Backcalculation of asphalt pavement materials’ moduli considering absolute and relative errors

Backcalculation is a procedure used to estimate the material properties of pavement layers from the results of non-destructive tests, such as the Falling Weight Deflectometer (FWD). This procedure is important to assess the quality of a pavement structure during its construction and/or to monitor its condition during its lifespan. The Finite Element Method (FEM) can be used to evaluate the pavement deflections, provided that the loading, geometry, and material properties of each pavement layer are known. Thus, assuming a linear elastic behavior and known Poisson’s ratios and layer thicknesses, the backcalculation procedure consists of the determination of the set of elastic moduli that minimize the differences between the simulated (FEM) and measured (FWD) deflections. Different error measures can be adopted to assess the quality of the model fitting. The resulting Nonlinear Least Squares (NLS) problem can be solved using classical algorithms, such as Gauss-Newton and Levenberg–Marquardt methods. However, these algorithms present convergence problems for NLS with large errors. In this case, it can be necessary to use of hybrid algorithms based on a combination of Gauss-Newton and BFGS methods. The robustness, accuracy, and computational efficiency of classical and hybrid algorithms are compared in the backcalculation of asphalt pavements.