Bedrock-soil layer slopes (BSLSs) are widely distributed in nature. The existence of the interface between bedrock and soil layer (IBSL) affects the failure modes of the BSLSs, and the seismic action makes the failure modes more complex. In order to accurately evaluate the safety and its corresponding main failure modes of BSLSs under seismic action, a system reliability method combined with the upper bound limit analysis method and Monte Carlo simulation (MCS) is proposed. Four types of failure modes and their corresponding factors of safety (Fs) were calculated by MATLAB program coding and validated with case in existing literature. The results show that overburden layer soil's strength, the IBSL's strength and geometric characteristic, and seismic action have significant effects on BSLSs' system reliability, failure modes and failure ranges. In addition, as the cohesion of the inclination angle of the IBSL and the horizontal seismic action increase, the failure range of the BSLS gradually approaches the IBSL, which means that the damage range becomes larger. However, with the increase of overburden layer soil's friction angle, IBSL's depth and strength, and vertical seismic actions, the failure range gradually approaches the surface of the BSLS, which means that the failure range becomes smaller.

Considering the occurrence of an earthquake, the bearing capacity of a strip footing placed on a saturated cohesive-frictional soil mass has been computed by performing a pseudo-static rigorous analysis incorporating the existence of (i) excess pore water pressures, and (ii) additional seismic-tractions and body forces. The analysis has been carried out by using lower and upper bounds finite elements limit analysis (FELA) in conjunction with the second order cone programming (SOCP) using the Mohr-Coulomb (MC) yield criterion. The generation of the excess pore water pressure in the event of an earthquake has been incorporated by defining a pore pressure coefficient ru-a ratio of the excess pore water pressure to the total vertical overburden stress at any point. The analysis has revealed that the bearing capacity reduces considerably with an increase in the magnitude of horizontal earthquake acceleration. For a given magnitude of earthquake acceleration, the bearing capacity reduces extensively further with an increase in the value of ru. All the computational results have been presented in a non-dimensional manner, and for the validation purpose, necessary comparisons have also been made. The study will be useful for designing foundations in a seismically active zone.

The finite element method is used to investigate the ultimate lateral pressure of snowflake pile group in undrained clay in this paper. The parametric analyses are performed to study the effects of the geometry of cross-section, the pile-soil adhesion coefficient, the loading direction, and the normalized pile spacing on the ultimate lateral pressure and the damage mechanism of the snowflake pile. The analysis results show that the ultimate lateral pressure of snowflake pile group decreases with the increasing of the length-thickness ratio of the pile flange and increases with the increasing of the pile-soil adhesion coefficient. When the loading direction is considered, the snowflake pile group with the number of piles of 4 is less affected by the loading direction, it has a larger ultimate lateral pressure. The ultimate lateral pressure of the pile group significantly decreases with the increasing of the number of piles. When the pile spacing is smaller, the decreasing of the ultimate lateral pressure is more obvious with the increasing of the number of piles. On the basis of finite element analysis, the empirical formula of ultimate lateral pressure of snowflake pile group is proposed and calibrated with the finite element results.

In existing studies, most slope stability analyses concentrate on conditions with constant temperature, assuming the slope is intact, and employ the Mohr-Coulomb (M-C) failure criterion for saturated soil to characterize the strength of the backfill. However, the actual working temperature of slopes varies, and natural phenomena such as rainfall and groundwater infiltration commonly result in unsaturated soil conditions, with cracks typically present in cohesive slopes. This study introduces a novel approach for assessing the stability of unsaturated soil stepped slopes under varying temperatures, incorporating the effects of open and vertical cracks. Utilizing the kinematic approach and gravity increase method, we developed a three-dimensional (3D) rotational wedge failure mechanism to simulate slope collapse, enhancing the traditional two-dimensional analyses. We integrated temperature-dependent functions and nonlinear shear strength equations to evaluate the impact of temperature on four typical unsaturated soil types. A particle swarm optimization algorithm was employed to calculate the safety factor, ensuring our method's accuracy by comparing it with existing studies. The results indicate that considering 3D effects yields a higher safety factor, while cracks reduce slope stability. Each unsaturated soil exhibits a distinctive temperature response curve, highlighting the importance of understanding soil types in the design phase.

As urbanization accelerates, the demand for efficient underground infrastructure has grown, with rectangular tunnels gaining prominence due to their enhanced space utilization and construction efficiency. However, ensuring the stability of shallow rectangular tunnel faces in undrained clays presents significant challenges due to complex soil behaviors, including anisotropy and non-homogeneity. This study addresses these challenges by developing a novel failure mechanism within the kinematic approach of limit analysis, integrating soil arching effects alongside anisotropic and non-homogeneous undrained shear strength. The mechanism's analytical solutions are rigorously validated against finite element simulations using PLAXIS 3D and existing models, demonstrating superior accuracy. Key findings show that the proposed model improves predictive performance for critical support pressure, with relative differences as low as 5% for wide rectangular tunnels compared to numerical simulations. Results reveal that limit support pressure decreases with increasing non-homogeneity ratios and rises with higher anisotropy factors. However, both effects diminish in wider tunnels, where increasing width in soils with high non-homogeneity and low anisotropy factors significantly enhances stability. Practical implications of this study are substantial, offering design formulas and dimensionless coefficients for estimating critical face pressures in shallow rectangular tunnels. These tools enable engineers to account for soil anisotropy and non-homogeneity, optimizing design and ensuring safety in urban environments. Furthermore, the proposed model's applicability extends to circular tunnels, where it offers comparable accuracy. This study bridges a critical gap in understanding the stability of rectangular tunnels, providing a robust framework for tackling the challenges of modern urban construction.

The study deals with reliability analysis of strip foundation on spatially variable c - phi soil. The spatial variability of soil strength parameters, namely cohesion c and friction angle phi is modelled using anisotropic uncorrelated random fields, generated with the Fourier series method. Random finite element limit analysis (RFELA) providing a rigorous lower and upper bound for bearing capacity for individual Monte-Carlo simulations is employed. Additional use of adaptive meshing refinement algorithm leads to a significant reduction of the relative difference between statistical moments of obtained lower and upper bound results. The influence of the horizontal and vertical scales of fluctuation and foundation depths on the mean and standard deviation of the obtained bound moments is investigated. Additionally, the rigorousness of the mean and standard deviation of both considered bounds estimation is checked. As a result of the analysis, a novel approach based on a mixed distribution that combines lower and upper bound moments is introduced. As shown, this approach offers significant benefits by providing conservative and relatively precise measures of reliability which can be obtained in reasonable computation time. The proposed method seems to be adequate for practical engineering reliability analysis of foundation bearing capacity and other limits states problems.

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek-Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis. (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-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

When a shield tunnel is excavated in water-rich strata with soft upper and hard lower layers, the failure mode of the tunnel face may shift from an overall failure mode to a partial failure mode. To address this issue, three-dimensional discrete failure mechanisms for both partial and overall failure modes are established on the basis of the upper bound theorem and spatial discretization techniques. The influence of pore water pressure is also considered, leading to the development of a method for calculating the critical support force of tunnel faces in such strata, while taking into account both failure modes and the effects of groundwater. Through parameter analysis, factors such as the tunnel diameter, proportion of soft soil, stratum cohesion, and pore water pressure coefficient significantly influence the tunnel face failure mode. A comprehensive critical support force, which takes both partial and overall failure modes into account, is proposed. The parameter analysis reveals that this comprehensive critical support force exhibits complex variations under the influence of multiple parameters. At the same time, a method is proposed to determine the upper and lower bounds of the ultimate support force, based on the calculation results under no seepage and free seepage conditions at the excavation face. The entire method provides a valuable reference for the stability analysis of tunnel faces in water-rich strata with soft upper and hard lower layers.

Sandy cobble soil is a composite made of soil matrix and cobbles, and the estimation of its shear strength always requires expensive large-scale experiments. The strength of the sandy cobble soil exhibits macroscopic anisotropy with respect to the direction of the major stress due to the observed dominant distribution of the cobble dip angle. In the present paper, a numerical homogenization procedure for anisotropic strength identification of the sandy cobble soils is established, which can take into account the influencing factors of the size, shape, and inclination of the cobbles and the mesoscopic strength of the soil-rock interface. To consider the condition of plain strain, the particle size distribution of the cross of the stratum is derived based on the fractal theory and the transformation method of Walraven. The mesostructure of the sandy cobble soils is randomly produced using ellipses to model the cross of the cobbles. An iterative procedure is utilized to represent the major stress orientation-dependent macroscopic strengths. The results are validated against the data from indoor experiments and global mesoscopic computations. It is shown that the macroscopic strength of the sandy cobble mixtures can be accurately determined and the iterative multiscale limit analysis method is reliable and efficient. Parameter analysis is finally conducted to discuss the effect of the mesoscopic properties on the macroscopic strength.

It is well perceived that the shear strength properties of natural soil stratum are inherently anisotropic and spatially heterogeneous due to the depositional, geological and environmental factors. In this study, the concurrent effect of inherent anisotropy and spatial heterogeneity of undrained shear strength of clay on stability of sloped ground is examined by using a numerical lower bound limit analysis approach. The inherent anisotropy of the undrained shear strength of clay is incorporated into the numerical model by the application of an iterative process, and the random field technique is utilized to account for clay's spatial variability. The numerical tool for slope's safety factor determination is based on the combination of lower bound theory, finite element method, second-order conic optimization and the strength reduction method. Probabilistic analyses of slopes with/without external tractions showed a remarkable effect of concurrent consideration of anisotropy and heterogeneity of soil on the evaluated safety factor of slope.