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Seismic stability analyses of soil slopes in the presence of weak interlayers are rather challenging within the framework of plasticity theory, due to the construction of kinematically admissible velocity fields and statically allowable stress fields at limit state. Finite-element limit-analysis procedures including finite-element upper-bound (FEUB) and finite-element lower-bound (FELB) approach are introduced in this study, retaining the merits of FEM and limit analysis theory to tackle above issues. Incorporating modified pseudo-dynamic approach, seismic slope stability analyses are transformed to linear programming models, in terms of lower- and upper-bound formulations. Pseudo-static and modified pseudo-dynamic solutions of the factor of safety (FoS) are sought through optimization with an interior-point algorithm. An appealing merit of the proposed procedure is that both lower and upper bounds are searched, aiding to better estimate the true solution of FoS. Limit equilibrium and Abaqus are applied to validate FEUB and FELB results. Effects of dual weak interlayers’ position and dimension on seismic slope stability are investigated. Critical failure surface and velocity field are plotted by post-processing, demonstrating a rotational-translational failure mechanism. Based on less than 5% difference between lower- and upper-bound solutions, the proposed procedure is capable of providing a reliable guidance for slope design and assessment.

The probabilistic bearing capacity of the strip footing placed near a two-layered cohesive soil slope is evaluated using random adaptive finite element limit analysis with anisotropic random field modeling and Monte Carlo simulation techniques. To account for the combined effect of geometric parameters (i.e., normalized slope heights, and slope angles), soil properties (i.e., ratio of undrained shear strength from two-layer soils) and spatially variable strengths of two-layered soil, the bearing capacity is quantitatively examined in stochastic analysis. Moreover, a sensitivity analysis is exhibited, and the optimal layout of footings near a two-layered slope is estimated through a multivariate adaptive regression splines procedure. The associated results demonstrate that the slope angle has the most significant impact on the mean bearing capacity, while the coefficient of variation of the ultimate bearing capacity factor could be greatly reduced by decreasing the variability of the upper layer soil. The interaction effects between these influencing factors are numerically investigated. This study highlights the prominent role of the variability in lower layer soil when the coupled influence of geometric conditions and soil properties is considered.

Risk assessment of earth dams is concerned not only with the probability of failure but also with the corresponding consequence, which can be more difficult to quantify when the spatial variability of soil properties is involved. This study presents a risk assessment for an earth dam in spatially variable soils using the random adaptive finite element limit analysis. The random field theory, adaptive finite element limit analysis, and Monte Carlo simulation are employed to implement the entire process. Among these methods, the random field theory is first introduced to describe the soil spatial variability. Then the adaptive finite element limit analysis is adopted to obtain the bound solution and consequence. Finally, the failure probability and risk assessment are counted via the Monte Carlo simulation. In contrary to the deterministic analysis that only a factor of safety is given, the stochastic analysis considering the spatial variability can provide statistical characteristics of the stability and assess the risk of the earth dam failure comprehensively, which can be further used for guiding decision-making and mitigation. Besides, the effects of the correlation structure of strength parameters on the stochastic response and risk assessment of the earth dam are investigated through parametric analysis.

The cap geometry and formation mechanism play a key role in influencing the hole-making quality on the bore exit side and must be the focus of research in orbital drilling of aeronautical metal materials. For a “bowl shape” cap geometry formed in orbital drilling process, the corresponding undeformed cap periphery geometry, generated by the cap periphery cutting edges, is simulated and given the parametric description. Especially, the cap periphery is simplified as a simply supported annular plate under uniform load with arbitrary loading radius based on the characteristics of the cap periphery shape and mechanical analysis of processing. Then its unified plastic limit analysis is developed. The ultimate load, stress field, and plastic deformation at the periphery of the cap are derived from the unified strength theory. Furthermore, the numerical solutions are obtained in terms of the Tresca yield, Huber–von Mises, and twin-shear yield criteria. The conclusions enabled an in-depth understanding of the cap periphery formation mechanism in the orbital drilling of holes from the unified plastic limit analysis perspective.

Highlights•A state of art approach to evaluate the elliptical tunnel stability of Hoek–Brown rock mass.•Rigorous upper bound and lower bound solutions of elliptical tunnel stability are derived using advanced finite element limit analysis.•Comprehensive design tables and equations are proposed for stability evaluation.

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.

Accurately estimating the stability of horseshoe tunnel faces remains a challenge, especially when excavating in rock masses. This study aims to propose an analytical model to analyze the stability of the horseshoe tunnel face in rock masses. Based on discretization and “point-by-point” techniques, a rotational failure model for horseshoe tunnel faces is first proposed. Based on the proposed failure model, the upper-bound limit analysis method is then adopted to determine the limit support pressure of the tunnel face under the nonlinear Hoek–Brown failure criterion, and the calculated results are validated by comparisons with the numerical results. Finally, the effects of the rock properties on the limit support pressure and the 3D failure surface are discussed. The results show that (1) compared with the numerical simulation method, the proposed method is an efficient and accurate approach to evaluating the face stability of the horseshoe tunnel; (2) from the parametric analysis, it can be seen that the normalized limit support pressure of the tunnel face decreases with the increasing of geological strength index, GSI, Hoek–Brown coefficient, mi, and uniaxial compressive strength, σci, and with the decreasing of the disturbance coefficient of rock, Di; and (3) a larger 3D failure surface is associated with a high value of the normalized limit support pressure.

The aim of this paper is to present an in-depth numerical investigation on the statics of historical masonry stellar vaults, a special class of masonry ribbed vaults whose three-dimensional geometry features a star-shaped projection on the horizontal plane. In particular, the mechanical behavior of the masonry stellar vault belonging to the church of Santa Maria del Monte in Cagliari (Italy) is analyzed and illustrated as an especially meaningful case study. This church, which was built during the second half of the sixteenth century, is a beautiful example of Gothic-Catalan style, and its ribbed stellar vault is one of the most representative of this type in the town of Cagliari. The geometric outline of the vault has been obtained through laser scanning techniques and a procedure of reverse engineering. Starting from a three-dimensional representation of its geometry, the ultimate load-bearing capacity of the stellar vault can be accurately estimated through a recently developed, NURBS-based upper-bound limit analysis scheme. A comparison with incremental nonlinear analyses carried out with the commercial finite element code DIANA is presented. Furthermore, the paper also includes a sensitivity study aimed at investigating the role of ribs on the ultimate load-bearing capacity of the structure.

This study investigates the effect of multivariate cross-correlated random fields on the failure behaviour of passive trapdoors in c-ϕ soil utilising random finite element limit analysis (RFELA). Failure mechanisms of a trapdoor in c-ϕ soil depend on an activity of the soil unit weight (γ), thus triggering downward and a restriction of soil shear strength (c, ϕ). The cross-correlated coefficients between any two soil parameters were used to generate the spatial variability of correlation, single and multiple dependent random fields. The failure mechanism and probability of design failure were explored with these random fields for a shallow to a deep passive trapdoor in c-ϕ soil. The results indicated that considering the greater cross-correlated coefficients produced a lower probability of design failure. Ignoring multivariate cross-correlated random fields can result in either an underestimation or an overestimation of the probability of design failure, depending on the specific scenarios. This study also provided a required factor of safety to satisfy the probability of design failure for each random field and normalised depth of the trapdoor. Additionally, the multivariate adaptive regression spline model was applied to predict passive load, thereby reducing computational time in practical applications.

The experimental data shows that most rocks behave nonlinearly in nature. The modified nonlinear Hoek–Brown failure criterion was considered to investigate the bearing capacity problem of shallow rigid foundations on rock masses subjected to horizontal seepage forces. Two multi-wedge translational failure mechanisms, including symmetrical and non-symmetrical mechanisms were used in the closed-form of the upper bound method of the limit analysis theory. The symmetrical failure mechanism was used in the case of no seepage, while the seepage effect was considered in the non-symmetrical mechanism. The variation of seepage forces was obtained as a function of gradient ratio i(γw/γsub) in the developed formulation. The bearing capacity coefficients Nγ, Nq and Nσ are introduced for the case of seepage flow condition. The results show that the magnitude of the bearing capacity coefficients reduces continuously with an increase in the value of gradient ratio i(γw/γsub). The obtained results were compared and offered for functional use in foundation engineering.