cases have to be converted to modulus of subgrade reaction values for use with Westergaard model based solutions. This conversion was made with the relation proposed by Parker et al. (1979). The subgrade modulus of elasticity values of 4,000, 10,000, 20,000, 35,000, and 50,000 lb/in. 2 were estimated to be equivalent to modulus of subgrade reaction values of 50, 103, 177, 274, and 361 lb/in. 2/in. In general, the proposed design method allows somewhat thinner equivalent slab thicknesses and appreciably thinner unbonded overlays. As noted in the previous section, the proposed design method's added interface friction for partially bonded overlays does not reduce the overlay required thickness appreciably from the thickness required for unbonded overlays. However, both the CE and FAA design approaches greatly reduce the required overlay thickness for partially bonded 221 Table 34 Comrarison of Overlaz Desian Procedure Results Desis;n Procedure Thickness .(in.) Case Aircraft 1 F-4 2 F-4 3A F-4 4 B-727 5 B-727 6 B-727 7 B-727 SA B-727 9 C-141 10 C-141 11 C-141 12 C-141 13 B-747 14 B-747 Notes: h eq Proposed AEEroach h h h h ~ u _L ~ 8.5 7.3 7.2 9.2 10.6 9.5 9.3 11.2 10.0 4.9 10.8 16.0 14.2 13.9 17.4 14.2 6.4 6.0 15.2 14.4 7.9 7.8 15.4 13.7 9.8 9.1 14.3 17.5 10.9 17.8 19.0 6.5 19.2 21.5 14.0 21.0 14.2 12.6 15.3 22.3 12.1 11.7 19.2 16.2 14.5 17.1 19.6 ll.5 20.1 equivalent thickness. h = unbonded overlay thickness. u CE h u 8.2 10.6 6.0 16.9 9.4 11.0 12.3 14.4 10.6 18.8 14.8 15.6 16.3 16.3 h = partially bonded overlay thickness. p 222 h h ___..E.__ ~ 7.0 9.5 7.0 15.8 16.5 6.2 15.3 7.9 15.1 10.0 14.9 11.2 17.3 6.6 15.8 13.6 12.2 14.8 16.2 12.7 18.9 FAA h h u _E__ 16.0 14.8 !i ,, 11.3 8.9 111 m 10.5 7.5 r.l II• ill 13.0 10.7 111 II 13.8 10.6 15.4 13.8 14.8 11.2 overlays. In most cases, the partially bonded overlay thickness for these two approaches are approximately equal to the proposed design method's unbonded overlay thickness. Again it is illustrated that the partially bonded overlay equation is a best fit to data, whereas the unbonded overlay equation is a conservative upper bound. Since the partially bonded overlay equation is not always conservative and it cannot model the interactions of different parameters such as overlay and base modulus of elasticity values and load configuration, its con- tinued use is questionable. Figure 52 shows the results of the equivalent slab and unbonded overlay thicknesses for three design approaches. In general, the FAA approach requires thinner pavements than the CE approach. The pro- posed design approach results usually in thinner equivalent slabs and always in thinner overlays. The criterion proposed by Parker et al. (1979) for use with the layered elastic model is shown with the pro- posed design methods relations for c0 and CF in Figure 12. For any given coverage level the Parker criterion requires a lower design factor than does the relation for c0 . Consequently, the Parker criterion for use with the layered elastic model results in a thinner pavement than does the proposed design method with c0 as the design performance level. The proposed design method results in pavement thicknesses that are similar to those required by existing CE and FAA design methods. Required overlay thicknesses by the proposed design method are appre- ciably thinner, however, due to the improved modeling of the base pavement and the overlay. The empirical unbonded overlay equation is a conservative upper bound to the proposed design method. 223 24 22 20 z ui 18 Ul w 2 ~ () :X: f- :X: 16 () ..: 0 a: a. a. ..: z " 14 Ul w 0 0 w tJ) 0 a. 12 0 a: a. 10 8 6 4 EQUIVALENT SLAB 0 e:. 0 0 0 0 • 6 8 0 THICKNESS UNBONOED OVERLAY • ~ • • • • 0 • 0 • • F-4 CE METHOD B-727 CE METHOD C-141 CE METHOD B-747 CE METHOD B-727 FAA METHOD B-747 FAA METHOD . ~ ~ . • • • • ~ • • 10 12 14 16 18 EXISTING DESIGN METHODS THICKNESS, IN. 0 a 20 Fig. 52. Comparison of Proposed Method, Corps of Engineers, and Federal Aviation Administration Design Results 224 22 Jill !Ill !ill I ill Ill' 1;1 ill ill ill Effect of Previous Traffic The previous sections have treated the base pavement as intact and undamaged by traffic before the overlay. As was discussed in Part VII, traffic applied to the base pavement before the overlay con- sumes a portion of its fatigue capacity and this effect has to be included in the analysis. For the specific parameters of case 5 in Table 31, a 6.4-in.- thick overlay is adequate to support 25,000 coverages of a B-727 before deterioration as predicted using the relation for c0 • This prediction assumes there has been no previous traffic. As discussed in Part VII, a fatigue damage factor, d , could be defined as where d d = a fatigue damage factor between 0.0 and 1.0 C the equivalent traffic applied to the base c0 = the coverage level to cause the onset of deterioration in the base In the previous analyses the base pavement has been assumed to be untrafficked, so the fatigue factor was zero. Figure 53 shows the effect of including fatigue in the prediction of the performance of the overlay for case 5. As fatigue from traffic before the overlay is increased, the predicted coverage levels before deterioration decrease. ·At a fatigue factor value of 1.0, the base slab was on. the 225 N u N "' 0\ 100 BO 60 40 20 0 100 CASE 5 h0 = 6.4" (/) () 0" .... -.J -n -n 0 II rn 0 0 :..... 0 U1 0 II II 0 0 ·-..~ U1 1,000 10,000 COVERAGES Fig. 53. The Effect of Fatigue and Initial Base Slab Cracking on the Predicted Performance of the Case 5 Overlay 100,000 verge of starting to deteriorate before the overlay. Its deteriora- tion with decreased support under the overlay traffic reduces the number of coverages to reach c0 in the overlay by almost half. If the pavement has been cracked and is deteriorating at the time of the overlay, its reduced support to the overlay has to be included in the analysis. The existing CE overlay design equation uses the condition factor in Table 2 to account for the deterioration. In Figure 53 deterioration has been calculated for the overlay in case 5 forCE condition factors of 0.75, 0.50, and 0.25. The equiva- lent SCI values for these factors were estimated from the relationship in Figure 15 and were used to determine the initial cracked slab effective modulus for the analysis. The effect of existing structural deterioration in the base slab is very pronounced. Obviously, the inclusion of any fatigue or structural damage to the base pavement before the overlay has to be an integral part of any overlay design. As shown previously in Table 34 and Figure 52, the existing CE and FAA design procedures result in thicker overlays. Figure 54 com- pares the predicted performance of the 6.4-in.-thick overlay required by the layered elastic approach and the 9.4-in.-thick overlay required by the CE design for case 5. The CE design without any consideration for fatigue or structural condition of the base slab results in a pre- dicted capacity about 20 times greater than the required 25,000 cover- ages. Including the effect of fatigue reduces this prediction to as little as a four-fold increase over the design coverage level. When the structural condition of the base slab before the overlay is included in the CE design using the condition factor, the predicted performance of the resulting design thickness falls between these two 227 N I'-' CXl u Ul 100 CASE 5 80 60 40 20 0 1,000 EFFECT OF FATIGUE LAYERED ELASTIC C = 1.0 F = 1.0 h 0 = 6.4" 10,000 CORPS C = 1.0 LAYERED ELASTIC C = 1.0 F = 0.0 h0 = 6.4" 100,000 COVERAGES CORPS C = 1.0 F = 0.0 h0 = 9.4" CORPS C = 0.75 170 =11.1" 1,000,000 Fig. 54. Comparison of the Corps of Engineers and the Proposed Design Method Overlay Performance for Case 5 10,000,000 extremes. Although the CE overlay design procedure does not include previous fatigue damage to the base pavement, the method is suffi- ciently conservative that adequate capacity is provided. The addi- tional overlay thickness required by the condition factors for cracking in the base slab before the overlay also provides adequate capacity to exceed the design coverage level. The required increase in the overlay thickness due to the condi- tion factor in the CE overlay equation is shown in Figure 55 along with the predicted performance of cases 4, 5, and 7. Only in case 5 did the base slab undergo a decrease in support due to fatigue. As the fatigue factor increased from 0.0 to 1.0, the thickness to reach c0 at 25,000 coverages increased from 6.4 to 7.4 in. The effect of the structural condition of the base slab at the time of the overlay is seen to have very significant influence on the required thickness of overlay in Figure 55. In the specific example of case 5 the required overlay thickness almost doubled as it went from 6.4 in. to 12.7 in. to account for the condition of the base slab. As before, the CE overlay equation with the condition factor provides conserva- tive results. The proposed overlay design approach using the layered elastic analytical model results in thinner overlays than required by existing design approaches. Because it attempts to predict performance and more closely models the pavement structure, the proposed layered elas- tic design approach requires much more accurate assessment of material properties and the structural condition of the base pavement. Factors such as fatigue damage from previous traffic that did not crack the pavement must be assessed if this approach is to be used. The 229 1.0 C" "' .c ui (/) w z :,.,: ~ 0.8 J: f- (Jl ~ __J Ul f- z w 0.6 __J ~ ~ :J 0 ~ 0 0.4 N .c w ui 0 Ul w 2 "' ~ J: f- 0.2 >- ~ __J a: w > 0 0 0 h = h o eq 0.2 0.4 0.6 0.8 1.0 1.2 1.4 BASE SLAB THICKNESS, hb/EOUIVALENT SLAB THICKNESS, heq LEGEND 6 c = 1.0 '/ RANGE OF FATIGUE 6 FROM 0.0 TO 1.0, C = 1.0 0 c = 0.75 0 c = 0.50 0 c ~ 0.25 1.6 1.8 2.0 Fig. 55. Effect of Fatigue and Initial Base Cracking on Overlay Relationships conservativeness of the existing empirical approach was sufficient to allow these factors to be ignored previously. The importance of these factors is increased as the structural value of the base pavement increases. 231 PART X: CONCLUSIONS ~~ RECOMMENDATIONS Conclusions A proposed new overlay design and analysis procedure has been presented for rigid airfield pavements. It predicts pavement deteri- oration in terms of a Structural Condition Index (SCI) varying between 0 and 100. The basis for the procedure is the layered elastic analy- tical model. Effects of fatigue damage to the base pavement, progres- sive cracking in the base pavement, and substandard load transfer at the pavement joints are included in the analysis. The proposed new overlay design procedure was found to require thinner overlays than existing design procedures. This reduction in required thickness is particularly true for thick base pavements that contribute significantly to the structural capacity of the overlay and base pavement system. The difference is mainly due to the proposed design procedure's improved modeling of the base pavements contribu- tion to the system compared with the existing empirical design proce- dures. The proposed design procedure predicts pavement performance, and therefore requires accurate material, structural condition, and fati- gue characterization of the pavement. The existing Corps of Engineers (CE) unbonded overlay design equation is a conservative upper bound to the solutions from the pro- posed design procedure. Consequently, it remains as a simple con- servative design method. The CE partially bonded overlay equation is 232 not conservative, however, and its continued use is highly question- able and subject to further study. The proposed design approach using the BISAR computer program is capable of handling any degree of interface condition from friction- less to fully bonded. A fully bonded overlay may have major problems in constructing a satisfactory joint capable of adequate load transfer if a thick overlay is used. Therefore, the fully bonded overlay for airfields should be limited to thin overlays of 2- to 5-in. thickness to correct surface deficiencies and provide limited structural improvement of the pavement. The limited data on the overlays nor- mally referred to as partially bonded suggest that there is increased friction or bonding which improves their performance compared to unbonded overlays. However, accurately characterizing the appropriate friction level to use in design is difficult. The BISAR computer program was used to calculate layered elastic stresses for this study. Other layered elastic computer programs may be used if they provide stress solutions of the same accuracy as the BISAR program. Most of these programs can only handle the fully bonded and unbonded overlays because they lack models for intermediate levels of friction. The proposed design procedure gives reasonable results and pro- vides general agreement with the available data. However, the data upon which the proposed and existing design procedures are based are very limited. Major efforts are needed to develop new trafficking data and to collect field performance data for overlays. 233 The proposed design procedure predicts structural deterioration of a pavement due to load induced stresses. There are other causes of deterioration in pavements that must be addressed separately. The proposed design procedure is analytically much more powerful than the existing empirical procedures and allows direct analysis of the effects of a variety of design parameters such as material pro- perties or interface friction. However, load characterization, major simplifications of material properties, and simple assumptions con- cerning time-dependent effects such as variation in load transfer or temperature are needed to simplify the problem to a point where anal- ytical solutions are feasible. While the analytical solutions provide the engineer with results to evaluate, all analytical solutions should be tempered and adjusted with judgment and experience. Recommendations for Further Research The proposed design procedure and the existing overlay design procedures are based on limited historic data. A program of full- scale test sections and field monitoring of in-service parameters and overlays is badly needed. Some specific areas that require further work include: a. Validate the-proposed rigid performance model presented in Part IV from in-service pavements. b. Determine what factors affect the structural deterioration besides the design factor. c. Gather more data on the effective cracked slab model. d. Validate or improve the load transfer adjustment developed in Part VI. 234 e. Determine appropriate friction levels to use in analysis of unhanded and partially bonded overlays. f. Develop other models to include durability and pumping related deterioration. ~· Extend the improved design method to include flexible overlays. The proposed design approach should be used to study the optimal point for pavement rehabilitation and to compare rehabilitation strat- egies (e.g., should an overlay try to protect the base pavement from further cracking or is it more cost effective to allow the base to crack with a thinner overlay). The effective cracked slab model should be investigated as a method of designing overlays for "crack and seat" construction. A long-term assessment and monitoring of load transfer in rigid airfield pavements is needed to determine the actual values and varia- bility of this parameter. 235 APPENDIX A CORPS OF ENGINEERS RIGID PAVEMENT TEST SECTION DATA 236 Table A1 Hate rial Properties for Lockbourne No. 1 Test Sections Concrete Surface Base Course Subgrade E (x 126 h E E Item h (in.) lb/in. ) (in.) Type (lb/in. 2)* \) Type (lb/in. 2)* \) -- A 1. 60 5. 72 3.8 Silty clay 16,000 0.4 A 2.60 5. 72 3.8 Silty clay 16,000 0.4 B 1.66L 5.50 3.8 6 Loose gravel 6,700 0.3 Silty clay 9,500 0.4 B 2.661 5.50 3.8 6 Loose gravel 6,700 0.3 Silty clay 9,500 0.4 c 1.66S 5.50 3.8 6 Sand 10,000 0.3 Silty clay 4,900 0.4 N c 2.665 5.50 3.8 6 Sand 10,000 0.3 Silty clay 4,900 0.4 w '-1 D 1. 66 5.50 3.8 6 Sand and 10,000 0.3 Silty clay 4,900 0.4 gravel D 2.66 5.50 3.8 6 Sand and 10,000 0.3 Silty clay 4,900 0.4 gravel E 1.66H 5.75 3.8 6 Crushed stone 18,000 0.3 Silty clay 6,000 0.4 E 2.66H 5.75 3.8 6 Crushed stone 18,000 0.3 Silty clay 6,000 0.4 F 1.80 7.75 3.8 Silty clay 4, 100 0.4 F 2.80 7.75 3.8 Silty clay 4,100 0.4 K 1.100 9.44 3.8 Silty clay 8,200 0.4 K 2.100 9.44 3.8 Silty clay 8,200 0.4 (Continued) * Estimated from Log E = 1. 415 + 1. 284 log k from Parker et al. (1979). k = Modulus of subgrade reaction .. N w co Table A1 (Concluded) Concrete Surface Base Course E (x 196 h E Item h (in.) lb/in. ) (in.) Type (lb/in. 2)* \} -- N 1.86 8.0 3.8 6 Sand and gravel 10,000 N 2.86 8.0 3.8 6 10,000 0 1.06 9.46 3.8 6 Sand and gravel 10,000 0 2.06 9.46 3.8 6 Sand and gravel 10,000 p 1.812 7.58 3.8 12 Sand and gravel 15,000 p 2.812 7.58 3.8 12 Sand and gravel 15,000 Q 1.1012 9.44 3.8 12 Sand and gravel 15,000 Q 2.1012 9.44 3.8 12 Sand and gravel 15,000 R 1.612 5.88 3. 77 60 Sand and gravel 59,800 R 2.612 5.67 3.53 60 Sand and gravel 59,800 s 1.66 5.83 3. 77 66 Sand and gravel 55,800 s 2.66 5.69 3.53 66 Sand and gravel 55,800 T 1.60 5.63 3. 77 72 Sand and gravel 51,800 T 2.60 5.68 3.53 72 Sand and gravel 51,800 u 1.60 5.83 3.8 72 Sand 23,000 u 2.60 5.83 3.8 72 Sand 23,000 * Estimated from LogE= 1.415 + 1.284 log k from Parker et al. (1979). k = Modulus of subgrade reaction. 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 Suhsrade E Type (lh/in. 2)* \} Silty clay 4,900 0.4 Silty clay 4,900 0.4 Silty clay 4,900 0.4 Silty clay 4,900 0.4 Silty clay 3,200 0.4 Silty clay 3,200 0.4 Silty clay 3,900 0.4 Silty clay 3,900 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Silty clay 5,800 0.4 Table A2 Performance for Lockbourne No. 1 Test Sections C a c b Slabs Ite'll' Cover a !:lies SCI 0 F Analyzed Load A 1.60 18 80 13 59 NE and SE 37-kip single wheel load 59 0 (SWL) 94 0 A 2.60 294 93 225 10,084 SE 20-kip SWL 520 78 B 1. 66L 14 55 3 96 NW, SW 37-kip SWL 56 13 91 3 225 0 B 2. 66L 76 86 59 522 sw 20-kip SWL 298 42 388 0 c 1. 668 15 93 13 92 NE, SE 37-kip SWL 56 23 91 2 225 0 c 2. 668 78 78 54 599 SE 20-kip SWL 300 42 390 17 526 0 D 1. 66 20 55 6 104 NW, sw 37-kip SWL 56 28 91 0 (Continued) a Calculated onset of deterioration DF ; 0.5234 + 0.3924 Log C . 0 b Calculated absolute failure (SCI = 0) DF = 0.2967 + 0.3881 Log CF. DF = design factor = flexural strength + calculated stress. (Sheet 1 of 4) 239 Table A2 (Continued) co CF Slabs Item Covera~es SCI Analzzed Load D 2.66 300 100 289 3 '776 SE 20-kip SWL 390 86 526 78 E 1. 66M 21 100 50 212 NE, SE 37-kip SWL 57 100 92 45 226 0 E 2.66M 556 100 SE 20-kip SWL F 1.80 111 55 70 195 NW, SW 37-kip SWL 195 0 287 0 F 2.80 550 100 20-kip SWL K 1.100 412 78 259 1,995 NW, SW 37-kip SWL 722 44 982 42 1,482 12 K 2.100 42 42 1 1,435 sw 60-kip SWL 722 12 982 0 N 1.86 107 100 105 284 NW, SW 37-kip SWL 191 36 283 3 N 2.86 6 100 6 32 NW, SW 60-kip SWL 16 39 32 0 0 1.06 418 93 347 1,606 NE, SE 37-kip SWL 728 45 988 27 1488 11 (Continued) (Sheet 2 of 4) 240 Table A2 (Continued) co CF Slabs Item Cove rases SCI Analyzed Load 0 2.06 42 100 41 155 NE, SE 60-kip SWL 80 45 138 11 205 0 p 1.812 106 100 NW, SW 37-kip SWL 272 93 1,148 0 p 2.812 6 42 NW, SW 60-kip SWL 190 0 Q 1.1012 457 100 NE, SE 37-kip SWL 988 100 1,487 93 Q 2.1012 42 100 36 209 NE, SE 60-kip SWL 80 45 138 13 205 13 R 1. 612 105 100 217 557 NW, SW 37-kip SWL 262 80 492 13 1,022 0 R 2.612 1.5 58 1.0 4.2 NW, sw 60-kip SWL 19 26 42 0 s 1.66 90 93 222 549 NE, SE 37-kip SWL 271 78 497 11 1,027 0 s 2.66 1.5 25 1.0 42 NE, SE 60-kip SWL 19 17 42 0 (Continued) (Sheet 3 of 4) 241 Table A2 (Concluded) co CF Slabs Item Covera~es SCI Anall':zed Load T 1.60 87 86 215 559 NW, SW 37-kip SWL 268 77 494 13 1,184 0 T 2.60 19 100 19 137 NW, SW 60-kip SWL 42 58 138 0 u 1.60 81 100 123 488 NE, SE 37-kip SWL 262 45 488 0 u 2.60 1.5 12 1.0 42 NE, SE 60-kip SWL 19 2 42 0 (Sheet 4 of 4) 242 Table A3 Naterial Properties for Lockbourne No. 2 Test Section and Hodification Concrete Surface Base Course E (x 106 h E (x 10 3 Item h (in.) lb/in. 2) (in.) Type lb/in. 2)* \) -- E-2 15 4.0 72 Sand and gravel 16,000 0.3 E-6 20.26 4.0 l1 1 12 4.12 M 2 15 4.12 M 3 20 4.12 * Estimated from LogE= 1.415 + 1.285 log k from Parker et al. (1979). k = Hodulus of subgrade reaction. Subgrade E (x 103 Type lb/in. 2)* Silty clay 6,600 Silty clay 9,300 Silty clay 4,400 Silty clay 4,400 Silty clay 4,400 v 0.4 0.4 0.4 0.4 0.4 Table A4 Performance for Lockbourne No. 2 Test Section and Modification Item Coverages SCI C a 0 c b F Slabs Analyzed Load E-2 1,430 78 1,280 2,241 D 10.150 150-kip SWL 2,023 16 E-6 500 98 1,040 52,554 F and G 7.20; F, G, 150-kip SWL 1,000 96 H, I, and J 8.2 1,430 91 1,725 89 N 2,023 82 ~ ~ M 1 125 91 93 353 R, s, and Q 0 .120, 150-kip twin- 144 83 1.120' and 2.120 tandem 150 57 Wheel Spacing: 154 56 31.25 "x 62.75" 169 49 188 35 235 18 324 15 384 0 (Continued) a Calculated onset of deterioration DF = 0.5234 + 0.3920 Log c 0 b Calculated absolute failure (SCI = 0) DF = 0.2967 + 0.3881 Log CF. DF = Design Factor = flexural strength f calculated stress. Table A4 (Concluded) Item Coverages SCI C a 0 c b F Slabs Analyzed M 2 29 95 1,693 6 '774 u 1,500 92 2,000 88 2,204 81 M 3 2,204 100 X a Calculated onset of deterioration DF = 0.5234 + 0.3920 Log C . 0 and V 0.150, and 2.150 and y 0.200, and 2.200 b Calculated absolute failure (SCI = 0) DF = 0.2967 + 0.3881 Log CF. OF = Design Factor = flexural strength f calculated stress. 1.150, 1.200 Load 150-kip twin- tandem 150-kip twin- tandem N ""' 0'\ Table AS Material ProEerties for Sharonville Heavl Load and Multiple Wheel Heavl Concrete Surface Base Course E (x 106 h E (x 10 3 Item h (in.) lb/in. 2) (in.) ~ lb/in. 2)* 72 28 4.2 4 Sand Not modeled 73 24 4.2 4 Sand Not modeled l-C5 10 6.0 2-C5 12 6.0 2-DT 12 6.0 3-CS 14 6.0 3-DT 14 6.0 4-C5 8 6.0 * Estimated from Log E = 1. 415 + 1. 284 log k from Parker et al. (1979). k = Modulus of subgrade reaction. TyEe CL-CH clay CL-CH clay CH clay CH clay CH clay CH clay CH clay CH clay Gear Load Tests Subgrade E (x 103 lb/in. 2)* \1 -- 6,000 0.4 6,000 0.4 7,500 0.4 7,500 0.4 7,500 0.4 7,500 0.4 7,500 0.4 7,500 0.4 Table A6 Performance for Sharonville Heav:r: Load and MultiEle Wheel Heavy Gear Load Tests Item Coverages SCI C a 0 c b F Load 72 1,000 85 420 147,210 325-kip twin- 1,260 82 tandem 1,440 79 Tire spacing 3,700 63 31.25" X 62.75" 73 1,000 89 668 7,054 325-kip twin- 1,200 68 tandem 1,650 58 2, 115 55 1-C5 112 92 150 936 360-kip 192 85 12-wheel C-5 251 81 gear assembly 288 56 592 26 2-DT 40 93 128 476 166-kip dual- 150 86 tandem 290 43 Wheel spacing 410 8 44 11 X 58 11 3-DT 150 8 177 960 166-kip dual- 260 78 tandem 410 45 Wheel spacing 530 43 44" X 58" 680 17 4-CS 180 80 165 258 325-kip 240 16 12-wheel C-5 gear assembly a Calculatd onset of deterioration DF = 0.5234 + 0.3924 Log C . 0 b Calculated absolute failure (SCI = 0) DF = 0.2967 + 0.3881 Log CF. DF = design factor = flexural strength + calculated stress. 247 N -10- (Y) Table A7 Material ProEerties for Keyed Lon~itudinal Join.t Stud)!: and Soil Stabilization Pavement Studl Concrete Surface Base Course E (x 106 h E 2 (lb/in. 2)a Item h (in.) lb/in. ) (in.) Type KLJS-1 8 6.0 24 Clayey, gravelly 20,000 sand KLJS-2 11 6.0 KLJS-3 10 6.0 4 Sand 7,500 KLJS-4 10 6.0 6 Cement 250,000 stabilized SSPS-3 15 6.0 6 Bituminous b stabilized SSPS-4 15 6.0 6 Cement 200,000 stabilized a Estimated from Log E = 1.415 + 1. 284 log k from Parker et al. (1979). k Modulus of subgrade reaction. b E 200,00 in Lane 1 under 200-kip gear load. E 100,000 in Lane 2 under 240-kip gear load. Subgrade E (x 103 lb/in. 2)a v Type -- 0.3 CH clay 7,500 CH clay 7,500 0.3 CH clay 7,500 0.2 CH clay 7,500 0.4 CH clay 7,500 0.2 CH clay 7,500 v -- 0.4 0.4 0.4 0.4 0.4 0.4 Item KLJS 1-CS KLJS 3-CS KLJS 3-CS KLJS 4-DT SSPS 3-200 SSPS 4-200 Table AS Performance for Keyed Longitudinal Joint Study and Soil Stabilization Pavement Study Coverages 54 144 344 504 144 344 504 688 22 116 164 364 320 630 880 950 200 1770 2050 3000 4460 1770 4660 5220 SCI 68 38 30 0 85 80 52 9 80 45 15 3 78 34 23 1 84 60 52 12 3 74 20 0 C a 0 16 292 ll 228 937 1179 (Continued) c b F 683 783 395 1094 4258 5934 Load 360-kip C-5 gear assembly 360-kip C-5 gear assembly 360-kip C-5 gear assembly 166-kip dual- tandem 200-kip dual- tandem 200-kip dual- tandem a Calculated onset of deterioration DF = 0.5234 + 0.3924 Log C . 0 b Calculated absolute failure (SCI = 0) DF = 0.2967 + 0.3881 Log CF. DF = design factor = flexural strength + calculated stress. 249 Table AS (Concluded) Item Coverages SCI C a 0 c b F Load SSPS 4-240 40 80 22 377 240-kip dual- 100 42 tandem 200 27 350 1 250 Table A9 Calculated Stress and Desi8n Factors Flex. Str. Layered Elastic Design Test Section Item (lb/in~ Stress (lb/in. 2) Factor Lockbourne No. 1 A 1.60 780 599 1.302 A 2.60 740 405 1. 827 B 1. 66 C 780 759 1. 028 B 2.66 c 740 504 1. 468 c 1.66 s 780 853 0.914 c 2.66 s 740 558 1.326 D 1.66 780 877 0.889 D 2.66 740 572 1. 294 E 1.66 M 780 771 1. 012 E 2. 66 M 740 505 1.465 F 1.80 780 625 1.248 F 2.80 740 396 1.869 K 1.100 780 410 1.902 K 2.100 735 570 1.290 N 1.86 780 560 1.383 N 2.86 735 785 0.936 0 1.06 780 458 1.703 0 2.06 735 647 1.136 p 1.812 780 632 1.234 p 2.812 735 883 0.832 Q 1.1012 780 465 1.677 Q 2.1012 735 659 1.115 R 1.612 780 332 2.349 R 2.612 735 381 1.929 s 1.66 780 344 2.267 s 2.66 735 381 l. 929 T 1. 60 780 364 2.143 T 2.60 735 397 1. 85 l u 1.60 780 527 1.480 (Continued) 251 Table A9 (Concluded) Flex. Str. Layered Elastic Design ·2 Stress (lb/in. 2) Test Section Item (1b/in. ) Factor u 2.60 735 651 1.129 E-2 680 574 1.185 E-6 700 397 1.763 M 1 725 600 1.208 M 2 725 446 l. 626 M 3 725 295 2.458 Sharonville Heavy 72 800 319 2.508 Load 73 800 401 1.995 Multiple Wheel 1-C5 725 580 1. 250 Heavy Gear Load 2-C5 800 473 1. 691 2-DT 700 566 1.234 3-C5 660 396 1. 675 3-DT 700 461 1. 518 4-C5 775 735 1.054 Keyed Longitudinal 1-CS 905 656 1.380 Joint Study 2-C5 730 522 1.399 3-C5 810 580 1.397 4-C5 860 522 1.648 4-DT 860 643 1.338 Soil Stabilization 3-200 900 463 1.944 Pavement Study 4-240 900 564 1.596 4-200 870 463 1.879 4-240 870 555 1.568 252 APPENDIX B SLAB TEST DATA 253 Fig. Bl. Crane and Headache Ball Used to Crack Slabs Fig. B2. Dynatest Falling Weight Deflectometer, Model 8000 254 Fig. B3. Initial Condition, Slab l Fig. B4. Initial Condition, Slab 2 255 (]J <( --' U) Cl w 1- U) w 1- "' t-..l z " ::J "' Ll1 1- 0'1 z w u <( --, Cl <( .. f \ '· ~ / ! ': ! ; SLAB 1 ADJACENT CONCRETE WASH RACK SLAB 2 POSITION 100.5\ ) POSITION 100 ----!(,-_~,;..,· ({ -----+ ..-------- ) POSITION 200 l . /POSITION 300.5 { :,_{ !POSITION 3~0 RADIAL FOR ---'·:~---8 POSITION 100 DEFLECTION ~: MEASUREMENTS ~ t 21' t DIRECTION OF t DIRECTION OF PHOTOGRAPHS P/-10 TOG RAPHS Fig. B5. Initial Cracking For Slabs 1 and 2 Fig. B6. Initial Cracking, Slab 1, SCI 80 Fig. B7. Initial Cracking, Slab 2, SCI 80 257 N lJ1 (X) rn ::) en Cl w 1-- Ul w ;, I- " 5 .... 1- z w u <{ ..., Cl <{ SLAB 1 POSITION TOO - ADJACENT CONCRETE WASH RACK SLAB 2 _/"'POSITION 300.5 () POSITION 300 RADIAL FOR DEFLECTION ~~ MEASUREMENTS t DIRECTION OF PHOTOG RAPffS I POSITION 100 POSITION 20U 21' t DIRECTION OF PHOTOGRAPHS fig. 88. Second Cracking for Slabs 1 and 2 Fig. B9. Second Cracking, Slab l, SCI 58 --::'"·/ _/,.,,··- Fig. BlO. Second Cracking, Slab 2, SCI 80 at Position 100 259 t<> 0"1 0 w <{ ...J Ul 0 w I- Ul w I- z :::> I- z UJ u <{ -, a <{ "' ...: "' -- RADIAL FOR DEFLECTION ~~ MEASUREMENTS 21' t DIRECTION OF PHOTOGRAPHS SLAB 1 ADJACENT CONCRETE WASH RACK SLAB 2 21' t DIRECTION OF PHOTOGRAPHS Fi Bll 1'll1'rd Cracking Phase for Slabs I and 2 g. . Fig. B12. Third Cracking, Slab 1, SCI = 23 Fig. B13. Third Cracking, Slab 2, SCI = 39 261 Fig. Bl4. Fourth Cracking, Slab 1, SCI = 0 Fig. B15. Slab 1 Next Morning 262 L Fig. Bl6. Fourth Cracking, Slab 2, SCI 23 Fig. Bl7. Initial Condition, Slab 3 263 Fig. Bl8. Initial Condition, Slab 4 -- Fig. Bl9. First Cracking, Slab 3, SCI = 39 264 ------------------------------------------------------------------------ ~,_ ·,~"· · ..,~~,~~·-.: ~f:~;~ '. Fig. B20. Second Cracking, Slab 3, SCI = 23 Fig. B21. First Cracking, Slab 4, SCI 58 265 Fig. B22. Second Cracking, Slab 4, SCI 23 Fig. B23. Initial Conditions, Slab 5 266 Fig. B24. Initial Conditions, Slab 6 Fig. B25. First Cracking, Slab 5 and 6, - SCI = 39 and 55 267 Fig. B26. Second Cracking, Slab 5 and 6, SCI = 23 Fig. B27. Third Cracking, Slabs 5 and 6, SCI 0 268 Table B1 Falling Weight Results Slab 1, Position 100 b Deflection -3 (x 10 in.) Load Position a (lb) D c D c D 24 c D 36 c D 48 c D c D c 0 12 60 72 100 22,278 28.0 24.6 18.9 14.0 10.3 7.7 5.7 100 22,421 26.9 23.6 18.0 13.5 10.0 7.5 5.6 100 22,405 27.1 23.4 18.0 13.5 10.0 7.5 5.6 100 22,437 27.3 23.6 18.0 13.5 10.0 7.5 5.6 101 22,071 45.7 47.2 30.2 20.7 14.1 9.5 6.7 101 22,389 42.7 41.7 28.3 19.4 13.1 9.0 6.3 101 22,357 42.6 40.7 28.3 19.3 13.0 8.9 6.3 101 22,373 42.6 40.4 28.3 19.2 13.0 8.9 6.3 102 13,109 67.2 55.6 31.9 19.0 11.6 7.4 5.0 102 13, 109 67.2 55.0 32.0 19.1 11.7 7.4 5.0 102 13,141 67.3 54.8 32.2 19.3 11.7 7.5 5.0 102 13,125 67.2 54.4 32.4 19.2 11.7 7.4 5.0 103 13,093 65.7 56.0 32.2 19.0 ll.5 7.7 5.0 103 13,173 64.0 52.2 31.1 18.2 11.1 7.4 4.9 103 13,125 64.4 52.4 31.2 18.2 11.0 7 .4 4.9 103 13,093 64.6 52.3 31.3 18.2 10.8 7.3 4.9 104 7,627 d 64.0 32.0 16.7 7.2 3.3 2.6 79.3d 104 7, 770 80.9d 63.7 32.4 16.8 7.6 3.4 2.6 104 7,818 82.0d 65.0 32.5 16.9 7.5 3.4 2.5 104 7,850 83.0 64.4 32.7 17.0 7.5 3.4 2.6 104 8,215 d 63.1 29.6 15.3 7.3 84.9d 3.0 2.5 104 8,326 84 .6d. 63.2 29.9 15.4 7.4 3.1 2.6 104 8,358 85.6d 64.3 30.4 15.6 7.4 3.2 2.6 104 8,390 86.5 65.0 30.8 15.7 7.5 3.1 2.6 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b Measured on plate. c Sensor location D0 at center of plate, Dl2 at 12 in. of plate, n24 at 24 in. from center of p ate, d Overranged sensor maximum capacity of 75 x 10-3 in. 269 from center Table B2 Falling Weight Results Slab 1' Position 100.5 -3 in.) b Deflection (x 10 Load Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 101.5 22,278 39.7 32.8 23.7 16.8 ll. 7 8.2 5.9 101.5 22,294 39.2 32.4 23.3 16.6 u.s 8.1 5.8 101.5 22,294 39.4 32.3 23.4 16.6 11.4 8.1 5.8 101.5 22,294 39.4 32.2 23.5 16.6 11.4 8.1 5.8 102.5 13,538 61.8 42.6 26.0 16.1 10.7 6.7 4.6 102.5 13,570 61.5 42.6 26.0 16.1 10.2 6.7 4.6 102.5 13,538 61.7 42.8 26.1 16.2 10.4 6.7 4.6 102.5 13,538 61.9 43 .l 26.2 16.3 10.4 6.7 4.6 103.5 13,808 45.5 35.6 22.4 14.4 9.1 6.1 4.3 103.5 13' 872 45.2 34.7 22.2 14.2 9.3 6.1 4.4 103.5 13,856 45.4 34.8 22.3 14.1 9.3 6.1 4.4 103.5 13,840 45.5 34.8 22.3 14.3 9.0 6.0 4.3 104.5 7,484 65.6 45.8 25.0 9.1 3.8 3.7 2.8 104.5 7,548 66.5 46.8 25.6 9.3 3.8 3.8 2.8 104.5 7,580 67.0 47.3 25.9 9.4 3.6 3.7 2.8 104.5 7,611 68.1 48.1 26.5 9.6 3.6 3.8 2.9 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b c Measured on plate. Sensor location D0 at center of plate, n12 at 12 in. from center of plate, n24 at 24 in. from center of p ate. 270 Table B3 Fallin~ Weight Results Slab 1, Position 200 b -3 in.) Deflection (x 10 Load Position a (lb) D c 0 12 c 024 c 0 36 c D48 c D60 c 0 72 c 0 200 23,025 32.6 26.3 19.6 14.6 9.8 7.9 5.7 200 23,501 31.0 25.0 18.7 14.1 9.6 7.6 5.6 200 23,517 31.5 25.2 18.8 14.0 9.7 7.7 5.6 200 23,470 32.0 25.5 19.0 14.1 9.8 7.6 5.6 201 22,087 48.0 37.0 26.3 18.8 12.5 9.3 6.5 201 22' 119 47.5 36.2 25.9 18.4 12.3 9.2 6.5 201 22,119 54.4 36.1 26.1 18.5 12.4 9.3 6.5 201 22,039 48.2 36.2 26.3 18.7 12.4 9.3 6.5 202 13,967 43.5 32.0 21.4 14.8 10.0 6.8 4. 9 202 14,047 41.8 30.8 20.6 14.3 9.8 6.1 4.9 202 14,031 42.2 31.1 20.7 15.6 9.8 6.0 5.1 202 14,015 42.4 31.3 20.9 14.4 9.6 5.5 5.4 202 18,369 56.3 41.9 27.8 19.3 12.6 9.1 6.7 202 18,337 57.0 42.6 28.3 19.4 12.7 8.8 6.9 202 18,337 57.8 43.0 28.7 20.7 12.8 9.3 6.9 202 18,369 58.5 43.4 28.9 20.0 13.0 9.4 7.0 202 21,483 67.9 50.4 33.5 22.9 15.7 10.9 8.3 202 21,563 68.6 51.1 33.8 23.6 15.8 11.0 8.3 202 21,563 69.8 51.5 33.9 23.3 16.1 11.1 8.3 202 21,610 70.4 51.7 34.1 23.5 16.1 11.1 8.3 203 18,591 44.3 35.4 24.8 16.1 10.3 7.3 5.4 203 18,639 40.2 32.4 22.2 15.0 9.8 7.1 5.4 203 18,655 40.3 32.3 22.1 15.0 9.4 7 .1 5.5 203 18,639 40.6 32.5 22.2 15.0 9.6 7 .1 5.5 203 21,388 52.2 42.2 26.3 17.8 11.7 8.4 6.5 203 21,420 51.9 40.2 26.7 16.7 10.3 6.9 6.3 203 21,404 52.6 41.9 26.9 17.6 12.2 8.5 6.2 203 21,356 53.0 41.1 27.0 17.7 12.3 8.5 6.1 (Continued) a Third digit in position number shows cracking level; i.e. 100 initial b c condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location n0 at center of plate, n12 at 12 of plate, n24 at 24 in. from center of p ate. 271 in. from center Table B3 (Concluded) b -3 in.) Deflection (x 10 Load Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 204 8,374 19.3 17.8 14.2 9.8 6.1 3. 7 2.6 204 8,453 18.9 17.5 14.0 9.8 6.1 3.7 2.7 204 8,422 18.9 17.5 14.0 9.8 6.1 3.7 2.8 204 8,422 19.0 17.6 14.1 9.8 6.1 3.7 2.8 204 14,094 35.2 31.9 24.8 16.9 10.4 6.4 4.8 204 14,158 35.0 31.9 24.6 16.8 10.4 6.5 5.0 204 14,142 35.2 32.0 24.8 16.9 10.4 6.5 5.0 204 14,142 35.4 32.3 24.8 16.9 10.4 6.5 5.0 204 21 '515 59.3 54.1 40.2 27.4 16.4 10.2 8.1 204 21,595 59.2 53.0 40.2 27.4 16.1 2.8 8.3 204 21,610 59.5 53.1 39.9 27.6 14.9 8.6 8.4 204 21,595 59.8 53.5 41.4 27.2 15.1 8.1 8.4 204 13,475 65.4 48.3 29.2 13.5 7.4 4.8 7.2 204 13,522 65.0 47.8 29.3 13.6 7.6 4.8 4.8 204 13,554 65.2 47.9 29.4 13.8 7.5 4.9 5.2 204 13,554 65.2 47.9 29.4 13.9 7.6 4.9 4.9 a Third digit in position number shows cracking level; i.e. 100 initial b c condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, n24 at 24 in. from center of p ate, 272 Table B4 Falling Weight Results Slab 1, Position 300 Loadb Positiona (lb) 300 300 300 300 301 301 301 301 302 302 302 302 303 303 303 303 304.5 304.5 304.5 304.5 304 304 304 304 304.5 304.5 304.5 304.5 304.5 304.5 304.5 304.5 21,912 21,976 21,992 21,992 22,262 22,262 22,167 22,055 21,849 21,912 21,896 21,881 21' 642 21,817 21,833 21,849 7,595 7,627 7,675 7,691 8,088 8,120 8,136 8,120 8,072 8,088 8,024 8,009 13,220 13,205 13,220 13,220 D c 0 30.4 30.2 30.4 30.6 35.4 34.5 34.6 34.7 36.5 36.4 37.1 36.9 66.3 61.7 61.6 61.6 43.2 43.3 44.0 44.3 60.3 60.5 60.6 60.5 38.8 38.7 38.9 39.2 75.6 75.7 75.9 76.1 26.6 26.0 26.2 26.2 33.7 32.8 33.1 33.3 35.7 33.5 33.2 33.1 57.8 55.7 53.9 51.2 36.1 35.8 36.6 37.1 42.1 42.2 42.3 42.2 34.4 34.1 34.5 34.9 66.7 66.2 66.3 67.0 Deflection (x 10-3 in.) 20.2 20.0 20.0 20.0 26.3 25.7 25.9 26.0 27.5 26.5 26.4 26.5 42.6 40.3 40.6 40.9 19.0 18.8 19.2 19.3 21.1 21.3 21.3 21.3 16.6 16.8 17.1 17.2 35.1 35.4 35.2 35.4 15.3 14.9 14.9 14.9 20.0 19.6 19.6 19.6 20.7 20.2 20.0 20.2 29.6 29.1 27.9 27.9 11.4 11.2 11.4 11.4 11.7 11.8 11.9 11.8 9.5 9.6 9.7 9.8 18.9 19.0 19.1 19.3 11.2 11.0 11.0 11.0 14.1 13.9 14.0 14.1 14.8 14.4 14.4 14.4 18.7 18.1 18.0 18.1 7.8 7.7 7.8 7.9 6.2 6.3 6.3 6.3 6.5 6.7 6.7 6.7 12.6 12.6 12.6 12.8 8.2 8.1 8.7 8.1 10.3 10.2 10.1 10.1 10.6 10.3 10.1 10.3 11.1 11.3 11.3 11.3 5.3 5.3 5.4 5.3 3.4 3.4 3.5 3.4 4.8 4.8 4.8 4.8 8.5 8.6 8.7 8.7 6.0 5.9 5.9 5.9 4.8 4.2 4.0 2.1 7.7 7.8 7.7 7.8 7.8 8.1 8.1 8.1 3.4 3.5 3.5 3.4 2.6 2.7 2.7 2.7 3.2 3.2 3.2 3.2 5.7 5.7 5.7 5.8 a Third digit in position number shows cracking level; i.e., lOO.ini- tial condition, 101 first cracking, 102 second cracking, etc. b Measured on plate. c Sensor location D0 at center of plate, n12 at 12 in. from center of plate, D24 at 24 in. from center of p ate. 273 Table B5 Falling Weight Results, Slab 2, Position 100 b -3 in.) Deflection (x 10 Load Position a (lb) 0 c 0 12 c D24 c D36 c D48 c D60 c D72 c 0 100 22,246 26.7 24.2 19.4 14.9 10.9 7.6 5.4 100 22,246 26.0 23.4 18.8 14.5 10.7 7.5 5.5 100 22,294 26.1 23.5 18.9 14.6 10.7 7.6 5.5 100 22,278 26.2 23.5 18.9 14.6 10.7 7.6 5.6 1000 23,025 26.3 24.2 19.1 14.9 11.5 9.0 6.8 1000 23,009 26.3 23.8 18.9 14.8 11.6 9.0 6.8 1000 22,913 26.3 23.7 19.0 14.9 11.6 9.0 6.9 1000 22,897 26.4 23.6 19.1 15 11.5 9.0 6.9 101 22,516 30.2 27.0 21.9 17.1 12.8 9.5 7.1 101 22,484 29.5 26.3 21.5 16.7 12.6 9.4 7.2 101 22,389 29.6 26.4 21.5 16.8 12.6 9.5 7.2 101 22,357 29.6 26.4 21.5 16.8 12.6 9.5 7.2 102 22,135 32.6 31.1 22.6 17.6 13.2 9.8 7.4 102 22,135 30.2 27.8 22.3 17.4 13.0 9.8 7.4 102 22,151 30.2 27.6 22.3 17.4 13.0 9.8 -7.5 102 22' 135 30.2 27.4 22.3 17.4 13.1 9.7 7.4 103 21,706 52.8 48.8 34.3 25.1 17.9 12.4 8.9 103 21,896 49.7 43.9 32.8 24.1 17.2 12.2 9.1 103 21,896 49.6 43.9 32.7 24.1 17.3 12.3 9.2 103 21,881 49.7 43.9 32.8 24.1 17.2 12.3 9.3 104 21,769 61.1 49.9 34.1 23.2 15.5 10.4 7.7 104 21,881 57.0 47.0 32.8 22.7 15.3 10.6 8.0 104 21,881 56.9 46.7 32.9 22.7 15.5 10.7 8.1 104 21,896 57.1 46.9 33.1 22.8 15.6 10.7 8.1 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b Measured on plate. c Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, o24 at 24 in. from center of p ate. 274 Table B6 Fallin~ Wei~ht Results, Slab 2, Position 200 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 200 22,516 28.8 24.2 19.4 15.5 10.7 8.7 6.6 200 22,548 27.1 24.1 19.3 15.2 10.8 8.7 6.7 200 22,437 27.2 24.0 19.2 15.1 11.5 8.7 6.7 200 22,389 27.4 24.1 19.3 15.2 11.5 8.7 6.7 2000 22,818 28.4 27.4 19.6 15.0 10.9 8.5 6.4 2000 22,850 27.0 24.9 19.7 15.0 11.1 8.6 6.5 2000 22,802 26.7 25.0 19.6 15.0 11.2 8.6 6.5 2000 22 '770 26.1 26.1 19.6 15.0 11.3 8.6 6.5 201 22,500 30.0 26.1 20.7 16.2 12.2 9.2 6.9 201 22,453 29.4 25.6 20.4 16.1 12.2 9.3 7.0 201 22,532 29.4 25.8 20.4 16.1 12.3 9.3 7.0 201 22,580 29.4 25.6 20.6 16.2 12.4 9.3 7.0 202 22,754 34.3 29.4 23.1 17.9 13.5 10.1 7.5 202 22,723 33.3 28.3 22.4 17.3 13.1 9.8 7.2 202 22,611 33.4 28.2 22.4 17.3 13 .l 9.8 7.3 202 22,564 33.5 28.5 22.4 17.3 13.1 9.8 7.3 203 21,769 61.2 53.6 40.7 29.8 21.5 15.0 10.7 203 21,896 58.4 50.7 39.8 29.3 21.5 15.4 11.0 203 21,928 58.7 50.7 40.4 29.4 21.6 15.5 11.1 203 21,896 58.9 50.9 39.8 29.5 21.6 15.6 11.1 204 18,432 51.5 45.0 33.5 24.3 16.2 11.5 7.9 204 18,575 49.4 43.5 32.0 23.4 14.8 11.3 7.8 204 18,560 49.6 42.0 31.9 23.4 13.8 11.4 7.8 204 18,560 49.8 42.9 32.0 23.5 13.0 11.5 7.8 204 21,753 60.2 50.6 41.1 28.1 19.9 13.6 9.4 204 21,785 59.6 50.9 39.1 28 19.9 13.7 9.4 204 21,785 59.9 51.3 38.6 28.3 20.0 13.7 9.5 204 21,769 60.2 51.2 38.8 28.4 20.0 13.7 9.5 a Third digit in position number shows cracking level; i.e., 100 ini- b c tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, D12 at 12 in. from center of plate, D24 at 24 in. from center of plate. 275 Table B7 Fallin~ Wei~ht Results, Slab 2' Position 300 Load b Deflection (x 10- 3 in.) a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c Position 0 300 22,357 30.6 25.2 19.6 15.1 10.4 8.7 6.5 300 22,421 27.7 24.6 19.0 14.8 9.4 8.5 6.4 300 22,421 27.9 24.2 19.1 14.8 9.3 8.5 6.4 300 22,437 28.0 24.4 19.1 15.0 10.6 8.5 6.5 3,000 22,405 27.8 24 18.9 14.7 11.3 8.3 6.3 3,000 22,516 27.4 23.7 18.9 13.8 9.7 8.2 6.3 3,000 22,532 27.4 23.5 18.3 14.1 8.9 8.3 6.3 3,000 22,532 27.5 23.9 18.0 14.1 9.8 8.2 6.0 301 22,024 42.9 37.2 25.4 18.6 13.5 9.9 7.4 301 22,230 41.0 34.1 24.3 17.8 13.0 9.7 7.2 301 22,278 41.2 33.5 24.2 17.7 12.9 9.6 7.1 301 22,325 41.5 33.4 24.3 17.7 13.0 9.6 7.2 302 21,372 61.0 58.3 47.3 38.3 30.2 24.6 17.8 302 21,563 57.7 54.1 44.8 36.4 28.9 23.3 17.1 302 21,626 60.3 53.9 45.0 36.7 28.8 23.3 17.2 302 21,626 58.1 53.7 45.0 37.1 28.4 23.4 17.2 303 21,007 80.2 74.6 62.8 50.5 35.1 25.6 17.2 303 21,181 75.1 69.7 59.3 49.4 36.2 26.3 17.8 303 21,197 75.7 69.8 59.8. 50.0 38.9 26.3 18.0 303 21,102 76.1 70.5 60.3 50.4 39.4 26.5 18.1 303 18,226 66.0 61.7 53.9 43.8 33.2 23.8 16.0 303 18,242 66.1 62.3 53.0 44.2 33.6 24.1 16.1 303 18,210 66.1 61.5 53.1 44.3 33.1 24.0 16.1 303 18,242 66.3 61.5 53.2 44.4 32.8 24.1 16.2 304 21,245 76.7 71.5 59.1 43.6 24.8 16.0 10.5 304 21,420 72.6 69.6 58.2 44.3 51.4 16.9 11.0 304 21,404 73.2 69.6 59.4 45.5 27.3 17.2 11.1 304 21,404 73.6 70.3 59.7 45.7 28.0 17.0 11.0 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b Measured on plate. c Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, n24 at 24 in. from center of p ate. 276 Table B8 Fallin~ Weil!;ht Results, Slab 3, Position 100 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 a 2 3 100 22,-802 21.2 19.9 15.7 12.0 8.3 6.5 4.8 100 22,993 21.0 19.1 15.4 11.9 6.9 6.5 4.8 100 22,977 21.1 19.2 15.5 12.0 7.0 6.5 4.8 100 23,009 21.1 19.1 15.7 11.9 7.4 6.5 4.8 101 22,659 30.0 34.7 19.8 14.6 10.3 7.5 5.2 101 22,786 28.8 28.8 19.2 14.2 10.1 7.3 5.2 101 22,786 28.7 28.5 19.2 14.2 10.1 7.3 5.2 101 22,786 28.6 28.5 19.1 14.2 10.1 7.3 5.2 102 22,325 41.4 43.7 26.3 19.7 14.0 9.9 6.7 102 22,437 38.7 39.3 23.8 18.0 13.1 9.4 6.4 102 22,421 38.6 38.9 24.0 17.4 13.0 9.3 6.4 102 22,437 38.6 38.8 22.4 17.4 12.9 9.2 6.3 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, n24 at 24 in. from center of p ate. 277 Table B9 Fallin~ Wei~ht Results, Slab 3, Position 200 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 a b c 200 21,944 37.6 29.5 20.4 13.8 9.6 7.0 5.2 200 22,437 38.6 29.9 20.7 14.1 9.6 7.0 5.1 200 22,405 39.8 30.5 21.0 14.3 9.6 7.1 5.0 200 22,437 40.7 31.0 21.4 14.4 9.6 7.2 5.2 201 13' 713 65.9 36.6 17.8 8.3 5.6 4.6 3.6 201 13,729 65.6 36.7 17.7 8.3 5.9 4.7 3.7 201 13,761 65.6 36.1 16.8 8.6 5. 1 4.7 3.7 201 13 '729 65.6 36.2 17.0 8.5 5.9 4.7 3.7 202 13,634 68.3 38.2 18.0 9.6 5.3 4.4 3.7 202 13,650 69.4 38.2 18.3 9.9 5.5 4.5 3.7 202 13' 618 68.0 38.0 18.3 9.6 5.5 4.4 3.6 202 13,618 67.9 38.0 18.4 9.7 5.5 4.4 3.6 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location, D0 at center of plate, n12 at 12 in. from center of plate, n24 at 24 in. from center of plate. 278 Table B10 FallinB; WeiB;ht Results, Slab 3, Position 300 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c 048 c D60 c D72 c 0 a b c 300 22,580 28.8 26.1 18.0 12.1 8.5 6.6 4.9 300 22,659 28.3 24.6 16.7 12.1 7.8 6.6 5.0 300 22,611 28.4 24.5 17.1 12.7 8.3 6.7 5.0 300 22,627 28.4 24.9 17.3 12.0 8.1 6.7 5.0 301 22,389 37.5 32.4 21.7 13.9 9.2 6.5 4.7 301 22,468 35.9 30.9 21.1 13.5 9.1 6.6 4.9 301 22,421 36.0 30.4 21.1 13.4 9.1 6.7 4.9 301 22,389 36.3 30.7 20.9 13.5 9.1 6.6 4.9 302 22,246 47.9 45.0 27.2 14.1 9.2 7.2 5.5 302 22,310 44.0 40.2 25.4 14.0 9.4 7.4 5.6 302 22,294 44.4 39.8 25.3 14.1 9.5 7.5 5.7 302 22,278 44.8 39.7 25.0 14.1 9.6 7.5 5.7 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl2 at 12 of plate, n24 at 24 in. from center of p ate. 279 in. from center Table Ell Fallins; Wei12ht Results, Slab 4, Position 100 Load b Deflection (x 10- 3 in.) Position a (lb) D c Dl2 c D24 c D36 c D48 c D60 c D72 c 0 a b c 100 22,850 18.0 16.0 12.9 10.1 7.4 5.9 4.3 100 22,961 17.8 15.9 12.8 10.0 7.6 5.8 4.3 100 22,929 17.8 15.9 12.8 10.0 7.6 5.8 4.3 100 22,897 17.9 15.9 12.8 10.0 7.6 5.9 4.4 101 22,310 38.0 32.4 22.9 16.3 11.2 8.1 5.4 101 22,532 35.5 29.3 22.0 15.6 10.7 7.9 5.3 101 22,516 35.4 28.9 21.6 15.5 10.7 7.8 5.2 101 22,516 35.4 28.8 21.5 15.5 10.6 7.8 5.2 102 21,912 50.1 45.0 28.4 16.7 10.7 7.9 5.7 102 21,928 46.8 40.9 27.4 16.3 10.4 7.8 5.7 102 21,912 46.8 40.6 27.4 16.3 10.4 7.8 5.7 102 21,912 46.8 40.6 27.4 16.1 10.4 7.8 5.7 Third digit in position number shows cracking level; i.e. 100 initial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location, D0 at center of plate, D12 at 12 in. from center of plate, n24 at 24 in. from center of plate. 280 Table Bl2 Fallin8 Weight Results, Slab 4, Position 200 Load b Deflection (x 10- 3 in.) Position a (lb) D c 0 12 c 0 24 c 036 c 0 48 c 0 60 c D72 c 0 a b c 200 22,246 51.4 38.9 25.0 16.1 10.4 6.9 5.0 200 22,310 51.3 38.5 24.7 16.1 10.4 7.0 5.0 200 22,262 52.0 38.9 24.6 16.3 10.6 7.0 5.0 200 22,262 52.4 38.8 24.6 16.4 10.6 7.0 5.1 201 21,499 72.4 52.7 32.1 16.8 ll.S 8.0 5.4 201 21,674 66.7 47.7 29.6 15.8 11.0 7.9 5.6 201 21,595 66.4 47.7 29.7 15.7 10.9 7.8 5.7 201 21,610 66.8 48.1 29.8 15.5 10.9 7.9 5.6 202 18,051 74.9 53.2 29.3 9.9 5.6 4.6 4.1 202 18' 115 74.0 52.6 29.6 10.1 5.8 4.6 4.1 202 18,051 75.9 52.7 29.7 10.0 5.8 4.3 4.0 202 18' 115 75.2 53.1 29.9 10.2 5.8 4.3 4.1 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location 00 at center of plate, n12 at 12 in. from center of plate, o24 at 24 in. from center of plate. 281 Table B13 Fallins Weight Results, Slab 4, Position 300 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 a b c 300 22,818 20.7 18.3 14.1 10.6 7.3 5.8 4.4 300 22 '770 20.4 18.0 14.0 10.5 7.5 5.7 4.4 300 22' 770 20.5 17.9 14.1 10.6 7.5 5.8 4.4 300 22,739 20.6 17.9 14.0 10.6 7.6 5.8 4.4 301 22,484 23.6 20.9 16.3 12.1 8.7 6.2 4.7 301 22,580 22.8 20.2 15.8 11.8 8.5 6.2 4.7 301 22,564 22.7 20.2 15.8 11.8 8.5 6.2 4.8 301 22,468 22.8 20.1 15.8 11.8 8.5 6.3 4.8 302 21,960 40.2 37.2 26.3 16.1 9.2 6.1 4.7 302 21,976 35.2 31.7 23.8 15.2 9.2 6.3 4.8 302 21,960 35.1 31.5 23.9 15.1 8.9 6.3 4.8 302 22,008 35.2 31.5 23.7 15.2 8.9 6.3 4.9 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl 2 at 12 in. from center of plate, n24 at 24 in. from center of p ate. 282 Table B14 Falling Weight Results, Slab 5, Position 100 Load b Deflection (x 10- 3 in.) Position a (lb) D c 0 12 c D24 c D36 c 048 c 060 c D72 c 0 100 20,371 4.3 4.0 3.7 3.3 3.0 2.6 2.3 100 20,466 4.2 4.0 3.7 3.3 3.0 2.6 2.4 100 20,419 4.3 4.0 3.7 3.3 2.9 2.6 2.3 100 20,419 4.3 4.0 3.7 3.3 3.0 2.6 2.4 1,000 21,213 4.8 4.3 3.9 3.5 3 .1 2.7 2.3 1,000 21' 134 4.6 4.2 3.8 3.4 3.0 2.6 2.3 1,000 21,150 4.6 4.2 3.8 3.4 3.0 2.6 2.3 1,000 21,118 4.4 4.3 3.8 3.4 3.0 2.6 2.2 101 20,482 9.4 8.2 7.0 5.8 4.8 3.9 2.9 101 20,546 9.1 8.0 6.9 5.6 4.5 3.8 2.8 101 20,466 9.1 8.0 6.9 5.7 4.6 3.8 2.8 101 20,562 9.2 8.0 6.9 5.8 4.7 3.8 2.9 102 20,721 13.7 11.2 9.4 7.8 5.9 4.9 3.6 102 20,784 13.1 10.7 9.0 7.5 5.9 4.8 3.5 102 20,641 12.9 10.6 9.0 7.4 5.4 4.7 3.4 102 20,530 14.6 10.5 9.0 7.4 5.2 4.7 3.4 1020 20641 13.6 15.4 9.8 8.1 6.6 5.1 3.8 1020 20705 13.5 15.3 9.8 8.1 6.5 5.1 3.8 1020 20689 13.7 15.4 9.8 8.1 6.5 5.2 3.8 1020 20641 13.8 15.6 9.8 8.1 6.5 5.1 3.8 103 20053 29.7 34.7 14.1 9.4 7.5 5.8 . 4.4 103 20069 27.6 31.9 13.3 9.3 7.5 5.9 4.5 103 20021 27.6 31.7 13.2 9.3 7.5 5.9 4.5 103 20069 27.7 31.7 13.2 9.2 7.4 5.9 4.5 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b c Measured on plate. Sensor location D0 at center of plate, n12 at 12 in. from center of plate, n24 at ~4 in. from center of p ate. 283 Table Bl5 Fallin!!! Wei8ht Results, Slab 5, Position 200 Load b Deflection (x 10- 3 in.) Position a (lb) D c 012 c 024 c 036 c 048 c 060 c D72 c 0 200 22,071 10.1 8.5 7.4 6.4 5.1 4.4 3.5 200 22,214 9.9 8.4 7.5 6.5 4.4 4.0 3.5 200 22,071 7.2 8.4 7.6 6.5 4.8 3.5 2.3 200 21,881 7.3 8.4 7.6 6.4 4.9 3.5 3.1 2,000 20,435 9.4 8.3 7.2 6.2 5.3 4.5 3.5 2,000 20,816 9.3 8.1 7.0 6.1 4.9 4.5 3.5 2,000 20,736 9.2 8.1 7.1 6.1 5.2 4.4 3.5 2,000 20,768 9.2 8.1 7.0 6.1 5.2 4.3 3.5 201 20,657 16.8 14.2 ll.5 8.8 6.5 4.6 3.5 201 20,625 16.3 13.9 11.1 8.6 6.4 4.6 3.6 201 20,625 16.3 13.8 11.1 8.6 6.3 4.6 3.7 201 20,657 16.4 13.9 11.2 8.6 6.4 4.6 3.7 202 20,403 23.8 19.6 15.7 12.0 8.3 5.3 3.9 202 20,530 22.3 18.6 14.8 11.4 8.1 5.3 4.1 202 20,450 22.3 18.6 14.8 11.4 8.0 5.3 4.1 202 20,498 22.4 18.7 14.8 11.4 8.1 5.5 4.1 2020 20,180 22.2 18.7 13.5 10.8 7 .1 4.4 4.0 2020 20,498 22.2 18.1 14.0 10.8 7.1 4.4 4.3 2020 20,546 22.3 18.5 14.6 10.7 7.2 4.4 4.3 2020 20,546 22.4 18.5 14.6 10.7 7.2 4.4 4.4 203 19,386 64.2 49.4 28.9 16.5 8.7 5.9 3.7 203 19,513 58.0 35.0 28.3 15.7 8.5 6.4 4.5 203 19,449 57.7 41.1 24.5 15.4 9.2 6.7 4.6 203 19,449 57.4 42.2 27.0 15.4 9.2 6.7 4.8 a Third digit in position number shows cracking level; i.e., 100 ini- b c tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, n24 at 24 in. fro~ center of p ate. 284 Table B16 Fallin~ Wei~ht Results, Slab 5. Position 300 -3 in.) b Deflection (x 10 Load Pcsitiona (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 a b c 300 27,680 8.2 7.8 7.2 6.8 6.4 5.9 5.4 300 27,394 8.3 7.4 7.2 7.0 5.9 6.1 5.5 300 27,251 8.2 7.5 7.2 7.0 6. 1 5.9 5.4 300 27,220 8.1 7.5 7.0 7.0 5.2 5.9 5.4 3,000 20,879 5.7 5.4 5.0 4.6 4.3 3.9 3.5 3,000 20,943 5.6 5.2 4.9 4.5 4.2 3.8 3.4 3,000 20,895 5.6 5.2 4.9 4.5 4. 1 3.8 3.4 3,000 20,879 5.6 5.2 4.9 4.5 4.2 3.8 3.4 301 20, 911 9.6 9.5 8.0 6.7 5.4 4.4 3.5 301 20,975 9.6 9.4 8.0 6.7 5.4 4.4 3.4 301 20,848 9.6 9.4 8.0 6.7 5.5 4.4 3.4 301 20,832 9.6 9.5 8.0 6.7 5.4 4.4 3.4 302 19,878 22.8 12.6 10.5 8.6 5.8 5.0 3.6 302 19,831 22.2 12.6 10.4 8.7 6 5.0 3.7 302 19,783 22.4 12.6 10.5 8.2 6.8 5.0 3.8 302 19,783 22.6 12.6 10.5 8.3 6.9 5.1 3.8 3,020 19,862 23.8 13.0 10.8 8.7 6.9 5.2 3.7 3,020 19,878 24.0 13.0 10.8 8.7 6.9 5.2 3.7 3,020 19,831 24.2 13.0 10.8 8.7 6.9 5.2 3.8 3,020 19,767 24.4 13.0 10.8 8.8 6.9 5.2 3.7 303 19,354 41.9 19.7 13.1 10.9 8.3 5.8 4.2 303 19,608 39.1 18.9 11.4 11.0 8.1 6.0 4.3 303 19,561 39.1 18.7 11.7 10.9 8.3 6.1 4.4 303 19,561 39.1 18.6 11.9 11.0 8 .1 6.1 4.4 Third digit .in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location DQ at center of plate, Dl2 at 12 in. from center of plate, D24 at ~4 in. from center of p ate. 285 Table B17 Falling Weight Results, Slab 6' Position 100 Load b Deflection (x 10- 3 in.) Position a (lb) D c Dl2 c D24 c D36 c D48 c c D72 c 0 D60 a b c 100 20,975 3.7 3.6 3.5 3.4 3.3 3.3 3.3 100 20,705 3.8 3.6 3.5 3.4 3.3 3.3 3.2 100 20,657 3.8 3.6 3.5 3.4 3.3 3.3 3.2 100 20,498 3.7 3.5 3.5 3.4 3.2 3.2 3.1 1,000 20,975 3.9 3.7 3.6 3.4 3.3 3.1 3.0 1,000 20,991 3.9 3.7 3.6 3.4 3.2 3.1 3.0 1,000 21,070 3.9 3.7 3.6 3.4 3.3 3.1 3.0 1,000 21,007 3.9 3.7 3.6 3.4 3.3 3.1 3.0 101 20,546 6.5 6.1 5.5 5.0 4.3 3.9 3.4 101 20,625 6.4 6.0 5.4 4.9 4.3 3.8 3.4 101 20,625 6.4 6.0 5.4 5.0 4.3 3.9 3.4 101 20,578 6.3 5.9 5.4 4.9 4.3 3.8 3.4 102 20,546 9.3 8.8 7.7 6.6 5.5 4.4 3.5 102 20,466 8.9 8.5 7.4 6.3 5.3 4.3 3.4 102 20,578 8.9 8.5 7.4 6.3 5.3 4.3 3.4 102 20,562 8.9 8.5 7.4 6.3 5.3 4.3 3.4 103 20,403 17.2 14.6 11.7 9.2 7.6 5.5 4.1 103 20,419 16.5 14.0 11.2 8.9 7.2 5.4 4,0 103 20,387 16.5 14.0 11.2 9.0 7.3 5.4 4.1 103 20,323 16.6 15.0 11.3 9.0 7.2 5.4 4.1 Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, Dl2 at 12 in. from center of plate, n24 at 24 in. from center of p ate. 28 6 Table B18 Falling Wei~ht Results, Slab 6, Position 200 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c 036 c D48 c 0 60 c D72 c 0 200 20,879 7.7 6.4 5.5 4.7 4.1 3.5 2.9 200 20,800 7.6 6.4 5.4 4.7 4.0 3.4 2.9 200 20,752 7.6 8.7 5.5 4.6 3.9 3.4 2.8 200 20,530 7.5 7.1 5.5 4.7 3.9 3.4 2.9 201 20,546 10.2 8.6 7.2 5.9 5.0 4.3 3.5 201 20,562 9.5 8.1 6.8 5.6 4.9 4.2 3.6 201 20,466 9.5 8.1 6.8 5.6 4.8 4.2 3.5 201 20,482 9.5 8.1 6.9 5.8 4.8 4.2 3.5 202 20,149 13.4 10.7 8.2 5.9 5.0 4.2 3.5 202 20,021 12.4 10.0 7.8 5.7 4.8 4.3 3.5 202 19,799 12.3 10.0 7.9 5.9 4.9 4.3 3.5 202 19,799 12.3 10.2 7.8 5.8 4.6 4.2 3.5 203 20,260 23.4 19.0 14.2 9.1 6.7 4.8 3.5 203 20,180 21.5 17.8 . 13.6 9.1 6.7 5.2 3.5 203 20,021 21.4 17.7 13.7 9.1 6.8 5.1 3.6 203 20,037 21.6 17.8 13.7 9.3 6.7 5.2 3.6 a Third digit in position number shows cracking level; i.e., 100 ini- b c tial condition, 101 first cracking, 102 second cracking, etc. Measured on plate. Sensor location D0 at center of plate, n12 at 12 in. from center of plate, n24 at 24 in. from center of p ~te. 287 Table B19 Falling Weight Results, Slab 6, Position 300 Load b Deflection (x 10- 3 in.) Position a (lb) D c D12 c D24 c D36 c D48 c D60 c D72 c 0 301 20,466 6.5 6.2 5.5 ·4.9 4.3 3.9 3.5 301 20,530 6.5 6.1 5.5 4.8 4.3 3.9 3.5 301 20,514 6.4 6.1 5.4 4.8 4.3 3.9 3.5 301 20,593 6.4 6.1 5.4 4.8 4.2 3.9 3.5 302 20,307 10.5 9.3 8.4 7.2 5.8 5.2 4.4 302 20' 180 10.2 8.9 8.0 6.9 5.6 5.0 4.2 302 20,133 10.2 9.1 8.0 6.9 5.9 5.2 4.4 302 20' 164 10.2 8.8 8.0 6.9 5.4 5.1 4.1 303 19,926 27.0 18.0 14.5 11.2 8.3 6.2 4.7 303 19,894 25.4 17.4 14.0 11.0 7.9 6.2 4.4 303 19,910 25.5 17.3 14.1 10.9 8.1 6 .1. 4.7 303 19,878 25.7 17.3 13.2 10.9 7.8 6.2 4.4 a Third digit in position number shows cracking level; i.e., 100 ini- tial condition, 101 first cracking, 102 second cracking, etc. b Measured on plate. c Sensor location D0 at center of plate, D12 at 12 in. from center of plate, n24 at 24 in. from center of plate. 288 APPENDIX C WESTERGAARD AND LAYERED ELASTIC STRESS CALCULATIONS 289 Table C1 Stresses Calculated From Corps of Engineers Test Sections (after Parker et al 1979) Layered Elastic Westergaard Edge Test Item Stress (lb/in. 2) Stress ? (lb/in. -) Lockbourne No. 1 A-1 405 836 A-2 599 1,215 B-1 504 1,035 B-2 759 1,527 C-1 558 1,051 C-2 853 1,553 D-1 572 1,035 D-2 877 1,527 E-1 505 907 E-2 771 1,331 F-1 396 700 F-2 625 1,072 K-3 570 973 K-2 410 729 N-2 564 945 N-3 785 1,248 0-2 458 759 0-3 647 1,019 P-2 632 961 P-3 883 1,249 Q-2 465 699 Q-3 659 925 U-2 527 1,091 U-3 651 1,327 A-Rec 390 601 Lockbourne No. 2 E-1 629 1,061 E-2 574 961 (Continued) (Sheet 1 of 3) 290 Table C1 (Continued) Layered Elastic . Westergaard Edge Test Item Stress (lb/in. 2) Stress (lb/in. 2) E-3 663 1,043 E-4 642 943 E-5 454 764 E-6 397 673 E-7 312 529 M-1 600 959 M-2 446 724 M-3 295 485 Lockbourne No. 3 976 1, 785 Sharonville 57 315 596 Channelized 58 373 692 59 394 780 60 416 872 61 349 717 62 274 571 Sharonville 71 249 479 Heavy 72 319 621 73 401 780 MWHGL 1-CS 580 1,093 2-C5 473 843 3-C5 394 680 4-CS 735 1,352 2-D7 566 1,039 3-D7 461 849 KLJS 1-C5 656 996 2-C5 522 855 3-C5 580 1,017 4-CS 522 768 4-D7 643 945 (Continued) (Sheet 2 of 3) 291 Table Cl (Concluded) Layered Elastic Westergaard Edge Test Item Stress (lb/in. 2) Stress (lb/in. 2) SSPS 3-200 463 828 3-240 564 993 4-200 463 784 4-240 555 941 (Sheet 3 or 3) 292 Table C2 Calculated Wester8aard and Lal':ered Elastic Stresses for Different Aircraft and Sub grade Conditions Subgrade Pavement Westergaard Layered Elastic Aircraft k (lb/in. 2 /in.)* Thickness (in.) Stress (lb/in. 2) Stress (lb/in. 2) B-707 50 6 3,123 1,420 50 10 1,591 834 50 30 322 187 50 40 199 121 200 6 2,125 714 200 10 1,166 459 200 30 257 129 200 40 165 87 400 6 1,758 499 400 10 966 325 400 30 .228 101 400 40 147 70 B-727 so 6 2,335 1,210 50 10 1,150 639 (Continued) * Value of subgrade E for layered elastic calculations estimated from k using relation of Parker et al. (1979). (Sheet 1 of 4) Table C2 (Continued) Sub grade Pavement Hestergaard Layered Elastic Aircraft k (lb/in. 2/in.)* Thickness (in.) Stress (lb/in. 2) Stress (lb/in. 2) B-727 50 30 201 126 50 40 122 79 200 6 1,675 661 200 10 866 399 200 30 172 94 200 40 106 61 N 400 6 1,404 473 1.0 .p. 400 10 740 296 400 30 156 79 400 40 98 52 B-747 50 6 2, 774 1 '510 50 10 1,550 894 50 30 329 207 50 40 214 132 200 6 1,843 791 200 10 1,047 489 200 30 261 140 (Continued) * Value of subgrade E for layered elastic calculations estimated from k using relation of Parker et al. (1979). (Sheet 2 of 4) Table C2 (Continued) Sub grade Pavement Westergaard Layered Elastic Aircraft k (lb/in. 2/in.)* Thickness (in.) Stress (lb/in. 2) Stress (lb/in. 2) B-747 200 40 170 93 400 6 1 ,Sll S86 400 10 852 351 400 30 22S 109 400 40 151 74 C-141 50 6 2,782 1,460 N so 10 1,497 850 '-!) Ln so 30 306 187 so 40 194 120 200 6 1,781 722 200 10 1,041 471 200 30 244 130 200 40 160 88 400 6 1,413 498 400 10 842 331 400 30 218 103 400 40 142 71 (Continued) * Value of subgrade E for layered elastic calculations estimated from k using relation of Parker et al. (1979). (Sheet 3 of 4) N \0 (j\ Table C2 (Concluded) Sub grade Pavement Westergaard Layered Elastic (lb/in. 2/in.)* (in.) 2 2 Aircraft k Thickness Stress (lb/in. ) Stress (lb/in. ) F-4 50 6 1 '377 898 50 10 613 395 50 30 90 54 50 40 53 31 200 6 1 '091 653 200 10 506 305 200 30 82 44 200 40 49 25 400 6 958 535 400 10 455 260 400 30 78 39 400 40 47 23 * Value of subgrade E for layered elastic calculations estimated from k using relation of Parker et al. (1979). (Sheet 4 of 4) APPENDIX D CORPS OF ENGINEERS RIGID OVERLAY TEST SECTION DATA 297 Table Dl Overlay Hate rial Pro~erties Sub grade Flexural 2 Elastig Modulus2 Elastic Test Strength (lb/in. ) (x 10 lb/in. ) Modulus 2 Test Series Item Base Overlay Base Overlay (lb/in. ) Lockbourne A 2.7-60 740 760 3.8 3.8 16,000 l 2.7-66 740 760 3.8 3.8 a No. D 4,900b E 12.14-100 740 760 3.8 3.8 6,000 F 2.7-80 760 760 3.8 3.8 4,100 Lockbourne F 12.14-100 735 735 4.0 4.0 16,880 N No. 2 \0 G 12.14-100 735 735 4.0 4.0 17,580 CP L 14.14-80 735 735 4.0 4.0 26,500 M 14.14-80 735 735 4.0 4.0 19,700 Sharonville 23 775 840 4.4 4.8 6,300-12,000 24 775 840 4.4 4.8 4,800-12,000 25 775 840 4.4 4.8 4,900-12,800 26 775 840 4.4 4.8 5,100-12,800 27 775 840 4.4 4.8 4,700-12,800 28 775 840 4.4 4.8 3,800-12,800 Sharonville 69 615-770 710-825 4.4 4.4 9,600 Heavy Load 70 615-770 710-825 4.4 4.4 9,600 a Overlain by a 6-in. base lb/in.~. b with an E of 10,000 Overlain by a 6-in. base with an E of 18,000 lb/in. . Table D2 Observed Field Deterioration Data Item Coverages SCI D 2.7-66 138 78 712 45 E 2.7-66 138 100 712 58 F 2.7-80 138 100 712 58 F 12.14-100 10 71 63 45 1,000 ll 1,430 0 G 12.14-100 10 100 370 100 887 71 1,430 50 L 14.14-80 5 58 1,000 0 M 14.14-80 36 58 807 0 69 180 85 240 80 2,750 60 3,310 51 3,750 42 3,810 38 3,940 31 4,630 20 299 Table D3 Base Slab Stress Calculations for Unbonded Overlays Sub grade After Overlay Item E(lb/in. 2) Stress (lb/in. 2) c CF 0 23 12,800 229 2 X 10 7 9 X 107 23 6,300 263 1.5 X 10 6 6,7 X 106 24 12,800 277 634,056 2.8 X 10 6 24 4,800 326 53,621 229,609 25 12,800 345 24,851 105,596 25 4,900 402 3,827 15,957 26 12,800 372 9,537 40,136 26 5' 100 444 1,311 5,408 27 12,800 430 1,830 7,577 27 4,700 513 330 1,343 28 12,800 536 226 914 28 3,800 656 48 190 69a 9,600 335 2,228 9,242 69b 9,600 335 8,301 34,885 a Low flexural strength values used in analysis. b Average flexural strength values used in analysis.- 300 Table D4 Overla~ Stress Calculations for Unbonded Overla~s Overlay Base Overlay Subgrade 2 Traffic 2 Stress2 co CF Item E (lb/in. ) Covera~es E-Ratio E (lb/in. ) (lb/in. ) 23 12,800 0-2x10 7 1.000 4,400,000 373 25,687 109,178 23 6,300 0-1.5x10 6 1.000 4,400,000 405 9,032 37,991 24 12,800 0-634,056 1.000 4,400,000 357 46,473 198,712 24 4,800 0-53,621 1.000 4,400,000 395 12,296 51,877 25 12,800 0-24,851 1.000 4,400,000 340 92,751 399,356 w 0 24,851-38,758 o. 748 3,291,268 374 24,795 105,353 1-' 38,758-51,764 0.525 2,310,980 413 7,134 29,934 51' 764-69,133 0.330 1,450,639 459 2,154 8,932 69,133-105,596 0.161 710,245 518 633 2,593 105,596+ 0.020 89,800 649 96 385 25 4, 900 0-3,827 1.000 4,400,000 370 28,596 121,678 3,827-5,933 0.748 3,291,268 410 7,785 32,697 5,933-7,894 0.525 2,310,980 456 2,312 9,593 7,894-10,503 0.330 1,lf50,639 512 708 2,903 10,503-15,957 0.161 710,249 588 204 825 15,957+ 0.020 89,800 760 31 121 (Continued) (Sheet 1 ·of 4) Table D4 (Continued) Overlay Base Overlal: Subgrade 2 Traffic (lb/in. 2) Stress2 co CF Item E (lb/in. ) Coverages E-Ratio E (lb/in. ) 26 12,800 0-9,537 1.000 4,400,000 499 910 3,741 26 5,100 0-l J 3112 1.000 4,400,000 517 310 1,260 27 12,800 0-1,830 1.000 4,400,000 437 3,701 15,429 1,830-2,831 0.748 3,291,268 477 1,436 5,929 2,831-3,762 0.525 2,310,980 521 599 2,454 w 3,762-4,998 0.330 1,450,639 572 258 1,046 0 4,998-7,557 0.161 710,245 636 108 435 N 7,557+ 0.020 89,800 777 26 105 27 4,700 0-330 1.000 4,400,000 486 1,186 4,886 330-508 0.748 3,291,268 533 484 1,978 508-672 0.525 2,310,980 587 207 837 672-892 0.330 1,450,639 652 89 359 892-1,343 0.161 710,245 738 37 147 1,343+ 0.020 89,800 933 9 36 28 12,800 0-226 1.000 4,400,000 318 253,128 1.1x10 6 226-347 0.748 3,291,268 382 18,809 79,698 347-459 0.525 2,310,980 467 1, 792 7,416 (Continued) (Sheet 2 of 4) Table D4 (Continued) Overlay Base Overlal Subgrade2 Traffic E (lb/in. 2) Stress2 co CF Item E (lb/in. ) Cove rases E-Ratio (lb/in. ) 28 459-607 0.330 1,450,639 584 216 874 607-914 0.161 710,245 760 31 121 914+ 0.020 89,800 1,170 3 12 28 3,800 0-48 1.000 4,400,000 343 81,694 351,304 48-73 0.748 3,291,268 418 6,184 25,910 73-96 0.525 2,310,980 518 633 2,593 w 0 96-127 0.330 1,450,639 661 81 324 w 127-190 0.161 710,245 884 12 48 190+ 0.020 89,800 1,460 1 5 69a 6,900 0-2,228 1.000 4,400,000 250 812,257 3.6x10 6 2,228-3449 0.748 3,291,268 283 116,114 501,080 3,449-4584 0.525 2,310,980 325 17,290 73,199 4,584-6,093 0.330 1,450,639 377 2,945 12,249 6,093-9,242 0.161 710,245 454 451 1,841 9,242+ 0.020 89,800 653 27 109 69b 9,600 0-8,301 1.000 4,400,000 250 3.3xl0 6 14.8x10 6 8,301-12,903 0.748 3,291,268 283 403,399 1.8x10 6 (Continued) (Sheet 3 of 4) Table D4 (Concluded) Overlay Subgrade 2 Traffic Item E (lb/in. ) Coverages E-Ratio 69b 12,903-17,193 0.525 22,912-34,886 0,161 34,886+ 0,020 a Low flexural strength values used in analysis. b Average flexural strength values used in analysis. Base E (lb/in. 2) 2,310,980 710,245 89,800 Overlay Stress2 (lb/in. ) co CF 325 51,139 218,876 454 980 4,033 653 47 188 (Sheet 4 of 4) Table D5 Calculated ComEosite Unhanded Overla;z Deterioration Item Subgrade2 E (lb/in. ) Coverages SCI Remarks 23 12,800 25,687 100 Base did not crack 109,178 0 23 6,800 9,032 100 Base did not crack 37,991 0 24 12,800 46,473 100 Base did not crack 198,712 0 24 4,800 12,296 100 Base did not crack 51,877 0 25 12,800 40,426 100 51,764 34 25 4,900 55,162 0 7,357 100 26 12,800 7,894 85 9,926 0 910 100 Base did not crack 3,791 0 26 5,100 310 100 Base did not crack 1,260 0 26 12,800 2,556 100 2,831 88 3,762 28 4,105 0 27 4,700 609 100 672 81 892 5 901 0 28 12,800 615 100 706 0 (Continued) 305 Table DS (Concluded) Item Subgrade2 E (lb/in. ) CoveraBes SCI 28 69a 69b a b 3,800 134 100 170 0 9,600 6,297 100 7,687 0 9,600 23,067 100 26,128 0 Low flexural strength values used in analysis. Average flexural strength values used in analysis. 306 Remarks Table D6 Base Slab Stress Calculations for Partiall~ Bonded Overlays Before Overlay After Overlay Bond K Stress (lb/in. 2) co CF Equiv. (lb/in. 2) co CF Item Factor SCI Traffic Stress D 2.7-66 1,000 549 127 511 42 385 529 171 692 750 549 127 511 42 403 526 179 725 500 549 127 511 42 444 520 197 799 250 549 127 511 42 570 505 253 1,026 0 549 127 511 42 1,957 442 862 3,543 w E 2.7-66 1,000 485 361 1,469 100 301 495 301 1,223 0 -....! 750 485 361 1,469 100 317 492 317 1,391 500 485 361 1,469 100 354 486 354 1,441 250 485 361 1, 469 100 462 472 462 1,884 F 2.7-80 1,000 381 4,164 17,379 100 27 519 200 812 750 381 4,164 17,379 100 31 510 232 942 500 381 4,164 17,379 100 40 495 301 1,223 Table D7 Overla~ Stress Calculations for Partially Bonded Overlays Overlay Base Overla~ Bond K Traffic E (lb/in. 2) (lb/in~ co CF Item Factor Covera1:2es E-Ratio Stress ) D 2.7-66 1,000 0-70 0.330 1,252,824 596 83 332 70-307 0.161 613,394 661 40 158 307+ 0.020 77' 554 821 11 42 750 0-74 0.330 1,252,824 565 125 503 74-322 0.161 613,394 635 52 209 w 0 322+ 0.020 77' 554 816 11 43 OJ 500 0-81 0.330 1,252,824 519 251 1,020 81-335 0.161 613,394 600 79 316 335+ 0.020 77,554 809 12 45 250 0-104 0.330 1,252,824 443 1,100 4,528 104-456 0.161 613,394 542 175 706 456+ 0.020 77' 554 801 12 48 0 0-362 0.330 1, 252' 824 248 3x106 13x106 362-1' 586 0.161 613,394 413 2,286 9,485 1,586+ 0.020 77,554 790 13 52 E 2.7-66 1,000 0-157 0.748 2,842,459 468 642 2,629 157-306 0.525 1,995,846 506 314 1 '275 (Continued) (Sheet 1 of 3) Table D7 (Continued) Overlay Base Overlay Bond K Traffic (lb/in. 2) (lb/in~ co CF Item Factor Coverages E-Ratio E Stress E 2.7-66 306-502 0.330 1,252,824 552 150 607 502-922 0.161 613,394 614 66 266 922+ 0.020 77' 554 768 15 61 750 0-166 0.748 2,842,459 437 1,263 5,208 166-323 0.525 1,995,846 476 547 2,236 323-530 0.330 1,252,824 523 235 955 w 530-974 0.161 613,394 590 89 359 0 \0 974+ 0.020 77 '554 763 16 63 E 2.7-66 500 0-185 0.748 2,842,459 391 4,201 17,532 185-360 0.525 1,995,846 430 1,491 6' 160 360-592 0.330 1,252,824 480 506 2,066 592-1,087 0.161 613,394 555 144 581 1,087+ 0.020 77' 5542 756 17 67 250 0-242 0.748 842,459 310 82,968 356,836 242-4 71 0.525 1,995,846 351 15,430 65,251 471-774 0.330 1,252,824 407 2,681 11,142 774-1,423 0.161 613,394 499 355 1,445 1,423+ 0.020 77.554 748 18 71 (Continued) (Sheet 2 of 3) Table D7 (Concluded) Overlay Base Overlaz Bond K Traffic E (lb/in. 2) (lb/in: co CF Item Factor CoveraBes E-Ratio Stress ) F 2.7-80 1,000 0-174 1.000 3,800,000 322 48 '511 207,517 174-278 0.748 2,842,459 367 8,863 37,270 278-377 0.525 1,995,846 420 1,910 7,907 377-507 0.330 1,252,824 488 434 1' 771 507-785 0.161 613,394 586 94 378 785+ 0.020 77,554 817 11 43 \...<.) 1-' 0 F 2.7-80 750 0-202 1.000 3,800,000 293 191,327 115 '815 202-323 0.748 2,842,459 336 27,225 115,786 323-437 0.525 1,995,846 388 4,588 19,167 437-588 0.330 1,252,824 455 843 3,462 588-911 0.161 613,394 554 146 589 911+ 0.020 77,554 809 12 45 500 0-261 1.000 3,800,000 251 2 .4xl0 6 lO.Ox10 6 261-418 0.748 2,842,459 291 212,449 922,393 418-567 0.525 1,995,846 341 22,406 95,104 567-763 0.330 1,252,824 407 2,681 11' 142 763-1,183 0.161 613,394 511 288 1,169 1,183+ 0.020 77,554 798 12 49 (Sheet 3 of 3) Table DB Calculated Com12osite Partially Bonded Overlaz Deterioration Bond K Item Factor Coverages SCI D 2.7-66 1,000 76 100 194 0 750 95 100 252. 0 500 134 100 355 4 357 0 250 262 100 456 46 479 0 0 1,592 100 1,631 0 E 2.7-66 1,000 362 200 502 53 640 0 750 481 100 530 86 781 0 500 661 100 1,087 1 1,088 0 250 1,088 100 1,423 53 1,460 0 F 2.7-80 1,000 571 100 785 15 793 0 (Continued) 311 Table D8 (Concluded) Bond K Item Factor Coverages SCI F 2.7-80 750 707 100 911 37 929 0 1,029 100 1,183 69 1,213 0 312 REFERENCES AASHTO. 1986. 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"Development of Probabilistic Rigid Pavement Design Methodologies for Military Air- fields," Technical Report GL-83-18, US Army Engineer Waterways Exper- iment Station, Vicksburg, Miss. Yoder, E. J., and Witczak, M. W. 1975. Principles of Pavement Design, 2nd Edition, John Wiley and Sons, Inc., New York. 318 BIBLIOGRAPHY Burns, C. D., et al. 1974. "Comparative Performance of Structural Layers in Pavement Systems," Technical Report S-74-8, US Army Engi- neer Waterways Experiment Station, Vicksburg, Miss. Grau, R. W. 1972. "Strengthening of Keyed Longitudinal Construction Joints in Rigid Pavements," Miscellaneous Paper MP S-72-43, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Huntington District. 1951. "Specifications for Constructions of Overlay Test Track, Sharonville Engineer Depot, Sharonville, Ohio," US Army Corps of Engineers, Huntington, W. Va. 1953. "Specification for Construction of Overlay Test Track No. 2," US Army Corps of Engineers, Huntington, W. Va. 1957. "Specifications for Construction of Heavy Load Test Tracks at Sharonville, Ohio," US Army Corps of Engineers, Huntington, W. Va. Ohio River Division Laboratories. 1944. "Design and Construction Report Lockbourne Test Track," US Army Corps of Engineers, Mariemont, Ohio. No date. "Lockbourne No. 1, Test Track Lockbourne Army Air Base-Photographs," US Army Corps of Engineers, Mariemont, Ohio. 1945. "Report of Reconstruction Lockbourne Test Track," US Army Corps of Engineers, Mariemont, Ohio. 1950. "Final Report Lockbourne No. 2 Experimental Mat," US Army Corps of Engineers, Mariemont, Ohio. 1950, "Final Report Lockbourne No. 2 -Modification, Multiple Wheel Study," U.S. Army Corps of Engineers, Mariemont, Ohio. 1954. "Overlay Test Track, Sharonville, Ohio, Report of Construction," US Army Corps of Engineers, Mariemont, Ohio. No date. "Photographs of Sharonville No. 1 and 2," US Army Corps of Engineers, Mariemont, Ohio. · No date. "Overlay Test Track, Sharonville, Representa- tive Photographs," US Army Corps of Engineers, Mariemont, Ohio. 1958. "Ohio River Division Laboratory Participation in Joint Conference on Military Investigational Programs," US Army Corps of Engineers, Mariemont, Ohio. 1959. "Weekly Progress Reports 20 Feb 1957 - Sept 1959," US Army Corps of Engineers, Mariemont, Ohio. 1961. "Heavy-Load Test Tracks, Report of Construction," Technical Report 4-17, US Army Corps of Engineers, Mariemont, Ohio. US Army Engineer Waterway Experiment Station. 1953. "Subgrade Pre- paration for Overlay Test Track No. 2, Sharonville, Ohio," US Army Corps of Engineers, Vicksburg, Miss. 319 L Walthen, T. R. 1959. "Heavy Load Investigation Consultants Brief- ing," Ohio River Division Laboratories, US Army Corps of Engineers, Mariemont, Ohio. 320 L ------------·· ·----·-- CURRICULUM VITAE Name: Raymond Sydney Rollings, Jr. Permanent Address: Rt. 2 Box 45, Pinewood, S.C. 29125. Degree and date to be conferred: PhD, 1987. Date of birth: July 3, 1950. Place of birth: Wright-Patterson AFB, Ohio. Secondary Education: Edmunds High School, Sumter, South Carolina, May 1968 Collegiate institutions attended U.S. Military Academy University of Illinois Mississippi State University, Vicksburg Graduate Extension University of Maryland Major: Geotechnical Engineering Dates 1968-1972 1972-1974 1979-1980 1980-1987 Minors: Structural Engineering, Mathematics Professional publications: Degree Date of Degree BS 1972 MS 1974 PhD 1987 Rollings, R. S. 1987. "Using Marginal Materials in Pavements," VIIth Pan American Conference on Soil Mechanics and Foundation Engineering, Cartagena, Colombia. Kohn, S.D., and Rollings R. S. 1987. "Overlay Design," Concrete Pavements, A. Stock editor, Elsevier Applied Science Publishers, Ltd, Essex, England. Rollings, R. S. 1986. "Pavement Construction with Marginal Mate- rials," Sixth African Highway Conference, Cairo, Egypt. 1986. "Evaluation of Concrete Block Pavement Design Methods,'' Second International Workshop on Block Paving, Australian Road Research Board, Melbourne, Australia. 1986. "Field Performance of Steel Fiber Reinforced Air- field Pavements," DOT/FAA/PM-86/26, US Federal Aviation Administra- tion, Washington, DC. Rollings, R. S., and Armstrong J, 1986. "Concrete Block Paving for Marine Terminals," Ports 86, American Society of Civil Engineers, Oak- land, Calif. L Rollings, R. S. 1985. "Review of Rigid Airfield Pavement Design," Pavement Design Seminar, University of New South Wales, Duntroon, Australia. Rollings, R. S. 1984. "Corps of Engineers Design Procedure for Con- crete Block Pavements," Second International Conference on Concrete Paving Blocks, Delft University, Delft, Netherlands. 1983. "Concrete Block Pavements," Technical Report GL-83-3, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Rollings, R. S. and Chou, Y. T. 1981. "Precast Concrete Pavements," Miscellaneous Paper GL-81-10, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Rollings, R. S. 1981. "Corps of Engineers Design Procedures for Rigid Airfield Pavements," Second International Conference on Concrete Pavement Design, Purdue University, West Lafayette, Ind. 1980. "Minimum Concrete Strength for Pavements and Floor Slabs," Miscellaneous Paper GL-80-3, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. 1979. "Field Test of Expedient Pavement Repairs," ESL TR-79-08, Air Force Engineering and Services Center, Tyndall AFB, Fla. 1979. "Summary Report on Amalgapave Testing, January 1976-August 1978," AFESC TR-79-70, Air Force Engineering and Services Center, Tyndall AFB, Fla. 1978. "Laboratory Evaluation of Expedient Pavement Repair Materials," CEEDO TR-78-44, Air Force Civil and Environmental Engineering Development Office, Tyndall AFB, Fla. 1976. "AM-2 Base Course Requirements on Debris Sub- grades," AFCEC TR-76-45, Air Force Civil Engineering Center, Tyndall AFB, Fla. 1975. "Comparison of the British Class 60 Trackway and AM-2 Mat for Bomb Damage Repair Application," AFWL TR-75-149, Air Force Weapons Laboratory, Kirtland AFB, N. Mex. Hokanson, L. D., and Rollings, R. S. 1975. "Bomb Damage Repair Ana- lysis of a Scale Runway, Project ESSEX," AFCEC TR-75-27, Air Force Civil Engineering Center, Tyndall AFB, Fla. 1975. "Field Test of Standard Bomb Damage Repair Tech- niques for Pavements," AFWL TR-75-148, Air Force Weapons Laboratory, Kirtland AFB, N. Mex. Professional positions held: 1978 - Present. Research Civil Engineer, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss. 1975-1978, Captain, USAF, Research Geotechnical Engineer, Air Force Civil Engineering Center, Tyndall AFB, Fla. 1974-1975, First Lieutenant, USAF, R&D Project Officer, Air Force Weapons Laboratory, Kirtland AFB, N. Mex. Professional awards and associations: Registered Professional Engineer, Florida. 1984 Herbert D. Vogel Award for Engineering Excellence, US Army Engi- neer Waterways Experiment Station, Vicksburg, Mississippi. American Society of Civil Engineers, Member. , Construction Division, Technical Committee on Construction ------Inspection, member. American Concrete Institute, member. ------ , Committee 215, Fatigue of Concrete, member. , Committee 325, Concrete Pavements, member. ----- -------' MidSouth Chapter, Secretary. National Society of Professional Engineers, member. Mississippi Engineering Society, member.