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The frame beam anchor plate is a new supporting structure reinforcing fill slopes. At present, only a few studies have evaluated its static stability based on the two-dimensional plane assumption. In this paper, the limit analysis method is combined with the three-dimensional spiral failure mechanism to evaluate the factor of safety (Fs) of a slope supported by a frame beam anchor plate. The pseudo-static approach is used to express the seismic effects. When calculating the internal energy dissipations, both the pull-out failure of anchor plates and tensile failure of tie rods are considered. The accuracy of the approach is verified by comparison with calculation results from the finite element method. Parameter analysis summarizes the influence law of each supporting structure design parameter on the Fs. Therefore, this study develops a theoretical basis for evaluating slope stability reinforced by frame beam anchor plates, which can better guide the design of slopes reinforced by this supporting structure. [ABSTRACT FROM AUTHOR]

Host rock deformation associated with sill emplacement is used to constrain magma transfer and storage within the upper crust. In contrast to classic models suggesting that the host rock above mafic sills is dominated by elastic bending, recent studies show that bounding faults that limit the uplift area can occur at the peripheries of a mafic sill. However, the accurate dip of this type of fault, named peripheral faults here, is still not well constrained. Their origin is also controversial in some cases. In this study, kinematic modeling and limit analysis are performed to better constrain the structure and mechanical properties of the peripheral faults based on seismic interpretation of a mafic sill from the Tarim Basin, China. The trishear kinematic model successfully reproduces peripheral faulting and associated folding of the host rock by performing a displacement of 58 m on a vertical fault plane with a fault propagation (P) to fault slip (S) ratio of 2.5. The limit analysis also predicts vertical damage at the sill tip by sill inflation. These results suggest that the dip angle of the fault in the case study is 90°, which is more accurate than that from the seismic interpretation with an 88° inward dip. This value may vary in other cases as it depends on the sill geometry (such as diameter and inclination), thickness, depth, and mechanical properties of the host rock. The study supports that peripheral faulting and associated folding can occur at the tips of the mafic sill due to the vertical uplift of the host rock caused by sill inflation. It is also suggested that trishear kinematic modeling and limit analysis are effective methods for studying the geometry of peripheral faults. [ABSTRACT FROM AUTHOR]

Reasonable support force is crucial for the stability of the excavation face in sandy pebble tunnels. By utilizing the existing failure mode of the logarithmic spiral curve, this study combined the collapse arch model with the limit analysis method to establish a failure model for the excavation face in sandy pebble tunnels. A calculation method for the ultimate supporting force applicable to the excavation face of sandy pebble tunnels was also proposed. Then, the theoretical analysis presented in this paper was compared with numerical simulation and existing theories to determine the failure areas under different internal friction angles and cohesion values. Finally, the excavation face stability of a shield tunnel in Beijing was analyzed using theoretical analysis and numerical simulation methods. The results showed that the analytical solution proposed in this paper was in good agreement with the limit supporting force derived from existing research, with convenient and accurate calculations. The limit supporting force decreased nonlinearly with the increase of the internal friction angle, and was more sensitive to changes in the friction angle when the angle was small. The limit supporting force decreased approximately linearly with the increase in cohesion. When the burial depth was small, it had a more significant impact on the limit supporting force. When the C / D ratio exceeded 1. 0, the increase of the burial depth of the tunnel had no obvious effect on the limit supporting force, and the friction angle had a very significant effect on the failure area. With the increase of internal friction angle, the failure area decreased significantly. Cohesion had little impact on the failure area, i. e., the size of the energy dissipation surface remained nearly unchanged under different cohesion values. For the shield tunnel in Beijing, the calculation based on the limit analysis method optimized the collapse range and shape, making the failure mode more reasonable while increasing the failure range, achieving excellent engineering application results. [ABSTRACT FROM AUTHOR]

Groups of contiguous unreinforced stone masonry buildings are a common type of housing seen in old European downtowns. However, assessing their response to earthquakes poses several challenges to the analysts, especially when the housing units are laid out in compact configurations. In fact, in those circumstances a modeling technique that allows for the dynamic interaction of the units is required. The numerical study carried out in this paper makes use of a rigid block modeling approach implemented into in-house software tools to simulate the static behavior and dynamic response of an aggregate stone masonry building. Said approach is used to reproduce the results of bi-axial shake-table tests that were performed on a building prototype as part of the activities organized within the Adjacent Interacting Masonry Structures project, sponsored by the Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe. The experimental mock-up consisted of two adjacent interacting units with matching layout but different height. Two rigid block models are used to investigate the seismic response of the mock-up: a 3D model allowing for the limit analysis of the building on one hand, and a 2D model allowing for the non-linear static pushover and time-history analysis on the other. The 3D model was built for the blind prediction of the test results, as part of a competition organized to test different modeling approaches that are nowadays available to the analysts. The 2D model was implemented once the experimental data were made available, to deepen the investigation by non-linear static pushover and time-history analysis. In both models, the stonework is idealized into an assemblage of rigid blocks interacting via no-tension frictional interfaces, and mathematical programming is utilized to solve the optimization problems associated to the different types of analysis. Differences between numerical and experimental failure mechanisms, base shears, peak ground accelerations, and displacement histories are discussed. Potentialities and limitations of the adopted rigid block models for limit, pushover and time-history analyses are pointed out on the basis of their comparisons with the experimental results. [ABSTRACT FROM AUTHOR]

The soil is usually unsaturated in practical engineering, and the slope failure surface generally presents three-dimensional (3D) characteristics. Therefore, the traditional plane problem calculation method does not accurately describe the slope's stability and safety assessment results strengthened through frame beam anchor plates (FBAPs). This work introduces a novel approach based on the limit analysis (LA) technique for assessing the 3D stability of unsaturated soil slopes supported by FBAPs to address this issue. The slope safety factor (Fs) expression was derived based on the energy balance principle. The soil slope stability the FBAP reinforces was quantitatively expressed as a function of slope parameters. Nonlinear distribution features of soil matrix suction and effective unit weight, as well as the internal energy dissipation rate created by the anchor plate, must be taken into account when calculating the internal energy dissipation and external work rate. The impact of the 3D effect, seismic parameters, unsaturated soil characteristics, and supporting structure on slope stability was discussed. Some design suggestions for slope reinforcement are put forward. According to the findings, the suction effect's beneficial effects on stability should be considered. Slopes with a width-to-height ratio (B/H) of less than 10 should consider the 3D effect's beneficial effects. The seismic action significantly negatively impacts slope stability, while using FBAP reinforcement structures can dramatically improve slopes' static and seismic stability. [ABSTRACT FROM AUTHOR]

The critical aspect of the seismic bearing capacity of footings holds significant importance in the field of geotechnical engineering. Past research has primarily focused on deterministic analyses, mainly neglecting or ignoring the spatial variability of the soil. This study aims to address this gap by employing a probabilistic approach to assess the seismic bearing capacity of foundations while considering the seismic force effect by adopting the pseudo-static approach. To achieve this goal, this study utilizes the random adaptive finite element limit analysis technique and Monte Carlo simulations to cover a wide range of potential outcomes, taking into account the uncertainties in the parameters. This research investigated the influence of soil strength variability on three key factors: the horizontal seismic coefficient, coefficient of variation, and dimensionless correlation length. The study revealed that an increase in the coefficient of variation of the undrained shear strength (COVsu) and the dimensionless correlation length (Θsu) leads to a reduction in the mean of the random seismic bearing capacity factor (μNran). Conversely, the horizontal seismic coefficient (kh) negatively impacts the seismic bearing capacity, thereby diminishing the overall soil stability. Additionally, the factor of safety must be selected with caution to ensure that the probability of failure is less than a specified value, particularly when the coefficient of variation of the undrained shear strength (COVsu) is high. To establish surrogate models capable of predicting the random seismic bearing capacity, multivariate adaptive regression spline (MARS) models have been developed. Utilizing the proposed MARS surrogate models offers a more convenient and computationally efficient means of evaluating the impact of variability in soil strength properties on geotechnical stability calculations. [ABSTRACT FROM AUTHOR]

Abstract The frame beam anchor plate is a new supporting structure reinforcing fill slopes. At present, only a few studies have evaluated its static stability based on the two-dimensional plane assumption. In this paper, the limit analysis method is combined with the three-dimensional spiral failure mechanism to evaluate the factor of safety (Fs) of a slope supported by a frame beam anchor plate. The pseudo-static approach is used to express the seismic effects. When calculating the internal energy dissipations, both the pull-out failure of anchor plates and tensile failure of tie rods are considered. The accuracy of the approach is verified by comparison with calculation results from the finite element method. Parameter analysis summarizes the influence law of each supporting structure design parameter on the Fs. Therefore, this study develops a theoretical basis for evaluating slope stability reinforced by frame beam anchor plates, which can better guide the design of slopes reinforced by this supporting structure.

Degradation of rock mass produced by rock blasting, stress relief, and other causes is an important factor in the assessment of rock strength. Quantified as a disturbance factor, such degradation varies depending on blasting control, stress state and stress relief, and rock mass quality. This study focuses on the impact of disturbance on the safety of slopes. The disturbance in the rock mass is characterized by the geometry of the disturbed zone, its size, the magnitude, and the decaying rate with the distance away from the slope surface. A method accounting for decay of rock disturbance is presented. A study of the impact of rock disturbance characteristics on the quantitative stability measures of slopes was carried out. These characteristics included disturbed zone geometry, its thickness, the maximum magnitude of the disturbance factor, and the rate of disturbance decaying. The thickness of the disturbed zone and the maximum factor of disturbance were found to have the greatest impact. For example, the factor of safety for a 45° slope in low-quality rock mass can decrease from 1.96 to 1.09 as the thickness of the disturbed zone increases from 1/4 of slope height H to the double of H and the maximum disturbance factor increases from 0.5 to 1. Uniform thickness of a disturbed zone was found to yield more conservative outcomes than the triangular zones did. The critical failure surfaces were found to be shallow for high rates of disturbance decay, and they were the deepest for spatially uniform disturbance factors.

A prediction model for the bearing capacity estimation of strip and ring footing embedded in layered sand is proposed using soft computing approaches, namely, artificial neural network (ANN) and random forest regression (RFR). The required data for the model preparation were generated by performing lower- and upper-bound finite-elements limit analysis by varying the properties of the top and bottom layers. Two types of layered sand conditions are considered in the study: (a) dense on loose sand; (b) loose on dense sand. The investigation for strip footing was carried out by varying the thickness of the top layer, embedment depth of the foundation and friction angles of top and bottom layers. For a ring footing, the internal-to-external diameter ratio forms an additional variable. In total, 1222 and 4204 data sets were generated for strip and ring footings, respectively. The performance measures obtained during the training and testing phase suggest that the RFR model outperforms the ANN. Also, following the literature, an analytical model was developed to predict the bearing capacity of strip footing on layered sand. The ANN and the generated analytical model predictions agreed with the published experimental data in the literature. [ABSTRACT FROM AUTHOR]

Research on the stability of tailings dam is often achieved through the finite element method with strength reduction. The influence of shear strength parameters(c) of tailings dam stability varies. In this paper, the theory of shortest path strength reduction is introduced to conduct a stability analysis of a large tailings dam in Northeast China. The main conclusions are as follows: 1) Approximating the actual unit weight of tailings using Optum G2, stability analysis of tailings dam with shortest path strength reduction under seepage conditions is conducted to obtain the minimum safety factor of the slope and potential failure surfaces. 2) During unequal strength reduction, as the reduction ratio increases, the length of the reduction path first decreases and then increases, indicating that the minimum safety factor obtained by the shortest reduction path corresponds to the most unfavorable limit state of the tailings dam. 3) The minimum safety factor obtained through the limit analysis of shortest path strength reduction is slightly lower than the results of the Swedish slip circle method and simplified Bishop method, but overall, it is in good agreement. 4)With the increase in height of the tailings dam, the minimum safety factor continues to decrease, and the range of potential sliding bodies of the tailings dam increases, with the corresponding sliding surface expanding towards the reservoir. [ABSTRACT FROM AUTHOR]

An innovative approach that combines isogeometric analysis (IGA), limit analysis, machine learning, and the multivariate adaptive regression splines (MARS) model is presented in this paper to investigate sinkhole stability of circular cavity. The upper bound limit analysis method using IGA and second-order cone programming (SOCP) is employed to analyze circular cavity stability. Based on Bézier extraction, the non-uniform rational B-spline (NURBS) is used to generate a set of NURBS surfaces that define the boundary of the soil domain. The proposed approach is validated through comparative analysis with previous studies, demonstrating its effectiveness in accurately predicting soil stability. A large dataset consisting of 5000 randomly generated runs is used to train the machine learning algorithm that is integrated with the MARS model. The results show high accuracy, with a small mean squared error of 10–3, in predicting the undrained stability of circular cavities. The integration of IGA, limit analysis, machine learning, and the MARS model contributes significantly to advancing computational techniques for assessing soil stability. The proposed approach offers a comprehensive and precise tool for engineers and researchers, providing an accurate design formula for evaluating the undrained stability of circular cavities. [ABSTRACT FROM AUTHOR]

A novel unified numerical limit analysis method is proposed to study variably saturated soils reinforced by flexible inclusions. An effective stress-based criterion is utilized to determine the shearing resistance of variably saturated soil-reinforcement interfaces, which is verified through available experimental results. Soils are then treated as single-phased materials and equivalent forces are respectively established within the soil mass and along the interface. In this way, the role of matric suction profiles in stabilizing the reinforced soils under different hydraulic conditions can be analyzed in a more efficient way. To represent the limited tensile strength and negligible compressive strength of the flexible reinforcement, a strategy is proposed to calculate its plastic dissipation rate without the incorporation of stress variables. Plastic dissipation rates of the soil, the reinforcement, and their interfaces are computed using only kinematic variables. The solution domains of the soil, the reinforcement, and the interface are discretized using linear and constant strain finite elements, respectively. Finally, numerical examples are provided to discuss the effect of matric suction on the stability of reinforced structures made of marginal soils. [ABSTRACT FROM AUTHOR]

Seismic activity on a tunnel damages the tunnel support systems. The extent of the tunnel damage depends on the soil type, the magnitude of the earthquake acceleration, and the tunnel cover depth. Hence, analyzing the stress induced by the seismic event from the surrounding ground on the tunnel facilitates a safe tunnel design. Based on the pseudostatic method, this study examined the seismic stability of square and rectangular tunnels placed in cohesive-frictional soil. The tunnel collapse load was found using the lower-bound theorem of limit analysis in combination with the finite-element method. From the distribution of stresses along the periphery, the normal stress at each tunnel node was calculated, and the maximum of stresses was reported as the support pressure. Thus, the systems safeguarding the tunnel against devastating lateral earthquake forces are expected to offer the ultimate resistance equal to the maximum normal stress on the tunnel periphery. With the increase in tunnel cover depth, aspect ratio, seismic acceleration coefficients, and a decrease in soil cohesion and friction angle, the support pressure was noted to enhance. The distribution of normal stresses around the tunnel periphery depends on the tunnel geometry, the soil's shear strength parameters, and the magnitude of earthquake acceleration. For a square tunnel, the magnitude of stress was maximum on the walls, followed by the roof and base, implying that collapse will be more prone from the side walls. However, the rectangular tunnels are noted to be susceptible to collapse from the roof, followed by walls and base. [ABSTRACT FROM AUTHOR]

The paper proposes a refined CT-based FE modelling strategy that implements a limit analysis numerical procedure, namely the Elastic Compensation Method (ECM), to estimate a lower bound to the collapse load of a human femur. In particular, the model geometry was obtained from CT images by segmentation of a fresh-frozen human cadaveric femur that was discretized with second-order tetrahedral 3D finite elements. A yield criterion of Tsai–Wu-type, expressed in principal stress space, was adopted to model the bone tissues for which the strength limit values in tension, compression and shear are computed locally from the femoral density distribution also derived from CT images. The developed CT-based numerical technique showed the ability to predict, at least for the examined femur for which the experimental collapse load is available, a lower bound to the collapse load. The proposed approach seems a promising and effective tool that could be adopted into clinical practice to predict the fracture risk of human femur starting from patient-specific data given by medical imaging. [ABSTRACT FROM AUTHOR]

Existing methods for calculating the ultimate support pressure of tunnel faces do not consider the control of seepage flow. Therefore, a model for calculating the ultimate support pressure under seepage conditions was established based on a two-dimensional water head distribution model and the upper bound theorem of limit analysis. The reliability of this method was verified through comparisons with other studies. Subsequently, the influence of water level and tunnel face water pressure coefficient on stability was analyzed. The results indicate that the ultimate support pressure is linearly positively correlated with the water level and tunnel face water pressure coefficient; as the water level increases and the water pressure coefficient decreases, the failure area extends and enlarges. Finally, an existing seepage flow calculation formula was introduced, and a method for calculating the ultimate support pressure based on seepage control was proposed. The appropriate tunnel face water pressure coefficient is determined through the seepage flow calculation formula, and the corresponding ultimate support pressure is then calculated. The results demonstrate that this method can provide better theoretical guidance for seepage control in tunnel faces in practical engineering. [ABSTRACT FROM AUTHOR]

Material optimization was one of the challenges for achieving cost-competitive solutions when concrete was introduced in construction, leading to new structural shapes for both civil works and buildings. As concrete construction became dominant, saving material was given less significance, and the selection of the structural typology was mostly influenced by construction or architectural considerations. Simple and non-time-consuming methods for building thus arose as the dominant criteria for design, and this led to the construction of less efficient structures. Currently, the awareness of the environmental footprint in concrete construction has brought the focus again to the topic of structural efficiency and material optimization. In addition, knowledge of material technology is pushing the use of cements and binders with lower environmental impact. Within this framework, Fiber-Reinforced Concrete (FRC) has been identified as a promising evolution of ordinary concrete construction. In this paper, a discussion is presented on the structural properties required for efficient design, focusing on the toughness and deformation capacity of the material. By means of several examples, the benefits and potential application of limit analysis to design at the Ultimate Limit State with FRC are shown. On this basis, the environmental impact of a tailored mix design and structural typology is investigated for the case of slabs in buildings, showing the significant impact that might be expected (potentially reducing CO2-eq emissions to half or even less in slabs when compared to ordinary solutions). [ABSTRACT FROM AUTHOR]

This paper presents a novel analytical approach for predicting the volume loss of a tunnel face during advancement with different longitudinal slope angles. The proposed approach utilizes the continuous velocity field of a circular tunnel face in undrained clay and combines the upper-bound limit analysis with the mobilized strength design method to derive the relationship between the load factor and the volume loss. An analytical expression is proposed for the relationship between the face support pressure and surface deformation, accounting for the longitudinal slope angle. Parametric studies are conducted to explore the impact of the longitudinal slope angle on the ground surface settlement during tunnel face advancement. The results reveal that the ground surface settlement increases with the tunneling longitudinal gradient in a downward direction but decreases for tunneling in an upward direction when the supporting pressure remains unchanged and the ground surface is horizontal. As the tunneling direction is parallel to the inclined ground surface, the impact on the ground surface settlement becomes more significant and cannot be ignored in engineering practice. [ABSTRACT FROM AUTHOR]

This paper presents a generalised Newmark method (GNM) incorporating a displacement hardening mechanism for the prediction of permanent displacements accumulated by diaphragm walls during earthquakes. A key feature of the proposed approach is the adoption of an evolution law for the critical acceleration, which links its current value to the accumulated wall permanent displacements. This displacement hardening mechanism is based on a simplified relation between the average plastic shear deformations experienced by the passive zone of soil below dredge level and the mobilised soil friction angle. This relation is determined indirectly by the evolution of the passive earth-pressure coefficient with wall displacement/rotation, as obtained in quasi-static model wall experiments. The proposed approach has been validated by comparing its predictions with the experimental data obtained in centrifuge model tests of cantilevered and propped walls. In spite of the simplifying assumptions on which it is based, the GNM has demonstrated that it is capable of capturing the essential features of the retaining structures' kinematics and provides realistic predictions of permanent wall displacements. [ABSTRACT FROM AUTHOR]

A seismic-induced landslide is a common geological catastrophe that occurs in nature. The Wangjiayan landslide, which was triggered by the Wenchuan earthquake, is a typical case in point. The Wanjiayan landslide caused many casualties and resulted in enormous property loss. This study constructs a simple surficial failure model based on the upper bound approach of three-dimensional (3D) limit analysis to evaluate the slope stability of the Wangjiayan case, while a traditional two-dimensional (2D) analysis is also conducted as a reference for comparison with the results of the 3D analysis. A quasi-static calculation is used to study the effect of the earthquake in terms of horizontal ground acceleration, while a parametric study is conducted to evaluate the critical cohesion of slopes. Rather than employing a 3D analysis, using the 2D analysis yields an underestimation regarding the safety factor. In the Wangjiayan landslide, the difference in the factors of safety between the 3D and 2D analyses can reach 20%. The sliding surface morphology as determined by the 3D method is similar to actual morphology, and the parameters of both are also compared to analyze the reliability of the proposed 3D method. [ABSTRACT FROM AUTHOR]

This article introduces an innovative approach to optimize steel reinforcement in reinforced concrete structures using the equilibrium-based formulation described in Ferradi et al. (Comput Struct 286:107095, 2023). The objective is to enhance structural performance and cost-effectiveness by efficiently distributing steel reinforcement within an arbitrary volume representing the concrete, while ensuring external loading equilibrium. To achieve this goal, two approaches are proposed: the first approach focuses on optimizing the cross section of 1D rebars that are already defined in the concrete volume as curves, while the second approach optimizes the steel bulk densities throughout the entire volume, with or without assuming predetermined principal directions for the reinforcement, represented by a steel stress tensor. The latter approach does not rely on any prior knowledge of the geometric distribution of rebars and can be seen as an automated strut and tie method for three-dimensional problems , where the struts are derived from the compression flow, and the ties originate from the tensile flow. Both approaches are formulated as optimization problems, enabling the utilization of the interior point method for effective problem-solving. Numerical examples and comparisons with existing results vividly illustrate the flexibility and potential efficiency gains achievable through the proposed approaches. [ABSTRACT FROM AUTHOR]

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Due to natural sedimentation and artificial filling, slopes exhibit heterogeneity in the form of multi-layer soils, namely, layered slopes. Compared with homogenous slopes, the failure mechanism of layered slopes is more complex owing to the different shear strengths of each soil layer. Therefore, it is of great importance to gain insight into the stability of layered slopes. In this study, the upper bound theorem of limit analysis incorporated with a pseudo-static approach is utilized to investigate the seismic stability of two kinds of two-layered slopes: one with a stiff lower soil layer and the other with a weak lower soil layer. Three failure patterns, namely face failure, toe failure and base failure, are taken into account. A depth coefficient (Δ) is introduced to describe the distribution of two soil layers. The layer-wise summation method is adopted to calculate the safety factor and yield acceleration coefficient more conveniently. Based on Newmark's method, the earthquake-induced horizontal displacement is estimated. The calculated results are validated by comparisons with published literature and the numerical method in terms of safety factor, critical failure surface and yield acceleration coefficient. The results show that the depth coefficient has a significant influence on the failure mechanism of two-layered slopes by determining whether the stability of upper-layered soil is dominant in the overall slope stability or not. Inaccurately identifying the failure patterns will overestimate the seismic performance of two-layered slopes in the aspects of safety factor and yield acceleration coefficient, leading to an underestimation of earthquake-induced horizontal displacement. [ABSTRACT FROM AUTHOR]

High geostress, a typical attribute of tunnels located at significant depths, is crucial in causing stress-induced failure and influencing the stability of the tunnel crown. This study developed an analytical method for the failure mechanism that occurs in deep-buried tunnel roofs, taking into account the influence of geostress. The limit analysis theory was utilized for deriving analytical solutions about the geometry of the collapsing surface and the limit supporting pressure. The collapsing surface obtained by the analytical solution was validated by the findings of the physical model test, which shows a high level of agreement with the actual one. An extensive investigation was done to explore the effects of the lateral pressure coefficients, the tunnel buried depth, the geological conditions of the surrounding rock, the long-short axis ratio, and the size of the tunnel profile. The findings indicate that an increase in the lateral pressure coefficient from 0.5 to 1.5 results in a reduction in the height of the collapsing zone by 2.08 m and the width of the collapsing zone by 1.15 m, while simultaneously increases the limit supporting pressure by 18.9%. The proposed upper bound method accurately determines the limit supporting pressure and the geometry of the collapsing surface, which aligns well with the results acquired through numerical modelling and on-site monitoring in actual engineering applications. The proposed analytical method can serve as a reference for similar crown failure issues of deep-buried tunnels. [ABSTRACT FROM AUTHOR]

In this work, the three‐dimensional stability of deep tunnel faces is evaluated in rock masses characterized by the generalized Hoek–Brown (H–B) criterion from the perspective of the limit analysis theorem. Considering that underground engineering is gradually developing towards larger burial depths and larger sizes, and the tensile strength of rocks is usually overestimated, the concept of tension cutoff (T‐C) is introduced to substitute the parabolic form of the H–B envelope in the tensile region with a circular arc. The multitangent technique is used to piecewise approximate the H–B envelope, instead of the conventional linear substitution, accounting for the nonlinear dependence of the shear strength on the pressure. Meanwhile, the earthquake loading is considered by the classic pseudostatic method. The tunnel face stability is measured by a stability number, which is calculated based on a newly developed multicone failure mechanism. Parameter studies indicate that the T‐C has almost no impact on the critical support pressure, while has a significant effect on the critical stability number, especially in the presence of earthquakes. Nearly all stress points back‐calculated from the rupture angles fall within the T‐C region, except for the first stress point associated with the first segment. Interestingly, the influence of the geological strength index (GSI) on the face stability is inverse to that of mi due to the brittleness of rocks. Moreover, the critical stability number is not sensitive to mi, but sensitive with the introduction of earthquake loadings. [ABSTRACT FROM AUTHOR]

AbstractUnder the nonlinear Mohr-Coulomb (MC) failure criterion, based on the upper-bound limit analysis theorem, the three-dimensional(3D) stability of piled unsaturated inhomogeneous slopes is analyzed. By incorporating the nonlinear strength parameters ct and φt, the energy balance equation is established, and the explicit expression of slope safety factor (FS) is derived by the gravity increase method (GIM). In addition, a genetic algorithm (GA) is used to calculate the minimum FS. The results obtained were compared with those of existing literature to verify the effectiveness of the method used in this paper. The influence of nonlinear parameters on slope stability was studied through parameter analysis. The results show that the nonlinear parameters of soil have a significant influence on the stability of piled slopes. The FS increases with the increase of nonlinear coefficient and uniaxial tensile strength and decreases with the increase of initial cohesion of soil. In addition, the critical slip surface of the slope becomes shallower with the weakening of soil nonlinearity. Furthermore, ignoring the suction effect will overestimate the slope stability, and the slope stability intensified with decreased soil inhomogeneity. [ABSTRACT FROM AUTHOR]

A displacement-based dislocation map has been used to build the eigenstress stress, which is the base of the structure's limit analysis. The limit load has been calculated as the upper bound of any equilibrated stress that respects the compatibility inequalities by means of a linear optimization program. The eigenstress stress nodal parameters were assumed as the design variables, and the compatibility inequalities have been obtained from the Mises–Schleicher criterion, assuming that the stress belongs to the corresponding plastic domain. The numerical application has considered a linear secant representation of the domain, with a penalty factor on stresses, to correct the linearization error. Examples concerning a simply supported cantilever beam, a pipe section, and a plate with a circular hole highlighted the accuracy of the procedure with respect to the established literature. Moreover, the procedure has been applied to investigate plane structure examples. A square plate with variable elliptic holes has been analyzed, and the influence of ellipticity on the collapse load has been shown. The effects of porosity and heterogeneity of the structure with respect to the collapse load are shown considering the porous cantilever and representative volume element. The evaluation of the limit load along different element directions envisaged a point-wise calculation of the compatibility domain of the porous material to be used in the macro-scale analysis of the structures made of porous micro-cells. [ABSTRACT FROM AUTHOR]

Tunneling efforts that use shield machines often encounter weak and fractured rock formations, where the stability of the tunnel face is the principle safety control factor during tunnel construction operations. Within the framework of the limit analysis method, an improved model was proposed. The model consists of two failure modes, effectively addressing the shortcomings that arise from the incomplete contact interface between the traditional model and the tunnel face. Furthermore, the proposed model introduces the nonlinear Hoek–Brown criterion and improves the shape of the sliding failure surface within the cover layer to account for the arching effect. Subsequently, the proposed model was validated by comparison with numerical simulations and results in the literature. Further parameter analysis was conducted to investigate the influence that the Hoek–Brown parameters and tunnel depth have upon the critical support pressure and effectively identify the characteristics of failure mechanisms. The resulting data show that a reduction in the geological strength index (GSI), Hoek–Brown parameter (mi), or uniaxial compressive strength (σci) or an increase in the disturbance coefficient (D) leads to a nonlinear increase in the critical support pressure and an expansion of the failure zone of the tunnel face. Conversely, as the tunnel depth increases, the extent of the failure zone gradually expands, and the stability of the tunnel face exhibits a trend of initially decreasing and then increasing. [ABSTRACT FROM AUTHOR]

The fundamental issue of bearing capacity of footings on anisotropic clays holds significant importance in geotechnical engineering. Previous investigations predominantly focused on deterministic analyses, disregarding the spatial variability of soil. A probabilistic analysis of the bearing capacity of footings is conducted in this paper, incorporating the spatial variability of anisotropic clays. To achieve this, Random Adaptive Finite Element Limit Analysis (RAFELA) and Monte Carlo simulations are utilised to capture the full spectrum of potential outcomes under parametric uncertainty. The impact of anisotropic soil strength variability is explored across three input parameters such as the anisotropic strength ratios, coefficients of variation, and dimensionless correlation lengths. In order to establish surrogate models capable of predicting random bearing capacity of anisotropic clays, Artificial Neural Network (ANN) models are developed. The use of the proposed ANN surrogate models presents a more convenient and computationally efficient approach for predicting the ultimate vertical load of footings on spatially random anisotropic clays. [ABSTRACT FROM AUTHOR]

Evaluation of seismic bearing capacity is to be vital for design of strip foundations in earthquake areas. Combining the upper bound theorem of limit analysis, the discrete technique is successfully extended in this study to investigate the seismic ultimate bearing capacity of shallow strip foundations on rock masses considering the Rayleigh waves, in which the nonlinear HB failure criterion is used to describe the constitutive relation of rock masses. The failure model of foundation soil is generated using the discretization method, a “point by point” technique. The variations of shear modulus G of rock masses and seismic acceleration varying with the depth are taken into consideration. The generalized tangential technique is employed to avoid the difficulty resulting from the nonlinear HB failure criterion. A linear corresponding to the Mohr–Coulomb failure criterion, tangent to the nonlinear Hoek–Brown failure criterion, is used to derive the objective function that is to be minimized. By comparing with the existing results, the present approach is verified. The widely parametric studies are made to investigate the effect of different parameters, e.g. shear modulus G, mi, GSI, σci, γ, D, VR, on the seismic bearing capacity of strip foundations. The present method provides a reference for strip foundations designed in earthquake areas.

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters, while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability. To overcome these limitations, this study proposes an efficient framework for conducting reliability analysis and reliability-based design (RBD) of tunnel face stability in spatially variable soil strata. The three-dimensional (3D) rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability, and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm (iHLRF) as well as its inverse analysis formulation. The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability. To demonstrate the feasibility and efficacy of the proposed framework, an illustrative case of tunnelling in frictional soils is presented, where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields. The results show that the proposed method can accurately estimate the failure probability (or reliability index) regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account. Furthermore, this study reveals the impact of various factors on the support pressure, including coefficient of variation, cross-correlation between cohesion and friction angle, as well as autocorrelation distance of spatially variable soil strata. The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method (FORM) in high-dimensional stochastic problems. It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

In order to improve rib stability, failure criteria and instability mode of a thick coal seam with inter-band rock layer are analysed in this study. A three-dimensional mechanical model is established for the rib by considering the rock layer. A safety factor is defined foy the rib, and it is observed that the safety factor exhibits a positive correlation with the thickness and strength of the inter-band rock. A calculation method for determining critical parameters of the rock layer is presented to ensure the rib stability. It is revealed that incomplete propagation of the fracture at the hard rock constitutes a fundamental prerequisite for ensuring the rib stability. The influence of the position of the inter-band rock in the coal seam on failure mechanism of the rib was thoroughly investigated by developing a series of physical models for the rib at the face area. The best position for the inter-band rock in the coal seam is at a height of 1.5 m away from the roof line, which tends to provide a good stability state for the rib. For different inter-band rock positions, two ways of controlling rib by increasing supports stiffness and flexible grouting reinforcement are proposed.

Jacques Heyman’s 1966 article “The Stone Skeleton” has been influential in the assessment of masonry arches in general, including masonry bridges and gothic architecture. Heyman’s article relies on limiting assumptions about arch behavior, and concludes that an arch can be declared stable based on the location of a statically admissible thrust line within the arch. In the following commentary, we assess the validity of the assumptions made by Heyman and the uses that have been made of his application of the lower bound theorem of plasticity. We conclude that Heyman’s methods have enduring value, but that the user needs to recognize the limitations of the assumptions made and the limits on the validity of conclusions imposed by these assumptions.

Under the forces of expansive soil and landslides, the construction of the tunnel entrance is more likely to cause engineering disasters, such as surface cracking and landslides. The application of micro piles in the tunnel has advantages over anti slide piles. Based on the homogenization theory and upper limit analysis, this study calculates the stability of expansive soil landslide at the entrance of an expressway tunnel, and evaluates the treatment effect of different combinations of micro pile groups and cutting-unloading. In the calculation, to improve the calculation efficiency, the micro pile groups and soil around the piles are equivalent to the plus solid conforming to the Mohr-Coulomb strength criterion based on the homogenization theory. the results then are verified by monitoring the landslide deformation after the cutting and micro pile group reinforcement treatment in the field. This study indicates that compared with the strength parameters of soil, the internal friction angle of equivalent reinforcement remains constant, and the cohesion increases from 26 kPa to 85.36 kPa. The evaluated landslide stability before and after treatment show that the sliding surface of the landslide extends from the rock-soil interface above the landslide to the front of the tunnel portal without treatment; when only using micro pile group reinforcement, the landslide safety factor is about 1.17, and the sliding surface extends from the rock-soil interface to the tunnel portal; when only using both micro pile group reinforcement and cutting-unloading, the safety factor increases from 1.26 to 1.28, and the upper edge of the sliding surface moves forward from the rock-soil interface. The field deformation monitoring shows that the deformation of surface and deep soil are less than 3 mm, which can keep the landslide stable, and also verifies the effectiveness of the calculation method. This study provides beneficial information for similar projects.

Jacques Heyman's 1966 article "The Stone Skeleton" has been influential in the assessment of masonry arches in general, including masonry bridges and gothic architecture. Heyman's article relies on limiting assumptions about arch behavior, and concludes that an arch can be declared stable based on the location of a statically admissible thrust line within the arch. In the following commentary, we assess the validity of the assumptions made by Heyman and the uses that have been made of his application of the lower bound theorem of plasticity. We conclude that Heyman's methods have enduring value, but that the user needs to recognize the limitations of the assumptions made and the limits on the validity of conclusions imposed by these assumptions. [ABSTRACT FROM AUTHOR]

Predicting the lateral load-carrying capacity of dry-joint unreinforced masonry (URM) walls is often challenging due to the complex interactions between the governing parameters (i.e. geometrical and mechanical properties). The capacity and behavior of dry-joint URM walls depend on boundary conditions, size and location of the openings, bond pattern, vertical load, and aspect ratio, among other factors. In this context, the present research investigates the effect of bond pattern, aspect ratio, vertical load, and boundary condition on the in-plane (IP) behavior and capacity. Two computational methods, the discrete element method (DEM) and micro limit analysis (micro LA), are employed. Through a comprehensive parametric assessment, the result indicates a good agreement between the two approaches. The computational investigations underline the direct relationship of the IP capacity of walls with respect to aspect ratio and applied vertical pressure. Furthermore, fixed-no rotation boundary condition is associated with the increased IP capacity. Finally, a simple analytical equation is proposed to predict the lateral capacity of dry-joint URM walls. [ABSTRACT FROM AUTHOR]

For the purpose of reliability quantitative assessment of the surrounding rock of the deeply embedded karst tunnel and the geological body around the cavern in the case of the cavern in the forepart of the tunnel face, on the basis of the upper bound limit analysis method, the energy dissipation theory, as well as the reliability theory, the dimensionless performance function of each damage area of the deeply buried karst tunnels could be established in the case of the cavern in the front of the tunnel face. Subsequently, the probability of failure and the reliability index of each damage region of the deep–bedded karst tunnel in the case of the cavern in the front of this tunnel face should be calculated through the Monte Carlo simulation sampling approach. The investigation has demonstrated that the larger the cohesion of the geotechnical body and the larger the internal friction angle within the geotechnical body, the larger the reliability indexes of the geotechnical bodies around the tunnel. The larger the diameter of the cavern and the larger the tunnel burial depth, the greater the probability of failure in the left part of the geotechnical body around this cavern, and the smaller the reliability indexes of these damage areas. [ABSTRACT FROM AUTHOR]

Earthquake-induced slope failures are common occurrences in engineering practice and pre-stressed anchor cables are an effective technique in maintaining slope stability, especially in areas that are prone to earthquakes. Furthermore, the soil at typical engineering sites also exhibit unsaturated features. Explicit considerations of these factors in slope stability estimations are crucial in producing accurate results. In this study, the seismic responses of expansive soil slopes stabilized by anchor cables is studied in the realm of kinematic limit analysis. A modified horizontal slice method is proposed to semi-analytically formulate the energy balance equation. An illustrative slope is studied to demonstrate the influences of suction, seismic excitations and anchor cables on the slope stability. The results indicate that the stabilizing effect of soil suction relates strongly to the seismic excitation and presents a sine shape as the seismic wave propagates. In higher and steeper slopes, the stabilizing effect of suction is more evident. The critical slip surface tends to be much more shallow as the seismic wave approaches the peak and vice versa. [ABSTRACT FROM AUTHOR]

Fully grouted bolts are widely used to reinforce road cutting slopes because of their low cost and high efficiency. However, there is a lack of research on the anchorage failure mechanism and stability assessment of bolt-supported road cutting dip slopes (BRCDSs). In this work, a progressive failure process of BRCDSs was captured via a triangular block model in the Universal Distinct Element Code (UDEC). A kinematically admissible velocity field of BRCDSs was innovatively established based on their sliding shear failure and the Mohr–Coulomb criterion. As a consequence, a novel method for evaluating the stability of BRCDSs was proposed using the upper bound theorem of limit analysis. The reinforcement effects of BRCDSs with different bolt angles were subsequently evaluated by UDEC simulations, and the obtained slope safety factors and bolt-supporting forces were compared with the results calculated by the proposed method. In addition, the influence of various parameters (bolt angle, bolt diameter, slope angle, and strengths of rock and discontinuity) on the reinforcement effect was investigated. The results obtained using the proposed method showed good agreement with those obtained via UDEC. There is an optimal bolt angle in BRCDSs, at which the bolt generates the largest supporting force and thus promotes the highest safety factor of the slope, and the value of this angle is approximated as the friction angle of the discontinuity. The safety factor of the slope also increases with the increase of bolt diameter, and the variation increasing according to a power function. The method proposed provided a convenient theoretical tool for the stability assessment and reinforcement design of BRCDSs. [ABSTRACT FROM AUTHOR]

There are numerous slope projects involved in railway and highway constructions, and ensuring the stability of slopes, especially those with cracks, is very important. Compared with the limit equilibrium method, the limit analysis method takes into account the soil's stress-strain behavior and boundary conditions, thereby yielding more rigorous and accurate results. The stability of slopes with cracks was examined using the finite element limit analysis method in this study. Results indicate that the stability of the slope decreases with the crack length, especially for slope with small slope ratio (i.e., α ≤ 1:1.5) and when l[sub c]/H exceeds 25%. The influence of crack inclination angle on slope stability increases with crack length, and the safety factor is larger in cases of negative inclination value cases as compared to those in positive inclination value cases when l[sub c]/H ≥ 0.33. Values of safety factor are larger in cases of slope with reinforcement as compared to those without reinforcement, and the values of F increase by about 20%. Additionally, the slip planes for slopes with reinforcement are located 10% further away from the slope surface compared to those without reinforcement, and reinforcements enhance the slope integrity. [ABSTRACT FROM AUTHOR]

This paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures. [ABSTRACT FROM AUTHOR]