nonlinear dynamic backcalculation app [nbak]

The primary purpose of nbak is to provide an unparalleled assessment of the structural capacity of pavements used in highways, ports, and airports, covering flexible, rigid, and composite pavement types. nbak employs state-of-the-art nonlinear dynamic implicit finite element analyses, coupled with the Newton-Raphson method, for the reliable backcalculation of pavement layer properties in the time domain using the F/HWD’s full load and deflection time histories.

dynamic implicit finite element analysis

linear elastic, linear viscoelastic and nonlinear elastic models

backcalculation at multiple load levels

energy calculation

modeling techniques

The dynamic nature of F/HWD testing, along with the diverse range of pavement materials, is addressed through the implementation of the Hilber, Hughes, and Taylor (HHT) α-method or the Newmark-β method. These approaches incorporate inertial, damping, elastic, and external forces within the equations of equilibrium governing the dynamic response of the system.

axisymmetric models

Pavement structures are formulated in nbak through axisymmetric models using two-dimensional finite elements due to the symmetry observed under F/HWD loading.

finite element meshing

A separate finite element mesh can be employed for every F/HWD test point, allowing for variations in layer thicknesses between those test points.

load-level backcalculation

Backcalculation can be conducted at a single load level or simultaneously at multiple load levels for a given F/HWD test point. Performing backcalculation at multiple load levels is essential to capture the nonlinearity of unbound materials.

layer properties

Pavement layers can be modeled in nbak as linear elastic (LE), temperature- and frequency-dependent linear viscoelastic (LVE), and nonlinear elastic (NLE). Rayleigh damping can be considered for all layers. For the nonlinear elastic materials, various options exist to relate modulus to stress, including the Uzan 1985 model (Universal model), k-θ model (θ = bulk stress) and k-τ_oct model (τ_oct = octahedral shear stress).

distinct or common variables

Backcalculation can be executed for single or multiple F/HWD test points during the same optimization process. Any layer property can be set as a distinct variable. A variable can also be shared for the same property between different layers of the same test point or the same layer(s) of multiple test points; this shared variable is referred to as a common variable. The use of common variables can enhance the robustness of the backcalculation process in scenarios such as testing at different temperatures for structures containing temperature-dependent layers, or when dealing with questionable F/HWD data.

F/HWD parameters

The F/HWD deflection time histories contain valuable information unique to each pavement structure. nbak utilizes a combination of time and deflection F/HWD parameters to accurately represent the shape and magnitude of the deflection time history for every sensor.

deflections smoothing

Robust locally weighted regression plays a pivotal role in the refinement of scatterplots depicting the time histories of measured and calculated F/HWD deflections. This method is designed to effectively smooth out irregularities, offering resilience against the potential distortion caused by outlier points that could disrupt the overall trend. The technique employs a weighted least squares polynomial fitting, attributing higher weights to neighboring data points and lower weights to more distant ones using the tricube weight function. This strategic approach significantly enhances the robustness of the regression process, ensuring a more precise representation of the underlying patterns within the scatterplots.

weight factors

Objective function weights are introduced into the optimization process to reflect the relative importance of different responses. This involves assigning higher or lower weights to certain responses, making them more or less influential in determining the optimal solution. Weights relative to one can be assigned to any of the seven combinations encompassing F/HWD drops, parameters, and offsets (spacings).

energy calculation

Ensuring the accuracy and reliability of simulation results, especially in models involving nonlinear materials, involves checking the total energy. nbak calculates various energy components (internal energy, viscous energy dissipated, kinetic energy, and external work of applied forces) from which the total energy is derived. Deviations in total energy over time could indicate numerical instability or other issues, emphasizing the importance of validating the simulations.