The flexible joints and segmental lining serve as effective seismic measures for tunnel in high-intensity seismic area. However, the tunnel axial deformation at flexible joints has not been fully incorporated into analytical models. This study presents a novel mechanical model for flexible joints that considers tension (compression)shear-rotation deformations, replacing the traditional shear-rotation springs model. An improved semi-analytical solution has been developed for the longitudinal response of a tunnel featuring a three-way flexible joint mechanical model subjected to fault movement. The nonlinear elastic-plastic foundation spring, the soil-lining tangential interaction, and the axial force of tunnel lining have been considered to improve the applicability and precision of proposed method. The proposed solution is compared with existing models, such as short beams connected by shear and rotation springs, by examining the predictions against numerical simulations. The results indicate that the predictions of the proposed model align much more closely with the outcomes of the numerical simulations than those of the existing models. For the working conditions selected in 4, neglecting the tension-compression deformation at flexible joints an 81.8% error in the peak axial force of the tunnel and a 20.2% error in the peak bending moment. The reason is that ignoring the axial deformation of these joints results in a larger calculated axial force on the lining, which subsequently leads to increased bending moment and shear force. Finally, a parameter sensitivity analysis is conducted to investigate the effect of various factors, including flexible joint stiffness, segmental lining length, and the length of the tunnel fortification zone.

This paper proposes a semi-analytical solution for one-dimensional consolidation of viscoelastic unsaturated soil considering a variable permeability coefficient under exponential loading. The governing equations of excess pore air pressure (EPAP) and excess pore water pressure (EPWP) were acquired by introducing the Merchant viscoelastic model. By employing Lee's correspondence principle and the Laplace transform, the solutions for EPAP and EPWP were derived under the boundary conditions of the permeable top surface and impermeable bottom surface. Crump's method was then used to execute the inverse Laplace transform, yielding a semi-analytical solution in the time domain. Through typical examples, the dissipation of EPAP and EPWP and the change of the average degree of consolidation over time under the influence of different elastic moduli, viscoelastic coefficients, and air-to-water permeability ratios were studied. The variation of the permeability coefficient and its influence on consolidation were also analyzed. The findings of this research show that the consolidation rate of viscoelastic unsaturated soil is slower than that of elastic unsaturated soil; however, an acceleration in the consolidation of the soil is observed when changes in the permeability coefficient are considered. These discoveries enhance our comprehension of the consolidation behaviors exhibited by viscoelastic unsaturated soil, thereby enriching the knowledge base on its consolidation traits.

Accurately predicting pile penetration in marine soft clays is crucial for effective construction, load-bearing design, and maintenance of offshore pile foundations. A semi-analytical solution employing the combined expansion-shearing method (CESM) is introduced to model pile penetration in soft clays. This method innovatively simplifies the Pile penetration into undrained cavity expansion and vertical shearing. Using the S-CLAY1S model, which incorporates the anisotropy and structure of natural soft clays, an exact semi-analytical solution was developed to describe soil behavior around the pile under undrained vertical shearing, expanding upon existing undrained cavity expansion solutions. The accuracy and innovation of the CESM were validated through the results of field tests and finite element simulations. Additionally, a comprehensive parametric study highlighted the significant impact of soil's initial structure and stress state on pile penetration response. The study findings strongly align with theoretical calculations, field Measurements, and numerical simulations. Compared to the conventional cavity expansion method, CESM excels in resolving soil stresses at the pile shaft, albeit with a slight limitation in evaluating excess pore water pressure of soils at the pile shaft. The proposed solution considers the fundamental properties of soft clays, including their anisotropy and structural behavior, while incorporating the vertical shearing experienced by the soil during pile installation, thereby providing a simplified yet precise theoretical framework for addressing pile penetration challenges.

Prefabricated vertical drains (PVDs) are highly effective in hastening the consolidation process of soil and enhancing the strength of the foundation. Enhanced computational precision is achieved by utilizing a twodimensional (2D) plane strain model throughout the analytical procedure. The pronounced layering characteristic of saturated soils, coupled with the obstruction of pore water drainage across interfaces, results in a pronounced flow contact resistance effect. A comprehensive investigation into the 2D plane strain consolidation behavior of layered saturated soils under continuous drainage boundary conditions is facilitated by the presentation of the interfacial flow contact model. Subsequently, semi-analytical solutions for pore water pressure and the degree of consolidation are derived using the Laplace transform and the Crump inverse method. The proposed solution is analyzed for its degradation and compared against the experimental results and numerical solutions, to ascertain the accuracy and reliability of the presented solution. The research delves into the effects of flow contact resistance on parameters, including the permeability coefficient ratio (kv / kh) and boundary coefficients (rt and rb) throughout the consolidation process. Additionally, the impact of the flow contact resistance on the degree of consolidation is discussed. The results indicate that both the permeability coefficient ratio and boundary parameters have a close association with the flow contact resistance effect. Ignoring this effect may lead to inaccurate predictions of pore water pressure distribution and an overestimation of the soil consolidation.

Permeable pipe pile, a novel pile foundation integrating drainage and bearing functions, improves the bearing capacity of the pile foundation by accelerating the consolidation of the soil around the pile. In this study, a mathematical model is established to simulate the consolidation of surrounding clayey soils and the pile-soil interaction, where the rheological properties of the soils are described with the fractional derivative-based Merchant model, and the impeded drainage boundary is used to simulate the pile-soil interfacial drainage boundary. Corresponding solutions for pile-soil relative displacement, skin friction, and axial force on the pile shaft are derived by means of semi-analytical methods, and they are validated by comparing with experimental results and numerical simulation results. Based on the proposed semi-analytical model, a series of parametric analyses are conducted to investigate the influences of fractional orders, viscosity coefficients, pile-soil interface parameters, and pile-head loads on the pile-soil interaction characteristics. It is observed that during the transition stage, the axial force increases linearly with depth in the plastic segment, and then increases nonlinearly in the elastic segment until it decreases after reaching the neutral plane. In the elastic segment, the axial force on the pile shaft for a given time increases with the increases in the fractional order or the pile-soil interface parameter, but decreases with the increase of viscosity coefficient.

The transient response of porous media is an important aspect of dynamic research. However, existing studies seldom provide solutions to the transient response problem of layered unsaturated porous media. Based on the Biot-type unsaturated wave equations, dimensionless one-dimensional wave equations are established. An appropriate displacement function is introduced to homogenize the boundary conditions. Subsequently, the transfer matrix method is used to obtain the eigenvalues and eigenfunctions of the homogeneous governing equations. Leveraging the orthogonality of the eigenfunctions, the original problem is transformed into solving a series of initial value problems of ordinary differential equations. The temporal solution within the time domain is then obtained through an improved precise time integration method. The validity of the solution presented in this paper is verified by comparing it with existing solutions in the literature. Analysis of numerical examples shows that reflection waves of opposite phases will be generated at the hard-soft and hard-harder interface, which helps in the accurate identification of weak interlayers in practical engineering applications. With increasing saturation, there is a noticeable increase in the velocities of the P1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{1}$$\end{document} and P3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{3}$$\end{document} waves, whereas the velocity of the P2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{2}$$\end{document} waves tends to decrease, which can be used to assess the mechanical property of medium. The peak value of pore pressure in unsaturated can be 1.64 times higher than those in saturated condition.

The self-weight stress in multilayered soil varies with depth, and traditional consolidation research seldom takes into account the actual distribution of self-weight stress, resulting in inaccurate calculations of soil consolidation and settlement. This paper presents a semi-analytical solution for the one-dimensional nonlinear consolidation of multilayered soil, considering self-weight, time-dependent loading, and boundary time effect. The validity of the proposed solution is confirmed through comparison with existing analytical solutions and finite difference solution. Based on the proposed semi-analytical solution, this study investigates the influence of self-weight, interface parameter, soil properties, and nonlinear parameters on the consolidation characteristics of multilayered soil. The results indicate that factoring in the true distribution of self-weight leads to a faster dissipation rate of excess pore water pressure and larger settlement and settlement rate, compared to not considering self-weight. Both boundary drainage performance and soil nonlinearity have an impact on consolidation. If the boundary drainage capacity is inadequate, the influence of soil nonlinearity on consolidation diminishes.

In recent earthquakes, tunnels in earthquake-prone zones have suffered significant damage. The cracks in these tunnels contain a mix of transverse, longitudinal and inclined cracks, suggesting a complex 3D tunnel response in these zones. In this article, we semi-analytically solve for the complete 3D response of a shallow lined tunnel embedded in a linear elastic homogeneous half-space under seismic waves that are incident on the tunnel from arbitrary directions. The waves scattered by the tunnel are represented using cylindrical waves, and the coefficients of these waves are estimated by enforcing the stress-free condition at the tunnel and ground surface, and the compatibility condition at the soil-liner interface. Accurate enforcement of the ground surface stress-free condition is accomplished by solving an improper contour integral that requires special treatment at branch points, removable singularities and poles. The convergence of the solution series is investigated, and the converged stresses and displacements at various locations in the soil and tunnel liner are compared with the results from past semi-analytical and numerical studies for 2D and 3D scenarios. Robustness and accuracy of the algorithm over a wide range of tunnel liner-to-soil stiffness ratios, tunnel depth-to-radius ratios, tunnel liner thickness-to-radius ratios, incident wave frequencies and directions are then tested to demonstrate the applicability of this algorithm as a fast and reliable tool for the initial design of a tunnel in an earthquake-prone zone.