SENSITIVITY ANALYSIS OF THE VESYS PROGRAM TO PREDICT CRITICAL PAVEMENT RESPONSES FOR RUTTING AND FATIGUE PERFORMANCES OF PAVEMENT INFRASTRUCTURES

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1 SENSITIVITY ANALYSIS OF THE VESYS PROGRAM TO PREDICT CRITICAL PAVEMENT RESPONSES FOR RUTTING AND FATIGUE PERFORMANCES OF PAVEMENT INFRASTRUCTURES Ghazi G. Al-Khateeb 1, Raghu Satyanarayana 2, and Katherine Petros 3 ABSTRACT. A sensitivity analysis was conducted in this study to evaluate the effect of major variable inputs on the predictions of the VESYS 5W program for primary pavement responses. These variable inputs included: the modulus of the hot-mix asphalt (HMA) layer, the modulus of the base layer, the thickness of the HMA layer, and the applied load intensity. The effect of the variation of these inputs on primary pavement responses including tensile strain, tensile stress, vertical stress, and vertical deformation, was investigated. The relative significance of the variable inputs on the primary responses was also evaluated. In general, the relative significance of the applied load intensity on primary response was found to be constant with the increase in the load intensity, while, the relative significance measures of the HMA modulus and the base modulus on primary response decreased logarithmically with the increase in the variable input. KEY WORDS Sensitivity Analysis, VESYS, Critical Response, Pavement Response, Primary Response, Rutting Performance, Fatigue Performance, Tensile Strain, Vertical Stress, HMA, Asphalt Pavement, Pavement Infrastructures. 1 Assistant Professor of Civil Engineering, Department of Civil Engineering, Jordan University of Science and Technology, P. O. Box 33, Irbid 2211, Jordan, Tel Ext , ggalkhateeb@just.edu.jo. 2 Research Engineer and Vice President, Engineering & Software Consultants, Inc., Whitfield Place, Ste. 22, Sterling, VA 2165, USA, 3 Katherine Petros, Team Leader, Pavement Modeling Team, TFHRC, FHWA, 63 Georgetown Pike, McLean, VA 2211, USA. 1

2 INTRODUCTION The concepts of the VESYS program were originally developed at the Massachusetts Institute of Technology in the United States. The work was further refined and modified by the Federal Highway Administration (FHWA) in The modified version as called VESY-IIM was widely publicized at that time. Then this version experienced several refinements and improvements since that time till current times by different agencies, organizations, and research groups (Huang, 1993). VESYS program has the capability of predicting the structural primary response of asphalt pavements as well as the pavement performance of the pavement structures. Current versions of the VESYS program can be used to predict three levels of output: Type I for primary response and single load axle, Type II for primary response and multiple loads axle, and finally Type III for pavement performance (rutting, fatigue, and low-temperature). The version used in this study is VESYS 5W (VESYS 5Ws User Manual, 23), which has various major features including: analysis of multilayer pavement systems (up to seven layers), temperature variation by season, analysis of both single and multiple loads axles, considering the viscoelastic properties of the asphalt layer, analysis of single, tandem, and tridem axle groups, and predictions of primary response as well as performance of pavement structures, and estimation of rutting in each layer of the pavement system. Empirical design methods have been long used in pavements. These methods, however, lack the understanding of the pavement mechanism and behavior, and therefore fail at times when pavements experience traffic loading in certain environmental conditions that lead to pavement damage. Consideration of mechanistic-empirical design methods in pavement technology thus becomes essential on account of their advantages over the empirical methods in providing more accurate predictions and better understanding of the pavement performance. The first step in any mechanistic-empirical design method is to conduct a mechanistic analysis of the pavement and to determine the stresses and strains the pavement perceives under traffic loading. Rutting and fatigue cracking are two major distresses that are primarily considered in mechanistic-empirical pavement designs. Vertical stress/strain at the top of the subgrade layer and tensile strain at the bottom of the HMA layer are two critical pavement responses for rutting and fatigue performances determined from mechanistic analysis. However, accurate mechanistic analysis leads to accurate predictions of pavement performance. Consequently, a proper selection of a good mechanistic model or program is a crucial step in the entire process. OBJECTIVES The main objective of this study is to investigate the effect and relative significance of different variable inputs on the critical pavement responses for rutting and fatigue performances of HMA pavements as obtained from the VESYS 5W program. 2

3 METHODOLOGY What is Sensitivity Analysis? There are different definitions of sensitivity analysis in general (not necessarily used in pavement engineering). Below is a summary of some of these definitions: 1. Sensitivity analysis is simply defined as the variation in the output of a model qualitatively or quantitatively to changes in the inputs. 2. Sensitivity analysis is a method to check the output dependency on the different input parameters of a model. 3. Sensitivity analysis is a simple technique to assess the resulted changes of the outcome of a model based on changes in the variable inputs. 4. Sensitivity analysis is the study about the relations between the input and the output of a model according to Saltelli et al. (2). Why Sensitivity Analysis Sensitivity analysis is conducted for different objectives summarized below: 1. It is a measure of the quality of a given model as well as a powerful tool for investigating the robustness and reliability of the model and is considered a basis for a model validation and optimization 2. It is used to assess the variable inputs one at a time (combinations can also be assessed) to identify the key variables of the model and the factors that mostly contribute to the output variability. 3. It can help in identifying critical control points, prioritizing additional data collection or research, and verifying and validating the model as mentioned in Frey and Patil (22). 4. Baker et al. (1999) identified sensitivity analysis as one of the principal quantitative techniques used for risk management in the United Kingdom. 5. Jones (2) indicated that sensitivity analysis can provide the basis for planning adaptation measures to mitigate the risk of climate change. 6. Sensitivity analysis can play an important role in model verification and validation throughout the course of model development and refinement (Kleijnen, 1995, Kleijnen and Sargent, 2, and Fraedrich and Goldberg, 2). Methods of Sensitivity Analysis Saltelli et al. (22) provides an overview and further insight into the different categorizations of the sensitivity analysis methods. Sensitivity analysis methods may be categorized according to the outcome of the related sensitivity measures: 1. Qualitative methods, 2. Quantitative methods, 3. Local methods, 4. Global methods, and 5. Methods that depend on or are independent of the model characteristics. 3

4 Frey and Patil (22) identified sensitivity analysis methods based on the type of the analysis and the model: 1. Mathematical methods, 2. Statistical methods, and 3. Graphical methods. Variable Inputs Used in the Sensitivity Analysis of the VESYS 5W Program In order to conduct the sensitivity analysis in this study, a three-layered pavement structure was used as shown in Figure 1 below: a 15 mm (6 in) asphalt concrete layer, a 2 mm (8 in) crushed aggregate base, and an A-6 class subgrade. The traffic data used in the analysis are: 1,, load applications after 2 years, deterministic traffic stream, season length of one year, and a single axle group. On the other hand, the seasonal temperature used is 2. C (68 F), and the material properties are shown in Table 1 below. HMA Layer Base Layer 15 mm (6 in.) 2 mm (8 in.) Sugrade Layer Figure 1. Three-layered pavement structure Table 1. Material properties used in the analysis. Layer Modulus of Elasticity, MPa Variation Coefficient for Poisson s Ratio (psi) Layer Moduli Asphalt Variable, 1,379 (2,).33.2 Base 29 (42,), Variable.4.3 Subgrade 27.6 (4,).4.3 The loading data included: intensity of applied loading of 69 kpa (1 psi), and radius of applied loading of 14. cm (5.6 in.). The grid data including the number of radial offset points and the number of vertical positions within the depth of the pavement structure, at which primary response predictions are desired, covered six offsets and three depths as shown in the tables below. Table 2. Radial offsets considered for primary response predictions. Point Radial Offset, cm (in.). (.) 15. (6.) 3. (12.) 6. (24.) 9. (36.) 18. (72.) 4

5 Table 3. Vertical positions considered for primary response predictions. Point Depth, cm (in.). (.) 15. (6.) 35. (14.) A matrix of variable inputs was considered in the sensitivity analysis with a practical range of values for each of these inputs as shown in Table 4 below. These variable inputs included: (1) HMA modulus of elasticity, (2) base modulus of elasticity, (3) thickness of HMA layer, and (4) intensity and radius of applied loading. Depth within the pavement structure was also considered in all cases. On the other hand, four target outputs or pavement responses of the VESY 5W program were selected to study the effect of each variable input on these outputs. They included: (1) tensile strain, (2) tensile stress, (3) vertical stress, and (4) vertical deformation. Variable Input HMA Modulus, MPa (psi) Base Modulus, MPa (psi) HMA Layer Thickness, mm (in.) Intensity of Applied Loading, kpa (psi) Associated Radius of Applied Loading Area, cm (in.) Table 4. Matrix of variable inputs. Range of Values Run #1 Run #2 Run #3 Run #4 Run # (2,) (4,) (6,) (8,) (1,,) (24,) (3,) (36,) (42,) (48,) (4) (6) (8) (1) (12) (8) (9) (1) (11) (12) 15.8 (6.3) 14.8 (5.9) 14. (5.6) 13.5 (5.4) 13. (5.2) The sensitivity analysis was conducted in this study based upon the following main processes: 1. The target outputs (responses) of the VESYS 5W program as well as the variable inputs of interest were selected. 2. The distribution functions for the selected variables were defined. 3. A matrix of the variable inputs using the defined distributions was generated. 4. A way to assess the impact or relative significance of each variable input on the target outputs was defined. The way to investigate the effect of each variable input on the target outputs is described as follows: 1. A relationship between the variable input and the target output was established. 2. A best-fit function was developed for each relationship. 3. Based on the developed functions, the effect of each variable input on each of the target outputs (primary responses) was described. 4. The impact or relative significance of each variable input on each of the target outputs was then determined and compared with the impact of the other variable inputs as shown in the equation below: 5

6 Percent Absolute Change in Output RS = 1 Percent IncreaseinVariable Input Where: RS = relative significance parameter, percent. ( 1) Impact of the Variable Inputs on the Target Outputs The relationship between each of the variable inputs including: HMA modulus of elasticity, base modulus of elasticity, HMA layer thickness, and intensity and radius of applied loading, and each of the target outputs of the VESYS 5W program was developed. The selected range for each variable input is shown in Table 4. Type I analysis (primary response analysis) of the VESYS 5W program was conducted. Several runs were performed using these values for each of the variable inputs. Each time a variable input was used, the other variable inputs were fixed at default values to separate the effect of each input from the effect of others. The logarithm function (ln) was found to be the best fit to describe the relationship between each of the variable inputs and each of the target outputs (primary responses) except for the relationship of the intensity of the applied loading, which was linear. Plots of the developed relationships were obtained for each of the variable inputs. Due to the similarity of the type of these relationships, only some examples are provided in this paper but inclusive explanation of each one of them is given. Figures 2 through 5 below show the relationships between the HMA modulus and each of the tensile strain, the tensile stress, the vertical stress, and the vertical deformation, respectively. Both the tensile strain and the vertical deformation decrease logarithmically with the increase in HMA modulus. Tensile Strain (me) y = Ln(x) inch Depth R 2 =.9998 y = Ln(x) R 2 =.9997 y = Ln(x) R 2 = HMA Modulus (psi) Figure 2. Tensile strain vs. HMA modulus 6

7 Tensile Stress (psi) inch Depth y = Ln(x) R 2 =.9995 y = -.63Ln(x) R 2 =.9429 y = Ln(x) R 2 = HMA Modulus (psi) Figure 3. Tensile stress vs. HMA modulus Vertical Stress (psi) y = Ln(x) - 2 R 2 =.9989 y = -1 R 2 = #N/A y = Ln(x) R 2 = inch Depth HMA Modulus (psi) Figure 4. Vertical stress vs. HMA modulus On the other hand, the tensile and vertical stresses increase as the HMA modulus increases. The decrease in the primary response is remarkable at lower HMA modulus values. Nevertheless, this reduction becomes insignificant at higher HMA modulus values; this is due to the nature of the logarithmic relationship. The effect of depth within the pavement structure is apparent in these figures, where the primary response value diminishes at higher depth values. 7

8 Vertical Deformation (inch) y = -.66Ln(x) R 2 = 1 y = -.74Ln(x) R 2 = inch Depth y = -.51Ln(x) R 2 = HMA Modulus (psi) Figure 5. Vertical deformation vs. HMA modulus The effect of the base modulus on the primary response is established in Figures 6 and 7 where the relationships between the base modulus and each of the tensile strain and the vertical deformation are developed, respectively. Both the tensile strain and the vertical deformation decrease as the base modulus increases as shown in these two figures with considerable reduction at lower base modulus values and less reduction at higher modulus values. Tensile Strain (µε µε) y = Ln(x) R 2 =.9985 y = Ln(x) R 2 = 1 y = Ln(x) R 2 = 1 6-inch Depth Base Modulus (psi) Figure 6. Tensile strain vs. base modulus 8

9 Vertical Deformation (inch).5.4 y = -.64Ln(x) R 2 = 1 y = -.95Ln(x) R 2 = 1 y = -.95Ln(x) R 2 = 1 6-inch Depth Base Modulus (psi) Figure 7. Vertical deformation vs. base modulus Results obtained from the VESYS 5W program also show that the primary response decreases logarithmically as the HMA layer thickness increases (Figures 8 and 9). However, the tensile strain at the bottom of the HMA layer decreases linearly with the increase in the HMA layer thickness as shown in Figure 8. Consequently, the reduction in the primary response is more significant at smaller values of HMA layer thickness except for the tensile strain at the bottom of the HMA layer, which has similar reduction at different values of HMA layer thickness due to the linearity of the relationship. Tensile Strain (µε µε) y = Ln(x) R 2 =.9647 y = x R 2 =.9922 y = Ln(x) R 2 =.993 Bottom of HMA HMA Layer Thickness (inch) Figure 8. Tensile strain vs. thickness of HMA layer 9

10 Vertical Deformation (inch) Bottom of HMA y = -.23Ln(x) R 2 =.998 y = -.221Ln(x) +.81 R 2 =.9986 y = -.135Ln(x) +.6 R 2 = HMA Layer Thickness (inch) Figure 9. Vertical deformation vs. thickness of HMA layer An applied load intensity of a range of 552 to 827 kpa (8 to 12 psi) was considered in the analysis. The effect of the applied load intensity on the primary response was linear. In other words, the primary response increases with the increase in the applied load intensity linearly (Figures 1 and 11). This variable input affected the primary response differently relative to the other variable inputs, which impacted the primary response logarithmically. Relative Significance of the Variable Inputs on the Target Outputs In order to investigate the effect of a variable input on the primary response, it is not enough, though, to only describe the relationship between the two. But rather, the relative significance (RS) of the variable input has to be estimated. The RS of each variable input on each of the primary responses was determined using Equation (1) above. The RS parameter defined in this paper as equivalent to the ratio of the percent absolute change in the primary response to the percent increase in the variable input is a powerful measure to assess the impact of the variable input on the primary response. Therefore, the RS values were determined for each variable input at different predicted primary response values. This is essential in assessing the change in the primary response with the change in the variable input. For instant, a linear relationship provides a constant RS value if plotted against the percent increase in the variable input, while a logarithmic-decreasing RS is obtained for a logarithmic relationship as shown in Figure 12. A comparison between the effects of the different variable inputs on the primary response of the VESYS 5W program using the RS measure was conducted. Additionally, a comparison between the effects of the same variable input on the different primary responses using the RS measure was also performed. Primary responses at the bottom of the HMA layer were considered for these comparisons. 1

11 6 4 y =.7342x R 2 = inch Depth Tensile Strain (µε µε) y = 1.977x R 2 =.9994 y = x R 2 = Load Intensity (psi) Figure 1. Tensile strain vs. applied load intensity.5 Vertical Deformation (inch).4 y = 6E-5x R 2 =.855 y = 5E-5x R 2 =.7524 y = 3E-5x R 2 = inch Depth Load Intensity (psi) Figure 11. Vertical deformation vs. applied load intensity It was found that the relative significance of the HMA modulus on the tensile stress was the highest and that on the vertical deformation was the lowest. The RS in this case decreased logarithmically for all primary responses as shown in Figure 13. Similar results were obtained for the RS of the base modulus. It has to be noted herein that both the RS of the HMA modulus and the RS of the base modulus decreased in a logarithmic manner with the increase in the variable input, which explains the diminishing of the relative significance impacts of both variable inputs on primary responses as their values increase. 11

12 1. 1. RS for Logarithmic Relationship RS for Linear Relationship RS, % y = Ln(x) R 2 = Percent Increase in x Figure 12. Relative significance of a variable input: linear vs. logarithmic RS, % Tensile Strain y = Ln(x) R 2 =.9991 Tensile Stress Vertical Deformation Vertical Stress y = -1.93Ln(x) R 2 =.9999 y = Ln(x) R 2 =.9981 y = Ln(x) R 2 = Percent Increase in HMA Modulus Figure 13. Relative significance of HMA modulus on primary responses The relative significance of the applied load intensity on primary responses was also investigated. The RS of the load intensity on the tensile stress and strain was the highest and that on the vertical deformation was the lowest. This is evident in Figure 14. Nevertheless, the RS of the load intensity for all primary responses was constant with the percent increase in the load intensity as shown in Figure 14. In other words, the relative significance impact of the load intensity on primary responses does not degrade with the increase in the load intensity but rather stays approximately the same at higher intensity values and is as significant as that at lower values. 12

13 RS, % Tensile Strain Tensile Stress Vertical Deformation Vertical Stress Percent Increase in Load Intensity Figure 14. Relative significance of applied load intensity on primary responses On the other side, the RS of the HMA layer thickness on the vertical stress was the highest and that on the vertical deformation was the lowest. In both cases, however, the RS decreased logarithmically. That is to say that the relative significance of the HMA layer thickness on these two responses is more at lower values of HMA layer thickness. Nevertheless, the RS of this variable input on the tensile stress and strain at the bottom of the HMA layer was approximately constant indicating that the relative impact of the HMA layer thickness on these two responses at higher thickness values is as significant as that at lower thickness values. Considering the RS measure of different variable inputs on the same primary response, the applied load intensity was found to have the highest relative impact on the tensile strain at the bottom of the HMA layer, whereas the HMA modulus had the lowest relative impact on the tensile strain at the bottom of the HMA layer as predicted from the VESYS 5W program and that is shown in Figure 15. Nevertheless, the RS values are constant with the percent increase in the load intensity and the HMA layer thickness, which indicates that the relative effect of these two variable inputs on the tensile strain stays significant at higher values of load intensity and HMA layer thickness. On the other hand, the RS of the base modulus and that of the HMA modulus on primary responses decrease logarithmically with the percent increase in the variable input. In other words, their relative impacts on the tensile strain at the bottom of the HMA layer are more remarkable at lower input values than those at higher input values. Using the RS of the different variable inputs on the vertical deformation, the HMA layer thickness was found to have the highest relative impact on the vertical deformation and the applied load intensity had the lowest relative effect on the vertical deformation (Figure 16). Conversely, the HMA modulus and the base modulus had medium relative impacts on the vertical deformation. Nonetheless, the RS measures of the three variable inputs: HMA layer thickness, HMA modulus, and base modulus decline in a logarithmic mode with the increase in their values, which means that their relative impacts on the vertical deformation are greater at lower input values (Figure 16). Yet, the RS measure of the load intensity maintains the same 13

14 RS on Tensile Strain, % HMA Modulus Base Modulus y = Ln(x) R 2 Load Intensity =.9846 y = Ln(x) R 2 = Percent Increase in Variable Input Figure 15. Relative significance of different variable inputs on tensile strain RS on Vertical Deformation, % HMA Modulus Base Modulus Load Intensity y = Ln(x) R 2 HMA Thickness =.9912 y = Ln(x) R 2 =.9867 y = Ln(x) R 2 = Percent Increase in Variable Input Figure 16. Relative significance of different variable inputs on vertical deformation value at different input values. In other words, the relative effect of the load intensity on the vertical deformation at higher input values is as significant as that at lower input values. CONCLUSIONS The following conclusions were drawn based upon the results of this study: 1. The best function that fitted the relationship between the variable inputs and the primary responses was a logarithmic one except for the applied load intensity, which was linear. 14

15 2. The RS measures of both the HMA modulus and the base modulus on the tensile stress was found to be the highest and that on the vertical deformation was the lowest. 3. The RS measures for both the HMA modulus and the base modulus decreased logarithmically for all primary responses. 4. The RS of the applied load intensity on the tensile stress and strain was the highest and that on the vertical deformation was the lowest; it was constant, though, with the increase in load intensity for all primary responses. 5. The RS of the HMA layer thickness decreased logarithmically for the vertical stress and the vertical deformation. However, it was approximately constant for the tensile stress and strain at the bottom of the HMA layer. 6. The applied load intensity was found to have the highest relative impact on the tensile strain at the bottom of the HMA layer, whereas the HMA modulus had the lowest relative impact on the tensile strain at the bottom of the HMA layer. 7. The RS measures of the applied load intensity and the HMA layer thickness on the tensile strain were found to be constant with the increase in the variable input. On the other hand, the RS measures of the base modulus and the HMA modulus on primary responses decreased logarithmically with the percent increase in the variable input. 8. The HMA layer thickness was found to have the highest relative impact on the vertical deformation and the applied load intensity had the lowest relative effect on the vertical deformation, while the HMA modulus and the base modulus had medium relative impacts on the vertical deformation. 9. Nevertheless, the RS measures of the three variable inputs: HMA layer thickness, HMA modulus, and base modulus declined in a logarithmic mode with the increase in their values, yet, the RS measure of the load intensity maintained the same value at different input values. REFERENCES Baker, S., Ponniah, D., and Smith, S. (1999). "Survey of Risk Management in Major UK Companies," Journal of Professional Issues in Engineering Education and Practice, 125(3), Fraedrich, D. and Goldberg, A. (2). "A Methodological Framework for the Validation of Predictive Simulations," European Journal of Operational Research, 124(1): Frey, H.C., and Patil, S.R. (22). Identification and Review of Sensitivity Analysis Methods", Risk Analysis, 22(3), Huang, Y.H. (1993). Pavement Analysis and Design. Prentice Hall. Jones, R.N. (2). "Analyzing the Risk of Climate Change Using an Irrigation Demand Model", Climate Research, 14(2), Kleijnen, J.P.C. (1995). "Verification and Validation of Simulation-Models", European Journal of Operational Research, 82(1), Kleijnen, J.P.C. and Sargent, R.G. (2), "A Methodology for Fitting and Validating Metamodels in Simulation, European Journal of Operational Research, 12(1), Saltelli, A., Chan, K., and Scott, E.M. (2). Sensitivity Analysis, John Wiley and Sons, Ltd.: West Sussex, England. VESYS 5Ws User Manual (23). Truck Pavement Interaction Program, Office of Infrastructure Research and Development, Federal Highway Administration. 15