3D-FAST: Three-Dimensional Fourier Analysis of Pavement Structures Under Transient Loading
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3D-FAST is a finite-layer model to compute pavement mechanical responses under dynamic (i.e., time-variable) non-uniform load of any shape. Surface loads, including vertical load and braking shear loads are discretized into waves propagating in time domain and spatial domains employing three-dimensional (3-D) Fourier transform. This transformation allows 3D-FAST to integrate the frequency-dependent material characterization with the harmonics composing the surface loads. In the model formulation, the main unknowns are displacements, and all other responses (i.e. stresses, strains, velocities and acceleration) are determined based on the displacement field. Layer interface boundary conditions were incorporated into 3D-FAST and may be adjusted to account for interface slippage. The equilibrium equations are set to be satisfied for every wave in the frequency domain for a representative differential element and for each time step. Using inverse Fourier transform, the responses can be obtained at the desired depths for the full spatial domain, generating informative graphical 3-D surface plots animated with time. Some practical applications of 3D-FAST are modelling FWD with any pulse shape and pavement analysis for roughness-induced dynamic loads. The runtime of the model is considerably shorter when compared to finite-element methods with no concern regarding mesh identification. The unique formulation of the model also allows for further computational efficiency by incorporation with parallel processing. 3D-FAST is a computationally effective model for computing pavement responses, specifically for integrating with mechanistic empirical (ME) approaches. The superposition principle represented by Boltzmann’s equation can be effectively integrated with 3D-FAST because it simplifies to multiplication in frequency domain. The non-uniform Fourier transform was proposed as a means of reducing computational runtime, however, it should be noted that it introduces some approximation to the results. 3D-FAST was verified and validated, and a sample application was demonstrated. The 3D-FAST verification process was performed by investigating rheological model, specifically, Kelvin, Maxwell, and Burger models. The results obtained by 3D-FAST were compared to classical solutions derived for strain amplitude and phase angle of these models and were matched very well. 3D-FAST results were validated by one of the experiments conducted at the full-scale Box facility at the University of Nevada, Reno. The measured deflections from LVDTs and stresses from pressure cells were compared with 3D-FAST results in terms of both response pulse shape and peak value. The comparison revealed a descent match between 3D-FAST results and data collected by the experiment instrumentation. As for the 3D-FAST application, the roughness-induced vehicle dynamic loading was investigated for a sample road profile. The dynamic load was obtained using quarter-car simulation, and was used as the load input for 3D-FAST. A variety of response types were computed for this example at different locations within pavement structure.