A space-time boundary mapped collocation method based on tensor decomposition with adaptive temporal discretization for dynamic analyses of fluid-saturated porous media

A space-time boundary mapped collocation method, incorporating tensor decomposition and adaptive temporal discretization, is proposed for dynamic analysis of fluid-saturated porous media under moving loads. In this method, the time domain is treated as an additional spatial dimension, and tensor decomposition is employed to construct space-time shape functions and generate computational nodes. To address temporal multiscale behavior caused by rapid pore-pressure variation followed by long-term dissipation, the adaptive compact support domain technique is introduced to achieve non-uniform temporal discretization while maintaining computational efficiency. The accuracy and stability of the proposed method are validated through a classical fluid-saturated soil column problem. Numerical results show that: (1) the non-uniform space-time boundary mapped collocation model accurately captures the initial peak excess pore water pressure, increasing the predicted peak value by 82.8% compared with the uniform discretization; (2) a horizontal displacement amplification zone with an antisymmetric double-peak pattern develops at the mid-depth of the soil layer and moves synchronously with the applied load; (3) the migration speed of this zone varies with load speed, while its location and extent remain unchanged. The proposed method provides an efficient approach for solving temporal multiscale dynamic problems in fluid-saturated porous media.