Subgrade Shear Failures

JOINT C­SHRP/SASKATCHEWAN BAYESIAN APPLICATION

Prepared for: Canadian Strategic Highway Research Program (C­SHRP)

Prepared by:

Allan Widger Senior Materials Engineer

Randy Schmidt Materials Standards Engineer

Saskatchewan Highways and Transportation

October, 1995

Executive Summary

In 1994, Saskatchewan Highways and Transportation (SHT) became involved in evaluating Subgrade performance (Subgrade Study). The Canadian Strategic Highway Research Program (C­SHRP), which operates within the Transportation Association of Canada (TAC), was also promoting their newly developed Bayesian Software by sponsoring Joint C­SHRP/Agency Applications, whereby technical assistance was provided to the provincial highway agencies towards the development of Bayesian performance models.

Saskatchewan's Bayesian project, Subgrade Shear Failure, was accepted by C­SHRP and would incorporate data collected in the Subgrade Study. The main objective was to learn the Bayesian methodology and to develop a model incorporating field data and expert judgement. Field data was collected from two gravel haul roads in 1994 and the expert data was obtained from department and external experts in the spring of 1995.

The purpose of the subgrade model is to estimate road surface deflections, initially based on five variables: Crust Thickness, Crust Strength, Subgrade Material Strength, Total Loading and Repetitive Loading. The Repetitive Loading variable was ultimately dropped, due to a lack of field data.

The following model equation was derived, as a result of minimal available field data and the input of 10 experts:

• Deflection (mm) = 7.23 ­ 0.02(Crust Thickness (mm)) ­ 0.02(Crust Strength (CBR)) ­ O.O9(Subgrade Material Strength (CBR)) + 0.01(Total Loading (tonnes))

This first generation model has a large degree of variance, in part due to the limited field data available. It should be 'fine tuned' with additional field data, as it becomes available.

SHT's Bayesian Project was a success in confirming the Bayesian methodology is a valuable tool. This method provides a structured process to obtain first generation models, by combining expert judgement with limited data.

This methodology should be considered for future department research projects.

Acknowledgments

Saskatchewan Highways and Transportation would like to acknowledge the financial assistance provided by the Canadian Strategic Highway Research Program (C­SHRP), which operates under the Transportation Association of Canada (TAC). C­SHRP provided for much needed support and direction from Vemax Management Inc., in particular, Lyle Kajner and Mark Nickeson, as well as providing the opportunity to attend the Bayesian Workshop in Ottawa.

The time and effort spent by the experts providing us with their input, and the support of the department's Material Section, made this analysis possible.

Table Of Contents

• Executive Summary
• Acknowledgments
• 1. Introduction
• 1.1 Problem Statement /Need for a Model
• 1.2 Project Objectives
• 2, Team Members
• 3. Schedule and Methodology
• 4, Model Selection
• 4.1 Definition of Model Variables
• 5. Expert Encoding Package
• 5.1 Dependent Variable
• 5.2 Independent Variables
• 5.2.1 Crust Thickness
• 5.2.2 Crust Strength
• 5.2.3 Subgrade Material Strength
• 5.2 4 Total Loading
• 5.2.5 Repetitive Loading
• 5.3 Relationship Between Deflection and Independent Variables
• 5.4 Summary of Variables
• 6. Modeling
• 6.1 Model Type and Functional Form
• 6.2 Factual Data (Data) (DATA.XLS)
• 6.3 Expert Data (Prior) (EXPERT_A.XLS)
• 6.4 Sensitivity Analysis
• 6.5 Combining of Expert Judgments
• 7. Bayes Analysis
• 7.1 Five Variables (BAYES5.XLS)
• 7.2 Four Variables (BAYES4.XLS)
• 7.3 Four Variables ­ 61 DOF (BAYES4B.XLS)
• 7.4 Iterations Based On Degrees of Freedom
• 7.5 Matrix Modification (4EXP RAM.XLS)
• 7.6 Final Model
• 8. Interpretation and Discussion
• 8.2 Transformations
• 8.3 Factual Data Statistics
• 8.4 Compatibility Problems
• 8.5 Analysis
• 8.6 Interpretation of Results
• 8.7 Inference from Analysis
• 9. Conclusions
• 10. Satisfaction and Improvements
• 10.1 Use of Developed Model, Both Inside and/or Outside the Agency
• 10.2 Bayesian Methodology
• 10.3 XLBA YES Software
• l 0.4 'Joint Application ' Partnership Arrangement with C­SHRP
• 11. Future Modeling Needs and Direction
• 12. Appendices

'A ' ­ Figures

• • 1 Summary of Expert's Suggested Variables
  • 2 Dynamic Cone Penetrometer
  • 3 Typical pop Test Results
  • 4 Typical pop ­ CBR Calculation
  • 5 Factual Data Coverage Of Encoding Matrix
  • 6 Factual Data Chart (five variable)
  • 7 Factual Data ­ Five Variable Regression Analysis
  • 8 Typical Completed Expert Matrix
  • 9 Typical Expert Data File
  • 10 Sensitivity Graph
  • 11 Expert Data ­ Classical Regression (five variable)
  • 12 ­ 17 Factual Data ­ XLBAYES Analysis (five variable)
  • 18 ­ 23 Expert Data ­ XLBAYES Analysis (five variable)
  • 24 Factual Data Chart(four variable)
  • 25 ­ 29 Factual Data ­ XLBAYES Analysis (four variable)
  • 30 ­ 34 Expert Data ­ XLBAYES Analysis (four variable)
  • 35 Modified Expert Data ­ Classical Regression (four variable)
  • 36 ­ 41 Bayesian Analysis ­ Five Variable
  • 42 ­ 46 Bayesian Analysis ­ Four Variable (1885 Degrees of Freedom)
  • 47 ­ 51 Bayesian Analysis ­ Four Variable (220 Degrees of Freedom)
  • 52 ­ 56 Bayesian Analysis ­ Four Variable (122 Degrees of Freedom)
  • 57 ­ 61 Bayesian Analysis ­ Four Variable (61 Degrees of Freedom)
  • 62 ­ 66 Bayesian Analysis ­ Four Variable (30 Degrees of Freedom)

'B' ­ 'Filename'Summary

'C' ­ Expert Judgement Encoding Package

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