When tunnels in loess traverse sections of alternating soil and rock layers, variations in soil properties can induce an arching effect, potentially leading to the shear failure of the tunnel's structural components. Therefore, seismic design in these areas is particularly crucial. To address these challenges, this paper analyzes the mechanical behavior of damping joints under dynamic earthquake loads using a pseudo-static approach. Based on Bernoulli-Euler beam theory and Pasternak's dual-parameter elastic foundation beam theory, a closed-form solution is derived for the longitudinal response of tunnels in loess with damping joints under seismic loading. The solution is further validated through numerical modeling. Additionally, the study investigates the effects of filling materials (used in damping joints) and design schemes on the effectiveness of damping joints, supported by practical engineering cases. The findings indicate that installing damping joints can reduce the restraining forces on the tunnel lining, allowing the structure to better accommodate the deformation of the surrounding rock. Among the tested materials, rubber was identified as the optimal material for damping joints due to its excellent elasticity and energy absorption capacity. However, the exclusive use of damping joints may result in excessive localized deformation, potentially compromising the tunnel's normal operation. Therefore, careful design of these joints is essential. This research provides theoretical support for the seismic design of tunnels in loess in alternating soil-rock strata.

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.

The hypoplastic theory has gained significant attraction in the geomechanics community for constitutive modeling and numerical simulation. However, the absence of an analytical benchmark for numerical simulations incorporating the hypoplastic model remains a notable gap. This study revisits the basic hypoplastic model for normally consolidated soil, as proposed by Wu et al., by providing explicit formulations of the failure criterion and material parameters. Furthermore, closed-form hypoplastic solutions are derived for normally consolidated soil in three elemental tests: oedometer, simple shear and true triaxial tests. The solutions are assessed by comparing the analytical results with numerical integration and geotechnical test data. Additionally, a novel formula for estimating the at-rest earth pressure coefficient is derived, and compared to the widely adopted Jaky equation. Our solutions not only provide insights into hypoplastic model enhancement but also serve as robust benchmarks for numerical implementations.

Vibration-based damage detection techniques have gained popularity in structural health monitoring due to their non-destructive nature. Most of such damage detection techniques on buildings have developed considering fixed base foundation, that is without considering effect of soil underneath. The objective of the present study is to develop a closed-form expression for determining damage severity in a shear building considering flexible boundary condition that is soil-structure interaction (SSI) using frequency response function (FRF)-based approach. The main concern is to understand the influence of SSI on structural damage quantification during post-seismic mitigation through numerical as well as experimental study. A numerical simulation has been performed on a 14-storey shear building with various soil conditions, namely fixed, dense, medium and soft soil. In the experimental investigation, the dimensions of the soil mass have been considered in such a way that free-field response can be replicated. By similitude laws, a geometric scale factor has been applied to develop a small-scale model and an equivalent shear beam (ESB) container. Damage severity has been determined for both numerical and experimental studies. The effectiveness of the proposed approach has been further studied for a real structure. The novelty of the study lies in the mathematical development involving minimum number of sensors as well as in modelling the effect of semi-infinite soil layer under a scaled-down model. The proposed approach is effective in identifying intermediate and ground storey damage. However, further investigation is required for quantifying complex damage patterns.

In this paper, closed-form expressions to calculate both the mean annual failure rate and the confidence factor are proposed. Reliability indicators are estimated assuming a normalization between capacity and demand called IDC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{DC}$$\end{document}. Simplified closed-form expressions are obtained in accordance with the probability seismic demand analysis used in SAC/FEMA. Uncertainties associated to mechanical, geometrical, and epistemic properties are taken into account, as well as uncertainties related to the occurrence of earthquakes. A comparison of both the mean annual failure rate and the confidence factor with IDC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{DC}$$\end{document} and the expressions proposed by Cornell and collaborators is performed. The numerical approach for the mean annual failure rate is obtained to verify the approximation of the closed-form solutions. Reliability indicators are obtained using six continuous reinforced concrete bridges designed to comply with three drift thresholds (0.002, 0.003 and 0.004). The bridge systems are situated in transition soil of Mexico City. Maximum differences of 4.1% and 10.6% are obtained between the proposed expression and the numerical solution for the mean annual rate of failure, estimated for two limit states: serviceability and collapse. The confidence factor presents differences of 5.2% between the present study and the original formulation.

This study proposes a closed-form solution for axisymmetric electro-osmotic consolidation of unsaturated soil under semi-permeable boundary conditions. The governing equations are formulated to allow for vertical and radial flows of liquid and air phases. The techniques of eigenfunction expansion and Laplace transformation are employed to develop the exact solution for excess pore-air (EPAP) and pore-water pressures (EPWP). The proposed solution is first validated by comparing it to an existing solution, followed by verification through finite element simulations. Both methods of validation confirm the accuracy of the analytical solution. Then, based on the obtained solution, the effects of vertical flow, semi-permeable boundary conditions, electrical voltage, electro-osmosis conductivity and spacing ratio re/rw on the consolidation profile have been further investigated. Parametric studies show that the EPWP at the steady state depends on the electro-osmosis conductivity and applied electricity gradient. In addition, the dissipation rates of EPWP and EPAP in the axisymmetric electro-osmotic consolidation would be underestimated if the vertical flows are neglected. The semi-permeable boundary conditions have great influences on the dissipation rate and the steady-state solution. The proposed solution could serve as a theoretical basis for axisymmetric electro-osmotic consolidation of unsaturated soil.