1. Western Transportation Institute Montana State University-Bozeman Evaluation of Non-Linear and Tension Cutoff Material Modeling Features for Pavement Base Aggregate Jeffrey Sharkey Undergraduate Research Assistant Dr. Steven Perkins Assistant Professor

2. Western Transportation Institute Montana State University-Bozeman Outline Background Information Background Information Project Design/Methodology Project Design/Methodology Results and Findings Results and Findings Conclusions Conclusions

3. Western Transportation Institute Montana State University-Bozeman Background Pavement design analysis Pavement design analysis –Historical methods using empirical methods –Recent methods using Finite Element Analysis Finite Element Analysis Finite Element Analysis –Wide range of applications –NCHRP 1 Design Guide 1 National Cooperative Highway Research Program

4. Western Transportation Institute Montana State University-Bozeman Background

5. Western Transportation Institute Montana State University-Bozeman Background Goal: Simplify FE method Goal: Simplify FE method –Increase throughput of a system –Increased productivity –More accessible

6. Western Transportation Institute Montana State University-Bozeman Methodology Two ways of simplifying FE models: Two ways of simplifying FE models: –Reducing mesh resolution –Removing model features Time: Accuracy: Percentage (%)

7. Western Transportation Institute Montana State University-Bozeman Methodology Two features Two features –Tension cutoff formulation –Non-linear behavior  Issues choosing modulus Six source models Six source models –High, medium, and low traffic loads for Firm and Weak pavement surface designs.

8. Western Transportation Institute Montana State University-Bozeman Methodology Four sub-models: Four sub-models: A.Using both features B.Removing Non-linear Behavior C.Removing Tension- cutoff Formulation D.Removing both features Non-linear Behavior Linear Behavior Tension- cutoff AB No Tension- cutoff CD

9. Western Transportation Institute Montana State University-Bozeman Findings Examining completed models Examining completed models –Physical output variables –Pavement fatigue life –Cycles to permanent deformation

10. Western Transportation Institute Montana State University-Bozeman Findings: U 2 and E 22 U 2 is deformation in vertical direction U 2 is deformation in vertical direction –Actual movement E 22 is strain in vertical direction E 22 is strain in vertical direction –Ratio of deformation to size of original un-deformed object. E 22 = ΔL / L 0

11. Western Transportation Institute Montana State University-Bozeman High Firm E 22 High Firm E 22 –LE: 19.3% –LETC: 19.3% High Firm U 2 High Firm U 2 –LE: 22.3% –LETC: 22.4%

12. Western Transportation Institute Montana State University-Bozeman High Weak E 22 High Weak E 22 –LE: 4.8% –LETC: 4.8% High Weak U 2 High Weak U 2 –LE: 17.7% –LETC: 17.7%

13. Western Transportation Institute Montana State University-Bozeman Medium Firm E 22 Medium Firm E 22 –LE: 18.7% –LETC: 19.0% Medium Firm U 2 Medium Firm U 2 –LE: 21.2% –LETC: 21.2%

14. Western Transportation Institute Montana State University-Bozeman Medium Weak E 22 Medium Weak E 22 –LE: 19.7% –LETC: 19.6% Medium Weak U 2 Medium Weak U 2 –LE: 30.1% –LETC: 30.0%

15. Western Transportation Institute Montana State University-Bozeman Low Firm E 22 Low Firm E 22 –LE: 17.0% –LETC: 16.9% Low Firm U 2 Low Firm U 2 –LE: 14.8% –LETC: 14.8%

16. Western Transportation Institute Montana State University-Bozeman Low Weak E 22 Low Weak E 22 –LE: 16.7% –LETC: 15.5% Low Weak U 2 Low Weak U 2 –LE: 33.1% –LETC: 41.0%

17. Western Transportation Institute Montana State University-Bozeman Findings: U 2 and E 22 Physical output variables Physical output variables –Errors introduced into LE sub-models due to modulus calculation method. –Little difference noted when including or excluding tension cutoff formulation.  0.28% (E 22 ), 1.68% (U 2 ) –Uniform results across source models.

18. Western Transportation Institute Montana State University-Bozeman Findings Pavement fatigue life Pavement fatigue life –High error compared to NLETC (24.2%) –Average TC effect  0.0% (high), 3.235% (med), 5.736% (low) Sub- model High Firm High Weak Med Firm Med Weak Low Firm Low Weak LE19.2047.2284.67144.91722.65849.049 LETC19.2047.22811.14144.91728.87731.359

19. Western Transportation Institute Montana State University-Bozeman Findings Cycles to permanent deformation Cycles to permanent deformation –Again, high error compared to NLETC (22.0%) –Average TC effect  0.0% (high), 0.616% (med), 5.034% (low) Sub- model High Firm High Weak Med Firm Med Weak Low Firm Low Weak LE12.3327.2084.14649.83814.78316.480 LETC12.3327.2085.37849.83811.33929.991

20. Western Transportation Institute Montana State University-Bozeman Conclusions Non-linear behavior Non-linear behavior –Can be removed only when modulus is carefully chosen. Tension cutoff formulation Tension cutoff formulation –Little difference noted –More important for cycles calculations as traffic loads decrease. Recommendations Recommendations

21. Western Transportation Institute Montana State University-Bozeman Conclusions Goal: Simplify FE method Goal: Simplify FE method –Increase throughput of a system –Increased productivity –More accessible Thank you Thank you –Dr. Steven Perkins –Western Transportation Institute