Composed of a raft and pipe piles with embedded heat exchange devices, a pipe-type energy piled raft foundation can enhance both foundation performance and energy utilization efficiency. An urgently needed thermomechanical analysis method would facilitate the optimization design and the broader adoption of this fundamental form. Therefore, this paper proposes an efficient method for the thermo-mechanical analysis of pipe-type energy piles with a raft in layered transversely isotropic media. The pile-soil and raft-soil interaction equations are derived by coupled finite and boundary element method. A simplified approach is then proposed and applied to tackle the pile-raft-soil coupling interaction. The correctness and efficiency of the method are verified through comparisons with a field test and two finite element numerical cases. Finally, parametric analyses are conducted to investigate the influences of temperature increment, pile thickness, raft thickness, and soil anisotropy on the performance of the pipe-type energy piled raft foundation.

This study considers the saturated soil around the tunnel as a transversely isotropic medium and derives the dynamic response solutions of the tunnel lining and its surrounding medium under explosive loads in the Laplace and Fourier transform domains. When the transverse isotropic coefficient equals 1.0, this solution simplifies to the case where the tunnel is surrounded by a uniform medium. By performing inverse Fourier and Laplace transforms on the solution, we obtain the time domain solution. Compared with the results for a uniform medium surrounding the tunnel, it was found that the peak values of stress and pore water pressure increased, while the peak displacement slightly decreased. In addition, the peak arrival time is advanced, and the fluctuation attenuation is accelerated. The transverse isotropy of soil in engineering cannot be ignored.

A novel theoretical model is proposed to investigate the torsional response of a pile in fractional-order viscoelastic unsaturated transversely isotropic soil with imperfect contact. This model employs Biot's framework for three-phase porous media along with the theory of fractional derivatives. Unlike previous models that assume continuous displacement at the pile-soil interface, this study uses the Kelvin model to simulate relative slippage between pile-soil contact surfaces (imperfect contact). Incorporating fractional-order viscoelastic and transversely isotropic models to describe the stress-strain relationship, comprehensive dynamic governing equations are derived. Using the separation of variables method, inverse Fourier transform, and convolution theory, analytical solutions for the frequency domain response and semi-analytical solutions for the time domain response of the pile head under semi-sine pulse excitation are obtained. Using numerical examples, the effects of model parameters in the fractional-order viscoelastic constitutive model, pile-soil relative slip and continuity model, and soil anisotropy on the torsional complex impedance, twist angle, and torque are presented.

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.

An analysis for the torsional dynamic response of end-bearing pile foundations embedded in a layered transversely isotropic geomaterial (soil/rock) is presented. The deformation of the transversely isotropic soil or rock is described by the method of separation of variables. The elasticity theory for a viscoelastic medium with frequency independent hysteretic material damping, and the Extended Hamilton's Principle are utilised to derive the differential equations describing pile and soil motions. The differential equations are solved analytically in an iterative algorithm. The accuracy of the analysis is verified with existing studies reported in the literature for pile foundations embedded in a homogeneous and layered soil deposit. The effect of the degree of anisotropy on the pile-soil response - dynamic pile-head stiffness, distribution of pile rotation and torque with depth, dimensionless soil displacement function for various values of pile slenderness and pile-soil stiffness ratios in a homogenous soil deposit is investigated. Design charts of static pile-head stiffness in a homogeneous soil deposit for a wide range of pile-soil stiffness and pile slenderness ratios, and degree of anisotropy are also reported. The effect of soil layering for a pile embedded in a two-layered soil deposit is also studied.

We present an assumed enhanced strain finite element framework for the simulation of tensile fracturing processes in transversely isotropic rocks. Fractures along the weak bedding planes and through the anisotropic rock matrix are treated with distinct enrichment, and a recently proposed dualmechanism tensile failure criterion for transversely isotropic rocks is adopted to determine crack initiation for the two failure modes. The cohesive crack model is adopted to characterize the response of embedded cracks. As for the numerical implementation of the proposed framework, both algorithms for the update of local history variables at Gauss points and of the global finite element system are derived. Four boundary-value problem simulations are carried out with the proposed framework, including uniaxial tension tests of Argillite, pre-notched square loaded in tension, three-point bending tests on Longmaxi shale, and simulations of tensile cracks induced by a strip load around a tunnel in transversely isotropic rocks. Simulation results reveal that the proposed framework can properly capture the tensile strength anisotropy and the anisotropic evolution of tensile cracks in transversely isotropic rocks. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

This study offers a comprehensive and advanced understanding of the torsional response of piles partially embedded in fractional-order viscoelastic unsaturated transversely isotropic soils, accurately capturing the true viscoelastic properties and particle orientation of the soil as formed during deposition. Based on Biot's threephase porous media wave equations and considering the coupling effects between the immiscible fluids (water and air) in the pores, the dynamic governing equations for fractional-order viscoelastic unsaturated transversely isotropic soil are established. The soil vibration displacement is solved using the method of separation of variables. In the frequency domain, employing the transfer matrix method and considering the continuity and boundary conditions of the pile-soil system for both the embedded and exposed portions, the analytical solution for the torsional complex impedance at the pile head of a partially embedded single pile in fractionalorder viscoelastic unsaturated transversely isotropic soil is derived. Furthermore, a semi-analytical solution for the pile head response in the time domain under half-sine pulse excitation is obtained through inverse Fourier transform and convolution theorem. Numerical examples are presented to investigate the effects of the parameters of the fractional-order viscoelastic constitutive model and the pile-soil parameters on the torsional complex impedance at the pile head.

An analytical solution for investigating the torsional dynamic response of a pipe pile in unsaturated poroelastic transversely isotropic soil under time-harmonic load is proposed. By employing the Biot's type three-phase porous media model and the three-dimensional continuum theory, taking into account the transversely isotropic characteristics of the soil skeleton, as well as the viscosity and inertial coupling between different phases, distinct dynamic governing equations are derived for the soils surrounding and inside the pipe pile. By considering the boundary and continuity conditions at the interface between the pipe pile and the soils surrounding and inside the pipe pile in the frequency domain, a mathematical expression is derived to describe the torsional dynamic behavior of the pipe pile. A parametric study aimed to investigate how the anisotropy of the soils surrounding and inside the pipe pile (soil plug) impacts its torsional complex impedance, twist angle, and torque was conducted. The parametric study also considered variations in saturation, pile lengths, porosity, the height of the soil plug and excitation frequencies to explore the effects of these parameters on the torsional behavior of the pipe pile.

Understanding the dynamic response of soil is crucial in geotechnical engineering. Based on the Biot's theory of poroelastic soil, the integral transformation method is used to solve the wave equation of multilayered poroelastic soil. Analytical solutions for the dynamic displacement and stress fields in the spatial domain are then derived. This method accounts for the transverse isotropy properties and the discontinuous contact conditions between adjacent layers. The accuracy of the algorithm is verified by the degradation models. On this basis, the effect of varying interlayer contact parameters on the displacement fields of the poroelastic layered soil is examined. The results show that the interlayer discontinuity condition state significantly affects the dynamic response, with a greater degree of separation leading to a greater dynamic displacement response and increased susceptibility of the pavement to damage. Finally, an example is given to analyze the effect of heterogeneous properties of soil on the dynamic response of multi-layered system. Due to the existence of discontinuous contact between layers, the influence of the heterogeneous properties of the soil on the dynamic response of the pavement structure is weakened, but it still has a great influence on the soil below the discontinuous contact layer.

Considering the soil skeleton to be statically transversely isotropic, the viscous and inertial coupling among three phases, along with the capillary pressure, the torsional dynamic response of an end-bearing pile in homogeneous unsaturated transversely isotropic soil under time-harmonic torsional load is investigated. The separation of variables method is employed to derive the torsional dynamic governing equations of unsaturated transversely isotropic soil in a cylindrical coordinate system, and pile is modeled as a 1D elastic theory. By combining the boundary conditions of the pile and soil, as well as the continuity conditions at the pile-soil interface, further employing the inverse Fourier transform and convolution theorem, fundamental analytical solutions for the torsional behavior of the pile are derived in both the frequency domain and time domain. Comparisons between the proposed solution and the two existing solutions indicate that the presented model exhibits stronger applicability, as it can simultaneously transition to both saturated transversely isotropic soil and unsaturated isotropic soil. Eventually, a parametric study is conducted to examine the influence of soil anisotropy, degree of saturation, pile-soil shear modulus ratio and pile length on the torsional dynamic response of end-bearing pile.