Stabilized reduced-integration u-w coupled element for 3D dynamic modelling of saturated soils

Three-dimensional numerical analysis is crucial in revealing the complex dynamic behaviour of saturated soil under multidirectional loadings. In this study, the derivation and implementation of a stabilized reduced-integration coupled element based on the u-w formulated Biot theory are presented. The key improvement of this element is the modification of non-constant solid and fluid strains based on the enhanced strain method (ESM) and assumed strain method (ASM), which ensures its stability in the incompressible-impermeable limit while maintaining an efficient bilinear interpolation scheme. Additionally, a mixed integration scheme is also employed to reduce the computational cost. The performance of the proposed element is evaluated using two benchmark problems, and comparisons with analytical methods and other coupled elements demonstrate its superiority in terms of accuracy, stability, and efficiency. The applicability of the element in more complex geotechnical scenarios is further demonstrated by investigating soil liquefaction under uni- and bi- directional shakings. The results demonstrate that both the extent and severity of field liquefaction are significantly greater under bidirectional loadings compared to those under Airas-equivalent unidirectional loadings. This highlights the necessity of three-dimensional analyses for problems involving multidirectional loading conditions, as the negligence of out-of-plane loadings and strains in plane-strain analyses could result in unsafe engineering designs.