The focus of this contribution is to develop an improved 2.5-dimensional (2.5D) FE (finite element)-BE (boundary element) method for a tunnel structure-transversely isotropic saturated soil system subject to underground moving train loads. In the proposed model, the rectangular tunnel invert, the lining, and the region of interest within the soil continuum use the 2.5D FE method. The remaining region of half space is replaced with a viscous spring boundary along the lateral sides and boundary element along the bottom. The theory of acoustic propagation in saturated media is extended to include transversely isotropy, viscoelasticity and boundary elements. An existing case is calculated using the enhanced model, and the results are compared with the previous literature to validate the accuracy and reliability of the proposed method. A parametric analysis is further conducted, and the factors considered in the analysis of ground-borne vibrations induced by trains meeting in the rectangular tunnel include the soil permeability, the groundwater level, and the depth of the tunnel. Numerical comparisons show that the saturated soil above the tunnel moderates the displacement undulation caused by quasistatic axle loads of the train, but this is not the case if the load has a non-zero excitation frequency. Moving train loads with excitation produce larger excess pore water pressure amplitude than do the quasi-static loads over a wide range along the travelling direction. The effect of meeting trains depends on the running speeds of both lines in opposite directions to some extent. Other conclusions useful to practical engineers are contained in the parametric study.

This study constructs a multilayered transversely isotropic saturated model under thermal and horizontally circular loads, and further investigates the model's thermo-hydro-mechanical coupling response. Firstly, the ordinary differential matrix equations of thermoelastic saturated media in the integral transformed domain are derived. Secondly, the solution for multilayered thermoelastic saturated media is developed using the extended precise integration method (EPIM), along with the boundary conditions at both ends of the foundation and the continuity conditions between adjacent layers. After that, the solution in the physical domain is further attained with the use of Laplace-Hankel integral transform inversion. Finally, the accuracy of the proposed theory is confirmed through numerical examples, and the influences of anisotropic parameters, the soil's stratification and porosity on the thermo-hydro-mechanical coupling response of the media are studied.

In this study, we present a novel nodal integration-based particle finite element method (N-PFEM) designed for the dynamic analysis of saturated soils. Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner (HR) variational principle, creating an implicit PFEM formulation. To mitigate the volumetric locking issue in low-order elements, we employ a node-based strain smoothing technique. By discretising field variables at the centre of smoothing cells, we achieve nodal integration over cells, eliminating the need for sophisticated mapping operations after re-meshing in the PFEM. We express the discretised governing equations as a min-max optimisation problem, which is further reformulated as a standard second-order cone programming (SOCP) problem. Stresses, pore water pressure, and displacements are simultaneously determined using the advanced primal-dual interior point method. Consequently, our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation. Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy, obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches. This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/ by/4.0/).

This study investigates the interaction between energy piles and layered saturated soils, considering the consolidation induced by the thermal loads and mechanical loads. Initially, the coupled thermo-hydromechanical solution of layered media is obtained by utilizing the boundary element method (BEM) and the transformed differential quadrature method. Subsequently, the energy piles are discretized and modelled by the finite element method (FEM), and the solving equation for piles is established. To reflect the interaction between piles and soils, a coupled BEM-FEM matrix equation is formulated and solved by incorporating displacement coordination conditions and force equilibrium conditions. This approach facilitates the analysis of the temporal evolution of displacements and temperatures of piles and surrounding soils. The proposed methodology is validated through comparisons with monitoring data of field tests and results from simulations. Ultimately, the key factors, including the temperature increments, mechanical loads, length-diameter aspect ratio are examined through examples.