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Publication Number: FHWA-HRT-05-150
Date: February 2006

Review of The Long-Term Pavement Performance (LTPP) Backcalculation Results

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FOREWORD

This report is a comprehensive review and evaluation of the Long-Term Pavement Performance (LTPP) backcalculation data. In this study, a new approach, called forwardcalculation was developed to determine layered elastic moduli from in situ load-deflection data with procedures and results documented. the entire set of LTPP-computed parameters of backcalculation results was screened using forwardcalculated moduli.

Although users cannot reject any backcalculated modulus value merely because it is outside a reasonable or acceptable range, the forwardcalculated values were, in most cases, more stable on a section-by-section basis than the backcalculated values in the LTPP database. The exception was the portion of the backcalculated database based on slab-on-dense-liquid and slab-on-elastic-solid theory, where the correspondence between the two rigid pavement analysis techniques was excellent and both the backcalculated and forwardcalculated moduli and k-values were very stable.

It is recommended that the backcalculated database be retained as is, with the addition of the complementary forwardcalculated dataset and screening flags, so the database user can decide which method is more suitable to the application.

This report will interest highway agency engineers involved in pavement analysis, design, construction, and deflection data collection, as well as researchers who use LTPP load-deflection data to improve design procedures and standards for constructing and rehabilitating pavements.

Gary L. Henderson
Office of Infrastructure
Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. the U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this report only because they are considered essential to the objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

 

TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-05-150

2. Government Accession No.

3. Recipient's Catalog No.

4. Title and Subtitle

Review of the Long-Term Pavement Performance Backcalculation Results—Final Report

5. Report Date

February 2006

6. Performing Organization Code

7. Author(s)

R.N. Stubstad, Y.J. Jiang, M.L. Clevenson, and E.O. Lukanen

8. Performing Organization Report No.

9. Performing Organization Name and Address

Applied Research Associates, Inc.
Elkridge, Maryland 21075-7056

10. Work Unit No. (TRAIS)

C6B

11. Contract or Grant No.

DTFH61-02-D-00138

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development
Federal Highway Administration
6300 Georgetown Pike
McLean, Virginia 22101-2296

13. Type of Report and Period Covered

Final Report

14. Sponsoring Agency Code

15. Supplementary Notes

Contracting Officer’s Technical Representative (COTR): Larry Wiser, HRDI

LTPP Data Analysis Contract.

16. Abstract

A new approach to determine layered elastic moduli from in situ load-deflection data was developed. This “forwardcalculation” approach differs from backcalculation in that modulus estimates come directly from the load and deflection data using closed-form formulae rather iteration. the forwardcalculation equations are used for the subgrade and the bound surface course for both flexible and rigid pavement falling weight deflectometer (FWD) data. Intermediate layer moduli are estimated through commonly used modular ratios between adjacent layers.

The entire LTPP set of backcalculated parameters was screened using forwardcalculated moduli. Any assumed or fixed modulus value was left as is and not further screened (e.g., hard bottom). Further, any back- or forwardcalculated values outside a broad range of reasonable values were not further screened, but flagged as unreasonable. Finally, a set of broad range convergence flags (0 = acceptable, 1 = marginal, 2 = questionable, and 3 = unacceptable) were applied to the backcalculated dataset, depending on how closely the pairs of back- and forwardcalculated moduli matched. Since both techniques used identical FWD load-deflection data as input, the moduli derived from each approach should be reasonably close to each other (within a factor of 1.5 to qualify as acceptable, for example).

Although backcalculated values cannot be rejected merely because they are outside a reasonable or acceptable range, the complementary forwardcalculated values were usually more stable on a section-by-section basis. the exception was the portion of the database based on slab-on-dense-liquid or slab-on-elastic-solid theory, where the correspondence between the two approaches was excellent and very stable. therefore, it is recommended that the backcalculated database be retained as is, with the addition of checks and flags so the database user can choose the best method, depending on the application.

17. Key Words

Pavements, LTPP, FWD, deflection data, elastic modulus, backcalculation, forwardcalculation, screening.

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

97

22. Price

Form DOT F 1700.7 (8-72)    Reproduction of completed page authorized

SI* (Modern Metric) Conversion Factors


TABLE OF CONTENTS

1. INTRODUCTION
Background
Study Objectives and Scope
LTPP Data Source
Report Organization

2. INTRODUCTION TO BACKCALCULATION AND FORWARDCALCULATION METHODS
Literature Review
Introduction to Backcalculation
Introduction to Forwardcalculation

3. FORWARDCALCULATION METHODOLOGY
Background and Previous Developments
Centerline Subgrade Modulus Based on the Hogg Model
Bound Surface Course Modulus Based on the Area Method
Intermediate Layer Modulus Calculations

4. INITIAL LTPP BACKCALCULATION DATA SCREENING RESULTS
Overview
Organization of Data
Check for Errors or Anomalies in the Backcalculation Process
Subgrade Screening Results
Surface Course Screening Results
Intermediate (Base) Course Screening Results
Extra Layer Results from Backcalculation
Choice of Screening Limits and Codes

5. LTPP BACKCALCULATION DATABASE SCREENING METHODOLOGY
LTPP Data Source Used in this Study
Key Steps for Screening the LTPP Backcalculation Data

6. LTPP BACKCALCULATION DATABASE SCREENING RESULTS
Level E and Other Levels of Data Quality
Screening of the Flexible Pavement Backcalculation Parameters-Linear Elastic Model
Screening of the Flexible Pavement Backcalculation Parameters-Nonlinear Elastic Model
Adaptation of Forwardcalculation Technique for LTPP Rigid Pavement Sections
Screening of the Rigid Pavement Backcalculation Parameters-Linear Elastic Model
Screening of the Rigid Pavement Backcalculation Parameters-Slab-on-Elastic Solid Analysis
Screening of the Rigid Pavement Backcalculation Parameters -Slab-on-Dense Liquid Analysis
Screening of the Section Average Backcalculated Database

7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
Summary
Conclusions
Recommendations

APPENDIX A

REFERENCES

LIST OF FIGURES

Figure 1. Equation. Composited Subgrade Modulus at an Offset.
Figure 2. Equation. Hogg Subgrade Modulus.
Figure 3. Equation. Offset Distance Where Deflection is Half of Center Deflection.
Figure 4. Equation. Characteristic Length of Deflection Basin.
Figure 5. Equation. Theoretical Point Load Stiffness/Pavement Stiffness Ratio.
Figure 6. Equation. Composite Modulus Under FWD Load Plate.
Figure 7. Equation. 914-Millimeter (MM) (36-Inch) AREA Equation for Rigid Pavements.
Figure 8. Equation. 305-MM (12-Inch) AREA Equation for Flexible Pavements.
Figure 9. Equation. AREA Factor for Rigid Pavements.
Figure 10. Equation. AREA Factor for Flexible Pavements.
Figure 11. Equation. Stiffness or Modulus of the Upper PCC Layer.
Figure 12. Equation. Stiffness or Modulus of the Upper AC Layer.
Figure 13. Equation. Modulus of the Unbound Base Layer Using the Dorman and Metcalf Relationship.
Figure 14. Graph. Back-Versus Forwardcalculated Subgrade Moduli for 15 Trial LTTP Flexible Sections.
Figure 15. Graph. Back-Versus Forwardcalculated Subgrade Moduli for Three Trial LTTP Rigid Sections.
Figure 16. Graph. Back-Versus Forwardcalculated Asphalt Layer Moduli for 15 Trial LTPP Flexible Sections.
Figure 17. Graph. Back-Versus Forwardcalculated Concrete Layer Moduli for Three Trial LTPP Rigid Sections.
Figure 18. Graph. Back-Versus Forward-Based Base Layer Moduli for 15 Flexible LTPP Sections.
Figure 19. Graph. Back-Versus Forwardcalculated Asphalt Layer Moduli for 15 Flexible LTPP Sections.
Figure 20. Graph. Back-Versus Forwardcalculated Subgrade Moduli for Five Trial LTPP Flexible Sections with Two Intermediate Layers.
Figure 21. Graph. Back-Versus Forwardcalculated Base Course Moduli for Four Trial LTPP Flexible Sections with Two Intermediate Layers
Figure 22. Equation. Interquartile Range.
Figure 23. Charts. Screening Results of the Elastic Moduli of the Subgrade for All Flexible Sections in the MON_DEFL_FLX_BAKCALC_POINT Table Based on the Linear Elastic Model (the Level E Records Only)
Figure 24. Charts. Screening Results Of Elastic Moduli Of the Subgrade For All the Flexible Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model (contains Both Level E and Nonlevel E Records).
Figure 25. Charts. Screening Results Of Elastic Moduli Of the Asphalt Concrete Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model.
Figure 26. Charts. Screening Results Of Elastic Moduli Of the Subgrade For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model.
Figure 27. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model.
Figure 28. Charts. Screening Results Of Elastic Moduli Of the Asphalt Concrete Layer For the Flexible Sections In the MON_DEFL_FLX_NMODEL_POINT Table Based On the Nonlinear Elastic Model.
Figure 29. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Flexible Sections In the MON_DEFL_FLX_NMODEL_POINT Table Based On the Nonlinear Elastic Model.
Figure 30. Charts. Screening Results Of Elastic Moduli Of the Subgrade For the Flexible Sections In the MON_DEFL_FLX_NMODEL_POINT Table Based On the Nonlinear Elastic Model.
Figure 31. Equation. PCC Slab Modulus—100 Percent Unbonded Case.
Figure 32. Equation. PCC Slab Modulus—100 Percent Bonded Case.
Figure 33. Equation. Layer Thickness Relationship.both Cases.
Figure 34. Equation. Modular Ratio Beta—both Cases.
Figure 35. Charts. Screening Results Of Elastic Moduli Of the Interior Concrete Slab For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model For Backcalculation and A Bonded Condition Between the Slab and Base For Forwardcalculation.
Figure 36. Charts. Screening Results Of Elastic Moduli Of the Interior Concrete Slab For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model For Backcalculation and An Unbonded Condition Between the Slab and Base For Forwardcalculation.
Figure 37. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model For Backcalculation and A Bonded Condition Between the Concrete Slab and Base Layer For Forwardcalculation.
Figure 38. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model For Backcalculation and An Unbonded Condition Between the Concrete Slab and Base Layer For Forwardcalculation.
Figure 39. Charts. Screening Results Of Elastic Moduli Of the Subgrade For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear Elastic Model.
Figure 40. Charts. Screening Results Of Elastic Moduli Of the PCC Slab For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Elastic Solid Model For Backcalculation and Assuming Bonded Condition Between the Slab and the Base For Back- and Forwardcalculation.
Figure 41. Charts. Screening Results Of Elastic Moduli Of the PCC Slab For the Rigid Sections
In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Elastic Solid Model For Backcalculation and Assuming Unbonded Condition Between the Slab and the Base For Back- and Forwardcalculation.

Figure 42. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Elastic Solid Model For Backcalculation and Assuming Bonded Condition Between the Slab and the Base For Back- and Forwardcalculation.
Figure 43. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Elastic Solid Model For Backcalculation and Assuming Unbonded Condition Between the Slab and the Base For Back- and Forwardcalculation.
Figure 44. Charts. Screening Results Of Elastic Moduli Of the Subgrade For the Rigid Sections
In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Elastic Solid Model For Backcalculation.

Figure 45. Charts. Screening Results Of Elastic Moduli Of the PCC Slab For the Rigid Sections
In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense Liquid Model For Backcalculation and Assuming Bonded Condition Between the Slab and the Base For Back- and Forwardcalculation.

Figure 46. Charts. Screening Results Of Elastic Moduli Of the PCC Slab For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense Liquid Model For
Backcalculation and Assuming Unbonded Condition Between the Slab and the Base For
Back- and Forwardcalculation.

Figure 47. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections
In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense-liquid Model For Backcalculation and Assuming Bonded Condition Between the Slab and the Base For Back- and Forwardcalculation.

Figure 48. Charts. Screening Results Of Elastic Moduli Of the Base Layer For the Rigid Sections
In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense-liquid Model For Backcalculation and Assuming Unbonded Condition Between the Slab and the Base For Back- and Forwardcalculation.

Figure 49. Equation. Subgrade K-value.
Figure 50. Charts. Screening Results Of the Subgrade K-values For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense-liquid Model For Backcalculation.
Figure 51. Charts. Screening Results Of Elastic Moduli Of the Point Base Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_POINT Table Based On the Linear-Elastic Model.
Figure 52. Charts. Screening Results Of Elastic Moduli Of the Section Base Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear- Elastic Model.
Figure 53. Charts. Screening Results Of the Subgrade Point K-value Table For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_POINT Table Using the Dense-liquid Model For Backcalculation.
Figure 54. Charts. Screening Results Of the Subgrade Section K-value Table For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Using the Dense-liquid Model For Backcalculation.
Figure 55. Charts. Screening Results Of Section Average Elastic Moduli Of the Asphalt Concrete Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model.
Figure 56. Charts. Screening Results Of Section Average Elastic Moduli Of the Base Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model.
Figure 57. Charts. Screening Results Of Section Average Elastic Moduli Of the Subgrade For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model.
Figure 58. Charts. Screening Results Of Section Average Elastic Moduli Of the Asphalt Concrete Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Nonlinear Elastic Model.
Figure 59. Charts. Screening Results Of the Section Average Elastic Moduli Of the Base Layer For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Nonlinear Elastic Model.
Figure 60. Charts. Screening Results Of the Section Average Elastic Moduli Of the Subgrade For the Flexible Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Nonlinear Elastic Model.
Figure 61. Charts. Screening Results Of the Section Average Elastic Moduli Of the PCC Slab For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model Using MODCOMP.
Figure 62. Charts. Screening Results Of the Section Average Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model Using MODCOMP.
Figure 63. Charts. Screening Results Of the Section Average Elastic Moduli Of the Subgrade For the Rigid Sections In the MON_DEFL_FLX_BAKCALC_SECT Table Based On the Linear Elastic Model Using MODCOMP.
Figure 64. Charts. Screening Results Of the Section Average Elastic Moduli Of the PCC Slab For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Elastic-Solid Model.
Figure 65. Charts. Screening Results Of the Section Average Elastic Moduli Of the PCC Slab For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Dense-Liquid Model.
Figure 66. Charts. Screening Results Of the Section Average Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Elastic-Solid Model.
Figure 67. Charts. Screening Results Of the Section Average Elastic Moduli Of the Base Layer For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Dense-Liquid Model.
Figure 68. Charts. Screening Results Of the Section Average Elastic Moduli Of the Subgrade For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Elastic-Solid Model.
Figure 69. Charts. Screening Results Of the Section Average K-values Of the Subgrade For the Rigid Sections In the MON_DEFL_RGD_BAKCALC_SECT Table Based On the Slab-On-Dense-Liquid Model.

LIST OF TABLES

Table 1. Hogg Model Coefficients.
Table 2. Moduli Used For Screening Of LTPP Database Values.
Table 3. Statistics For Back- and Forwardcalculated Subgrade Moduli For 15 Trial Flexible Sections.
Table 4. Back- and Forwardcalculated Moduli For Two Trial Florida Sections.
Table 5. Back- and Forwardcalculated Moduli For Two Trial Nebraska Sections.
Table 6. Statistics For Back- and Forwardcalculated Surface Course Moduli For Flexible Sections.
Table 7. Statistics For Back- and Forwardcalculated PCC Moduli For Rigid Sections.
Table 8. Statistics For Backcalculated and Pseudobackcalculated Base Course Moduli For Flexible Sections.
Table 9. Statistics For Base Course Moduli From Backcalculation and From Forwardcalculation Using Dorman and Metcalf's Equation For Nine Trial Flexible Sections.
Table 10. Flagging Codes Suggested For Screening Of the Backcalculated LTPP Database Tables.
Table 11. LTPP Backcalculation Tables and Number Of Records Screened.
Table 12. Assignment Of Backcalculated Layers For Forwardcalculation Of Flexible Pavements.
Table 13. FWD- and Time-specific Sensor Positioning Anomalies In the LTPP Database.
Table 14. Reasonable Ranges For Various Pavement Layers In the LTPP Database.
Table 15. Flagging Codes Used To Screen the Backcalculated LTPP Database.
Table 16. Back- and Forwardcalculated Modulus Ratios For EPCC/EBase.
Table 17. Reasonable Ranges For Various Pavement Layers In the LTPP Database (same As Table 14).

FHWA-HRT-05-150

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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