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**Federal Highway Administration Research and Technology**

Coordinating, Developing, and Delivering Highway Transportation Innovations

REPORT |

This report is an archived publication and may contain dated technical, contact, and link information |

Publication Number: FHWA-HRT-15-036 Date: December 2015 |

Publication Number: FHWA-HRT-15-036Date: December 2015 |

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The Long-Term Pavement Performance (LTPP) database includes deflection basins measured on thousands of test sections across the United States. These deflection data were used to backcalculate the elastic layer modulus of both flexible and rigid pavements. This report documents the tools, data analyses, backcalculation and forward calculation packages, and procedures used to calculate the in-place elastic layer modulus of the LTPP test sections. It summarizes the backcalculated elastic layered modulus of both new and rehabilitated flexible and rigid pavements in the LTPP program and demonstrates their use in day-to-day practice for pavement design, rehabilitation, and management. Many agencies have used the LTPP deflection data for calibrating mechanistic-empirical distress transfer functions, including those in the *Mechanistic-Empirical Pavement Design Guide.*^{(1)}

An important outcome presented in this report is the documentation of methods and procedures for calculating in-place elastic layer modulus, including the pre- and post-processing tools so the results can be recreated by others to make the process less user-dependent. In addition, the elastic modulus computed parameter tables included in the LTPP database (Standard Data Release 27.0 released in 2013) are defined and explained in this report so agencies can use these results in multiple areas.^{(2)} This final report is intended for use by pavement researchers as well as by practicing engineers involved in rehabilitation design and management of agencies’ pavements.

Jorge E. Pagán-Ortiz

Director, 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.

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.

1. Report No. FHWA-HRT-15-036 |
2. Government Accession No. |
3 Recipient's Catalog No. | ||

4. Title and Subtitle Long-Term Pavement Performance Program Determination of In-Place Elastic Layer Modulus: Backcalculation Methodology and Procedures |
December 2015 | |||

6. Performing Organization Code | ||||

7. Author(s) Harold L. Von Quintus, P.E., Chetana Rao, and Lynne Irwin |
| |||

Applied Research Associates, Inc. |
| |||

11. Contract or Grant No. DTFH61-11-C-00051 | ||||

12. Sponsoring Agency Name and Address Office of Infrastructure Research and Development |
13. Type of Report and Period Covered Draft Final Report | |||

| ||||

15. Supplementary Notes The Contracting Officer’s Technical Representative (COTR) was Ms. Yan "Jane" Jiang. | ||||

16. Abstract Deflection data have been measured at periodic intervals with a falling weight deflectometer on all rigid, flexible, semirigid, and rehabilitated pavement test sections included in the Long-Term Pavement Performance (LTPP) program. A common use of deflection data is to backcalculate in-place layered elastic modulus values. The Federal Highway Administration sponsored earlier studies to backcalculate elastic layer modulus values from deflection basins measured on all LTPP test sections and included those computed values in the LTPP database. This report summarizes all activities completed to backcalculate the elastic layered modulus from deflection basins measured on all test sections included in the LTPP program. Specifically, the report documents the tools, data analyses, backcalculation and forward calculation packages, and procedures used to calculate, on a production basis, the in-place elastic layer modulus of the LTPP test sections. Multiple packages (including BAKFAA, EVERCALC | ||||

17. Key Words Backcalculation, Deflection data, Elastic modulus, EVERCALC |
18. Distribution Statement No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161. | |||

Unclassified |
Unclassified |
177 |
22. Price |

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

**SI* (Modern Metric) Conversion Factors**

**Chapter 2. Backcalculation Methodology and Packages**

**Types of Backcalculation Methods****Candidate Backcalculation Programs****Standardization of Backcalculation Process**

**LTPP Test Sections Selected for Case Studies****Comparison of Results from Candidate Backcalculation Programs****Case Study Summary**

**Chapter 4. Backcalculation Process**

**Chapter 5. Backcalculation Results**

**LTPP Data Source****Basic Facts about the Backcalculation Process****Evaluating the success of Backcalculation****CPTs**

**Chapter 6. Application and Use of Backcalculation Results**

**Setting Defaults for Material Types****Stress Sensitivity of Nonlinear Materials and Soils****MEPDG HMA Damage Concept: Fact or Fiction?****Differences between Field-Derived and Laboratory-Measured Moduli****Time and Seasonal Effects****Mixture Time-Dependent Moduli****Modulus of Fractured PCC Layers****Reclaimed asphalt pavement (RAP) and Virgin Mixtures**

**Appendix A: Best Fit Method—Calculating PCC Elastic Layer Moduli**

**Appendix B: LTPP Test Sections with a Moderate and High Percentage of Errors**

**Appendix C: Development of the Simulated Layer Structure for the Backcalculation Process Using Evercalc ^{©} and Modcomp^{©}^{}**

- Figure 1. Photo. Core recovered from an LTPP test section used to equate laboratory-measured modulus values to backcalculated elastic modulus values (Texas SPS-5 section)
- Figure 2. Photo. Cross-section of the pavement layers exposed during a forensic investigation to measure the rutting within individual pavement layers (Arizona SPS-1 section)
- Figure 3. Graph. Comparison of RMSE values between backcalculation programs for flexible pavement sections comparing MODULUS, MODTAG
^{©}, and EVERCALC^{©} - Figure 4. Graph. Comparison of RMSE values between backcalculation programs for rigid pavement sections comparing best fit method and EVERCALC
^{©} - Figure 5. Graph. Normal distribution of calculated elastic modulus for a crushed stone base aggregate
- Figure 6. Graph. Bimodal distribution of calculated elastic modulus for the weathered soil layer
- Figure 7. Graph. Comparison of backcalculated moduli from the candidate programs for the HMA layer
- Figure 8. Graph. Comparison of backcalculated moduli from the candidate programs for the asphalt stabilized base layer
- Figure 9. Graph. Comparison of backcalculated moduli from the candidate programs for the weathered soil layer modulus values
- Figure 10. Graph. Comparison of backcalculated moduli from the candidate programs for the natural subgrade modulus values
- Figure 11. Graph. Comparison of backcalculated moduli from the candidate programs for aggregate base layers
- Figure 12. Graph. Backcalculated layer PCC modulus from EVERCALC
^{©}compared to the elastic modulus calculated with the area - Figure 13. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the subgrade layer
- Figure 14. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the aggregate base layer
- Figure 15. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the PCC layer
- Figure 16. Graph. Comparison of backcalculated and laboratory-measured PCC moduli
- Figure 17. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Iowa SPS-1 project
- Figure 18. Graph. Comparison of backcalculated HMA base layer moduli and laboratory-measured moduli from the Iowa SPS-1 project
- Figure 19. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project
- Figure 20. Graph. Comparison of backcalculated HMA base layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project
- Figure 21. Graph. Comparison of backcalculated HMA overlay moduli and laboratory- measured moduli from the Mississippi SPS-5 project
- Figure 22. Graph. Comparison of backcalculated HMA surface layer moduli of the existing pavement after overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project
- Figure 23. Graph. Comparison of backcalculated HMA surface layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project
- Figure 24. Graph. Comparison of backcalculated HMA base layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project
- Figure 25. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated dynamic modulus for the Oklahoma SPS-6 project
- Figure 26. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated dynamic modulus for the Georgia SMP project
- Figure 27. Graph. Comparison of backcalculated elastic moduli of unbound layers using EVERCALC
^{©}and laboratory-derived resilient modulus - Figure 28. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODULUS and laboratory-derived resilient modulus
- Figure 29. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODTAG
^{©}and laboratory-derived resilient modulus - Figure 30. Flowchart. Major steps and decisions in linear elastic backcalculation process
- Figure 31. Equation. Skewness factor
- Figure 32. Equation. Kurtosis factor
- Figure 33. Equation. Jarque-Bera statistic used for verifying normality in data
- Figure 34. Photo. Cores recovered where moisture damage occurred, decreasing the in-place modulus of the layer/mixture (Texas SPS-5 project)
- Figure 35. Graph. Backcalculated elastic moduli for all aggregate base layers for the Georgia (GA(13)) LTPP test sections classified as an AASHTO A-1-a material
- Figure 36. Graph. Backcalculated elastic moduli for all aggregate base layers for the Minnesota (MN(27)) LTPP test sections classified as an AASHTO A-1-a material
- Figure 37. Graph. Comparison of backcalculated elastic moduli for the aggregate base layer from the Texas SPS-8 project 48-0801
- Figure 38. Graph. Comparison of backcalculated elastic moduli for the weathered fine- grained soil layer from the Texas SPS-8 project 48-0801
- Figure 39. Graph. Comparison of backcalculated elastic moduli for the fine-grained subgrade from the Texas SPS-8 project 48-0801
- Figure 40. Graph. Comparison of backcalculated elastic moduli for the aggregate base layer from the Utah SPS-8 project 49-0803
- Figure 41. Graph. Comparison of backcalculated elastic moduli for the weathered coarse-grained layer from the Utah SPS-8 project 49-0803
- Figure 42. Graph. Comparison of backcalculated elastic moduli for the coarse-grained subgrade from the Utah SPS-8 project 49-0803
- Figure 43. Graph. Comparison of backcalculated elastic moduli for the aggregate base layer from New York SPS-8 project 36-0802
- Figure 44. Graph. Comparison of backcalculated elastic moduli for the weathered coarse-grained layer from the New York SPS-8 project 36-0802
- Figure 45. Graph. Comparison of backcalculated elastic moduli for the coarse-grained subgrade from the New York SPS-8 project 36-0802
- Figure 46. Graph. Decreasing elastic moduli of the asphalt layer over time for use in rehabilitation design for Minnesota GPS section 27-6251
- Figure 47. Graph. Decreasing elastic moduli of the asphalt layer over time for use in rehabilitation design for Minnesota GPS section 27-1018
- Figure 48. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 ºF over time for use in rehabilitation design for Minnesota GPS section 27-1016
- Figure 49. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 ºF over time for use in rehabilitation design for Minnesota GPS section 27-6251
- Figure 50. Graph. Elastic moduli of the asphalt layer between the wheel path and non-wheel path lanes for Minnesota GPS section 27-6251
- Figure 51. Graph. Elastic moduli of the asphalt layer between the wheel path and non-wheel path lanes for Minnesota GPS section 27-1018
- Figure 52. Graph. Comparison of the dynamic moduli computed from the Witczak regression equation and the backcalculated elastic moduli for four SPS-1 projects
- Figure 53. Graph. Comparison of HMA backcalculated elastic layer moduli for Idaho SMP section 16-1010
- Figure 54. Graph. Comparison of HMA backcalculated elastic layer moduli for New Mexico SMP section 35-1112
- Figure 55. Graph. Comparison of HMA backcalculated elastic layer moduli for Minnesota SMP section 27-1018
- Figure 56. Graph. Comparison of HMA backcalculated elastic layer moduli for Texas SMP section 48-1077
- Figure 57. Graph. Comparison of aggregate base backcalculated elastic layer moduli for Idaho SMP section 16-1010
- Figure 58. Graph. Comparison of aggregate base backcalculated elastic layer moduli for New Mexico SMP section 35-1112
- Figure 59. Graph. Comparison of aggregate base backcalculated elastic layer moduli for Minnesota SMP section 27-1018
- Figure 60. Graph. Comparison of aggregate base backcalculated elastic layer moduli for Texas SMP section 48-1077
- Figure 61. Graph. Comparison of weathered soil backcalculated elastic layer moduli for Idaho SMP section 16-1010
- Figure 62. Graph. Comparison of weathered soil backcalculated elastic layer moduli for Minnesota SMP section 27-1018
- Figure 63. Graph. Comparison of weathered soil backcalculated elastic layer moduli for Texas SMP section 48-1077
- Figure 64. Graph. Comparison of SS backcalculated elastic layer moduli for Idaho SMP section 16-1010
- Figure 65. Graph. Comparison of SS backcalculated elastic layer moduli for New Mexico SMP section 35-1112
- Figure 66. Graph. Comparison of SS backcalculated elastic layer moduli for Minnesota SMP section 27-1018
- Figure 67. Graph. Comparison of SS backcalculated elastic layer moduli for Texas SMP section 48-1077
- Figure 68. Graph. Backcalculated PCC elastic moduli over time from EVERCALC
^{©}for selected SPS-2 test sections - Figure 69. Graph. Backcalculated PCC elastic moduli over time from the best fit unbonded method for selected SPS-2 test sections
- Figure 70. Graph. Comparison of backcalculated PCC elastic moduli from EVERCALC
^{©}and the best fit unbonded method for selected SPS-2 test sections - Figure 71. Graph. Backcalculated elastic moduli for the Oklahoma SPS-6 rubblized test sections
- Figure 72. Graph. Backcalculated elastic moduli for the Indiana SPS-6 crack and seat test sections
- Figure 73. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, and rubblized test sections for the Arizona SPS-6 test sections
- Figure 74. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, and rubblized test sections for the Michigan SPS-6 test sections
- Figure 75. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, and rubblized test sections for the Pennsylvania SPS-6 test sections
- Figure 76. Graph. Comparison of RAP and virgin backcalculated elastic HMA moduli from the Minnesota SPS-5 project
- Figure 77. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli from the Arizona SPS-5 project
- Figure 78. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli from the Mississippi SPS-5 project
- Figure 79. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli from the Oklahoma SPS-5 project
- Figure 80. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli from the Maine SPS-5 project
- Figure 81. Illustration. Transformation of design structure to effective structure used by the neural networks to compute mechanistic response
- Figure 82. Equation. Error function definition for best fit procedure
- Figure 83. Equation. Calculated deflection
- Figure 84. Equation. Radius of relative stiffness
- Figure 85. Equation. Error function in alternate form
- Figure 86. Equation. Partial derivative of
*F*with respect to*k* - Figure 87. Equation. Partial derivative of
*F*with respect to*l* - Figure 88. Equation.
*k*-value - Figure 89. Equation. Radius of relative stiffness
- Figure 90. Equation. Modular ratio
- Figure 91. Equation. Flexural stiffness
- Figure 92. Equation. Slab modulus from effective modulus for unbonded condition
- Figure 93. Equation. Base modulus from effective modulus for unbonded condition
- Figure 94. Equation. Sab modulus from effective modulus for bonded condition
- Figure 95. Equation. Base modulus for bonded condition
- Figure 96. Equation. Depth of the parallel axis from the surface
- Figure 97. Equation. Equivalent beta when multiple layers are combined into the base
- Figure 98. Equation. Equivalent thickness
- Figure 99. Equation.
*Expr*1 - Figure 100. Equation.
*Expr*2 - Figure 101. Equation. Depth of parallel axis from the surface when multiple layers are combined into the base
- Figure 102. Equation.
*Expr*3 - Figure 103. Equation.
*Expr*4

- Table 1. Backcalculation software packages used in the case studies
- Table 2. LTPP test sections used for the case studies
- Table 3. Comparison of datasets from selected LTPP flexible test sections
- Table 4. Comparison of datasets from selected LTPP rigid test sections
- Table 5. Tables from the LTPP database for evaluating data for the backcalculation process
- Table 6. Typical range of modulus for different paving materials and soils
- Table 7. Statistical parameters calculated for normality check
- Table 8. Critical chi-squared value for different degrees of freedom and levels of significance
- Table 9. Summary of LTPP data used in the backcalculation analyses by experiment
- Table 10. Summary of LTPP deflection basin data
- Table 11. Number of deflection basins analyzed and percentage of those deflection basins considered acceptable
- Table 12. Deflection basins analyzed and percentage classified as acceptable drops using EVERCALC
^{©}and MODCOMP^{©}for all pavements - Table 13. Deflection basins analyzed and percentage classified as acceptable drops using the best fit method for PCC-surfaced pavements
- Table 14. LTPP test sections identified as errors and eliminated from determining the test section statistics
- Table 15. Error flags used in the CPTs
- Table 16. Backcalculation results for the Oklahoma SPS-6 project—intact and rubblized test sections
- Table 17. Modular ratio to estimate the relative stiffness between PCC slab and base in the best fit procedure (for both bonded and unbonded conditions)
- Table 18. Effect of layer structure on base layer—number of layers underneath the PCC slab included in the effective base layer
- Table 19. LTPP test sections with a moderate percentage of errors
- Table 20. LTPP test sections with a high percentage of errors
- Table 21. AC surface with two layers between AC and subgrade
- Table 22. PCC surface with two layers between PCC and subgrade
- Table 23. AC surface with three layers between AC and subgrade
- Table 24. PCC surface with three layers between PCC and subgrade
- Table 25. AC surface with four layers between AC and subgrade
- Table 26. PCC surface with four layers between PCC and subgrade
- Table 27. AC surface with five layers between AC and subgrade
- Table 28. PCC surface with six layers between PCC and subgrade
- Table 29. AC surface with seven layers between AC and subgrade
- Table 30. PCC surface with seven layers between PCC and subgrade
- Table 31. AC surface with one layer between AC and subgrade
- Table 32. PCC surface with one layer between PCC and subgrade
- Table 33. AC surface with two layers between AC and subgrade
- Table 34. PCC surface with two layers between PCC and subgrade
- Table 35. AC surface with three layers between AC and subgrade
- Table 36. PCC surface with three layers between PCC and subgrade
- Table 37. AC surface with four layers between AC and subgrade
- Table 38. PCC surface with four layers between PCC and subgrade
- Table 39. AC surface with five layers between AC and subgrade
- Table 40. PCC surface with six layers between PCC and subgrade
- Table 41. AC surface with seven layers between AC and subgrade
- Table 42. PCC surface with seven layers between PCC and subgrade

AASHTO | American Association of State Highway and Transportation Officials |

AC | asphalt concrete |

ANN | artificial neural network |

ATB | asphalt-treated base |

CPT | computed parameter table |

CRCP | continuously reinforced concrete pavement |

FHWA | Federal Highway Administration |

FWD | falling weight deflectometer |

GB | granular base |

GPR | ground-penetrating radar |

GPS | General Pavement Studies |

GS | granular subbase |

HMA | hot mix asphalt |

JPCP | jointed plain concrete pavement |

JRCP | jointed reinforced concrete pavement |

LTE | load transfer efficiency |

LTPP | Long-Term Pavement Performance |

MEPDG | Mechanistic-Empirical Pavement Design Guide |

PCC | portland cement concrete |

RAP | reclaimed asphalt pavement |

RMSE | root mean squared error |

SDR | Standard Data Release |

SHRP | Strategic Highway Research Program |

SLIC | Sensor Location Independent Check |

SMP | Seasonal Monitoring Program |

SPS | Specific Pavement Studies |

SS | subgrade soil |

TB | treated base |

TS | treated subgrade |