This paper establishes a novel full-process numerical simulation framework for analyzing the 3D seismic response of mountain tunnels induced by active faults. The framework employs a two-step approach to achieve wavefield transmission through equivalent seismic load: first, a highly efficient and accurate FMIBEM (Fast multipole indirect boundary element method) is used for large-scale 3D numerical simulations at the regional scale to generate broadband ground motions (1-5 Hz) for specific sites; subsequently, using the FEM (Finite element method), a refined simulation of the plastic deformation of surrounding rock and the elastoplastic behavior of the tunnel structure was conducted at the engineering scale. The accuracy of the framework has been validated. To further demonstrate its effectiveness, the framework is applied to analyze the impact of different fault movement mechanisms on the damage to mountain tunnels based on a scenario earthquake (Mw 6.7). By introducing tunnel structure damage classification and corresponding damage indicators, the structural damage levels of tunnels subjected to active fault movements are quantitatively evaluated. The findings demonstrate that the framework successfully simulates the entire process, from fault rupture and terrain amplification to the seismic response of tunnel structures. Furthermore, the severity of tunnel damage caused by different fault types is ranked as follows: reverse fault > normal fault > strike-slip fault.

The subject of the current paper is the dynamic behaviour of anisotropic half-plane with surface relief containing a flexible or rigid foundation and two buried lined or unlined tunnels under time-harmonic waves radiated via embedded line source. The aim is to anticipate the influence of different model key factors such as (a) the soil topography; (b) the soil anisotropy; and (c) the soil-tunnels and soil-foundation-tunnels interaction. The computational tool is the direct boundary element method (BEM) based on the frequency-dependent fundamental solution for 2D general anisotropic solid derived by the Radon transform. The lined tunnels are implemented in the numerical model by the sub-structuring approach, which allows an efficient numerical processing of integrals along the interface boundaries. Numerical scheme verification and parametric studies are performed, and respective concluding remarks are summarized. The obtained results clearly illustrate the dynamic response sensitivity to the soil anisotropy, the soil topography and the complex soil-foundation-tunnels interaction.

To investigate the three-dimensional dynamic response of a deeply buried storage and drainage tunnel in saturated soil subjected to water hammer, we propose a frequency-domain finite element method and boundary element method (FEM-BEM) coupling model for the fluid-lining-saturated soil system. The fluid is modeled as an inviscid and compressible fluid, the lining as an elastic medium conceptualized as a hollow cylinder of finite length, and the soil as a saturated poroelastic medium. Initially, the governing equations for the fluid and lining are solved using FEM in the frequency domain, while those for the soil are solved using BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility, force equilibrium, and impermeable boundary conditions at their interfaces. The presented model is verified through the comparison with the existing models. Finally, a case study of internal water pressure (water-hammer load) and the displacement and pore pressure of the saturated soil in a fluid-filled lined tunnel due to water hammer is presented. The results show that: (1) The dynamic response caused by the water hammer presents significant periodicity and attenuation. (2) The radial displacement of soil is significantly larger than that of axial displacement. (3) Modeling soil as a single-phase elastic medium inaccurately evaluates the dynamic response. (4) The water hammer makes an extensive impact on the ground surrounding the storage and drainage tunnel. (5) The peak values of internal fluid pressure, the soil displacement and pore pressure decrease with the decrease of soil permeability.

This paper studies the time-dependent behavior of a pile drilled in layered saturated viscoelastic rock-soil mass due to a vertical load. By virtue of the finite element method (FEM), the pile is discretized into three-node axial bar elements. On the basis of the consolidation solution of layered transversely isotropic saturated rock-soil mass, the fractional Poyting-Thomson model and fractional Merchant model are used to simulate the rheological properties of rock and soil, respectively. The viscoelastic solution of layered saturated rock-soil mass under annular linear loads is derived according to the elastic-viscoelastic correspondence principle. Taking the above solutions as the kernel functions of the boundary element method (BEM), and combining with the stiffness matrix equation of a pile, a coupling formula of pile-soil-rock interaction is further established by the FEM-BEM coupling method. A MATLAB code is developed for numerical calculation, and the correctness of the present theory and calculation method are verified by comparing with the existing solutions, field tests and ABAQUS analyses. Finally, the key factors influencing the time-dependent behavior of piles are in-depth discussed.

This study proposes a rapid seismic resilience assessment framework of tunnels in mountain regions considering the topography amplification effect and tunnel-soil dynamic interaction based on the indirect boundary element method (IBEM) coupled with the finite element method (FEM). The high efficiency is achieved by using a surrogate model to determine the tunnel fragility curves. This model reflects the relationship between the geometric and material variables of mountains and tunnels, as well as the tunnel damage index. To obtain the surrogate model, the identification of model variables is first explored quantitatively based on the random forest algorithm due to the high variable quantity. The dataset for training and testing the random forest is constructed from 600 numerical simulations. The IBEM-FEM coupling scheme is employed to describe the large-scale site response for tunnel damage analysis and significantly reduce the number of finite element grids for each sample. This scheme solves the nonlinear dynamic response of mountain tunnels under near-fault earthquakes. The surrogate model is then used to obtain the tunnel functionality and resilience. Based on the proposed framework, the influence of the mountain material, mountain height-span ratio, and tunnel position on the seismic fragility, functionality, and resilience are investigated. The results reveal that a surrogate model can be employed to replace a series of nonlinear time-history analyses of tunnels, with a high accuracy and efficiency. The shear modulus of the surrounding rock, the height-to-span ratio of the mountain, and tunnel position have a significant impact on tunnel fragility and resilience. This impact is correlated with the tunnel height. The mountain topography can cause a difference of approximately 20 % in the tunnel resilience.

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.

The mechanical response of energy pile groups in layered cross-anisotropic soils under vertical loadings is studied with the aid of the coupled finite element method- boundary element method (FEM-BEM). The single energy pile is simulated based on the finite element theory, which then is extended to energy pile groups. The global flexibility matrix for soils is obtained by considering the coupling effects of vertical and thermal loadings. The coupled FEM-BEM equation for the interaction between energy pile groups and soils is derived based on the displacement compatibility condition at the pile-soil interface. According to the displacement coordination condition and force balance in the rigid cap, the displacement of the cap and axial forces of pile groups can be solved. The presented theory is validated by comparing the calculated results with numerical simulations and field test results in existing literature. Finally, effects of the thermal loading, pile-soil stiffness ratio, pile spacing, cross-anisotropy of Young's modulus and the stratification are discussed.

Dynamic stress responses of saturated soil around a fluid-filled lined tunnel caused by a water hammer are investigated by a frequency-domain FEM-BEM coupled model. The fluid is modeled as an inviscid and compressible fluid, the lining is modeled by elastic medium and conceptualized as a hollow cylinder of finite length, and the saturated poroelastic medium is adopted to model the soil. Initially, governing equations of fluid and those of lining are solved by FEM in the frequency domain, while those of soil are solved by BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility and force balance on their interfaces. Water pressure (inside the tunnel), the distribution of lining displacement and dynamic stress responses of saturated soil generated by the water hammer are presented. It is concluded that the dynamic stresses and the pore pressure change periodically in saturated soil under a water hammer. Modeling soil as an elastic medium inaccurately evaluates the distribution of lining displacement. The soil permeability has a significant influence on the normal stresses of soil and pore pressure but has a slight effect on the shear stresses of soil.

The current paper investigates wave propagation from time-harmonic embedded point source in a semi-infinite anisotropic medium containing underground structure by applying three different computational techniques. Firstly, direct BEM for 2D elastodynamics is applied using the fundamental solution derived by the Radon transform for general anisotropic continua. The second numerical technique is a computationally efficient two-and-a-half dimensional FEM, used to calculate the 3D wave field in the soil. At the boundaries of the mesh perfectly matched layers are instated to prevent spurious wave reflections. The FEM solutions realized by the built-in options in ANSYS are finally utilized with two types of absorbing boundary conditions. The results obtained by the three adopted modelling techniques are properly compared and respective insights regarding their applications are provided.