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.

Three simplified models for the analytic determination of the dynamic response of a crossanisotropic poroelastic half-plane to a load moving with constant speed on its surface are presented and compared against the corresponding exact model. The method of analysis of the exact and approximate models uses complex Fourier series to expand the load and the displacement responses along the horizontal direction of the steady-state motion and thus reduces the partial differential equations of the problem to ordinary ones, which are easily solved. The three simplified models are characterized by reasonable simplifying assumptions, which reduce the complexity of the exact model and facilitate the solution. In the first simplified model all the terms of the equations of motion associated with fluid acceleration are neglected. In the second simplified model, solid displacements are assumed to be equal to the corresponding fluid ones, while the third simplified model is the second one corrected with respect to the fluid pressure at the free boundary (top) layer. All three simplified models are compared with respect to their accuracy against the exact model and the appropriate range of values of the various significant parameters of the problem, like porosity, permeability, anisotropy indices, or load speed, for obtaining approximate solutions as close to the exact solution as possible is thoroughly discussed.

This paper investigates the pullout behaviours of horizontal rectangular plate anchors under inclined loading in sand using three - dimensional finite element (3D-FE) analysis. An advanced bounding surface plasticity model incorporating the critical state framework is developed to capture the stress-strain relationship of sand. The model is firstly validated against various analytical solutions and centrifuge test data. Then, a series of FE analysis is conducted to consider the effects of plate anchor aspect ratio, initial embedment depth, sand relative density and inclined loading angle on the pullout capacities. Results show that shallow anchors develop failure zones reaching the soil surface, and vertical pullout capacity exceeds that under pure vertical loading when the load is slightly inclined. For deep anchors, failure zones are confined below the surface, and horizontal pullout capacity exceeds that under pure horizontal loading when the load is slightly inclined. The transitional embedment depth depends on anchor aspect ratio and sand density. A modified analytical solution is proposed to estimate the vertical pullout capacity of plate anchors from shallow to deep depths. Failure envelopes established from probe tests provide practical guidance for assessing rectangular anchor failures under various inclined loadings.

During pile installation, construction disturbances alter soil mechanical properties near the pile, significantly affecting the dynamic response of the pile. This paper develops a three-dimensional (3D) analytical model to investigate the vertical dynamic response (VDR) of a pile in radially inhomogeneous saturated soil. Firstly, by employing the separation variable method and incorporating the continuity and boundary conditions of the soilpile system, the exact solution of the whole system in the frequency domain was derived. Subsequently, the timedomain velocity response under semi-sinusoidal vertical excitation is obtained using Fourier inverse transform and the convolution theorem. The accuracy and superiority of the proposed solution were validated through comparison with previous analytical solutions. Finally, the developed solution is then used to examine the impact of parameters of saturated soil and pile on the VDR of a pile. The results demonstrate that the proposed saturated model better captures the VDR of a pile in radially inhomogeneous saturated soil compared to the single-phase model. The VDR of a pile is significantly influenced by the pore water, porosity, disturbed degree and range of the saturated soil, as well as the elastic modulus of the pile.

The presence of desiccation cracks can affect rainfall-induced slope stability through both hydraulic and mechanical ways. Despite the valuable insights gained from physical tests in literature, there still lacks understanding how crack characteristics impact water flow dynamics and slope stability, especially considering the coexistence of vegetation. In this study, new analytical solutions were derived for calculating pore-water pressure and slope stability for an infinite unsaturated slope with cracks and vegetation. Both enhanced infiltration from water-filled cracks and water uptake by plant roots are considered. Using the newly developed solutions, two series of parametric analyses were carried out to improve understanding of the factors affecting crack water infiltration and hence the stability of vegetated slope. The calculated results show that slope failure at shallow depths is governed by the surface crack ratio, whereas deeper failures typically occur with greater crack depths. The surface crack ratio primarily influences the hydraulic response at shallow depths not exceeding 1.5 m, hence affecting the factor of safety for slip surfaces within the crack zone. Moreover, increasing the crack-to-root depth ratio from 0.5 to 1.5 results in a 25% reduction in suction at 1.5 m, threatening slope safety in deeper depth after 10-year rainfall.

This study presents an enhanced analytical approach for one-dimensional consolidation settlement by introducing a revised AJOP (arc joint via optimum parameters) equation assuming creep and strain rate effects can be neglected for both normally and overconsolidated clays. This modified equation integrates both curved and linear segments within a unified framework, enhancing accuracy across varying stress levels for normally consolidated clay. Additionally, the revised AJOP function, coupled with newly proposed equations for symmetrical and asymmetrical hysteresis, improves the modeling of overconsolidated clay. The findings from a comparative investigation using benchmark datasets and conventional methods, including the linear function (LF) and the curved function (CF), reveal that the revised AJOP method was found to reduce settlement prediction errors by up to 85% compared to LF method (particularly at shallow layers) and by 10-15% compared to the CF method (particularly at deep layers). The revised AJOP equation effectively resolves this error with a wide range of depths. Furthermore, results highlight the crucial impact of clay layering techniques on consolidation settlement predictions. Non-layered models yield lower settlement estimates compared to multilayer approaches, emphasizing the significance of the proper e-log sigma ' v relationship and layering techniques in enhancing prediction reliability.

During an earthquake, the strong interaction between the surrounding rock and lining structure causes the lining susceptible to extrusion or shear damage. To evaluate the damping effect of the shock-absorbing layer on seismic loads and mitigate the deformation-induced damage of tunnel structures in loess regions, the dynamic mechanical properties of loess seismic-isolated tunnels subjected to P-wave seismic loading were investigated. In this work, the dynamic behavior of loess seismic-isolated tunnel under seismic loads was converted into a static problem. Analytical methods were employed to derive solution for internal forces within the lining structure using a mechanical analysis model. Additionally, the impact of loess hardness and seismic intensity on the performance of the shock-absorbing layer were analyzed based on the analytical solutions. Numerical methods were then applied to examine the influence of shock-absorbing layer parameters on the mechanical properties of loess seismic-isolated tunnel subjected to P-wave loads. The results indicate that the analytical solutions, simplified numerical solutions, and theoretical results in the literature exhibit strong numerical consistency and similar trends. The analytical results demonstrate that the internal forces in the lining structure increase linearly with seismic intensity, while the effect of loess hardness on the bending moment is more complex. As the loess hardness decreases, the damping effect of the shock-absorbing layer on the internal forces gradually diminishes. Numerical analysis further reveals that reducing the elastic modulus and increasing the thickness of shock-absorbing layer significantly enhance its damping effect on the axial force, although the bending moment slightly increases. Additionally, the shock-absorbing layer effectively reduces the peak stress and strain responses in lining structure, but the peak stress at the hance position increases, with this increase becoming more pronounced as the elastic modulus of the damping material decreases. Moreover, the shock-absorbing layer significantly reduces the peak acceleration response of lining structure but also leads to increased deformation, which progressively intensifies with the thickness of shock-absorbing layer. These findings provide valuable theoretical insights for the seismic design of tunnel structures in loess regions, emphasizing the importance of balancing damping efficiency and deformation control in the lining structure.

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.

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.