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

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

Chapter 2. Introduction to Backcalculation and Forwardcalculation Methods


To review the approach through which backcalculation took place and the load-deflection data were used to create the computed parameter tables of the backcalculated database, two primary references were consulted:

  • FHWA, Backcalculation of Layer Parameters for Long-Term Pavement Performance (LTPP) Test Sections, Volume I: Slab on Elastic Solid and Slab on Dense-Liquid Foundation Analysis of Rigid Pavements, FHWA-RD-00-086, Washington, DC: FHWA, December 2001.(1)
  • FHWA, Backcalculation of Layer Parameters for LTPP Test Sections?Volume II: Layered Elastic Analysis for Flexible and Rigid Pavements, FHWA-RD-01-113, Washington, DC: FHWA, December 2001.(2)

These publications describe how backcalculation was calculated for rigid and flexible pavement sections, respectively. After review of these documents, the researchers determined that the described processes used to perform the backcalculation and prescreen the data for outliers were reasonable, though (at least in hindsight) perhaps somewhat imperfect.

The processing of the rigid pavement data appeared to be somewhat more effective than for the flexible pavement data, mainly because rigid pavements were generally divided into only two unknown structural layers, while flexible pavements generally used three, four, and sometimes even five unknown structural layers.

Additionally, the following documents were used, as needed:

These documents were helped to ensure the quality of the FWD load-deflection data and to verify the sensor positions used during FWD testing.


Most backcalculation programs, including those used to generate the backcalculated modulus data in the LTPP computed parameter tables, involve numerical integration subroutines that are capable of calculating FWD pavement deflections (and other parameters), given the stiffnesses (or moduli) of the various pavement layers and their thicknesses. If all assumptions are correct, (i.e., each layer is an elastic layer, isotropic and homogeneous, and all other boundary conditions are correct), then it is possible to iterate various combinations of moduli to reach a (virtually) perfect match between the measured and theoretical FWD deflections. In this manner, a solution to the problem of deriving moduli from deflections is obtained.

A serious drawback to this approach is that one or more of the many input assumptions mentioned above may be incorrect and therefore may not apply to the actual pavement system. In spite of this potential drawback, many of the moduli in the database appear to be reasonable and rational, based on common engineering sense and a working knowledge of pavement materials.


Forwardcalculation techniques were developed and used for the pilot study to generate moduli that are independent of the backcalculated values so they can be used for comparison to screen the backcalculated moduli in the database. This approach is based on the premise that two substantially different approaches to calculated layered elastic parameters from the same deflection data should produce at least somewhat similar moduli given that either approach is credible.

Forwardcalculation involves using certain portions of the FWD deflection basin to derive an apparent modulus or stiffness of the subgrade and/or the bound surface course, using closed-form as opposed to iterative solutions. The deflections measured at larger distances from the load mainly determine the subgrade modulus, while the surface course modulus is mainly a function of the near-load deflections and/or the radius of curvature of the deflection basin. Including the center deflection reading, which in effect is a reflection of the overall pavement system stiffness also enhances both of these forwardcalculation approaches.

The advantages of forwardcalculation are as follows:

  1. Since the subgrade and bound surface course stiffnesses obtained are not dependent on the other moduli within the pavement system, as is the case with backcalculation, each problem provides a unique solution.
  2. Forwardcalculation is easy to understand and use, whereas backcalculation is presently more of an art than a science. Anyone can perform forwardcalculation, while backcalculation requires expert engineering judgment along with the art of running the iterative program of choice. For backcalculation, the art is in the evaluation of the reasonableness of the results and selection of the model and other input parameters.
  3. The forwardcalculation techniques developed for this project produce considerably less scatter in the data (for the same layer and test section) than do backcalculation techniques.

Nothing in pavement analysis comes without its own unique drawbacks. As such, these drawbacks are not limited to backcalculation alone, for example:

  1. Since the subgrade and surface course stiffnesses are calculated independently, in combination the values obtained may or may not be reasonable with respect to the total center deflection.
  2. To obtain a third, intermediate layer stiffness (if present), such as a granular base, analysts could then assume that the surface and subgrade stiffnesses are correct and then fit the center deflection to the remaining unknown stiffness of, for example, a base course layer. This approach suffers from the same drawback as backcalculation—the layer’s modulus depends on another layer’s, or layers’, analysis results.
  3. It is also possible to use a ratio between the subgrade modulus calculated through forwardcalculation and apply the modular ratio relationship for unbound base materials. Certainly, there is no assurance that this method is correct; however, the test of reasonableness is best applied to the results.
  4. Since this method produces approximate values (particularly for the base or intermediate layer/s), these results should only be used as layer modulus estimates, for example, for screening or quality assurance/quality control (QA/QC) purposes.

In the following sections, the method used in forwardcalculation is described, followed by a section with the screening results from phase I (modified during phase II) of this study that compares the backcalculated (computed) parameters in the database to the forwardcalculated values for the 18 trial sections evaluated in the pilot study.


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