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