Mechanistic Roughness Model Based on Vehicle-Pavement Interaction

114 Transportation Research Record 1699 Paper No. 00 -1148 Mechanistic Roughness Model Based on Vehicle-Pavement Interaction Mofreh F. Saleh, Michael S. Mamlouk, and Emmanuel B. Owusu-Antwi A mechanistic roughness performance model that takes into account vehicle dynamics was developed for use in flexible pavement design and evaluation. The model was developed in the form of a relation between roughness and number of load repetitions, axle load, and asphalt layer thickness. The model is completely mechanistic and uses vehicle dynamics analysis to estimate the dynamic force profile and finite element structural analysis to estimate the change of pavement surface roughness for each load repetition. The model makes use of the fact that pavement roughness changes the magnitude of the vehicle dynamic forces applied on the pavement and that the dynamic forces change the road roughness. The developed mechanistic roughness performance model can be used to estimate the 80-kN (18-kip) equivalent single-axle load for mixed traffic. The model can also be used to design pavement so that it will last for a certain number of load repetitions before reaching a predetermined roughness level. Performance-based specifications can be developed using the methodology presented in this study. The model has been calibrated and verified with field data elsewhere. Unlike other structural systems, pavements deteriorate at a fast rate because of repeated traffic loads and environmental effects, although the stresses caused by traffic loads are typically far below the ultimate strength of the material. Therefore, the approach used in designing pavements is different from traditional approaches used in other structures. Typical pavement design methods are based on estimation of the number of load repetitions to failure, a process that is currently being performed mostly empirically. Although empirical relations are easy to use, they are not valid for conditions other than those used during their development. A number of mechanistic-empirical pavement design approaches are available and have been used with a certain degree of accuracy. These mechanistic-empirical approaches are based on either fatigue or rutting failure criteria (1). In many cases, pavements may fail because of roughness before they develop excessive fatigue or rutting distresses. Current roughness models are typically associated with empirical relations based on previous observations such as those obtained in the Road Test sponsored by the American Association of State Highway Officials (AASHO). At present, there is no pavement design method that uses a mechanistic roughness model. Road roughness is defined as the irregularities in the pavement profile that cause uncomfortable, unsafe, and uneconomical riding. Studies made at the AASHO Road Test showed that about 95 percent of the information about serviceability of a pavement is contributed by roughness (2). Roughness affects the dynamics of moving vehicles, increasing the wear on vehicle parts and the hanDepartment of Civil and Environmental Engineering, Arizona State University, Tempe, AZ 85287-5306. Current affiliation for M. F. Saleh: California Department of Transportation, District 3, 703 B Street, P.O. Box 911, Marysville, CA 95901. dling of vehicles. Thus, road roughness has an appreciable impact on vehicle operating costs and on the safety, comfort, and speed of travel. It also increases the dynamic loading imposed by vehicles on the surface, accelerating the deterioration of the pavement structure. Moreover, roughness can have adverse effects on surface drainage, causing water to pond on the surface, with consequent adverse impacts on both the performance of the pavement and vehicle safety. A number of studies have investigated the interaction between vehicles and pavement and how it is affected by axle load, suspension type, and pavement stiffness (3–7). The concept was suggested of a pavement performance model in which relations between present serviceability index and number of load repetitions were introduced (8). Currently, there is no mechanistic model that predicts pavement roughness as a function of axle load repetitions. The main objective of this study is to develop a mechanistic roughness model for use in the design of flexible pavements that takes into account vehicle dynamics. The model estimates the roughness in the wheelpath as a function of initial pavement roughness, pavement thickness, static axle load, and number of load repetitions. The model considers the elastic viscoplastic behavior of the asphalt concrete and the plasticity and nonlinearity of granular and subgrade materials. The model can augment current mechanistic-empirical pavement design methods that are based on fatigue and rutting criteria. VEHICLE-PAVEMENT INTERACTION Vehicles bounce as they move on the pavement, resulting in variable dynamic forces on the pavement surface. Figure 1 shows typical dynamic forces measured on an in-service pavement section (9). A number of vehicle dynamics models are available to predict the truck dynamic forces produced by different axle and wheel configurations at different locations on the pavement surface. Vehicle dynamics models represent the truck with a number of masses, springs, and dashpots. The models are typically implemented in time-domain computer simulation programs. Among the vehicle dynamics computer models is the Florida Comprehensive Pavement Analysis System (COMPAS) (10), which was used in the present study. The COMPAS model is capable of generating the dynamic force profile of wheel loads for different combinations of vehicle type, suspension type, vehicle speed, and level of pavement roughness. The results of COMPAS were verified by comparing the output of the program with field experimental data and with the output of other vehicle dynamics programs. Close agreement was obtained (11). The subject of vehicle-pavement interaction considers the effect of pavement roughness on vehicle dynamic forces and the effect of these forces on the pavement response and performance, as demonstrated in Figure 2. The roughness of the pavement surface excites and bounces traveling vehicles. Increasing surface roughness or vehicle speed increases the bouncing of vehicles and consequently Saleh et al. Paper No. 00 -1148 115 FIGURE 1 Typical instantaneous dynamic wheel force measured at 80 km /h for medium road roughness (10). increases the dynamic forces applied to the pavement. The forces applied by vehicles vary instantaneously above and below the static weight because of the interaction effect between vehicles and pavement. Several factors contribute to this load variation, such as road roughness, vehicle configuration, suspension type, tire type, and vehicle speed. Increasing dynamic forces increases the damage rate of pavement and shortens its service life. Nearly all roughness measurement systems measure a slope statistic. However, they do not obtain identical measurements because each device has unique sensitivities to different wavelengths in the road. One of the road roughness indicators is the international roughness index (IRI), which is a scale for roughness based on the response of a generic motor vehicle to the roughness of the road surface. Its true value is determined by obtaining a suitably accurate measurement of the profile of the road, processing it through an algorithm that simulates the way a reference vehicle would respond to the roughness inputs, and accumulating the suspension travel. Thus, it mathematically duplicates a roadmeter (12). For a perfectly smooth surface, the IRI value is zero. Typical IRI values range from about 1 m/km for a smooth pavement to 4 m/km and above for a rough pavement. RESEARCH APPROACH In order to estimate the change in roughness caused by traffic load applications of a specific pavement section with a certain initial surface profile, the dynamic wheel force profile developed by a truck, speed, and axle load are obtained using the Florida COMPAS vehicle dynamics model. Pavement structure is simulated using the ABAQUS finite element software and subjected to the dynamic wheel force profile, which moves at the same speed from one end of the pavement to the other 50 times. The permanent deformations due to creep and plasticity of materials at different locations in the wheelpath are then computed. Subtracting the permanent deformations from the initial surface profile produces a new pavement profile, which is used in the COMPAS model to estimate the new load pro- file. This process is repeated iteratively every 50 load repetitions until the required number of load repetitions is achieved. It is also repeated for different asphalt layer thicknesses, initial pavement roughness levels, and static axle loads. Statistical analysis was used to relate pavement roughness to load repetitions under different conditions. In this paper dynamic analysis was used to determine the forces applied by the vehicle, but a quasi-static analysis was used to determine the pavement response. In other words, the inertia of the vehicle was considered, but the pavement inertia was ignored. This method is justified since the vehicle bouncing is much larger than the pavement bouncing. The quasi-static analysis of pavement was used to analyze time-dependent material response such as viscoelasticity and plasticity. This approach was used to reduce the computational effort, especially because of the many load repetitions used (up to 500 repetitions in many cases). DEVELOPMENT OF ROUGHNESS MODEL Estimation of Dynamic Wheel Force Profile Pavement surface profile is characterized by the IRI value, which is a mathematically defined summary statistic of the longitudinal profile in the wheelpath. For a specific IRI value, the Florida COMPAS program (10) was used to estimate the dynamic tire forces at 0.3-m (1-ft) intervals when the tire moves along the pavement at a certain speed. The Florida COMPAS program simulates the truck with a number of masses, springs, and dashpots as shown in Figure 3. A three-axle tractor with a two-axle trailer (3-S2) (18-wheeler) truck type was used in this study. In addition, since the dynamic wheel load of the same truck type varies depending on pavement profile, different pavement roughness levels were considered. Figure 4 shows an example of pavement profile and the corresponding dynamic wheel force profile obtained by the Florida COMPAS program for a 3-S2 truck traveling at a speed of 100 km/h on a rough road profile with an IRI value of 5.33. FIGURE 2 Effect of pavement roughness on vehicle dynamic forces and consequent increase in pavement roughness. 116 Paper No. 00 -1148 FIGURE 3 Truck dynamics model used to estimate vehicle dynamic forces. Development of New Pavement Profile The pavement sections used in the study were assumed to consist of three layers—asphalt concrete surface, granular base, and cohesive subgrade. A two-dimensional plain-strain finite element model using the ABAQUS program (13) was developed to represent the pavement structure, as shown in Figure 5. A 12.2-m (40-ft) long wheelpath was used with two 4-m (13.1-ft) unloaded zones before and after the wheelpath to reduce the end effect. To minimize the effect of the boundary conditions, continuum infinite elements were used on both sides and at the bottom of the subgrade. The mesh dimensions were selected to obtain appropriate Transportation Research Record 1699 aspect ratios of the elements and to achieve the desired degree of accuracy. The results of the selected finite element mesh were compared with those of a three-dimensional finite element mesh and with the KENLAYER program using static analysis to verify its accuracy. Very close agreement was found. The asphalt concrete was modeled as an elastic viscoplastic material. In this case, permanent deformation is developed because of the creep and plasticity of the material. On the other hand, granular and subgrade materials were modeled as elastic-plastic with strain hardening using the Drucker-Prager model (Figure 6). If a stress below the yield value is applied, an elastic strain will result and will be completely removed upon unloading. If a stress larger than the yield value is applied (e.g., σ1) and removed, a permanent strain (⑀1) is developed, as demonstrated in Figure 6. When the pavement surface gets rougher because of continuous load applications, a higher stress (σ2) is applied because of the larger bouncing of vehicles, and consequently a new permanent strain (⑀2) will be developed. Typical material parameters were obtained from the literature and used in this study (Table 1). The load in the ABAQUS input file was simulated using a step function. The duration of the step function load was calculated by dividing the length of the element by the vehicle speed. The load is moved from one element to the next up to the last element in the mesh, whereas the value of the load changes from one element to another depending on the dynamic wheel force profile computed by Florida COMPAS. The end stress state of the pavement after the first load repetition is taken as the starting case for the second load repetition, and so on. A FORTRAN program was designed to automate the load repetition procedure in ABAQUS. The ABAQUS program was used to compute the permanent deformation at 0.3-m (1-ft) intervals after 50 load repetitions. The permanent deformation at each node was subtracted from the initial elevation of the node to estimate the new pavement profile, which was then used in the COMPAS vehicle dynamics model to obtain a new dynamic load profile. The ABAQUS program was used again to generate the new pavement profile. This process is repeated many times until the required number of load repetitions is reached. In each step, the pavement roughness was estimated by calculating the IRI value using the RoadRuf program (14). Development of Mechanistic Roughness Model In order to develop a roughness model that is applicable to a variety of load and pavement conditions, the process discussed earlier was performed many times for the following variables: • Axle load: 67 and 80 kN (15 and 18 kips), • Asphalt concrete layer thickness: 100 and 150 mm (4 and 6 in.), and • IRI: 0.38 m/km (smooth) and 5.33 m/km (rough) (24 and 336 in./mi). FIGURE 4 Pavement profile and corresponding dynamic load profile (3-S2 truck, 80-kN axle load, 100-km /h speed). A 3-S2 truck type with a speed of 100 km/h (62 mph) was used. The second axle of the truck was used in the analysis. In addition, the pavement section was assumed to have a granular base 200 mm (8 in.) thick and a silty clay subgrade. Statistical analysis was used to evaluate the effect of axle load, asphalt layer thickness, and initial surface roughness on pavement roughness. A half-fractional factorial statistical design was carried out Saleh et al. Paper No. 00 -1148 FIGURE 5 Finite element mesh used to estimate new pavement profile after many axle repetitions. using the statistical package Design-Expert 5 (15). Figure 7 shows the eight different combinations considered in this statistical design. The statistical analysis showed that initial roughness is the most significant factor that affects roughness at later ages. The other important factors in order of importance are axle load, the interaction between axle load and thickness, asphalt thickness, and the number of load repetitions. The roughness was very highly correlated with these factors, with an R2 value of 1.0. Statistical analysis showed that initial roughness is the dominating factor that affects final roughness, which explains the high R2 value. The Design-Expert 5 package was used to develop a roughness performance model in the form of a relation between roughness and number of load repetitions, axle load, and asphalt layer thickness as follows: IRI = −1.415 + 2.923 IRI 0 + 0.00129 N + 0.000113T −5.485 ∗ 10 −10 P 4 − 10 −5 T N + 5.777 ∗ 10 −12 P 4 N (1) where IRI N P T IRI0 = = = = = 117 international roughness index (m/km), number of load repetitions, axle load (kN), asphalt concrete layer thickness (mm), and initial IRI value (m/km). In order to evaluate how roughness is affected by various factors, Equation 1 was used for different values of axle loads, asphalt layer thicknesses, and initial IRI values. Figure 8 shows IRI versus number of load repetitions for an initially smooth pavement (IRI0 = FIGURE 6 Elastic-plastic base and subgrade materials with strain hardening properties. 1 m/km) for different asphalt layer thicknesses and axle loads. Figure 9 shows the same relations except for an initially rough pavement (IRI0 = 4 m/km). A general look at Figures 8 and 9 indicates that roughness increases with increasing number of load repetitions in all cases. As expected, larger axle loads result in greater roughness. Also, thicker asphalt concrete layers result in less development of roughness. Figure 10 shows the relation between the IRI value and number of load repetitions of a 50-mm asphalt concrete layer for different axle loads and initial roughness values. Figure 11 is similar to Figure 10, except for an asphalt concrete layer of 100 mm. An important conclusion can be drawn from Figures 10 and 11: when the pavement is initially smooth, roughness does not greatly increase with load repetitions because of the smaller dynamic effect of vehicle loads. However, when the pavement is initially rough, a large amount of roughness is developed because of the large interaction between vehicles and pavement and consequently larger dynamic vehicle loads. This conclusion shows the importance of having a smooth pavement surface during construction so that the pavement will stay smooth for a long time. This trend was observed in the sections developed for the Long-Term Pavement Performance (LTPP) Program and emphasizes the importance of proper quality control during construction (16). Performance-based specifications can be developed using the methodology developed in this study. An incentive-penalty table can be obtained to deal with contractors on the basis of the effect of initial roughness on pavement performance. TABLE 1 Material Properties Used in Developing Roughness Model 118 Transportation Research Record 1699 Paper No. 00 -1148 FIGURE 7 FIGURE 9 IRI versus number of load repetitions for different asphalt layer thicknesses and axle loads (IRI 0 = 4 m/km). Fractional factorial statistical design. CALCULATING EQUIVALENCY FACTORS FROM ROUGHNESS MODEL Using the roughness model developed in this study, equivalency factors based on roughness can be mechanistically determined. In this case, a mixed traffic spectrum can be converted into an 80-kN (18-kip) mechanistic equivalent single-axle load (mechanistic ESAL) value based on roughness by developing equivalency factors for different axle loads. In this case, Equation 1 can be rewritten as  IRI failure − 2.923 IRI 0 + 1.415     − 0.000113T + 5.485 ∗ 10 −10 P 4   N =   0.00129 − 10 −5 T + 5.777 ∗ 10 −12 P 4  American Association of State Highway and Transportation Officials (AASHTO) load equivalency factor using a structural number of 3 and terminal pavement serviceability index (PSI) of 2.5 is 2.4, which is slightly less than that obtained in this study. In this example, it was assumed that an IRI value of 4 m/km is equivalent to a PSI value of 2.5 using the following relation, which was developed by Gillespie (12): IRI( m km ) = 1.5875(5 − PSI ) (3) 2 (2) Equation 2 can be used once to estimate the number of load repetitions of an 80-kN standard axle load to reach failure (e.g., IRI of 4 m/km). The same equation can be solved another time to estimate the number of load repetitions of any other axle load to reach failure. The ratio between these two values is the equivalency factor for that axle load. For example, for an axle load of 80 kN, asphalt layer of 100 mm, IRI0 of 2 m/km, and IRIfailure of 4, the number of load repetitions to failure is 22.941 ⴱ 106. The corresponding 100-kN axle load repetitions to failure is 8.619 ⴱ 106. Thus, the mechanistic ESAL is (22.941 ⴱ 106)/(8.619 ⴱ 106), or 2.662. The corresponding Figure 12 shows a comparison between the load equivalency factors obtained in this study by Arizona State University (ASU) (T = 100 mm, IRI0 = 2 m/km, IRIfailure = 4) and the AASHTO load equivalency factors (single axle, structural number = 3, terminal serviceability = 2.5). By definition, both curves agree at a standard axle load of 80 kN and an equivalency factor of 1. For axle loads either less than or larger than 80 kN, the ASU study produced larger equivalency factors than those obtained by AASHTO. If the load spectrum of a mixed traffic fleet is known, a cumulative mechanistic ESAL can be estimated by multiplying the number of load repetitions of each axle load by the corresponding equivalency factor and adding the results. This mechanistic ESAL is more rational than the ESAL determined using the AASHTO equation since the latter is limited to the conditions that prevailed during the AASHO Road Test in the late 1950s and early 1960s. This process can be computerized and used in the mechanistic design of pavement. USE OF ROUGHNESS MODEL IN PAVEMENT DESIGN FIGURE 8 IRI versus number of load repetitions for different asphalt layer thicknesses and axle loads (IRI 0 = 1 m / km). The model developed can also be used for the mechanistic design of flexible pavement based on roughness. If a pavement is required to carry a certain number of ESAL repetitions before an IRIfailure value is reached, Equation 1 can be used to design the asphalt concrete layer thickness. For example, for an ESAL of 6 million, IRI0 of 2 m/km, and IRIfailure of 4, the required asphalt layer thickness is 150 mm. It should be noted, however, that the model developed in this study is preliminary and limited by the material properties and conditions assumed. Other equations can be developed to cover other conditions. This limitation, however, should not be viewed as empirical since the procedure can be computerized and repeated to produce results for other conditions. The effort needed for repeating the procedure for other conditions is much less than that required to conduct a major FIGURE 10 IRI versus number of load repetitions for different axle loads and initial roughness values (50-mm asphalt concrete layer). FIGURE 11 IRI versus number of load repetitions for different axle loads and initial roughness values (100-mm asphalt concrete layer). FIGURE 12 Comparison of AASHTO and ASU study load equivalency factors. 120 Paper No. 00 -1148 road test. The model presented in this paper was calibrated and verified with LTPP data and the results were submitted for publication elsewhere (17). SUMMARY AND CONCLUSIONS A completely mechanistic roughness performance model for use in flexible pavement design and evaluation under certain conditions that takes into account vehicle dynamics was developed. The model was developed in the form of a relation between roughness and number of load repetitions, axle load, and asphalt layer thickness. The model uses vehicle dynamics analysis to estimate the dynamic wheel force profile and finite element structural analysis to estimate the change of pavement surface roughness for each load repetition. The model makes use of the fact that pavement roughness changes the magnitude of the vehicle dynamic force applied on the pavement and dynamic forces change the road roughness. The developed mechanistic roughness performance model can be used to estimate the 80-kN ESAL for mixed traffic. It can also be used to design pavement so that it will last for a certain number of load repetitions before it reaches a predetermined roughness level. Although the model developed in this study is limited, it can be expanded to cover other conditions. The model was calibrated and verified with field data and the research was submitted for publication elsewhere. It was concluded that when pavement is initially smooth, the rate of increase of roughness with load repetitions is smaller because of the smaller dynamic effect of vehicle loads. However, when pavement is initially rough, a greater amount of roughness is developed because of the larger interaction between vehicles and pavement and consequently larger dynamic vehicle loads. Performance-based specifications can be developed using the methodology developed in this study. REFERENCES 1. Huang, Y. Pavement Analysis and Design. Prentice-Hall, Englewood Cliffs, N.J., 1993. 2. Haas, R., W. R. Hudson, and J. P. Zaniewski. Modern Pavement Management. Krieger Publishing Company, Melbourne, Fla., 1994. Transportation Research Record 1699 3. Mamlouk, M. S. Rational Look at Truck Axle Weight. In Transportation Research Record 1307, TRB, National Research Council, Washington, D.C., 1991, pp. 8–19. 4. Cebon, D., and C. B. Winkler. A Study of Road Damage Due to Dynamic Wheel Loads Using a Load Measuring Mat. Report SHRP-ID/UFR-91518. Strategic Highway Research Program, TRB, National Research Council, Washington, D.C., 1991. 5. Gillespie, T. D., S. M. Karamihas, M. W. Sayers, M. A. Nasim, W. Hanson, N. Ehsan, and D. Cebon. NCHRP Report 353: Effects of Heavy Vehicle Characteristics on Pavement Response and Performance. TRB, National Research Council, Washington, D.C., 1993. 6. Mikhail, M. Y., and M. S. Mamlouk. Effect of Vehicle-Pavement Interaction on Pavement Response. In Transportation Research Record 1570, TRB, National Research Council, Washington, D.C., 1997, pp. 78–88. 7. Mikhail, M. Y., and M. S. Mamlouk. Effect of Traffic Loads on Pavement Serviceability. STP 1348. ASTM, Philadelphia, Pa., 1998. 8. Mamlouk, M. S., and M. Y. Mikhail. Concept for Mechanistic-Based Performance Model for Flexible Pavements. In Transportation Research Record 1629, TRB, National Research Council, Washington, D.C., 1998, pp. 149–158. 9. Sweatman, P. F. A Study of Dynamic Wheel Forces in Axle Group Suspensions of Heavy Vehicles. Special Report 27. Australian Road Research Board, June 1983. 10. Fernando, E. G., et al. The Florida Comprehensive Pavement Analysis System (COMPAS), Vol. 1. Texas Transportation Institute, Texas A&M University, 1991. 11. Fernando, E. G., and R. L. Lytton. A System for Evaluation of the Impact of Truck Characteristics and Use on Flexible Pavement Performance and Life-Cycle Costs. Proc., Seventh International Conference on Asphalt Pavements, Nottingham, U.K., 1992. 12. Gillespie, T. D. Everything You Always Wanted to Know about the IRI, But Were Afraid to Ask. Presented at Road Profile Users Group Meeting, Lincoln, Nebraska, Sept. 1992. 13. ABAQUS, Finite Element Computer Program. Theory Manual, Version 5.4. Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, R.I., 1995. 14. RoadRuf Software for Analyzing Road Profiles. Transportation Research Institute, University of Michigan, Ann Arbor, 1996. 15. Design-Expert 5. Stat-Ease Corporation, Minneapolis, Minn., 1996. 16. Ali, H. A., and S. D. Tayabji. Mechanistic Evaluation of Test Data from LTPP Flexible Pavement Test Sections. FHWA, U.S. Department of Transportation, May 1997. 17. Saleh, M. F., and M. S. Mamlouk. Calibration and Verification of a Pavement Roughness Performance Model. Journal of Transportation Engineering, ASCE (to be published). Publication of this paper sponsored by Committee on Pavement Monitoring, Evaluation, and Data Storage.