A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers (2018)

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K-1 APPENDIX K. SENSITIVITY ANALYSIS OF TOP-DOWN CRACKING DESIGNING PROGRAM Sensitivity analysis is conducted using the computer program developed in this project to evaluate the effects of different design and environmental variables including traffic (AADTT), annual number of days at high temperature (above 32°C for aging effect), annual number of days at low temperature (below 0°C for thermal effect), modulus of asphalt layer, m-value, asphalt layer thickness, and base layer thickness. The change of variables is listed in Table K-1. It shows that the increase of AADTT, annual number of days for high temperature (HT) for the aging effect, annual number of days for low temperature (LT) for the thermal effect and asphalt layer modulus reduce both of the initiation time and pre-fatigue life. On the other hand, the increase of asphalt layer thickness and base layer thickness is beneficial to delay the initiation time and increase pre-fatigue life. Table K-1. Sensitivity Analysis for Top-Down Crack Initiation and Propagation Variable Climatic Zone AADTT HT (day) LT (day) E1 (MPa) m- value Air Void Content Binder Content Aggregate Parameter total asphalt thickness (inch) base thickness (inch) Case 1 (AADTT) WNF 1000 51 51 1000 0.20 4 6 0.42 4 6 500 51 51 1000 0.20 4 6 0.42 4 6 Case 2 (E1) WNF 800 51 51 1500 0.20 4 6 0.42 4 6 800 51 51 1000 0.20 4 6 0.42 4 6 Case 3 (Ha) WNF 800 51 51 1000 0.20 4 6 0.42 8 6 800 51 51 1000 0.20 4 6 0.42 4 6 Case 4 (Hb) WNF 800 51 51 1000 0.20 4 6 0.42 4 15 800 51 51 1000 0.20 4 6 0.42 4 6 Case 5 (m- value)_ WNF 800 51 51 1000 0.20 4 6 0.42 4 6 800 51 51 1000 0.23 4 6 0.42 4 6 Output t0 (day) ρ (day) β Case 1 1956 3532 1.57 3981 4793 0.53 Case 2 1544 1530 1.57 2457 3147 0.95 Case 3 2934 11235 0.47 2457 3147 0.95 Case 4 2459 4793 0.73 2459 5425 0.62 Case 5 2457 3147 0.95 5722 3147 0.95

K-2 (a) Effect of AADTT (b) Effect of Asphalt Layer Modulus 0 50 100 150 0 1000 2000 3000 4000 5000 6000 7000 8000 Lo ng itu di na l C ra ck  L en gh  (m ) Service Time(day) High AADTT Low AADTT 0 50 100 150 200 0 1000 2000 3000 4000 5000 6000 Lo ng itu di na l C ra ck  L en gt h  (m ) Service Time (day) High Modulus Low Modulus

K-3 (c) Effect of m-value (d) Effect of Asphalt Layer Modulus 0 50 100 0 2000 4000 6000 8000 Lo ng itu di na l C ra ck  L en gt h  (m ) Service Time (day) Small m‐value Large m‐value 0 50 100 150 200 0 1000 2000 3000 4000 5000 6000 Lo ng itu di na l C ra ck  L en gt h  (m ) Service Time (day) High Modulus Low Modulus

K-4 (e) Effect of Asphalt Layer Thickness (f) Effect of Base Layer Thickness Figure K-1. Sensitivity Analysis of Input and Environmental Variables 0 50 100 2000 2500 3000 3500 4000 4500 5000 5500 Lo ng itu di na l C ra ck  L en gt h  (m ) Service Time (day) High Ha Low Ha 0 50 100 0 1000 2000 3000 4000 5000 Lo ng itu di na l C ra ck  L en gt h  (m ) Service Time (day) Low Hb High Hb