Time-domain thin layer method for computing transient response due to sudden/moving loads

TL;DR: In this paper, the authors applied the thin-layer method (TLM) for developing explicit time domain solutions for the ground response due to impulse and moving loads, and applied the Fourier and Laplace transforms for space and time, respectively, to derive the transformed domain solution that satisfies given boundary conditions.

Abstract: In this study, the author applied the thin-layer method (TLM) for developing explicit time domain solutions for the ground response due to impulse and moving loads. The Fourier and Laplace transforms for space and time, respectively, are applied to derive the transformed domain solution that satisfies given boundary conditions. The eigenvalue decomposition in the Laplace parameter domain and the discrete wave number superposition for the horizontal wave field description lead to an accurate and efficient strategy for a stable time-space domain solution. Some demonstrations are given: The first example is a fundamental problem relating to interpretation of the causal transient responses of the P, S, and Rayleigh waves due to an impact loading. The second example is also fundamental, and treats the description of a compound wave field produced by a single moving load, detailing the kinematic as well as the inertial effects, with the speed being an important parameter. The third example is an engineering application that demonstrates the track response due to train passage in order to interpret the wave generation in ground by the high-speed passage. A comparison to measurement data is presented for validation.