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.

Upon completing large-area layered filling, the foundation soil exhibits transverse isotropy and is predominantly. unsaturated, making post-construction settlement prediction challenging. Additionally, the creep model considering transverse isotropy and unsaturated characteristics has not been proposed. Therefore, the true triaxial apparatus for unsaturated soil was enhanced, and transversely isotropic unsaturated loess samples were prepared. The relationship between matrix suction and moisture content at various depths in transversely isotropic unsaturated loess was determined using soil-water characteristic curve tests. The creep characteristics of loess fill under varying moisture content, degree of compaction, deviatoric stress, and net confining pressure were examined using a consolidation drainage test system. According to the creep curve, the expressions for six parameters in the modified Burgers element model were determined, establishing a post-construction settlement prediction method for transversely isotropic unsaturated loess fill foundations. The results show that the transversely isotropic unsaturated loess exhibits distinet creep characteristics, primarily nonlinear attenuation creep. The degree of compaction, moisture content, deviatoric stress and net confining pressure significantly affect its creep characteristics. Creep stability strain is linearly related to the degree of compaction. Enhancing soil compaction can effectively reduce post-construction settlement of the fill foundation. A prediction algorithm based on the modified Burgers model, which reflects the influence of degree of compaction, moisture content, and stress level, and accurately describes the post-construction settlement behavior of transversely isotropic unsaturated loess fill foundations, is established. Actual engineering monitoring results demonstrate that the proposed settlement prediction algorithm is simple, practical, and effective. The research results can enrich and advance the creep model of unsaturated soil, and provide a scientific basis for solving the problem of deformation calculation of high fill foundation.

Three approximate analytical solutions for the problem of the seismic response of two rigid cantilever walls retaining a transversely isotropic poroelastic soil layer over bedrock are presented under conditions of plane strain and time harmonic ground motion. These approximate solutions come as a result of various reasonable simplifications concerning various response quantities of the problem, which reduce the complexity of the governing equations of motion. The method of solution in all the cases is the same with that used for obtaining the exact solution of the problem, i.e., expansion of response quantities in the frequency domain in terms of sine and cosine Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations with respect to the vertical coordinate in conjunction with the boundary conditions. The first approximate solution is obtained on the assumption of neglecting all the terms of the equations of motion associated with the fluid acceleration. The second approximate solution is obtained on the assumption that the fluid displacements are equal to the corresponding solid displacements. The third approximate solution is obtained as the sum of the second approximate solution for the whole domain plus a correction inside a boundary layer at the free soil. All three approximate solutions are compared with respect to their accuracy against the exact solution and useful conclusions pertaining the approximate range of the various parameters, like porosity, permeability and anisotropy indices, for minimization of the approximation error are drawn.

Anisotropy is an inherent characteristic of subgrade soils, causing significant variations in the dynamic behavior of the pile embedded in them under different loading conditions. This research develops a novel model to examine, for the first time, the dynamic behavior of an end-bearing pile embedded in an anisotropic elastic medium subjected to vertical S-waves. The pile is modeled as a Euler-Bernoulli beam, while the surrounding soil is treated as a transversely isotropic (TI) elastic material. The one-dimensional free-field and three-dimensional scattered-field motions in the TI elastic medium under S-waves are obtained within the frame of dynamic continuum model. The developed model is checked for accuracy against established analytical solution. Key parameters, such as the anisotropic modulus ratio of the TI soil, pile radius, are systematically studied to assess their effects on the kinematic behavior of the system. Results reveal that the soil anisotropy would significantly alter the kinematic behavior of the pile and surrounding soil system, notably impacting the amplification factors for pile displacement and rotation and the horizontal movement of the soil. These findings highlight the necessity of considering soil anisotropy in the seismic design and analysis of pile foundations to ensure structural safety and performance under earthquake.

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.

Natural geotechnical materials are affected by sedimentation and exhibit significant anisotropy. To study the transverse isotropy characteristics of soil, the influence of intermediate principal stress and loading direction must be considered. Currently, research on transverse isotropy primarily focuses on the modified stress space, which is cumbersome to apply in multi-yield surface constitutive models. To describe the three-dimensional mechanical properties of geomaterials in real stress space, the alpha-Spatial Mobilized Plane strength criterion is introduced. Then, combined with the structure tensor, the transverse isotropic three-dimensional strength criterion can account for the effect of the loading angle. Finally, the three-dimensional strengths of Fukakusa clay, unsaturated SP-SC soils, uncemented Monterey sands, Yamaguchi marble, San Francisco Bay mud, Toyoura sand, and Santa Monica Beach sand are predicted on the pi-plane. The results show that the alpha n m- SMP criterion, in the context of transverse isotropy, can describe the three-dimensional mechanical properties reasonably, and it can provide an accurate strength criterion for geotechnical engineering practice.

A novel model is put forward to characterize the seismic response excited by vertical P-waves in a transversely isotropic and layered nonlocal poroelastic seabed. The proposed model integrates nonlocal parameter, anisotropy, and stratification to accurately examine wave propagation behavior. The fundamental equations for the underlying seabed are formulated using Biot's poroelastodynamic theory and Eringen's nonlocal theory. The wave equation for the overlying water is expressed in terms of the velocity potential. General solutions in both the poroelastic seabed and water layer are derived by solving the involved ordinary differential equations. Employing the newly devised and unconditionally stable propagator matrix scheme, semi-analytical solutions are derived for the time-harmonic response in a layered poroelastic seabed subjected to vertical P-wave excitation within the frequency domain. The validity of the proposed solutions is confirmed through rigorous comparison with the previously established analytical solutions. The influence of key material properties of seabed on the velocities of P-waves and free-field response in the poroelastic seabed is estimated in detail, along with the freefield response in a nonhomogeneous poroelastic seabed.

Large-diameter pipe piles are widely applied in various civil engineering fields due to their outstanding load- bearing capability. The unsaturated characteristics, anisotropy, and heterogeneity of the soil jointly affect the dynamic response of the pipe pile. However, most previous studies were limited to single-phase or two-phase soil. This paper develops an analytical model for the torsional vibration of a pipe pile in transversely isotropic unsaturated soils considering construction disturbance. Based on transversely isotropic unsaturated soil theory, a pipe pile-soil interaction model has been developed, while the effect of construction disturbance is simulated by the radial heterogeneity of the soil. The general solution for the unsaturated soil is obtained using the separation of variables method with the boundary conditions. Then, the solution for the whole pipe pile-soil system is derived by considering the pile-soil interface conditions. The accuracy of the proposed solution is verified through comparisons with previous research results. The results show that unsaturated characteristics, construction disturbance, and transverse isotropy of the soil have significant effects on the impedance of large- diameter pipe piles. Specifically, with a low degree of saturation, there will be significant prediction errors when using previous works based on single-phase or two-phase soil theory to predict the dynamic response of large-diameter pipe piles.

In shallow water regions, ocean waves commonly propagate in the form of cnoidal waves, with the response induced in the seabed obviously being different from that involving conventional linear waves. Computational models of waves and seabeds were established based on cnoidal wave theory and Biot's completely dynamic consolidation theory, respectively. A semianalytical solution for the dynamic response of the multilayered, transversely isotropic (TI), poroelastic seabed induced by cnoidal waves was derived via the scalar potential function and the dual variable and position method. The reliability and accuracy of the developed semianalytical solution was verified against existing solutions and experimental data. This parametric study demonstrated that cnoidal waves have a significant effect on the dynamic response of the seabed compared to linear waves. Also, the induced pore pressure/stresses and corresponding liquefaction potential were significantly affected by the anisotropy and layering of the seabed material. The newly developed solution can serve as a useful tool for estimating the liquefaction potential of a TI and multilayered poroelastic seabed in shallow water.

In this study, a theoretical approach is presented for analyzing how rectangular barrettes respond laterally in layered transversely isotropic soil deposits. To do this analysis, a modified Vlasov model is used. In this study, the barrette and the soil around it are treated as a continuum system. The deformation of the barrette is analyzed using the Timoshenko beam theory. By multiplying the barrette's displacement with a pair of decay functions, the horizontal soil displacement can be quantified. The equations that govern the barrette and soil are derived based on the principle of minimum energy, along with the appropriate boundary conditions. These equations are then solved using an iterative method. The accuracy of the results is confirmed by comparing the barrette response to two previously published results. Additionally, the impact of the shape of the rectangular cross and the anisotropy of the soil on the static responses of a barrette are explored. The results show that the ratio Esh/Esv between the horizontal modulus and vertical modulus for the transversely isotropic soil has significant influences for the response of barrette. An increase of Esh/Esv from 0.5 to 3.0 can lead to a reduction of around 75%, 54%, 30%, 40% for the maximums of lateral displacement, rotation, moment, and soil reaction, respectively.