Benkelman Beam Rebound AC Overlay Model

JOINT C­SHRP/MANITOBA BAYESIAN APPLICATION

Prepared for: Canadian Strategic Highway Research Program (C­SHRP)

Prepared by: Leonnie Kavanagh, P.Eng.

Manitoba Highways and Transportation Materials and Research Branch

October, 1995

EXECUTIVE SUMMARY

The Manitoba Department of Highways & Transportation (MDHT) attempted to model and predict the immediate and long term maximum Benkelman Beam Rebound BBR, or deflection, of a flexible pavement after an asphaltic concrete (AC) overlay. The purpose of the application was to verify the current rehabilitation design procedure for Manitoba, and to quantify the significant contributing variables and their impacts on the design.

A two­stage model to predict BBR was developed and analysed using the Bayesian approach. Model 1 was the first stage initiation model to predict the maximum BBR immediately after an overlay. The second stage, Model 2, was the propagation model to predict the rebound over time. The XLBAYES software was used to develop coefficients and statistical parameters for the combination of C­SHRP & SHRP field data and expert data in the models. Sensitivity analyses were performed and compared for each model, and each expert, to determine the magnitude and effect of the independent variables on the dependent rebound variable. Two iterations were performed on each model.

The Prior, Data, and Posterior models generated from the analysis generally had good statistical parameters, and the sensitivity analysis clearly indicated the importance and magnitude of the impacts of each variable on the BBR prediction. The Bayesian analysis was also successful in incorporating expert judgement information with limited field data to produce useable first models.

TABLE OF CONTENTS

1.0 Executive Summary

2.0 Introduction

2.1 What was Manitoba's Problem Statement?

2.2 Why the Need for a Model?

2.3 Who were the Team Members and Experts?

3.0 Bayesian Methodology

3.1 What was the Model Selection?

3.2 What was the 2­Stage Model Definition, Dependent

& Independent Variables?

3.3 What was the Model Type and Functional Form?

3.4 What were the Model Inputs?

4.0 Analysis and Interpretation of Results

4.1 Model Iterations, Results & General Findings

4.2 Sensitivity Analysis ­ General Findings

5.0 Discussion and Conclusions

5.1 Conclusion

5.2 General Impression /Satisfaction with Bayesian Methodology

5.3 Future Modelling Needs/Direction

Tables:

• Table 1: Model Evaluation - Model 1, Iteration 1
• Table 2: Comparison of Prior and Posterior Equations - Model 1, Iteration 1
• Table 3: Model Evaluation - Model 1, Iteration 2
• Table 4: Comparison of Prior and Posterior Equations - Model 1, Iteration 2
• Table 5: Model Evaluation - Model 2, Iteration 1
• Table 6: Comparison of Prior and Posterior Equations - Model 2, Iteration 1
• Table 7: Model Evaluation - Model 2, Iteration 2
• Table 8: Comparison of Prior and Posterior Equations - Model 2, Iteration 2

Figures:

• Figure 1: Variable Sensitivity by Expert - Model 1, Iteration 1 - Prior
• Figure 2: Variable Sensitivity by Expert - Model 1, Iteration 1 - Posterior
• Figure 3: Variable Sensitivity by Expert - Model 1, Iteration 2 - Prior
• Figure 4: Variable Sensitivity by Expert - Model 1, Iteration 2 - Posterior
• Figure 5: Variable Sensitivity by Expert - Model 2, Iteration 1 - Prior
• Figure 6: Variable Sensitivity by Expert - Model 2, Iteration 1 - Posterior
• Figure 7: Variable Sensitivity by Expert - Model 2, Iteration 2- Prior
• Figure 8: Variable Sensitivity by Expert - Model 2, Iteration 2 - Posterior
• Figure 9: Sensitivity of Posterior Standard Error to Prior DOF - Model 1, Iteration 1
• Figure 10: Sensitivity of Posterior Standard Error to Prior DOF - Model 2, Iteration 2

Appendices:

Appendix A: Expert Judgement Encoding Package

• Figure 1: Typical Road Cross Section
• Figure 2: Encoding Matrix: Model 1
• Figure 3: Encoding Matrix: Model 2

Appendix B: Field and Expert Data & Transformations

Appendix C: Model 1, Iteration 1 ­ Input & Output Spreadsheets & Graphs

Appendix D: Model 1, Iteration 2 ­ Input & Output Spreadsheets & Graphs

Appendix E: Model 2, Iteration 1 ­ Input & Output Spreadsheets & Graphs

Appendix F: Model 2, Iteration 2 ­ Input & Output Spreadsheets & Graphs

Appendix G: Sensitivity Analysis and Degree of Freedom Output & Graphs

Return to Main Page