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V . . m-vv "um IIIH/INLH’HMH/WIN/l tumult/mum , . 73 00787 0557 k—-""'"1 ‘ LIBRARY mom.“ State L University l ——i This is to certify that the dissertation entitled Factors Affecting Deterioration of Transverse Cracks In Jointed Reinforced Concrete Pavement (JRCP) presented by Zafar Iqbal Raja has been accepted towards fulfillment of the requirements for Ph.D. degreein Civil & Env. Engineering Date W / MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. msu Is An Affirmative Action/Equal Opportunity Institution cmmfld EACTORS AFFECTING DETERIORATION OF TRANSVERSE CRACKS IN JOINTED REINFORCED CONCRETE PAVEMENT (JRCP) BY ZAFAR IQBAL RAJA A DISSERTATION submitted to Michigan State university in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil and Environmental Engineering 1991 JKBSTRACflP FACTORS AFFECTING DETERIORATION OF TRANSVERSE CRACKS IN JOINTED REINFORCED CONCRETE PAVEMENT (JRCP) BY Zafar Iqbal Raja Transverse cracks in Jointed Reinforced Concrete Pavement (JRCP) deteriorate due to loss of aggregate interlock load transfer capacity. This thesis presents a synthesis of factors that may reduce aggregate interlock load transfer and describes the design, conduct, and results of experimental research conducted to evaluate the relative effects of several material and design factors on transverse crack deterioration in JRCP. The work involved the collection and analysis of load transfer data from cracks that have been induced in a series of large-scale reinforced concrete slab test specimens and are subjected to repeated applications of loads simulating the passage of heavy truck traffic. ‘ The test variables selected for the study included type of coarse aggregate, gradation of -coarse aggregate, treatment of coarse aggregate (virgin, recycled, and blend), amount of slab tension and foundation support. Results obtained show that the slabs cast using crushed limestone and. natural gravel graded. to meet Michigan Department of Transportation (MDOT) specification 6A (1.5-in. [4-cnfl top size, coarser" gradation) performed comparably while specimens cast using similarly graded slag deteriorated much more rapidly. It has also been observed that the use of nmme finely graded gravels meeting MDOT specification 17A (1.0—in. [2.5-cm] top size, finer gradation) resulted ixlaa performance only slightly poorer than that of the larger gravel. Test results also indicate that the specimens cast using 100% recycled gravel concrete (6A Gradation) or a blend of recycled gravel concrete (6A Gradation) and large crushed limestone (MDOT Gradation 4A: 2.5-in. [6-cm] top size) performed only slightly better than the slag specimen. It was observed that increase in the amount of slab tension significantly decreased the load transfer efficiency and endurance. Test results also suggest that the amount of temperature steel currently used in Michigan JRCP (0.16% by area of concrete) may be insufficient to endure the combined effects of repeated truck traffic and environmental loads. Finally, the test results indicate that transverse crack load ‘transfer efficiency’ and. endurance increases with increases in foundation stiffness. To my Parents, my wife Ameelia , and daughters Hina and Nida AIEQKMKEEDGEEHHMRS This work was sponsored by the Michigan Department of Transportation and the Great Lakes Center for Truck Transportation, which is administered by the University of Michigan Transportation Research Institute for the Federal Highway Administration. These organizations are gratefully acknowledged for providing the necessary financial and technical support. The following persons are gratefully acknowledged for their contributions to this research effort: Mr. C.J. Arnold and Dr. Gail Grove of the Michigan Department of Transportation Materials and Technology Division for their expertise and assistance throughout the project; Dr. Frank Hatfield of the Michigan State University Department of Civil and Environmental Engineering for his assistance in the structural design and analysis (both static and dynamic) of the project test stand; vi Mr. J.C. Brenton, the MSU Civil and Environmental Engineering lab technician, whose fabricating, welding, and general scavenging expertise helped us out of more than one tight spot; Mr. Mickey McGhee and Mr. Steve Lemons of Holloway Construction for their generous cooperation in the processing of the recycled aggregates that were necessary for the project work; Mr. Dave Fredline, Mr. Scott Johnson and the other employees at the Michigan DOT Grand Ledge maintenance facility who assisted in transporting materials to and from the recycling plant; Mr. Bob George, Mr. Carl Sivola, Mr. Mark Borns, and Mr. Rollie Hubble of MTS and the people at the MTS "HELPLINE" for their guidance in setting up and operating the truck load simulation portion of the test stand; Dr. Gary Cloud of the Michigan State University Department of Metallurgy, Mechanics, and Materials Science for lending his expertise in the selection and use of strain gages to this project; Vii All of the graduate and undergraduate students who hauled literally tons of aggregate, cement, fresh concrete, and broken concrete, and assisted in the design, erection, and maintenance of tflua test stand components, and performed other dirty little tasks too numerous to mention. These people include Ramez Butros, Doug Gatrell, "Edward" Hua Guo, Paul Hauschild, Julia Hoogerwerf, Jer-Wen Hsu, Dave Jeakle, Shamshad Khan, Ken Kucel, Gary Mekjian, Michael Miller, Fred Nazar, Jeni Nolan, Greg Soehnlen, Michael Thelen, Julie Vandenbossche, Keith Ward, Jack Wheatley, Brad Weiferich, and Geoff Wilkie; Dr. Gilbert Baladi, Dr. Parviz Soroushin, and Dr. Dennis Gilliland of the Michigan State University, who provided technical guidance in the conduct of this research effort; The writer wishes to express his sincere appreciation to his major advisor Dr. Mark B. Snyder, under whose direction this research was performed, for his guidance, encouragement, calm assurance and ongoing support. His energy and drive were a continuous source of inspiration and having the pleasure of his friendship was a distinguished privilege. viii EHUIEE CH?‘CONHEHWTS page LIST OF TABLES ......................................... xii LIST OF FIGURES ........................................ xiii CHAPTERS I. INTRODUCTION .................................. 1 1.1 Problem Statement ......................... 1 1.2 Objective ................................. 3 1.3 Scope ..................................... 3 II. BACKGROUND .................................... 5 2.1 Load Transfer Across Transverse Cracks....5 2.2 Aggregate Interlock Mechanism ............. 7 2.3 Aggregate Interlock Models ................ 8 III. SUMMARY OF AGGREGATE INTERLOCK LOAD TRANSFER RESEARCH ...................................... 13 3.1 Aggregate Interlock Performance ........... 13 3.1.1 Effect of the Width of Crack Opening ............................ 14 3.1.2 Effect of the Texture of the Crack Face ......................... 17 3.2 Aggregate Interlock Endurance ............. 23 3.3 Summary ................................... 26 ix IV. VI. LABORATORY STUDY FACTORS ...................... 28 4.1 Research Needs ............................ 28 4.2 Research Variables ........................ 31 EXPERIMENTAL PROGRAM .......................... 41 5.1 Test Equipment ............................ 41 5.1.1 Test Specimen Loading System ....... 41 5.1.2 Test Specimen Tensioning System....43 5.1.3 Test Specimen Support System ....... 44 5.2 Load Simulation ........................... 46 5.2.1 Loading due to Truck Traffic ....... 46 5.2.2 Loading due to Environment ......... 47 Instrumentation and Data Collection ....... 49 5.4 Test Materials ............................ 52 5.4.1 Artificial Foundation .............. 52 5.4.2 Portland Cement Concrete Slabs ..... 54 5.5 Test Procedures ........................... 63 5.5.1 Casting ............................ 63 5.5.2 Cracking ........................... 65 5.5.3 Loading ............................ 65 DISCUSSION AND ANALYSIS OF TEST RESULTS ....... 68 6.1 Evaluation of Load Transfer ............... 68 6.2 Test Results - Material Factors ........... 69 6.2.1 Effect of Type of Coarse Aggregate.69 6.2.2 Effect of Gradation of Coarse Aggregate .......................... 75 X 6.2.3 Effect of Treatment of Coarse Aggregate ....................... 79 6.3 Test Results - Design Factors ............. 84 6.3.1 Effect of Slab Tension ............. 84 6.3.2 Effect of Foundation Support ....... 89 6.4 Development of a Model 92 6.5 Equivalence of Performance 94 6.6 Discussion of Test Results 98 6.6.1 Significance of Rougher Crack Face ............................... 98 6.6.2 Effect of Aggregate Interlock Looseness .......................... 102 6.6.3 Effect of Repetitive Loading ....... 104 6.6.4 Design of Steel Reinforcement ...... 107 6.7 Summary 115 VII. CONCLUSIONS AND RECOMMENDATIONS ............... 116 7.1 Primary Conclusions ....................... 116 7.2 Other Related Findings .................... 117 7.3 Recommendations ........................... 118 REFERENCES ............................................. 129 APPENDIX A: LOAD-DEFLECTION HISTORIES OF TEST SPECIMENS (MATERIAL FACTORS) ............... 138 APPENDIX B: LOAD-DEFLECTION HISTORIES OF TEST SPECIMENS (DESIGN FACTORS) ................. 198 APPENDIX C: PRELIMINARY STATISTICAL ANALYSIS ........... 256 APPENDIX D: AREA UNDER CURVES OF TEST SPECIMENS ........ 266 xi LIST OF TABLES TABLE page 4.1 Laboratory study factors ........................... 32 Treatment combinations run in the experiment ....... 40 Mix characteristics and concrete properties — material factor specimens .......................... 56 Mix characteristics and concrete properties - design factor specimens ............................ 57 Physical characteristics of concrete aggregates... 6O Coarse aggregate gradation of 6A material ......... 61 Coarse aggregate gradation of 17A material ........ 62 Coarse aggregate gradation of 4A material ......... 64 Strength estimation of the three coarse aggregate types using flexural strength ...................... 73 Strength evaluation of the three coarse aggregate types using Los Angeles (LA) test (ASTM Test Method C131-89) .................................... 74 Differential deflection data of the two specimens used in the evaluation of effect of foundation support ............................................ 93 Differential deflection data - material factors....100 xii n LIST OF FIGURES FIGURE page 2.1 Local/Global roughness model of aggregate interlock mechanism [10] .......................... 9 2.2 Frictional sliding model of aggregate interlock mechanism [11, 12] ................................ 11 2.3 Two-phase model of aggregate interlock mechanism [13] .................................... 12 3.1 Relation of crack opening and per cent of load transferred (from Eq. 1) .......................... 15 3.2 Influence of joint opening on effectiveness percent (from Eq. 2) .............................. 16 3.3 Illustration of restraining effect of reinforcement on load transfer capacity of transverse cracks, after [1] ...................... 18 3.4 Effect of size of coarse aggregate on the relation between joint opening and joint efficiency ........................................ 21 3.5 Influence of aggregate size on joint effectiveness ..................................... 22 3.6 Effect of foundation strength on endurance index..25 3.7 Effect of joint opening on endurance index ........ 27 4.1 Test matrix A ..................................... 35 .10 .11 Test matrix B ..................................... 36 Test matrix C ..................................... 37 Test matrix D ..................................... 38 Test matrix E ...................... > ............... 39 Isometric view of the test frame .................. 42 Test stand ........................................ 43 Test specimen loading system ...................... 45 Test specimen tensioning system ................... 45 Load profile ...................................... 48 Test specimen instrumentation ..................... 50 Test control and data acquisition setup ........... 51 A plot of a data collection run ................... 53 Strength gain curves of the test specimens (material factors) ................................ 58 Strength gain curves of the test specimens (design factors) .................................. 59 A view of a failed specimen ....................... 67 Effect of coarse aggregate type on the relation between LTE% and number of load cycles ............ 70 Exposed crack faces of small test specimens, varying coarse aggregate type, 6A gradation xiv p o .10 .11 .12 .13 materials ......................................... 71 Effect of coarse aggregate type on the relation between peak deflection and number of load cycles ............................................ 76 Effect of coarse aggregate gradation on the relation between LTE% and number of load cycles ............................................ 77 Effect of coarse aggregate treatment on the relation between LTE% and number of load cycles ............................................ 80 Exposed crack face of 100% recycled gravel concrete specimen after loading ................... 81 Exposed crack face of 50-50 recycled blend specimen after loading ............................ 83 Effect of slab tension on the relation between LTE% and number of load cycles .................... 85 Aggregate looseness geometry ...................... 87 Effect of looseness on the relation between LTE% and load magnitude .......................... 88 Effect of foundation support on the relation between LTE% and number of load cycles ............ 90 Effect of foundation support on the relation between peak deflection and number of load cycles ............................................ 91 Equivalence of performance ........................ 96 XV 9 u .A 6.14 Illustration of effect of aggregate interlock looseness on load transfer capacity ............... 103 6.15 Effect of repetitive loading on aggregate interlock load transfer (data from 17A virgin gravel specimen ................................... 106 6.16 Details of 6"x12" wire mesh ....................... 110 6.17 A typical S—N curve for steel [25] ................ 113 7.1 Proposed test matrix 1 ............................ 124 7.2 Proposed test matrix 2 ............................ 125 7.3 Proposed test matrix 3 ............................ 126 7.4 Proposed test matrix 4 ............................ 127 7.5 Proposed test matrix 5 ............................ 128 A-1 Load and deflection curves for 6A virgin gravel .slab after cycle # 1 .............................. 138 A-Z Load and deflection curves for 6A virgin gravel slab after cycle # 1,000 .......................... 139 A-3 Load and deflection curves for 6A virgin gravel slab after cycle # 2,000 .......................... 140 A-4 Load and deflection curves for 6A virgin gravel slab after cycle # 5,000 .......................... 141 A-5 Load and deflection curves for 6A virgin gravel slab after cycle # 20,000 ......................... 142 A—6 Load and deflection curves for 6A virgin gravel slab after cycle # 50,000 ......................... 143 xvi A-lO A-ll A-12 A-l3 A-lS A-l6 A-18 and deflection curves after cycle # 100,000 Load slab and deflection curves after cycle # 300,000 Load slab and deflection curves after cycle # 600,000 Load slab and deflection curves after cycle # 900,000 Load slab Load limestone slab after cycle and deflection curves Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle xvii for 6A virgin gravel ....................... 144 for 6A virgin gravel ....................... 145 for 6A virgin gravel ..................... 14 for 6A virgin gravel ....................... 147 for 6A virgin # 1 .................... 148 for 6A virgin # 1,000 ................ 149 for 6A virgin # 2,000 ................ 150 for 6A virgin # 5,000 ................ 151 for 6A virgin # 10,000 ............... 152 for 6A virgin # 20,000 ............... 153 for 6A virgin # 50,000 ............... 154 for 6A virgin # 100,000 .............. 155 A-19 A-23 A-24 A-25 A-26 A-28 Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves limestone slab after cycle Load and deflection curves after cycle # 1 ............ Load and deflection curves after cycle # 1,000 ........ Load and deflection curves after cycle # 2,000 ........ Load and deflection curves after cycle # 5,000 ........ Load and deflection curves after cycle # 10,000 ....... Load and deflection curves slab after cycle # 20,000.. Load and deflection curves after cycle # 50,000 ....... Load and deflection curves after cycle # 100,000 ...... for 6A virgin # 300,000 .............. 156 for 6A virgin # 600,000 .............. 157 for 6A virgin # 900,000 .............. 158 for 6A virgin # 1500,000 ............. 159 for 6A virgin slag ....................... 160 for 6A virgin slag ....................... 161 for 6A virgin slag ....................... 162 for 6A virgin slag ....................... 163 for 6A virgin slag ....................... 164 for 6A virgin slag ....................... 165 for 6A virgin slag ....................... 166 for 6A virgin slag ....................... 167 xviii A-31 A-32 A-34 A-35 A-36 A-37 A-38 A-42 Load and deflection curves for 6A virgin slag after cycle # 250,000 ............................. 168 Load and deflection curves for 17A virgin gravel after cycle # 1 ............................ 169 Load and deflection curves for 17A virgin gravel after cycle # 1,000 ........................ 170 Load and deflection curves for 17A virgin gravel after cycle # 2,000 ........................ 171 Load and deflection curves for 17A virgin gravel after cycle # 5,000 ........................ 172 Load and deflection curves for 17A virgin gravel after cycle # 10,000 ....................... 173 Load and deflection curves for 17A virgin gravel after cycle # 20,000 ....................... 174 Load and deflection curves for 17A virgin gravel after cycle # 50,000 ....................... 175 Load and deflection curves for 17A virgin gravel after cycle # 100,000 ...................... 176 Load and deflection curves for 17A virgin gravel after cycle # 300,000 ...................... 177 Load and deflection curves for 17A virgin gravel after cycle # 600,000 ...................... 178 Load and deflection curves for 17A virgin gravel after cycle # 900,000 ...................... 179 xix A-43 A-44 A-45 A-46 A-47 A-48 A-49 A-50 A-51 A-53 A-54 Load and deflection curves for 6A 100% recycled gravel after cycle # 1 ............................ 180 Load and deflection curves for 6A 100% recycled gravel after cycle # 1,000 ........................ 181 Load and deflection curves for 6A 100% recycled gravel after cycle # 2,000 ........................ 182 Load and deflection curves for 6A 100% recycled gravel after cycle # 5,000 ........................ 183 Load and deflection curves for 6A 100% recycled gravel after cycle # 10,000 ....................... 184 Load and deflection curves for 6A 100% recycled gravel after cycle # 20,000 ....................... 185 Load and deflection curves for 6A 100% recycled gravel after cycle # 50,000 ....................... 186 Load and deflection curves for 6A 100% recycled _grave1 after cycle # 100,000 ............... i ....... 187 Load and deflection curves for 6A 100% recycled gravel after cycle # 300,000 ...................... 188 Load and deflection curves for 50-50 recycled blend after cycle # 1 ............................. 189 Load and deflection curves for 50-50 recycled blend after cycle # 1,000 ......................... 190 Load and deflection curves for 50-50 recycled blend after cycle # 5,000 ......................... 191 XX A-55 A-56 A-58 A-59 A-60 Load and deflection blend after cycle # Load and deflection blend after cycle # Load and deflection blend after cycle # Load and deflection blend after cycle # Load and deflection blend after cycle # Load and deflection blend after cycle # curves for 50-50 recycled 10,000 ........................ 192 curves for 50—50 recycled 20,000 ........................ 193 curves for 50—50 recycled 50,000 ........................ 194 curves for 50-50 recycled 100,000 ....................... 195 curves for 50-50 recycled 300,000 ....................... 196 curves for 50-50 recycled 350,000 ....................... 197 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 1 ........... Load and deflection curves for typical tenSion and 100 psi/in foundation modulus after cycle # 1,000 ....... Load and deflection and 100 psi/in foundation modulus after cycle # 2,000 ....... Load and deflection and 100 psi/in foundation modulus after cycle # 5,000 ....... Load and deflection and 100 psi/in foundation modulus after cycle # 10,000. ..... .............................. 198 .............................. 199 curves for typical tension .............................. 200 curves for typical tension .............................. 201 curves for typical tension .............................. 202 xxi Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 20,000 .................................... 203 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 50,000 ...................... ' .............. 204 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 100,000 ................................... 205 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 300,000 ................................... 206 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 600,000 ................................... 207 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 1200,000 .................................. 208 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 1800,000 .................................. 209 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 2400,000 .................................. 210 Load and deflection curves for typical tension and 100 psi/in foundation modulus after cycle # 2700,000 .................................. 211 xxii Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab and deflection curves after cycle # 1 .............................. 212 and deflection curves after cycle # 1,000 .......................... 213 and deflection curves and deflection curves after cycle # 5,000 .......................... 215 and deflection curves after cycle # 10,000 ......................... 216 and deflection curves after cycle # 20,000 ......................... 217 and deflection curves after cycle # 50,000 ......................... 218 and deflection curves after cycle # 100,000 and deflection curves after cycle # 250,000 and deflection curves after cycle # 1 .............................. 221 and deflection curves after cycle # 1,000 .......................... 222 and deflection curves after cycle # 2,000 .......................... 223 for for for for for for for for for for for xxiii high high high' after cycle # 2,000 .......................... 214 high high high high high high high tension tension tension tension tension tension tension tension foundation foundation foundation B-33 Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load ,slab Load slab Load slab Load slab Load slab and deflection curves for high foundation after cycle # 5,000 .......................... 224 and deflection curves for high foundation after cycle # 10,000 ......................... 225 [and deflection curves for high foundation after cycle # 20,000 ......................... 226 and deflection curves for high foundation after cycle # 50,000 ......................... 227 and deflection curves for high foundation after cycle # 100,000 ........................ 228 and deflection curves for high foundation after cycle # 300,000 ........................ 229 and deflection curves for high foundation after cycle # 600,000 ........................ 230 and deflection curves for high foundation after cycle # 1200,000 ....................... 231 and deflection curves for high foundation after cycle # 1800,000 ....................... 232 and deflection curves for high foundation after cycle # 2400,000 ....................... 233 and deflection curves for high foundation after cycle # 3000,000 ....................... 234 and deflection curves for high foundation after cycle # 3600,000 ....................... 235 xxiv Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab Load slab XXV and deflection curves for high foundation after cycle # 4200,000 ....................... 236 and deflection curves for high foundation after cycle # 4800,000 ....................... 237 and deflection curves for high foundation after cycle # 5400,000 ....................... 238 and deflection curves for high foundation after cycle # 6000,000 ....................... 239 and deflection curves for high foundation after cycle # 6600,000 ....................... 240 and deflection curves for 6A virgin gravel (replicate) after cycle # 1 .................. 241 and deflection curves for 6A virgin gravel (replicate) after cycle # 1,000 .............. 242 and deflection curves for 6A virgin gravel (replicate) after cycle # 2,000 .............. 243 and deflection curves for 6A virgin gravel (replicate) after cycle # 5,000 .............. 244 and deflection curves for 6A virgin gravel (replicate) after cycle # 10,000 ............. 245 and deflection curves for 6A virgin gravel (replicate) after cycle # 20,000 ............. 246 and deflection curves for 6A virgin gravel (replicate) after cycle # 50,000 ............. 247 v ‘ a a.., '- . .- ‘h! u e I . - eh. '- e . s c c ‘ . m u L x n . ." I V . I .- \ N ‘I \ V ‘ h . ‘ a. \. \ - Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 100,000 ............ 248 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 300,000 ............ 249 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 600,000 ............ 250 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 1200,000 ........... 251 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 1800,000 ........... 252 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 2400,000 ........... 253 Load and deflection curves for 6A virgin gravel slab (replicate) after cycle # 3000,000 ........... 254 Load and deflection curves for 6A virgin gravel -slab (replicate) after cycle # 3300,000 ........... 255 Area under the curve for 6A virgin gravel specimen used in the computation of El ............ 266 Area under the curve for 6A virgin limestone specimen used in the computation of El ............ 267 Area under the curve for 6A virgin slag specimen used in the computation of EI ............ 268 Area under the curve for 17A virgin gravel specimen used in the computation of EI ............ 269 Area under the curve for 6A 100% recycled gravel specimen used in the computation of El ............ 270 xxvi Area under the curve specimen used in the Area under the curve specimen used in the Area under the curve specimen used in the Area under the curve specimen used in the Area under the curve specimen used in the for 50-50 recycled blend computation of EI ............ 271 for 6A virgin gravel (year 2) computation of EI ............ 272 for 6A virgin gravel (year 2) computation of El ............ 273 for high tension computation of E1 ............ 274 for high foundation computation of El ............ 275 xxvii a... .- ‘v a...’ 've‘ an AV, ‘ ‘- (NUUNEER I INTRODUCTION 1.1 Problem. Statement Jointed reinforced concrete pavement (JRCP) typically develops transverse cracks over the first several years of its service life as contractions of the slab (caused by combinations of drying and thermal shrinkage) are restrained by friction between the slab and supporting layers. Transverse cracks may also be initiated by combinations of curling, warping, and load-related stresses. Most JRCP designs rely on grain or aggregate interlock to transfer shear loads across these cracks. These cracks deteriorate with time and traffic due to loss of aggregate interlock load transfer capacity. The loss of aggregate interlock due to opening of these cracks permits increased slab deflections, and the infiltration of water and intrusion of incompressibles into the cracks. These, in turn, lead to pumping and crack deterioration ‘through faulting' and. spalling. Continued pumping eventually leads to a loss of support beneath the 1 up. q ..-‘, ~e- ‘ve~- '1 v . T. "b. V -~ ‘ 'l I a“ ‘. ‘U‘A‘ . u 2 slabs, which greatly increases load—related stresses in the slab and can result in fatigue cracking. Thus, transverse cracks must exhibit good long-term load transfer 09,. - ' ' o fl...l.,‘ 0‘ 1‘ - cou‘s ore - - ° 0 It was recently observed that some of the recently-constructed JRCP in Michigan were exhibiting rapid transverse crack deterioration (spalling and faulting), which may lead to increased maintenance requirements and shortened service lives [1]. These newer JRCP contained important design modifications including, most notably, use of small-sized recycled concrete aggregates, and an open-graded untreated aggregate base course [2]. A preliminary evaluation of the causes of rapid deterioration of these cracks indicated. that, a combination. of jpoor aggregate interlodk (due to Luna of small-sized recycled concrete aggregate), increased slab tension. (due to the open-graded base course and inproperly functioning load transfer dowel bars at transverse joints), high deflections (due to soft support) and heavy traffic may be the major causes of crack deterioration. Many of these factors have not yet been evaluated in the context of JRCP transverse crack performance. The relative impacts of the above factors on JRCP transverse crack performance need to be quantified and documented to develop improved design guidelines and specifications for future JRCP design and construction. '—. Ix) ,... c...- -u- t" l .,-, .o‘. 1.2 Objective The overall objective of this study is to advance the state-of-the-knowledge on the subject of aggregate interlock load transfer across transverse cracks in JRCP. The specific purpose of this comparative laboratory study was to estimate the effects of several material and design variables on the aggregate interlock load transfer characteristics of transverse cracks in JRCP. Specific objectives include:- 1. Identify factors that may affect deterioration of transverse cracks in JRCP. 2. Develop and execute a laboratory experiment to evaluate the impact of selected factors on the performance of transverse cracks in JRCP. 3. Recommend construction materials that provide good load transfer across transverse cracks. 4. Recommend design modifications to improve the overall performance of JRCP. 5. Recommend variables for additional testing. 1.3 Scope This study incorporated examination of existing literature on time topic and £1 laboratory experiment involving collection and analysis of load transfer data from . n 4.- 4 the testing of a series of large-scale reinforced slab test specimens that are subjected to repeated applications of loads simulating the passage of heavy truck traffic. An extensive review of literature of previous field and laboratory studies aimed at evaluation of aggregate interlock load transfer characteristics of transverse cracks and weakened—plane transverse joints was conducted to identify 'variables that significantly' affect the load transfer through aggregate interlock. This information and recent Michigan Department of Transportation (MDOT) experience (as described above) was used as a basis for selection of the laboratory study factors. Due to financial and time restraints a singl§;fagtg; W was employed to obtain estimates of main effects only. This approach reduced the number of specimens that must be tested while quickly providing usable results and a solid foundation for future expansion of research. CRAPHEEIIII IBAIEKHMWEND 2.1 Load Transfer Across Transverse Cracks The ability of transverse cracks/joints to transfer load is a major factor in the structural performance of the crack or joint and the surrounding slabs. This ability, typically referred to as load transfer efficiency, can be described in different ways, including deflection load transfer efficiency euui stress load transfer efficiency. Several formulae for computing load transfer efficiency have been adopted by various researchers; the definitions referred to in this thesis are presented below: %LT = dUL/(dUL + dL) x 100 [3] (Eq. 2.1) %LT = 2 x dUL/(dUL + dL) X 100 [4,5,21] (Eq. 2.2) where %LT = percent load transfer deflection of unloaded side of the crack or joint 0.. c: L“ ll 5 6 dL = deflection of loaded side of the crack or joint Note that in the first formula (Eq. 2.1), the maximum load transfer that can be achieved is 50%. This is obtained when the two slabs deflect an equal amount. In this study, the following definition was used to compute the load transfer efficiency based on deflection. This formula was preferred for its conceptual simplicity and ease of application. %LTE = (dUL/dL)X 100 [23] (Eq. 2.3) where %LTE = percent load transfer efficiency dUL deflection of unloaded side of the crack or joint dL deflection of loaded side of the crack or joint Note that in the above formula, the maximum theoretical load transfer that can be achieved is 100%. This is obtained when the two sides deflect an equal amount. On the other extreme, if the two sides move with complete independence, the load transfer efficiency would be zero. Load transfer efficiency based on stress can be computed using formulae similar to those described above for load transfer based (M1 deflection. Sutherland anui Cashell [6] used the following definition to compute load transfer efficiency based on stress [11 ll (ff - fj)/ 'Load Leave—Side Load <0—- .175 .0122 .0122 Time (sec) 89:49—59:13 1 lb = 0.4536 kg Figure 5.5: Load Profile 49 slab measuring 41 ft [12.5 m] in length by 4.5 ft [1.4 m] wide. A tension of approximately 16000 lbs [71.3 KN] (3500 lb/ft width) [51 KN/m width] was induced in the test specimens by adjusting the two tensioning bars embedded in each test specimen and monitoring tension bar strain with the strain gages. To study the effects of high amount of tension one specimen was tensioned to 32000 lbs [142.6 KN] (7000 lb/ft width) [102 KN/m width], simulating an assumed coefficient of frictional resistance of 3.0. 5.3 Instrumentation and Data Collection Test specimens were instrumented for measurements of crack; openings, deflections under loadingy and. tensile strains (tensioning). Instrument locations aux; shown in Figure 5.6. Gage plugs and a vernier caliper were used to monitor crack openings. Linearly variable deflection transducers (LVDT's) were used for measuring deflections on either side of the crack. General purpose CEA-series strain gages were used to measure strain in the tensioning bars, thereby monitoring the amount of tension in the specimen. All testing and data collection operations were controlled using a 286-based personal computer equipped with a data acquisition system (Metrabyte I/O board and Labtech Notebook software). This system was connected directly to the hydraulic actuator control panel (MTS T/RAC controller) and signal conditioners. The arrangement, shown in Figure 5.7, allowed the coordinated control of both hydraulic 50 APPROACH SIDE LEAVE SIDE TRANSVERSE CRACK LVDT 4 . 5 ' 7 12" mummy. m LOAD puma: \bmo. 18" L___ I STRAIN GAGES GE PLUG FOR K)” FOR MONITORING ONITORING CRACK SLAB TENSION PENINGS .| Note: The distance between the edge of the crack and the LVDT's ranged between 1/2 to 3/4 inch. Figure 5.6: Test specimen instrumentation 51 286-PC MTS T/RAC SYSTEM Test. Definition & Control System LABTECH NOTEBOOK Data Acquisition Software —>| ans-nus 16 Bit Analog and Digital I/O Board T/RAC Controller Command Generation and Feedback ‘ optimization Unit A ‘ LVDT Signal Analog Conditioners Servocontrollers LVDT'S HYDRAULIC ACTUATORS Figure 5.7: Test control and. data acquisition setup rap. u-c‘ A.-- .- Vanna. 4:.“ 4.“- 5.4 52 actuators, as well as the collection of load data from both actuators and deflection data from two external LVDT's. The load. and.1def1ection. data. were collected following ‘the completion of 1” 1000, 2000, 5000, 10000, 20000, 50000, 100000, 300000, 600000, 900000, 1200000, 1500000, 1800000, 2400000, 3000000, 3600000, 4200000, 4800000, 5400000, 6000000, and 6600000 load applications. Each data collection channel was sampled 250 times per load cycle (about 1 sample per channel every 0.0008 seconds). Each data collection stage lasted one second (5 load cycles). This sampling rate and stage duration provided sufficiently close data points for plotting smooth curves and identifying peak loads and deflections (see Figure 5.8 and APPENDICES A and B). In this thesis, unless otherwise noted, all data pertaining to loads and relative deflections are based on the average of 5 sets of measurements. 5.4 Test Materials 5.4.1..Arti£icial Foundation Each test specimen was provided approximately uniform support through the use of an artificial foundation (FABCEL vibration isolation padding rated at specific "k" values). Since 54; is difficult tn) reproduce foundation properties accurately and consistently using real granular materials and this can introduce variability in test results, it was decided to use artificial material for the foundation 53 Deflection (in) Load (lbs) 0 fi 10000 -I .’\‘ ‘2 " V ‘ .- ;\ l \I“ j . '- - - . _. -_. . l ;i,. -_u g I ‘3 I . . l; : ' - s i : : I: 5 O I /' ‘\;‘\‘-.-“\ ll . . t“ \ _-_.__-i ll . o 02 01: <16 <13 1 Time (sec) .,..-, / -lnlh—m-aooo §—§ 6000 4000 ' r g .l l ' ------ Approach Deflection ' Leave Deflection § — Approach Load — Leave Load Figure 5.8: A plot of a data collection run 54 support. FABCEL is 21 high quality neoprene, molded into scientifically designed pads measuring 18" x 18" x 5/16" [46 cm x 46 cm x 3/4 cm]. The pad surfaces have molded recessed offset-cells to allow the neoprene to deform under load while maintaining lateral stability. Desired levels of foundation support are achieved. by providing various thickness and type combinations of these pads. Three layers of FABCEL—ZS were used to provide a foundation with a simulated modulus of subgrade reaction of approximately 100 psi/in [27 Kpa/m] under the entire test specimen. Two layers of FABCEL-25 were used under the high foundation specimen to simulate a modulus of subgrade reaction of approximately 250 psi/in [68 Kpa/m]. 5.4.2 Portland Cement Concrete Slabs The test specimens were PCC slabs measuring approximately 10 ft [12.5 m] long by 4.5 ft [1.4 m] wide and 9-in. [23-cm] thick at the crack. The cracks were of the plane-of-weakness type where load transfer is achieved solely by aggregate interlock. Each specimen contained 8 ft x 4 ft [2.8 m. x 1.2 m] of smooth steel wire mesh reinforcment (0.16% by area of concrete longitudinally) placed 3-in. [7.5-cm] below the slab surface. This reinforcment was typical of the size, quantity and type used in Michigan JRCP construction. The test program required the design of six concrete mixes for material factor specimens and four concrete mixes V . eon .y- C. r. ”A -~ "..4.» A. A. an A. av ~.. A. 2. a ‘ -\ . \ 3‘ ... .nc .. «a. :— it A: b~ L. h. an. e . 55 for design factor specimens. Mix designs provided by MDOT (mortar voids method of proportioning) were used as a starting point for trial batching to reach a final mix design (target slump 2—3 inches, air content 6-7 percent). Type I portland cement was used in each mix (cement factor of approximately six sacks per cubic yard of concrete). Air entrainment was provided through the addition of Microair air-entraining admixture. Tables 5.1 and 5.2 show the mix characteristics and other properties of the test specimens. Figures 5.9 and 5.10 show the average age—strength relationship of compression cylinders cast from the same mixes as the test specimens. Three types of virgin coarse aggregates were used in the concrete. One was natural gravel with rounded particles and smooth surfaces. The second aggregate was crushed limestone with angular edges and relatively rough surfaces. The third type was slag with rounded particles and rough surfaces. Physical characteristics of the three aggregates are shown in Table 5.3. Two different coarse aggregate gradations were used, designated as MDOT specification 6A (1.5-in. [4—-cm] top size, coarser gradation) and MDOT specification 17A (1.0-in. [2.5-cm] top size, finer gradation). The grading requirements for ‘these designations along' with. actual gradations of the materials are given in Tables 5.4 and 5.5. Test specimens incorporating recycled concrete were produced by breaking and crushing slabs cast using 6A gravel in commercial crushers, and then sieving, grading and 56 Table 5.1: Mix characteristics and concrete properties - material factor specimens Mix Proportions Entrained Compressive Strength Test. Specimens (oven-dry"weights) .Air (ZS-days) FA:FA:WATER:CEMENT % psi 6A Virgin Gravel 1966:1079z235z554 6.4 5681 GA Virgin Limestone 1817:1240:245:560 5.4 5295 61 Virgin Slag 1808:1297:305:744 6.7 5954 173 Virgin Gravel 1878:1163z283:548 6.0 4294 100% Recycled 1559:1209:263:523 6.7 4780 50-50 Recycle Blend 1682:1137:272:545 6.7 5352 Note: All weights are in pounds 57 Table 5.2: Mix characteristics and concrete properties - design factor specimens Test Specimens Mix Proportions (oven-dry weights) CA:FA:WATER:CEHENT Entrained Air Compressive Strength (28-days) psi Typical Tension and Foundation Typical Tension and Foundation High Tension nigh Foundation 1814:1264z221z570 1832:1238:217:549 1800:1238:234:563 1791:1250:234:563 6.5 7.4 6.8 6.8 4125 3645 4178 5837 Note: All weights are in pounds 58 6000 5mm« .17 n 3’ 4000 d m B . u E a . m 3000 g . GA VIRGIN sue H m a . (A saxnmenwemmmm a: 2000 - 5 g " 0 50-50 31mm 8 I: shimmenlnnummmu: £3 100% escrow) 1mm-i ' X inaxnmenweamnm 0 . u . u 0 1 0 20 30 AGE (days) Figure 5.9: Strength-gain curves of the test specimens (material factors) as .- VI,- .O\/ .- Ie.e"a ». (psi) STRENGTH COHPRESSIVE 59 6mm 5000- 4000- 3000 - HIGH FOUNDATION I wool“ 0 HIGH TENSION A mrczu. TENSION :. supponr 1000 + mucus O I 0 10 20 30 AG! (days) Figure 5.10: Strength-gain curves of aPecimens (design factors) the test 60 Table 5.3: Physical characteristics of concrete aggregates SPECIFIC psonrrow (24hr) AGGREGATE GRAVITY PERCENT Sand 2.62 2.20 SA Virgin Gravel 2 . 61 0 . 90 41/61 Virgin 2 . 60 0 . 66 Limestone GA Virgin Slag 2 . 41 3 . '71 173 Virgin Gravel 2 . 61 ‘ 0 . 90 100% 6A Recycled 2 . 40 4 . 66 Gravel 50-50 Recycle Blend 2 . 50 2 . 92 Note: Absorption capacity of sand for design factor specimens = 1.05 61 Table 5.4: Coarse aggregate gradation of 6A.material SIEVE TOTAL PERCENT PASSING 6A 6A 6A 6A 6A SIZE Spec Limestone Gravel Slag Recycled. 1.5 in 100% 100 100 100 100 1.0 in 95-100% 98 98 100 97 1/2 in 30-60% 38* 38 60 42 No. 4 0-8% 2 4 2 4 Note: *Gradation test run in the lab show only 16% passing 1/2 in sieve for 6A crushed Limestone 62 Table 5.5: Coarse aggregate gradation of 17A material S IEVE TOTAL PERCENT PASSING 17A 17A SIZE Spec gravel 1.0 in 100% 100% 3/4 in 90-100% 100% 1/2 in 50-75% 56% No. 4 0-8% 6% ' . A? v‘f‘ .- .vuo'“ .uov AAVV" “vol—nee . an. J‘s ~~"-‘ . -aa. I it“ 9 "V‘. b ~va..-. Veufiu. . 5.5 1 63 reblending this recycled material for use in test specimens. The 100% recycled test specimen was graded.tx> meet MDOT specification 6A. The 50-50 recycled blend specimen contained coarse aggregate composed of a blend of 50% (by weight) recycled. gravel concrete .graded t1) meet MDOT specification 6A and 50% virgin crushed limestone graded to meet MDOT specification 4A (2.5-in. [6-cm] top size). The 4A gradation requirements and actual 4A material gradation are presented in Table 5.6. 5.5 Test Procedures 5.5.1 Casting The concrete was mixed under careful laboratory control. First the coarse aggregates were sieved and blended (as required) to meet the appropriate gradation requirements. Then the coarse and fine aggregates were left in the laboratory to air dry. Tests were run to determine coarse and fine aggregate absorption capacities, unit weights and moisture contents. Trial batches were made to develop a final mix design for each test specimen. Prior to actual mixing, moisture contents (M5 the aggregates were again determined to adjust the mix water. The size of the test specimens and the capacity of the available drum mixers required mixing the concrete in a continuous stream of small batches to prevent the formation of cold joints. For each batch, one-half of coarse 64 Table 5. 6: Coarse aggregate gradation of 4A material S IEVE TOTAL PERCENT PASSING 4A 4A S I ZE Spec Limestone 2.5 in 100% 82 2.0 in 95-100% 47 1.5 in 65-90% 9 1.0 in 10-40% 2 1/2 in 0-20% - 3/8 in 0-5% - 65 aggregates, fine aggregates and water were blended first, followed by the addition of cement, the remaining one-half of the water (with air-entraining admixture), coarse aggregates and fine aggregates. The mixer was operated for five minutes after the addition of the final component. Concrete was hauled to the structural steel form in wheel barrows, where it was consolidated with a shaft-type vibrator. Each specimen was cast according to a schedule that generally allowed testing to begin after 28 days of curing*. Specimens were cured :U1 the laboratory' under polyethelene sheets. 5.5.2 Cracking The transverse crack was forced near midslab after approximateLy 18 hrs. of curing. A removable metal joint insert (1/4 in. x 1.0 in. [5/8 cm x 2.5 cm]) was used at the bottom of the 10—in. [ZS—cm] slab to form a plane-of-weakness at the midslab. The slab was cracked full-depth along the weakened plane by jacking one-half of *The first two specimens (6A gravel and 6A limestone) were tested. at 55 days and 52 days, respectively due to difficulties in getting the test program. to operate properly. According to 'Troxell, Davis and. Kelly [22] concrete made with 1.5-in. [4-cm] aggregates; 6 sacks cement per cu yd; and cured under standard conditions typically experiences a 9 percent gain in compressive strength between 28 and 55 days of curing. Thus, these specimens could have gained another 500 psi in compressive strength. However, actual increase in strength is expected to be less than this because of exposure to air after 28-days which may retard the hydration process due to drying. 66 the slab and frame while clamping the other half to the cracking frame. A hinge mounted on top of the casting frame assured a tensile mode of fracture. 5.5.3 Loading After 28 days of curing, each test specimen was moved to the test stand while still in the structural channel casting form, which was equipped with lifting loops. The slabs were held securely in the form during cracking and transportation by short steel studs, which were welded to the insides of the form around its perimeter. After each specimen was placed and centered on the test stand, the casting form was removed. This procedure ensured that the temperature steel was not over stressed prior to loading. Tension was induced in the specimens as described previously. LVDT's were then set to zero, the data acquisition system was initialized, and the repetitive loading was begun. Load-deflection data were collected an: the intervals described earlier. Each test was run until the temperature steel ruptured (see Figure 5.11). During the test, applied loads and slab tension were monitored and adjusted as needed. 67 Figure 5.11: A view of a failed specimen CHAPHEEK‘VI DISCUSSION AND ANALYSIS OF TEST RESULTS 6.1 Evaluation of Load Transfer The ability of transverse cracks to transfer load is a major factor in the structural performance of the crack and the surrounding slab fragments. In this study, the ability to transfer load was evaluated by comparing the deflections [of the two slab fragments using the following definition originally presented in chapter 2: %LTE = (dUL/dL) X 100 [23] (Eq. 2.3) where %LTE = percent load transfer efficiency dUL = deflection of unloaded side of the crack dL = deflection of the loaded side of the crack Note that in the above formula, the maximum theoretical load transfer that can be achieved is 100%. This is obtained 68 69 when the two sides deflect an equal amount. On the other extreme, if the two sides move with complete independence, the load transfer efficiency would be zero. 6.2 Test Results - Material Factors 6.2.1 Effect of Type of Coarse Aggregate The effect of coarse aggregate type on the aggregate interlock load transfer characteristics of transverse cracks was studied by comparing the performance of three test specimens, each containing a different type of coarse aggregate meeting the MDOT 6A gradation specifications. The three types of aggregates used were crushed limestone, gravel and slag. Figures 6.1 and 6.3 summarizes some of the test results for these materials. Detailed results are presented in APPENDIX A. The results show tflun: specimens containing’ crushed limestone and gravel coarse aggregates started with and retained higher load transfer efficiencies than the specimen containing slag coarse aggregate. This difference in performance is probably due to the different textures of the crack faces of these specimens, as illustrated in Figure 6.2. It is seen that the specimens containing crushed limestone and gravel have rougher crack faces (more large protrusions and macrotexture) than the specimen containing slag. This is due to the fact that slag aggregate apparently 70 Load Transfer Efficiency (%I 100 0 l l l l 0 300 600 900 1200 1500 Thousands of Load Cycles D 6A VIRGIN GRAVEL + 6A VIRGIN LIMESTONE 914 6A VIRGIN SLAG Figure 6.1: Effect of coarse aggregate type on the relation between LTE% and number of load cycles 71 imestone Crushed L Gravel Slag faces of small test crack 2 6 Figure Exposed 6A aggregate type, COII’SG varying specimens, gradation materials 72 fractured at the time of crack development, whereas limestone and gravel pulled out through the loss of bond, thus resulting in rougher crack faces. It is.pg§§ible that the test results are biased due to slight differences in the three coarse aggregate gradations. Table 5.4 indicates that, although all three materials meet the requirements of MDOT gradation designation 6A, the slag is somewhat finer than either the limestone or gravel. It is also possible that the results were affected by the slight differences in mix designs* and strengths between the three test slabs (see Table 5.1). However, it seems most likely that the observed differences in performance (endurance of load transfer efficiency) are mainly due to differences in the crack face texture (see Figure 6.2) and coarse aggregate particle strengths. The highly porous slag particles were obviously of lower strength (see Tables 6.1 and 6.2) and produced crack faces with little macrotexture. These conclusions should be verified in future tests through the use of more comparably graded aggregates and identical curing conditions for each specimen. Figure 6.3 shows the approach side peak deflections of the three test specimens after repeated loading. The crushed limestone specimen exhibited lower deflections than the gravel or slag at all times. Similarly, the gravel generally ' Recall that rough-textured, angular, elongated particles require more water to pmoduce workable concrete than do smooth, rounded, compact aggregates. Thus, aggregate particles that are angular require more cement to maintain the same w/c ratio. Hence, slight differences in mix designs are unavoidable when using' different types of coarse aggregate if workability and w/c ratio are to remain constant. 73 Table 6.1: Strength estimation of the three coarse aggregate types using flexural strength FLEXURAL STRENGTH CA TYPE (24 hrs) psi Gravel 253 Limestone 261 Slag 187 Note: ASTM C78-84, Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading) 74 Table 6.2: Strength evaluation of the three coarse aggregate types using Los Angeles (LA) test (ASTM Test Method C131-89) CA Type Percent Loss Gravel 19 Limestone 31 Slag 39 Note: It is generally believed that the abrasion resistance of aggregate is mainly related to its strength. The Los Angeles (LA) test has been widely used as an indicator of the relative quality of coarse aggregate particles. The LA test is a measure of degradation of mineral aggregates of standard gradings resulting from a combination of actions including mm and mm, impact andgrinding 75 the fact that the 17A gravel test specimen was able to performed better than the slag. Although the temperature reinforcement eventually ruptured lJliall three cases, the crushed limestone concrete was able to endure a significantly higher number of load repetitions than the other two specimens. This better endurance is probably due at least in part to the relatively low deflections that are attributable to the angularity of the crushed particles, which increase the sliding resistance of the crack faces. 6.2.2 Effect of Gradation of Coarse Aggregate The effect (Hf coarse aggregate gradation (n1 load transfer characteristics of transverse cracks was studied by comparing the results of two specimens, one cast using coarsely graded gravel (6A Gradation: 1.50-in. [4-cm] top size) and the other cast using more finely graded gravel (17A Gradation: 1.0-in. [2.5—cm] top size). The test results are summarized in Figure 6.4 (detailed results are presented in Appendix A). The results show that for initial loading cycles (up to 20,000 cycles) both test specimens performed comparably. As the number of load cycles increased, the load transfer efficiency of the 17A gravel test specimen dropped slightly. This is probably due to the relatively small size of coarse aggregates which, after initial attrition or abrasion of the crack faces, requires a larger vertical displacement of the two slab fragments to make contact and transfer load. However, this increase in looseness was not 76 Approach Peak Deflection (in) -0.01 — -* -003“: f, -0.05 i' - -4106 '4107 _ -0.08 1 1 ‘ 1 O 300 600 900 1200 1500 Thousands of Load Cycles U 6A VIRGIN GRAVEL + 6A VIRGIN LIMESTONE *6 6A VIRGIN SLAG Figure 6.3: Effect of coarse aggregate type on the relation between approach-side peak deflection and number of load cycles 77 Load Transfer Efficiency (%I 100 80 60 4O 20 O l l 0 300 600 900 Thousands of Load Cycles [3 6A VIRGIN GRAVEL X 17A VIRGIN GRAVEL Figure 6.4: Effect of coarse aggregate gradation on the relation between LTE% and number of load cycles 78 large enough to produce immediate failure, as evidenced by the fact that" the 17A gravel test specimen was able to endure a number of load cycles comparable to that of the 6A gravel test specimen before the steel reinforcement eventually ruptured. These results agree with the results of Nowlen [5], who observed the following relationship between top size of coarse aggregate and load transfer efficiency for two different joint openings (weakened-plane transverse joint). Joint Opening'iin) 0.035 0.065 Aggregate Top Size Load Transfer Efficiency 3/4" 45% 21% 1.5" 52% 23% 2.5" 96% 55% It is seen that an increase in top size of coarse aggregate from 3/4—in. [2—cm] to 1.5-in. [4-cm] improved the effectiveness of the 0.035-in. [0.089-cm] joint by only 11 percent. Effectiveness of the 0.065-in. [0.165-cm] joint did not change significantly. Thus, the results (ME this and previous studies show that effect of top size of coarse aggregate is not pronounced in the range of 3/4-in. [2—cm] 79 to 1.5—in. [4—cm] top size. 6.2.3 Effect of Treatment of Coarse Aggregate The effect of treatment of coarse aggregate on aggregate interlock load transfer characteristics of transverse cracks was studied by comparing the performance of three test specimens, each containing' a different treatment of coarse aggregate. The three treatments of aggregates included virgin gravel aggregates (MDOT gradation 6A), 100% recycled gravel concrete aggregates (MDOT gradation 6A), and a 50-50 blend of recycled gravel concrete (MDOT gradation 6A) and large virgin limestone (MDOT gradation 4A) aggregates. Figure 6.5 summarizes the test results of these treatments (details are presented in Appendix A). The results show that the specimen containing virgin coarse aggregates performed considerably better than the other two test specimens which contained recycled concrete as coarse aggregates. The examination of the crack faces of the 100% recycled specimen revealed that very few pull outs of aggregate particles existed (see Figure 6.6). The reason for this condition is probably related to the mode of fracture of recycled concrete aggregates. Coarse aggregates produced by recycling concrete consist of two materials (i.e., cement mortar and original aggregate) bonded together. At the time of crack development, recycled concrete aggregates apparently often fracture at the old 80 Load Transfer Efficiency (%I 100 'z‘. 'I. J a = e 60 *‘" O l l 0 300 600 900 Thousands of Load Cycles D 6A VIRGIN GRAVEL 1' 100% 6A RECYCLED 9* 50-50 RECYCLED BLEND Figure 6.5: Effect of coarse aggregate treatment on the relation between LTE% and number of load cycles 81 Figure 6.6: Exposed crack face of 100% recycled gravel concrete specimen after loading 82 bond interface, thus resulting in the above condition. Furthermore, the use of comparable quantities of recycled aggregate results in nearly a 50% reduction in the actual number of virgin coarse aggregate particles in the mix. If the shear transfer characteristics of the slab depend upon the number and quality of virgin aggregate particles at the crack interface, it stands to reason that concrete utilizing only recycled concrete aggregates may fare poorly. The unexpected poor performance of 50-50 recycle blend specimen may also be attributable to a reduction in the number of virgin aggregate particles at the crack face (see Figure 6.7). Not only are there fewer virgin particles present because of the use of recycled concrete materials, but the use of an equal weight of large aggregate also results in a smaller number of particles (although the few that are present are large enough to provide significant interlock for some time). The distribution of particles that protrude from the crack face can be fairly widespread, as seen in Figure 6.7. It should also be noted that during transportation of this specimen (50-50 recycle blend) from the cracking frame to the test stand, one of the lifting ropes broke, causing one end of the specimen to drop a distance of about 2-in. [5-cm]. This may have contributed to the observed performance since initial load transfer efficiency of this specimen was also low compared to all other specimens except one (6A virgin slag). It is recommended that this test cell (50-50 recycled 83 Figure 6.7: Exposed crack face of 50-50 recycled blend specimen after loading 84 blend) should be replicated in future tests to determine whether the observed results were influenced by the handling of the specimen or were truly indicative of the performance of this mixture. 6.3 Test Results - Design Factors 6.3.1 Effect of Slab Tension The effect of slab tension on aggregate interlock load transfer characteristics of transverse cracks was studied by comparing the performance of two test specimens (6A virgin gravel), one with an induced tension of 16000 lbs [71.3 KN] (3500 lb/ft width) [51 KN/m width] and the other with an induced tension of 32000 lbs [142.6 KN] (7000 lb/ft width) [102 KN/Hl width]. The amount of tension required. was computed using subgrade drag theory, modelling assumed coefficients of frictional resistance of 1.5 and 3.0, respectively, for a 9—in. [23-cm] slab measuring 41 ft [12.5 m] in length by 4.5 ft [1.4 m] wide. The test results are summarized in Figure 6.8. Detailed results are presented in APPENDIX B. The test results show that the specimen with lower tension started with and retained higher load transfer efficiencies than the specimen with higher slab tension. This difference in performance is probably due to the wide; crack opening and consequent higher level of stresses and strains in longitudinal steel in the high tension specimen. (\5 Fi be 85 Load Transfer Efficiency (%) 100 80 60 40 —-- I 20 0 l l l l 0 600 1200 1800 2400 Thousands of Load Cycles 9K Typical Tension + High Tension Figure 6.8: Effect of slab tension on the relation between LTE% and number of load cycles 86 The induction of 16000 lbs [71.3 KN] slab tension resulted in 0.015-in. [0.038-cm] crack width, whereas induction of 32000 lbs [142.6 KN] resulted in a 0.023-in. [0.058-cm] wide crack, an increase by a factor of 1.5. This increased crack opening may cause a partial loss of contact between the two crack faces, which, in turn, diminishes the bearing and crushing action of cement matrix. Thus, load is transferred solely through the sliding action of coarse aggregate particles. Hence, an increase in crack width results in an increase in looseness, requiring a vertical displacement of the loaded side of the slab to make contact and transfer load (see Figure 6.9). Analyses of the load-deflection data of the two specimens also shows the presence of significant looseness in the high tension specimen. Figure 6.10 illustrates the detrimental effects of increased looseness in the high tension specimen on its load transfer capacity. It is seen that at small loads, the load was not fully transferred to the unloaded slab fragment. This is due to lack of immediate contact of the two crack faces. However, with an increase in load, better contact was made between aggregate particles and the load transfer efficiency increased. Moreover, presence of excessive looseness suggests that for a fraction of time longitudinal steel is picking up the shear and while doing so is also being bent to accommodate the vertical displacement of the loaded slab fragment before aggregate interlock becomes effective. The combined effect of high tensile stresses (due to high tension) and high 87 Coarse Aggregate 1/2(2) Crack Width 1/2(Z) Looseness = z = 2 (r - For 1.5" top size coarse aggregate particle Crack width = 0.015" Z = 0.0003" Crack width = 0.023" Z I 0.0007" Figure 6.9: Aggregate looseness geometry [5] 88 LTE°/o 100 it 1.2 60 - 20 —~ -‘ 0 1 r 6 7 8 9 Load (1000 lbs) I + Typical Tension —I— High Tension I Figure 6.10: Effect of looseness on the relation between LTE% and load magnitude 89 shearing stresses (due to excessive looseness) under repeated heavy load applications may cause the accelerated rupture of steel. Note that the longitudinal steel in JRCP is not designed for shear loads. 6.3.2 Effect of Foundation Support The effect cu? foundation support (M1 the aggregate interlock load transfer characteristics of transverse cracks was studied by comparing the performance of two specimens (6A virgin gravel), one placed on three layers of FABCEL-25 simulating a modulus of subgrade reaction of approximately 100 psi/in [27 kPa/m], and the other placed on two layers of FABCEL-ZS simulating a modulus of subgrade reaction of approximately 250 psi/in [68 kPa/m]. The test results are summarized in Figures 6.11 and 6.12. Detailed results are presented in APPENDIX B. The results show that specimens placed on the stiffer foundation (250 psi/in [68 kPa/m]) started with and retained higher load transfer efficiency than the specimen placed on the relatively soft foundation (100 psi/in [27 kPa/m]). For example, the initial load 'transfer‘ efficiencies (after application of load cycle # 1) of these specimens were 96% and 91% respectively. Load transfer efficiencies at the end of two million load cycles were 91% and 87% respectively. The results also show that high foundation specimen was able to endure a considerably higher number of load cycles (6.6 million) compared to the low foundation modulus 90 Load Transfer Efficiency (%l 100 l 80 40—~—» O l l l l l l 0 1 2 3 4 5 6 Millions of Load Cycles *6 Low Foundation + High Foundation Figure 6.11: Effect of foundation support on the relation between LTE% and number of load cycles 91 Approach Peak Deflection (in) 0 -0.01 ._ ~ _CL02!_..WHW . 77H“ ...... -0.06 - ~ Illll -0.07 ‘0.08 l l I l l l 0 1.2 2.4 3.6 4.8 6 Millions of Load Cycles + High Foundation —i— Low Foundation Figure 6.12: Effect of foundation support on the relation between approach-side peak deflection and number of load cycles 92 specimen (2.7 million). Thus, it is apparent that the added stiffness of the high foundation modulus specimen contributed significantly to the long-term aggregate interlock load transfer characteristics of the transverse crack. This increased endurance is due to the fact that strong foundation support reduces the magnitude of the peak and differential deflections, thereby allowing the application of more load cycles for any given loss of interlock and load transfer. Figure 6.12 shows the approach side peak deflections of the two test specimens after repeated loading. It is seen that the high foundation modulus specimen exhibited lower deflections than the low foundation modulus specimen at all times. Similarly, Table 6.3 shows that the high foundation modulus specimen experienced a lower magnitude of differential displacements at all times compared. to ‘the low foundation modulus specimen. 6.4 Development of a Model One of the critical response variables in this testing program is the number of load cycles to failure (N). Based on the experience gained from other reliability studies and an examination of the load cycles to failure data generated from the 10 test runs, the N data were transformed by taking logarithms, resulting in the performance variable Y = Loglo N. An additive linear model was fit to the Y-data resulting in estimated effects for changes in the material and design 93 Table 6.3: Differental deflection data of the two specimens used in the evaluation of effect of foundation support differential deflection under peak load, mils slab # High Low cycle 8 Foundation Foundation 1 1.62 5.30 1000 1.62 5.98 2000 1.64 6.13 5000 1.64 6.50 10000 1.64 6.60 20000 1.75 6.60 50000 1.98 6.36 100000 2.05 6.92 300000 2.05 6.93 600000 2.05 7.72 1200000 2.82 7.12 1800000 3.30 ’7.13 2400000 4.76 8.78 2700000 - 43.48* 3000000 5.60 3600000 5.85 4200000 5.98 4800000 6.78 5400000 7.98 6000000 8.28 6600000 31.63” Note: * = steel had ruptured 94 factor levels. The predictive model developed is presented below: Loglo N = 6.48 + 0.23(LS) - 0.55(SL) - 0.41(RB) - O.47(R) - 1.08(HT) + O.34(HF) where LS = 6A Virgin Limestone SL = 6A Virgin Slag RB = 50-50 Recycled Blend R = 100% 6A Recycled Gravel HT = High Tension (7000 lb/ft width) HF = High Foundation (250 psi/in) The formal analysis is presented in APPENDIX C. The estimate of the standard deviation of the pure error in Y is 0.064 which transforms to an estimated error of about 16% in measured cycles to failure. Not surprisingly, only extreme differences ix: cycles tx> failure, PM are statistically significant because the pure error is estimated with only one degree of freedom. 6.5 Equivalence of Performance Maintenance of adequate load transfer through aggregate interlock over a large number of heavy truck load 95 applications 543 critical tn) the satisfactory' long-term performance of JRCP. An Endurance Index, EI, concept may be used to describe the long-term transverse crack performance. In this study, Endurance Index (expressed as percentage) is arbitrarily defined as the ratio of the area under the curve of load transfer efficency, LTE%, versus logarithm of number of load cycles, Loglo N, to the corresponding area under the curve obtained by setting LTE = 100% for Loglo N = 8 (i.e., 100 million load cycles). The results are summarized in Figure 6.13. Detailed results are presented in APPENDIX D. Figure 6.13 can be used to show equivalence of performance. It is seen that bars of approximately equal height indicate specimens with approximately equal endurance index values. For example, the high tension specimen and 6A virgin slag specimen exhibited comparable EI values i.e., 57 and 58 percent respectively. The reason for these low and comparable EI values is probably related to the inefficient functioning of the aggregate interlock mechanism in these two specimens. As pointed out earlier, significant looseness in the high tension specimen (caused by increased crack width due to high tensioning) prevented aggregate interlock from offering full resistance tx: the applied load. This resulted in lower load transfer efficiency and also subjected the longitudinal steel to higher level of stresses and strains. Similarly, in the 6A virgin slag specimen aggregate interlock mechanism was not effective in stress control due to lack of macrotexture and roughness at the crack face. Thus, it may be concluded that the effect of 96 Endurance Index (96) 81 n .._______________________________________:__________________________________________=_______ ESSSSSSSSESSS nae/Zigzag 63 58 100 " 804 60] 40— 20~ 0 d n m B 0 :w 0 5 1:3 100% Recycle - High Tension 6A Slag E 6A Limestone “IIIIIIIIII High Foundation a\\f\ 6A Gravel 17A Gravel Figure 6.13: Equivalence of performance 97 increase in crack opening on aggregate interlock mechanism is same as that of fracture of coarse aggregate particles since in both instances, aggregate interlock mechanism is prevented from functioning at full efficiency. A similar comparison can be made between the two recycled specimens. Figure 6.13 shows that 6A 100% recycled gravel specimen and 50-50 recycled blend specimen exhibited approximately comparable EI values i.e., 63 and 65 percent respectively. These low eumi approximately comparable EI values are also attributable to the inefficient functioning of aggregate interlock mechanism in these two specimens. The reasons for somewhat ineffective aggregate interlock mechanism were discussed previously. It was pointed out that very few pull outs of coarse aggregate particles existed at the crack interfaces of these specimens. However, note that the BI values for the recycled specimens are 9 to 14 percent higher than the BI value of 6A virgin slag specimen. This is due to the fact that crack face textures of the recycled specimens, though relatively smooth in time global sense, were somewhat rougher than the 6A virgin slag specimen (see Figures 6.2, 6.6 and 6.7). 6A virgin gravel specimen and 17A virgin gravel specimen exhibited approximately comparable EI values i.e., 74 and 72 percent respectively. This suggests that effect of coarse aggregate gradation is not significant in the range of 1.0-in. [2.54-cm] and 1.5-in. [4.0-cm] top size. However, note that these EI values are considerably higher than EI values of the four specimens discussed above. This 98 significant increase in E1 is attributable to the fact that in virgin gravel specimens, gravel pulled out through the loss of bond (due to high particle strength, see Tables 6.1 and 6.2) thus resulting in crack faces with more protrusions and macrotexture. Figure 6.13 shows. that, EI, further improves with the angularity of the coarse aggregate particles as evidenced by the BI value of 77 percent exhibited by 6A virgin crushed limestone specimen. The most significant improvement in E1 was observed when the stiffness of the foundation was increased from 100 psi/in [27 kpa/m] to 250 psi/in [68 kpa/m]. The EI values for these two specimens are 74 and 81 percent respectively. This increase in BI is due to the fact that strong foundation support reduces the magnitude of differential deflections, thereby allowing the application of more load cycles to produce a given loss of aggregate interlock and load transfer. 6.6 Discussion of Test Results 6.6.1 Significance of Rougher Crack Face The results of this study show that aggregate interlock load transfer efficiency and endurance is strongly related to texture of the crack face. The crack face texture is primarily a function of type, number and size of coarse aggregate particles at the crack face and the mode of fracture. It was observed that specimens in which cracks vii 1. >4 9‘ u 99 developed around the aggregate (virgin limestone and virgin gravel) developed higher initial load transfer efficiencies and. were able to ‘maintain this higher level over a considerably larger number of load cycles than specimens in which cracks developed through the aggregate (virgin slag and recycled slabs). The difference in performance is related to the texture of the crack face of these specimens as described previously. Specimens with rougher crack faces (virgin limestone and virgin gravel) exhibited lower approach-side peak deflections than specimens with relatively smooth crack faces (virgin slag and recycled). More importantly, specimens with rougher crack faces experienced much lower differential deflections (relative vertical displacements) than specimens with smooth crack faces. The magnitude of differential deflections of these specimens after various load cycles are tabulated in Table 6.4. It is seen that specimens with fracture through the aggregate had much higher (66% to 281%) initial differential deflections than specimens with fracture m the aggregate. The higher differential deflections of the two slab fragments results in higher level of shear stresses and strains in longitudinal steel. It is obvious that higher levels of strains and strain reversals would accelerate fatigue failure of longitudinal steel as is evidenced by the relatively small (and comparable) number of load cycles endured by the three specimens with smooth crack faces. Thus, it can be concluded that W fr. ,- . o o i - - iv- in on 01 f . ;- maoi', 0‘ 100 Table 6.4: Differential deflection data - material factors differential deflection under peak load, mils slab! A B C D E F cmfleil 1 1.94 2.92 3.68 7.40 6.20 6.13 1000 3.28 3.93 4.56 7.40 6.20 6.13 2000 3.54 4.34 5.28 8.83 7.94 6.13 5000 5.03 4.74 5.28 9.82 8.50 6.83 10000 5.38 6.43 6.84 10.85 8.98 7.04 20000 5.64 7.52 7.20 12.30 10.58 8.38 50000 5.64 7.80 9.33 13.53 10.98 15.60 100000 6.32 7.80 12.15 14.84 12.55 17.90 250000 - - - 65.40* - - 300000 6.62 9.35 15.60 72.08* 22.73 350000 - - - 63.40* 600000 7.58 11.66 18.63 900000 8.33 45.85* 83.64* 1500000 64.73* Notes * = steel had ruptured A = 6A virgin limestone B = 6A virgin gravel C = 17A virgin gravel D = 6A virgin slag E = 6A 100% recycled gravel F = 50-50 recycled blend 101 WW and thereby ensures that longitudinal steel is not subjected to a high level of stresses/strains and their reversals. This provides higher initial load transfer efficiency and better endurance. The fact that crushed limestone performed the best among the three types of coarse aggregates does not necessarily means that this is always the case. Sutherland and Cashell [6] indicate that, for a given size (1.0-in. [2.5-cm] and 2.5—in. [6.3-cm], gravel performed better than cmushed limestone. These researchers noted that crushed limestone fractured at the time of joint development (weakened-plane transverse joint). Thus, the advantages of angular, rough-surfaced crushed limestone aggregate particles were lost because fracture of aggregate results in a smooth crack face. Note that in this study crushed limestone was of good quality (see Table 6.1), thus, pulled out through the loss of bond. The key factor which determines the mode of fracture is paste/aggregate bond strength at the time of crack development. Therefore, it is desirable to have paste/aggregate bond low at the time of fracture so that the crack passes around the aggregate resulting in a rough crack face. On the other hand, high paste/aggregate bond is required to keep coarse aggregate particles embedded in the cement matrix under repeated heavy truck traffic. The paste/aggregate bond generally increases with increase in concrete strength i.e., age of concrete. Thus, the age of 102 concrete at the time of crack development may play an important role in determining the texture of the crack face. In view of the above, it is recommended that in future experimentation different types CHE aggregates should be evaluated in the context of age of concrete at the time of cracking (effect of fracture delay). 6.6.2 Effect of Aggregate Interlock Looseness The term looseness may be defined as conditions that prevent aggregate interlock from offering full resistance to applied load. Conditions which may affect the aggregate interlock looseness include top size of coarse aggregate particles, abrasion/attrition of coarse aggregate particles and sockets under repetitive loading, and opening of the crack due to thermal and drying shrinkage of the concrete. Aggregate interlock mechanism can function at full efficiency only after the looseness is taken Lu: by load displacement of the slab fragments. Thus, the effect of looseness is to reduce the potential usefulness of the aggregate interlock mechanism by an amount proportional to the degree of looseness present at the cmack interface. Figure 6.14 illustrates the above-described effect of looseness on load transfer capacity. This figure is drawn from the load-deflection data obtained for the high tension specimen after load cycle # 1” :n: is seen that, due to presence of significant looseness (caused by increased crack width due to high tension), the magnitude of differential 103 Differential Deflection (mils) LTE% 100 Load (1000 lbs) I 9* Differential Defl + LTE% I Figure 6.14: Illustration of effect of aggregate interlock looseness on load transfer capacity 104 deflections increases with increases in applied load. This increase in differential deflection is accompanied by a loss in load transfer capacity. However, after the looseness is taken up by load displacement of the slab fragments, the magnitude of differential deflection starts decreasing and the load transfer capacity begins to increase. However, note that as the load approaches the peak load the magnitude of differential deflection starts increasing again and consequently the load transfer efficiency begins tt> drop. This suggests that ‘this specimen. experienced slippage of the two vertical faces under the action of the peak load. This is probably related to high tensioning of this specimen which resulted in increased crack width, which, in turn, pulled apart the coarse aggregate particles from their respective sockets. In view of the above, it is recommended that the effect of large top size aggregates (e.g., 2.5-in) on aggregate interlock load transfer characteristics of transverse cracks should be evaluated in future tests, particularly for large crack openings (high tension specimens). 6.6.3 Effect of Repetitive Loading It. was observed. that aggregate interlock. load transfer efficiency of transverse cracks decreases with increasing load cycles, as would be expected. This reduction in load transfer capacity is attributable to the increase in looseness at the crack face caused by wearing out of 105 interlocking features through repeated slippage of the two vertical faces under accumulated load applications. Generally, load transfer efficiency was cmserved.tx> drop during initial load cycles, then typically remained approximately constant until the longitudinal steel began to yield, after which it dropped very sharply (due to opening of the crack). The effect (n5 repetitive loading' on load 'transfer capacity is illustrated in Figure 6.15. This figure is drawn from the load-deflection data collected from 17A virgin gravel specimen. As stated earlier, small amounts of initial looseness existed in this specimen due to relatively smaller top size coarse aggregate (1.0-in. [2.54-cm]), as is seen from the top curve in Figure 6.15, though the effect is not prounounced. However, as the number of load cycles increased the magnitude of differential deflections also started increasing at a sharper rate (see curves for cycle #50,000). This increase :hi looseness jproduced. decreases 1J1 load transfer capacity, as explained previously. As the number of load cycles further accumulated, the differential deflection curve (see curve for cycle # 100,000) shifted upward, indicating at significant increase th looseness, which in turn shifted the LTE curve further down. Note that LTE is now only 77% under the approach side peak load, a loss of approximately 15% from ‘the initial 91% load ‘transfer efficiency. The fact that this specimen was able to endure approximately another 800,000 load cycles suggests that 106 Relative Deflection (in) LTE% 0.014 100 (1012‘ "80 —8— no Cycle # 1 0°01 7 -8- LTE% Cycle # 1 0.008 ~ [6° ' RD Cycle # 60000 ' LTE% Cycle # 50000 0.006 d _ ee— no Cycle # 100000 40 ea— LTE% Cycle # 100000 0.00 4 _ t 20 (1002“ O I I I I O 0 2 ~4 6 a 10 Load (1000 lbs) RD - Relative Deflection Figure 6 . 15: Effect of repetitive loading on aggregate interlock load transfer (data from 17A virgin gravel specimen) 107 longitudinal steel had not begin to yield at this point i.e., there was no appreciable change in crack width. Thus, this increase in looseness is attributable to wearing out of the crack interface, more specifically, abrasion/attrition of the coarse aggregate particles and plastic deformation of the aggregate sockets (cement matrix) under repetitive heavy loads. From this description it is apparent that coarse aggregate particles with good abrasion and impact resistance and strong cement matrix should provide longer performance under accumulated heavy loading conditions. In view of the above, ii: is recommended that 1J1 future experimentation aggregates of different quality (source) should be evaluated e.g., limestone # 1 vs limestone # 2, gravel # 1 vs gravel # 2 etc. 6.6.4 Design of Steel Reinforcement As stated earlier, for transverse cracks to exibit good load transfer characteristics, it is imperative that steel reinforcement must serve its intended purpose i.e., hold the fractured concrete in close interlock. The unexpected relatively early rupture of steel during this study indicates that current longitudinal steel quantities (0.16 percent by area of concrete) may be inadequate for the combined tension and shear loading conditions encountered in the field. It is realized that the laboratory test is rigorous in nature in that each specimen is under adverse loading conditions (i.e., combined tension and shear) 108 constantly, whereas in the field due to daily and seasonal temperature changes, tensile stress in longitudinal steel varies with cyclic opening and closing of transverse cracks. Moreover, the rate of application of wheel loads in the field varies and is generally much lower than 5 cycles per second applied in this study; thus, allowing the pavement structure to recover between load applications. Thus, laboratory test specimens were subjected to more severe loading conditions than those encountered in the field. Nevertheless, rupture of steel during this study represents an rmxxi for developing improved reinforcement design procedure based on combined shear and tension failure criteria. Currently, in most design procedures the required amount of reinforcement in JRCP is determined by using subgrade drag theory i.e., area of steel is calculated to resist tensile stresses/strains that develop due to friction between the slab and the foundation. The shear stresses/strains caused by differential displacement of the two slab fragments are neglected. whereas, shear stresses and strains may become very high depending on magnitude of the load, crack interface roughness and level of support provided by the foundation. The cumulative effect of high shear stresses/strains and their reversals combined with tension, under' accumulated. heavy loads can result in shear-fatigue failure of the longitudinal steel. The following calculations based on the results of this study illustrate the above point. We know from strength of materials that 109 Strain, 8 (Elongation)/(Original length) (AL)/L in/in and the relation between the ultimate stress and strain is given by Tensile Strain, 3t (Tensile Strength)/(Elastic Modulus) = F E y/ Shear Strain, GS = (Shear Strengthl/(Shear Modulus) = 0.6Fy/G where E = 29,000,000 psi, and C) II 12,000,000 psi In this study MDOT's standard welded smooth wire mesh (see Figure 6.16) was used in each of the specimens. The properties of the mesh are tabulated below: - Area of longitudinal steel, Asl = 0.172 in2 [1.11 cm2] - Ultimate tensile strength or > 75,000 psi [5273 kg/cmz] - Transverse steel spacing 12—in. [BO-cm] - Cold rolled - Carbon Content 0.6% - 0.8 o\° 110 6" X 12" Standard Mesh Transverse steel: 0.300-ir. \ diameter Lmooth \ inmsat 12 in. c/c Longitudinal steel: 0.331-in. diameter smooth bars at 6 in. c/c Figure 6.16: Details of 6"x12" wire mesh reinforcement 111 Using these numbers the ultimate strain capacities of the longitudinal steel are: Tensile Strain, 8t 0.00259 in/in, and 0.00375 in/in- Shear Strain, 83 If ii; is assumed that aflJ. the stresses/strains are taking place over the width of the crack only (i.e., no debonding' due to slippage between the steel and ‘the concrete), then the magnitude of applied shear strain, computed for 51 crack opening CHE 0.015-in. [0.038-cm] and minimum differential displacement of 1.94 mils observed among all the data (see Table 6.4: virgin limestone, cycle # 1), equals 0.12933 in/in. This is far higher than the ultimate shear strain capacity of the steel. Since the steel had not ruptured at this point, this suggests that there is some debonding/slippage taking place between the steel and the concrete. Assuming debonding/slippage is taking place along 12-in. [30-cm] length of the longitudinal steel (i.e., center to center spacing of transverse steel), it can be shown that the crack. may open 0.031—in. [0.079-cm] before steel ruptures in tension, and that slab fragments may deflect differentially up to 45 mils before steel is sheared. A look at the maximum measured values (prior to steel rupture) of crack. openings (0.023-in. [0.058-cm]) and «differential displacements (22.73 mils) among all the specimens in this study show that they were well short of these limiting 112 values. This suggests that steel rupture was (hue to combined tension and shear fatigue. This contention is supported by the differential deflection data tabulated in Table 6.4. It is seen that the three specimens (6A virgin slag, 6A 100% recycled, and 50-50 recycled blend) in which steel ruptured at relatively low and comparable number of load cycles (about 300,000), exhibited considerably higher differential deflections throughout the course of their loading history; whereas the other three specimens (6A virgin limestone, 6A virgin gravel, and 17A virgin gravel) started with much lower differential deflections which started increasing generally after several hundred thousand load cycles. It is obvious that higher level of differential displacements (higher shear stresses/strains and their reversals) could not be sustained over a longer period of time as evidenced by the accelerated rupture of steel in the aforementioned three specimens. In view of the above, further research is needed to establish a reinforcement design procedure based on a more comprehensive approach (combined tension and shear—fatigue) than the conventionally used simple approach based on the drag theory. One possible approach would be to develop fatigue curves for longitudinal steel, in terms of stress levels and number of load cycles required to cause failure at a certain given level. The relationship between stress level and number of load cycles may be shown on an S-N curve (see figure 6.17). Such a curve, presented on a log-log 113 Stress (log scale) Cycles to failure (log scale) Figure 6.17: A typical S-N curve for steel [25] 114 basis, portrays the behavior of a specific structural steel detail for a given loading condition and can be expressed by [25] Fn = S(N/n)k where Fn = fatigue strength computed for failure at n cycles 8 = stress which produced failure in N cycles 7i” ll slope of the straight-line S-N curve Such a relationship can be developed for JRCP longitudinal steel by conducting cyclic loading tests on laboratory specimens. The tests should be conducted so that the stress level during the course of loading remains constant for all specimens. The slope of the straight-line S-N curve can be obtained by varying the magnitude of stress level from specimen to specimen. Once this relationship (for a typical type and quantity of longitudinal steel) has been developed, it can then be used to determine the fatigue limit of the longitudinal steel. This can be done by comparing the projected traffic (18000-1b [BO-KN] single-axle loads) and tflme estimated stress level in the outer lane of the "to be constructed" pavement section. Since traffic enui stress level, both increase with passage of time, Miner's hypothesis [25] may be used to analyze the fatigue behavior. For failure, 115 2(ni/Ni) = (nl/Nl) + (“Z/N2) + . . . . = 1 where ni = number of stress cycles at stress level i Z H. II number of stress cycles to produce failure at stress level i The use of above-described concepts in design of JRCP longitudinal steel would require development of a series of S-N curves representing different quantities of steel. 6.7 Summary The overall objective of this study is to advance the state-of-the-knowledge on the subject of aggregate interlock load transfer across transverse cracks in JRCP. The specific purpose of this comparative laboratory study was to estimate the effects of several material and design factors on the aggregate interlock load transfer characteristics of transverse cracks in JRCP. The general concept of the study involved the application of repeated loads (simulating the passage of heavy truck traffic) across transverse cracks that have been induced in a series of large-scale reinforced concrete slab test specimens and the collection and analysis of load transfer data at several points during the testing of each specimen. 116 This laboratory study has provided valuable information on the characteristics of aggregate interlock load transfer mechanism. The major conclusions drawn from the results of this study are summarized in the next chapter along with recommendations for future experimentation. CHAPHTEI‘VII CONCIIEHKNWS.AND smxxnnunmmurrons 7.1 Primary Conclusions The following primary conclusions were drawn from the results of this laboratory study: 1. When the type of coarse aggregate (gravel, limestone or slag) was varied while holding all other variables approximately constant, load transfer efficiency and endurance was significantly higher for 6A limestone and 6A gravel than for 6A slag. 2. When all other variables were held constant, transverse crack load transfer efficiency and endurance decreased (but only slightly) when the coarse aggregate gradation was changed from 6A (1.5-in. top size) to 17A (1.0-in. top size). 3. The use of 100% recycled 6A gravel concrete as coarse aggregate decreased the load transfer efficiency and 117 is -Q. 7 A V \Ha. ; s nH‘» .4: \c .h» . NY. a ken 5 — 118 endurance considerably as compared to concrete made using virgin 6A gravel. 4. The use of the blend of 50% virgin 4A (2.5-in. top size) limestone and 50% recycled 6A grave-1 concrete as coarse aggregate decreased the load transfer efficiency and endurance considerably as compared to concrete made using virgin 6A gravel. 5. While holding all other variables approximately constant and increasing the amount of slab tension from typical (3500 lb/ft width) [51 KN/m width] to high (7000 lb/ft width) [102 KN/m width] resulted in a significant reduction in load transfer efficiency and endurance of transverse crack. 6. The use of a stiff foundation (k = 250 psi/in) increased the endurance (ME good. load 'transfer efficiency 'under repeated load applications compared. to the use of .a relatively soft foundation (k = 100 psi/in). 7.2 Other Related Findings The following observations were also made from the results of this laboratory study: 1. Aggregate interlock load transfer efficiency of reinforced transverse cracks decreases with increasing load cycle applications. It was observed that load transfer I III [1; .I\ (a) u \.. V 119 efficiency (LTE) typically drops by 2 tx: 27 percent under repeated load applications until the longitudinal steel begins to yield, after which it drops sharply. 2. The aggregate interlock load ‘transfer capacity of transverse cracks is related to the texture of the crack face. The crack face texture is primarily a function of the type, size, and number of coarse aggregate particles at the crack face and the mode of fracture. It was observed that specimens in which the cracks developed argund the aggregate (i.e., virgin crushed stone and virgin gravel) developed higher initial load transfer efficiencies and were able to maintain this higher level over a considerably larger number of load cycles than specimens in which the crack developed W the aggregate (i.e., virgin slag and recycled aggregates). 3. The amount of aggregate interlock looseness (caused by excessive crack opening and/or attrition and wearing of crack interface) significantly affects the aggregate interlock. efficiency euui endurance, since :H: can. only function at full efficiency only after the looseness is taken up by displacement of the slab. 7.3 Recommendations The following recommendations are made from the results of this laboratory study: 120 1. The observed performance of the six specimens incorporating various material factors and the underlying reasons for differences in performance of these specimens suggest the use of a concrete mix that produces a rough crack interface (large protrusions and macrotexture). The key factor which determines the texture of the crack face is the mode of concrete fracture. The use of coarse aggregate particles with high tensile strength is recommended to ensure pullout of aggregate particles at the time of crack development. The results of this and some other previous studies suggest that large size, angular (rough-surfaced) coarse aggregate particles are beneficial in the preservation of aggregate interlock effectiveness (particularly for wide crack openings and high number of load repetitions). With regards to the use of recycled concrete as coarse aggregates, it is felt that increasing the number of virgin aggregate particles in a recycled blend may improve the performance of aggregate interlock. This can be verified in future experimentation by testing materials that have high percentages of large size virgin material (by weight) and/or by decreasing the top size of the virgin material to a gradation comparable to the recycled material. 2. Although the unexpected poor performance of the 50—50 recycled blend (6A recycled gravel concrete with 4A virgin limestone) concrete might be due to inadequate numbers of virgin coarse aggregate particles at the crack face or due ”c ...\_ IN“ an“ “A, l: .fia v «A ‘u 4 no. .. a. . C 121 to slab handling difficulties, there is enough concern about the results (Hi this particular specimen. to recommend replicating the test in future experimentation. 3. One of the unexpected findings of this study is the relatively early rupture of steel in all six test specimens. Although this laboratory test is rigorous in nature in that each test specimen is under adverse loading conditions (i.e., combined. tension. and. shear) constantly, it is possible that current longitudinal steel quantities (0.16% percent by area of concrete) are inadequate for the combined tension auui shear loading conditions encountered.:h1 the field. Further testing should include variations of steel quantities. The results of this and any future testing can be used as a basis for recommending an increase in the quantity of "temperature and shrinkage" steel to keep cracks tighter and reduce deterioration. Development of a mechanistic reinforcement design procedure (as described in chapter 6) is suggested to replace or supplement the conventionally used design procedure based on the subgrade drag theory. 4. Several other factors are likely to affect transverse crack performance. These include type of steel reinforcement (smooth wire vs deformed wire), source or quality of virgin coarse aggregate (limestone # 1 vs limestone # 2 etc), large top size aggregates (e.g., 2.5-in [6.3-cm]) and aggregate/paste bond strength (effect of fracture delay). 122 These factors should also be considered in future testing. 5. Replicate test specimens should be prepared for most of these specimens that were tested during this study to determine the variability of the test results and help in identifying true differences in specimen performance. A preliminary statistical analysis is presented in APPENDIX C. 6. Based on recommendations 1—5, test matrices presented in Figures 7.1-7.5 are proposed for expanding the current test program. Note that these matrices accomplish the following three major goals: - Provide replicate tests for selected cells to provide an better estimate of the blocking effect (as described in chapter 4 and APPENDIX C) and pure error. Testing a 6A virgin limestone specimen and a 50-50 recycled blend (see Figures 7.1 and 7.2) shall improve the precision of the estimate of the blocking effect. Moreover, the results of the 6A virgin limestone (under modified conditions) are needed to determine the effect of coarse aggregate source/quality (see Figure 7.1). Testing another 6A virgin gravel specimen (see Figure 7.1) shall increase the degree of freedom to two in the estimate of pure error. This will result SUI improved confidence levels 1J1 the statistical analysis. - Consider additional test factors that are likely to play 123 important roles in the JRCP transverse crack performance (i.e., reinforcing steel quantities and type, age of concrete at the time of fracture, source or quality of aggregate, and a larger top size aggregate. - Complete fractional factorial test matrices to identify possible interaction effects of selected test factors. It is felt that type of coarse aggregate and treatment of coarse aggregate are unlikely to interact. This contention is based on the examination of the crack faces of the recycled specimens, which revealed. that very feW' pull outs of aggregate particles existed. It was pointed out previously, that tuna of comparable quantities of recycled aggregate (100% recycled specimen) and use of an equal weight of large aggregate (50-50 recycled specimen) results in a significant reduction in the actual number of virgin aggregate particles in the mix. Thus, various combinations of coarse aggregate type and treatment are unlikely to produce significant differences in performance. However. it is felt that performance of recycled specimens may be improved by having high percentages of large size virgin material (by weight) and/or by decreasing the top size of the virgin material to a. gradation. comparable t1) the recycled. material. Yet, another possible approach would be to use recycled coarse aggregates produced by breaking and crushing slabs cast using ea large top size ‘virgin aggregates (e.g., MDOT gradation 10A/4A: 2.5-in. [6.35-cm] top size) (see Figure 7.2). Recycled aggregates thus obtained would contain 124 relatively large size virgin aggregate particles bonded to the old cement mortar, for a given gradation (e.g., 6A gradation). Notes: U'llbUJN 125 PTKNPCEHHD NBHERIXEII CH! SCXMRCEI (QEHELITH!) ca TYPE #1 #2 GRAVEL A o D M1 Ml LIMESTONE 11 M1 Ml A D Test cell run under matrix A (see Figure 4.1) Test cell run under matrix D (see Figure 4.4) M1 = Test cell being tested under proposed matrix 1 Foundation modulus = 100 psi/in Typical slab tension = 3500 lb/ft [51 KN/m width] (coefficient of friction = 1.5, slab length = 41 ft [12.5 m], crack face depth = 9-in. [23—cm] Longitudinal steel = 0.16% by area of concrete All coarse aggregates conform to MDOT gradation 6A Figure 7.1: Proposed test matrix 1 126 PROPOSED MATRIX 2 CA TREATMENT 100% 50-50 RECYCLED BLEND CA GRADATION VIRGDN 6A A.D D Ml C C 17A. 3 10A/ 4A MZ M2 M2 Notes: A = Test cell run under matrix A (see Figure 4.1) B = Test cell run under matrix B (see Figure 4.2) C = test cell run under matrix C (see figure 4.3) D 4.4) M1 = Test cell first filled in proposed matrix 1 = Test cell run under matrix D (see Figure M2 = Test cell being tested under proposed matrix 2 Foundation modulus = 100 psi/in Typical slab tension = 3500 lb/ft [51 KN/m width] (coefficient of friction = 1.5, slab length = 41 ft [12.5 m], crack face depth = 9—in. [23-cm] mummwal—I 9. Longitudinal steel = 0.16% by area of concrete 10. Aggregates type gravel 11. Treatments as defined in Table 4.1 12. 10A/4A gradation — top size = 2.5-in. [6.35—cm] Figure 7.2: Proposed test matrix 2 127 PROPOSED MATRIX 3 SLAB TENSION STEEL STEEL TYPICAL HIGH TYPE QUANTITY TYPICAL .A.D D M1 D SMOOTH HIGH M3 M3 TYPICAL M3 M3 DEFORMED HIGH M3 M3 Notes: \IOAUTLONH 10. 11. = Test cell run under matrix A (see Figure 4.1) D = Test cell run under matrix D (see Figure 4.4) M1 = test cell first filled in proposed matrix 1 M3 = Test cell being tested under proposed matrix 3 Foundation modulus = 100 psi/in Typical slab tension = 3500 lb/ft [51 KN/m width] (coefficient of friction = 1.5, slab length = 41 ft [12.5 m], crack face depth = 9—in. [23-cm] High slab tension = 7000 lb/ft width [102 KN/m width] (coefficient of friction = 3.0, slab length = 41 ft [12.5 m], crack face depth = 9-in. [23-cm] Typical longitudinal steel = 0.16% by area of concrete High longitudinal steel = 0.25% by area of concrete Aggregates type gravel Figure 7.3: Proposed test matrix 3 128 PROPOSHIIMATRIX 4 AGE (days) CA SOURCE 1 7 GRAVEL # 1 .A D D M1 MA GRAVEL # 2 MA MA Notes: 1. A = Test cell run under matrix A (see Figure 4.1) 2. D = Test cell run under matrix D (see Figure 4.4) 3. M4 = Test cell being tested under proposed matrix 4 4. Foundation modulus = 100 psi/in 5. Typical slab tension = 3500 lb/ft [51 KN/m width] (coefficient of friction = 1.5, slab length = 41 ft [12.5 m], crack face depth = 9-in. [23-cm] 6. Longitudinal steel = 0.16% by area of concrete 7. All coarse aggregates conform to MDOT gradation 6A Figure 7.4: Proposed test matrix 4 129 PROPOSED MATRIX 5 FOUNDATION SLAB 100 250 TENSION TYPICAL A.D D M1 E HIGH D 3M5 Notes: 1. A = Test cell run under matrix A (see Figure 4.1) 2. D = Test cell run under matrix D (see Figure 4.4) 3. M1 = Test cell first filled in proposed matrix 1 4. M5 = Test cell being tested under proposed matrix 5 5. Typical foundation modulus = 100 psi/in 6. High foundation modulus = 250 psi/in 1 7. Typical slab tension = 3500 lb/ft [51 KN/m width] (coefficient of friction = 1.5, slab length = 41 ft [12.5 m], crack face depth = 9-in. [23-cm] 8. High slab tension = 7000 lb/ft [102 KN/m width] (coefficient of friction = 3.0, slab length = 41 ft [12.5 m], crack face depth = 9-in. [23-cm] 9. Longitudinal steel = 0.16% by area of concrete 10. All coarse aggregates conform to MDOT gradation 6A 11. Aggregate type gravel Figure 7.5: Proposed.matrix 5 LIST OF REFERENCES LIST OF REFERENCES 1. Darter, M. 1., "Initial Evaluation of Michigan JRCP Crack Deterioration," a report prepared for Michigan Concrete Paving Association, December, 1988, Revised February, 1989, Mahomet, IL 61853. 2. McCarthy, G.J., and MacCreery, W.J., "Michigan Department of Transportation Recycles Concrete Freeways," Proceedings Third International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, April 23—25, 1983, W. Lafayette, IN., pp. 643-647. 3. Benkelman, A.C., "Tests of Aggregate Interlock at Joints and Cracks," Wm, Vol. III, N0. 8, August 24, 1933, New york, N.Y., pp. 227-232. 4. Colley, B.E., and Humphrey, H.A., "Aggregate Interlock at Joints in Concrete Pavements," Highnay_3esgarch_figggrd_NQ+ ‘189, Highway Research Board, National Research Council, Washington, D.C., 1967, pp. 1-18. 5. Nowlen, W.J., "Influence of Aggregate Properties on Effectiveness of Interlock Joints in Concrete Pavements," Journal of the PCA, Research and Development Laboratories, Vol. 10, No. 2, May 1968, pp. 2—8 6. Sutherland, E.C., and Cashell, H.D., "Structural Efficiency of Transverse Weakened-Plane Joints," mm Roads, Vol. 24, No. 4, April-May-June 1945. 130 bu? 131 7. Older, C., "Efficiency of Aggregate interlock in Concrete Roads," Engineering_fleus_fiecord, Vol. III, No. 8, November 23, 1933, New York, N.Y., pp 615—616. 8. Poblete, M., Valenzuela, R., and Salsilli, R., "Load Transfer in Undowelled Transverse Joints of PCC Pavements," Transportation Research Record 1207, Transportation Research Board, National Research Council, Washington, D.C. 1988. 9. Ioannides, A. M., and Korovesis, G. T., "Aggregate Interlock: Pure-Shear Load. Transfer' Mechanism," paper prepared for presentation at the 1990 Annual Meeting of the Transportation Research Board, Washington, D.C. 10. Laible, J. P., White, R. N., and Gergely, P., "Experimental Investigation of Siesmic Shear Transfer Across Cracks in Concrete Nuclear Containment Vessels," Reinforced Concrete Structures in Siesmic Zones. Detroit, American Concrete Institute, 1977. ACI Special Publication SP-53. 11. Jimenez, R., Gergely, P., and White, R. N., "Shear Transfer Across Cracks in Reinforced Concrete," Ithaca (N.Y.), Cornell University, August 1978, pp. 357. Report 78-4. 12. Fardis, M. N., and Bu yukozturk, o., "Shear Transfer Model for Reinforced Concrete," Proceedings of the American Society of Civil Engineers. Vol. 105, No. EM2. April 1979, pp. 225-275. 13. Walraven, J. C., "Fundamental Analysis of Aggregate Interlock," American Society of Civil Engineers, Journal of the Structural Division, Vol. 107, No. 11, November 1981, pp. 2245-2270. 14. Millard, S. (1”. and JOhnson, IR. P., "Shear Transfer Across Cracks in Reinforced Concrete Due to Aggregate Interlock and to Dowel Action," Magazine of Concrete IA . . . w. 8.. a ‘ AU -u s fi/L ¢ x, . 2.. «é a 132 Research, Vol. 36, No. 126, March 1984. 15. Soroushian, P., Obaseki, K., and Choi, K., "Analysis of Aggregate Interlock Behavior at Cracks in Reinforced Concrete," Magazine of Concrete Research, Vol. 40, No. 142, March 1988, pp. 43-49. 16. Darter, M.I., WWW WWW. — I I Contract Number DOT-FH—11—8474, Federal Highway Administration, Washington, D.C., June 1977. 17. Snyder, M. B., "Dowel Load Transfer Systems for Full—Depth Repairs of Jointed Portland Cement Concrete Pavements," Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1988. 18. Ball, C. G., and Childs, L.D., "Tests of JOints for Concrete Pavements," Research auui Development. Bulletin RD026.01P, Portland Cement Association, Skokie, IL, 1975. 19. Ciolko, A. T., Nussbaum, P. J., and Colley, B. E., "Load Transfer of Dowel Bars and Star Lugs," ‘Final Report, Construction Technology Laboratories, Skokie, IL, 1979. 20. Siriwat, C., "Development of a: Test Facility for Evaluation of Concrete Pavement Joints," Ph.D. Thesis, Oklahoma State University, Stillwater, Oklahoma, 1987. 21. Teller, L.W;, and. Cashell, H.D., "Performance of Dowelled JOints Under Repetitive Loading," Bulletin 217, Highway Research Board, Washington, D.C., 1959. 22. Troxell, G.E., Davis, H.E., and Kelly, J.W., Composition and Properties of Concrete, second edition, McGraw-Hill Book Company, N.Y., 1968, pp 238-247. 133 23.Tabatabai, A. M., Barenberg, E. J., and Smith, R. E., "Longitudinal Joint Systems in Slip-Formed Pavements, Vol. II - .Analysis of Load Transfer Systems for Concrete Pavements," Report No. FAA—RD-79-4, prepared for USDOT, FAA, 1979. 24. "Methods for Reducing Friction Between Concrete Slabs and Cement—Treated Subbases," an unpublished report by the Cement and Concrete Research Institute (a division of the Portland Cement Association) for the Federal Highway Administration, September 1971. 25. Gaylord, E. H., and Gaylord, C. N., W W, second edition, McGraw—Hill Book Company, 1979, pp. 4-1 to 4-12. 26. Hanson, .J. PL, Burton, I<. 1n, and..Hognestad, E., "Fatigue Tests of Reinforcing Bars - Effect of Deformation Pattern," Journal of the PCA, Research and Development Laboratories, Vol. 10, No. 3, September 1968, pp. 2-13. 27. Snyder, M. B., "Dowel Load. Transfer Systems for Full-Depth Repairs of Jointed Portland Cement Concrete Pavements," Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1988. 28. Snyder, M. B., Reiter, M. J., Hall, K.T., Darter, M.I., Voigt, G.E., et. al., "Rehabilitation of Concrete Pavements Volume I - Repair Rehabilitation Techniques Volume II - Overlay rehabilitation Techniques Volume III - Concrete Pavement Evaluation and Rehabilitation System Volume IV — Appendexis" Final Report, Prepared for Federal Highway Administration, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, I1, December 1987. 134 29. Darter, M.I., Becker, J., Snyder, M.B., and Smith, R.E., '0 coo ‘u‘c 00 ‘ ‘ ’. ‘u‘o . . '00 -u 0' , NCHRP Report No. 277, Transportation Research Board, 1984. 30. Paulay, T., euui Loeber, P.J., "Shear Transfer' by Aggregate Interlock," Shear in Reinforced Concrete, Detroit, American. Concrete Institute, 1974, Special. Publication SP-42, Vol. 1, pp. 1-16. 31. Christory, J.P., Nissoux, J. L., Orsat, P., and Verhee, F., "Load transfer Restoration at Joints," Proceedings, Fourth International Conference on Concrete Pavement Design and.IRehabilitation, Purdue 'University, .April 18-20, W. Lafayette, IN., pp. 1—18. 32. Gulden, W., and Brown, D., "Establishing Load Transfer in Existing Jointed Concrete Pavements," paper prepared for presentation at the 1985 Annual Meeting of the Transportation Research Board, Georgia Department of Transportation. 33. Kushing, J.W., and Fremont, W. 0., "Design of Load Transfer Joints in Concrete Pavements," Proceedings Vol. 20, Highway Research Board, Washington, D.C., 1940. 34. Bolourchi, 2., Temple, W. H., and Shah, S. C., Evaluation of Load Transfer Devices, Final Report, Report No. FHWA-2A—97, Federal Highway Administration, Washington, D.C., 1975. 35. Arnold, (S. J}, "Performance of Several Types of Corrosion Resistant Load Transfer Bars, for as much as 21 Years of Service in Concrete Pavements," Research Report No. R-1151, Michigan Department of State Highways and Transportation, Aug. 1980. 36. Peshkin, D. G., Smith, K. D., Darter, M. I., and Arnold, C. J., "Performance Evaluation of Experimental Pavement 135 Designs at Clare, Michigan," Transportation Research Record No. 1227, Transportation Research Board, National Research Council, Washington, D.C. 1989. 37. Kapernick, J. W., "Equipment for Studying Joint Performance in the Laboratory," Journal of the PCA, Research and Development Laboratories, Vol. 5, No. 2, May 1963. 38- Yoder, E. J., and Witczak, M. W., BriminlemLBaxement Design, second edition, John Wiley and sons, Inc., New York, new York, 1975. 39. WW ,Lflfljd American Association of State Highway and Transportation Officials, Washington, D.C., 1986. 40. Neter, J., Wasserman, W., and Kutner, M. H., Applied, Linear_SLatistieal_MQdele, second edition, Richard D. Irwin, Inc., Homewood, Illinois 60430, pp. 230-240. 41. flfifin_Mannal_iQL_LAEIEQH_NQIEBQQK_§XSIEMSI version 5-0, Laboratory Technologies Corporation, Inc., Wilmington, MA, 1990. 42. W, version 1-5-4r MTS Systems Corporation, Minneapolis, Minnesota, 1990. 43. AW, Vols. 04.02 and 04.03, 1991. 44. Highter, W. H., and Moore, E. L., "Prediction of Rigid-Pavement Performance from Cumulative Deflection History," Transportation Research Record 633, Transportation Research Board, 1977. 136 left intentionally blank 137 left intentionally blank APPENDIX A LOAD-DEELECTION HISTORIES OE TEST SPECIMENS (MATERIAL FACTORS) .F 1* o_o>o Bum 99m .996 £93 mm.._ III one; comocda< III cozooCoo o>mo4 coZoozoo comoad< ...... OOON I ooov 1 Doom 1 Doom 1 oooor an: 33 E: 528:3 F is. m_n_0>0 |_m_> <0 mod: 50.0: 00.01 mod: _ v0.0- mod: No.0: rod- 139 ooo; 1% 226 Loam 92m .055 593 (m .2 8230 838:8 new two; ”m-< 05am poo; 023.. Ill ooo; concedes. 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OOOOOOOOOIJ 0000000010 0000010000 0000100000 0001000000 0010000000 0100000000 0000001111 1111111111 Vector of Parameters = 9 n 1 1 0 0 0 0 0 0 1H— 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 O 0 1. 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1. 0 0 0 0 0 0 4 4 0 0 0 0 0 1 1 m 4 1 1. 1. 1 1 1 1.— __ w“ x 262 59.67 25.17 6.18 5.40 5.95 5.54 5.48 5.40 6.82 -— - 9X1 The least square normal equations for the general linear regression model are: A (X'X)]3 = X'Y A where 6 is the least square estimator Therefore, 103M4131+I§2+B3+fi4+35+36+37+738= 59-67 (I) 4304-461 fi7+fi8 = 25.17 (2) £0 £2 = 6.18 (3) £0 £3 = 5.40 (4) Bo 2‘4 = 5.95 (5) [30 35 = 5.54 (6) Ba 36 = 5.48 (7) 230431 37 = 5-40 (8) A A flo+fi1 fi8= 6-82 <9) 263 The solution of the above equations yields the following estimates: fib = 5.95 fl] =+o.53 (block effect) fiz =+O.23 (limestone vs gravel) B3:=-0.55 (slag vs gravel) fi4== 0.00 (17A gradation vs 6A gradation) fl5==—0.41 (SO-50 recycled vs virgin gravel) B5==—0.47 (100% recycled vs virgin gravel) [37 =-1.08 (high tension vs typical tension) flg==+0.34 (high foundation vs low foundation) We see that the best linear unbiased estimates for effects are (*): 31= 1/2(Y7 + Y8) - Y1 32= Y2 ' Y1 fi3= Y3 - Y1 é4= Y4 ' Y1 35= Y5 ’ Y1 36= Y6 - Y1 fi7= Y9 - 1/2 (Y7 + Y8) fi8= Ylo - 1/2 (Y7 + Y8) C.3.4 Studbnt t-tast The estimate of variance for l-degree of freedom for the observed data is 264 mean = (6.43 + 6.52)/2 = 6.48 32 = [(6.43 - 6.48)2 + (6.52 - 6.48)2]/(2-1) = 0.004 s = 0.064 = estimate of 0 From (*) A Var(p1) = 02 + (1/4)02 + (1/4)02 = (3/2)o2 A Var(B2) = 0'2 + 02 == 202 l‘ Var (fi3) = n = n ,4 Var (fi4) = u = n l‘ Var (fi5) = u .._. n A Var ([36) = n = n var(B7) = 02 + (1/4)02 + (1/4)02 = (3/2)o2 A Var(fig) = 02 + (1/4)02 + (1/4)02 = (3/2)o2 A Standard error for fii is given by A 53(fii) = 2 s i = 2,3,...,6 A A A Standard error for fil’ B7 and fi8 is given by A SE([31,7’8) = 1.5 S t-statistics is given by t = (estimate)/(SE) 265 The results are tabulated below: Contrast Block Effect Limestone v3 Gravel Slag vs Gravel 17A Gradation vs 6A Gradation 50-50 Recycled vs Virgin Gravel 100% Recycled vs Virgin Gravel High Tension vs Typical Tension Estimate A fl1=+0 . 53 A flf-f-O . 23 A flf-0.55 A fl4=0 . 000 A fi5B-0.41 fif-O.47 A flf-l. 08 A High Foundation vs Low Foundation flf+0.34 SE 0.078 0.090 0.090 0.090 0.090 0.090 0.078 0.078 * = statistically significant at a = 0.05 ** = statistically significant at a = 0.10 *** = statistically significant at a = 0.15 6.10 0.00 12.5 p-value 0.10** 0.10** 1.00 0.14*** 0.12*** 0.05* 0.14*** APPENDIX D AREA UNDER CURVES 03' TEST SPECIMENS 264 mean = (6.43 + 6.52)/2 = 6.48 52 = [(6.43 — 6.48)2 + (6.52 - 6.48)2]/(2-1) = 0.004 s = 0.064 = estimate of a From (*) Var(fi1) = 02 + (1/4)02 + (1/4)o2 = (3/2)o2 Var(B2) --- 02 + 02 = 202 Var(fi3) = " = " mum) = .. = .. Var(fi5) = " = " Var(fi6) = " = " var(B7) = 02 + (1/4)02 + (1/4)o2 = (3/2)o2 Var(fig) = 02 + (1/4)02 + (1/4)02 = (3/2)02 A Standard error for fii is given by 53(31) = 2 s i = 2,3,...,6 h A A Standard error for fil, fi7 and fi8 is given by A SE(fib7’8) = 1.5 s t-statistics is given by t = (estimate)/(SE) 265 The results are tabulated below: Contrast Estimate SE Block Effect 31=+0.53 0.078 Limestone vs Gravel fiz=+0.23 A 0.090 Slag vs Gravel §3=-0.55 0.090 17A Gradation vs 6A Gradation 34:0.000 0.090 so-so Recycled vs Virgin Gravel fif-OAl 0.090 100% Recycled vs Virgin Gravel. figB-0.47 0.090 High Tension vs Typical Tension fif~1.08 0.078 High Foundation vs Low Foundation Ek=+0.34 0.078 * = statistically significant at a = 0.05 ** = statistically significant at a = 0.10 *** = statistically significant at a = 0.15 6.10 0.00 12.5 4.50 p-value 0.10** 0.10** 1.00 0.14*** 0.12*** 0.05* 0.14*** APPENDIX D AREA UNDER CURVES OF TEST SPECIMENS "Ill’illlllllllllfllllr