This study proposes a three-dimensional transformed differential quadrature solution for the thermo-mechanical (TM) and thermo-hydro-mechanical (THM) coupling of transversely isotropic soils considering groundwater. Initially, the governing equations for TH coupling above the water table and THM coupling below the water table are introduced. Subsequently, twodimensional Fourier integral transform and Laplace integral transform are applied, and a series of equations are discretized along the depth according to the discrete rules of the transformed differential quadrature method. Then, the boundary conditions for stress, displacement, and temperature are introduced through integral transforms and stress-strain relationships. By solving the matrix equation, the solution for transversely isotropic soils is obtained. After verifying the theory in this study, continuity conditions, the water table depth, anisotropy of thermal diffusion coefficients, and seepage are analyzed, contributing to the design of radioactive waste disposal sites, energy piles, and other projects.

Energy pile groups transmit geothermal energy and have attracted widespread attention as one of new building energy-saving technologies. Accurately predicting the time-dependent behaviors of energy pile groups is a challenge, given the complex thermal and mechanical interactions between piles, surrounding soils and the pile cap. This study presents a semi-analytical solution for analyzing energy pile groups within heat exchangers. Utilizing the transformed differential quadrature method, a flexible coefficient matrix for the saturated surrounding soils is acquired, which accounts for both consolidation and heat transfer. The piles are segmented, and the discrete solving equations considering thermal stresses and expansion are formulated. To accurately reflect the interactions among piles-to-piles, piles-to-soils and piles-to-pile cap, the coupled matrix equations are constructed with involving both the displacement coordination and the force equilibrium at the pile-soil interface as well as the pile cap. The validity of the proposed solution is confirmed through comparisons with results from onsite tests and simulations using COMSOL. Pivotal parameters including temperature variations, pile spacing, and the relative stiffness are discussed through examples. Compared with traditional simulation and field test, the proposed solution enables fast and accurate prediction of displacement and load distribution across pile groups, facilitating the safety evaluation of heat exchangers.

This paper examines the thermo-hydro-mechanical (THM) coupling behavior of layered transversely isotropic media under axisymmetric and plane strain conditions by utilizing the transformed differential quadrature method (TDQM), taking groundwater into consideration. Initially, the coupled governing equations of layered transversely isotropic media in multi-dimensional coordinate systems are established with considering the influence of groundwater levels. Subsequently, appropriate integral transform methods are applied to derive ordinary differential equations under different coordinate systems. It can be seen that the equations in different coordinate systems after the discretization are similar. Boundary conditions and internal continuity conditions are defined through the stress-strain relationship in the transformed domains, which are integrated into the discretized equations to form the global matrix equations. After solving the matrix equations, this study verifies the solution and investigates the impact of groundwater levels and the key parameters of transverse isotropy, and compares the behaviors of the media in different coordinate systems.

In this study, a new method is proposed to solve the axisymmetric consolidation problem of transversely isotropic saturated soils. At first, based on the governing equations of axisymmetric Biot's consolidation, the transformed governing equations in the Hankel domain are derived via integral transform technology. Then, by introducing boundary conditions, and the transformed equations are solved with the TDQM, and the consolidation solution in the actual domain is obtained via numerical inversion. Several examples are provided to verify the proposed solution and discuss the convergence of the method. Furthermore, the effects of key parameters such as the anisotropy of the stiffness and permeability on the consolidation of the skeleton are studied. Compared with the traditional differential quadrature method (DQM), the transformed differential quadrature method (TDQM) simplifies the solution process and diminishes the quantity of algebraic equations by employing the integral transform technique. This adaptation avoids the exponential escalation of the equation count encountered when solving multidimensional problems and extends DQM's applicability to the infinite domain.

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.