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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]

Slope failures in nature and engineering are typically three-dimensional (3D). The rotational failure mechanism derived from the variational limit equilibrium (LE) method shows superior performance in the stability analysis of the 3D slope. In contrast to the traditional LE methods, it avoids arbitrary kinematical and statical assumptions. Stability charts obtained by the variational LE method are used to derive explicit expression equations of the safety factor, also known as the stability equations, for both 3D reinforced and unreinforced slopes. These equations are highly accurate and can provide a convenient means to assess slope stability in practical engineering. An example of a convex reinforced slope with a turning arc is illustrated in this study to investigate the effect of the 3D effects on the required reinforcement length for design. The results indicate that the 2D method underestimates the required reinforcement length when dealing with a 3D reinforced slope problem. Furthermore, a forensic analysis of the Yeager Airport reinforced slope is conducted within the framework of the variational LE method. The required strength for stability is found to be significantly less than the allowable strength of reinforcements without considering the decrease in soil shear strength. However, the required strength greatly exceeds the allowable strength when the decrease in soil shear strength is considered. The results verify that the decrease in shear strength of the weak layer is responsible for the collapse. [ABSTRACT FROM AUTHOR]

Seismic amplification effects are a common occurrence in V-shaped valleys. A method is presented for incorporating the amplification effects in the stability assessment of V-shaped fill slopes based on the limit equilibrium (LE) method coupled with the pseudo-static approach. The proposed LE method uses a variationally derived three-dimensional (3D) rotational failure mechanism to produce stability charts for slopes. A series of parameter analyses are conducted to investigate the influences of seismic load and the geometric parameters on the 3D stability and the most critical slip surface for V-shaped fill slopes. The findings indicate that the reduction in the slope stability triggered by the seismic amplification effects is notable. The boundary effects are positively correlated with the inclination of the valley side slope and negatively correlated with the width of the valley bottom. The face failure mode is dominated in the cases where the boundary effects are significant. Furthermore, an explicit expression equation of the safety factor, the stability equation, is obtained by regression analysis. This stability equation has excellent accuracy and can be used in practical engineering to provide a convenient assessment for V-shaped fill slopes. [ABSTRACT FROM AUTHOR]

Evaluating the stability of layered slopes, a common type of terrain in nature and engineering practice, poses a fundamental challenge in the field of geotechnique. The emergence and extension of tension cracks play a crucial role in the failure process of layered slopes, but accurately predicting the location of layered slope cracking and assessing its impact on layered slopes remains a challenge using conventional analytical methods. Herein, we present a closed-form solution for evaluating the layered slope stability with tension cracks without any priori assumptions. The presented closed-form solution enables the location and depth of tension crack, the critical failure surface in different soil layers, and the corresponding normal stress distribution to be determined for all single/layered slopes. Effects of tension cracks on layered slopes are investigated, considering slope inclination, soil properties, layer thickness, and dominant failure mechanism. Note that, the results show that the dominant failure mode of layered slopes could change from toe failure (without cracks) to face/base failure (with tension cracks), which has not been previously reported. Multiple cracks are possible to develop in layered slopes. The proposed closed-form solution can be applied to improve the stability assessment and engineering design of layered slopes considering tension crack. [ABSTRACT FROM AUTHOR]

Previous research has demonstrated that concave cross-sectional geometry can enhance slope stability, reduce sediment loss, and improve mining efficiency. However, studies on the use of concave facing in geosynthetic-reinforced soil (GRS) walls are limited. This study idealizes the concave facing as a circular arc whose concavity is determined by the wall height, batter and mid-chord offset. Based on the limit equilibrium analysis, a modified top-down procedure is proposed to investigate the impact of concave facing on the internal stability of GRS walls. Using the presented method, the distribution of required tension along the reinforcement layer and necessary connection load can obtain while considering the pullout capacity at a given layout and factor of safety. Sensitivity analysis, including the mid-chord offset, wall batter, reinforcement length, vertical spacing, and facing blocks, are carried out to explore the impacts of facing profile concavity on the internal stability of GRS walls. Results show that concave facing can significantly reduce the required tension along the reinforcement, and the required connection strength is sensitive to the variation in the facing profile. Increasing the wall batter can result in a greater reduction of maximum required tension for the concave wall, but it can also increase the connection load for most reinforcements. The concavity of the facing has no effect on the optimal reinforcement length, which is found to be 0.7 times the wall height. The differences in maximum required tension for various facing concavities gradually diminish when considering the toe resistance. [ABSTRACT FROM AUTHOR]

The mining of open-pit mines has a significant influence on the surrounding ecological environment and safety. Once the slope of an open pit is unstable, it will bring extremely severe disasters to the surrounding environment. The south slope of the Fushun West open-pit mine is a large bedding slope with weak interlayer and asymmetrical features between the eastern and western regions. The different deformation mechanisms are worth further discussion, and the deformation mechanism of the eastern region needs to be systematically investigated. In this study, a comprehensive method combining a numerical model, the limit equilibrium method, and a probabilistic approach is used. The different deformation mechanisms of the slope are explored. Thereafter, the sensitivity of the geometric and mechanical parameters of the slope is determined. Finally, the probability of failure (PF) and slope stability are evaluated. The results illustrate that the difference in geological characteristics and constraint conditions is the fundamental reason for the difference in deformation features of the slope. The sensitivity analysis results show that the friction angle of the weak layer exhibits the most sensitivity and that the unit weight is irrelevant to the slope stability. Taking the friction angle of the weak layer as a variable, when the thickness of the basalt layer is less than 140 m and the height of the slope is more than 360 m, the PF of the slope reaches a high value. When the inclination of the weak layer exceeds 30°, the PF of the slope increases to a high value. When the Ru coefficient exceeds 0.2, the slope presents a high PF. The results illustrate that decision-makers should pay attention to the strength degradation, transitional mining of the basalt layer, and establish a good drainage system. The comprehensive method can also provide an effective way to assess the stability and PF of similar large-scale bedding slopes under complex geological conditions. [ABSTRACT FROM AUTHOR]

The magnitude of seismic displacement is an important index to evaluate the safety of slopes. The traditional Mohr–Coulomb failure criterion may overestimate the slope stability in seismic displacement calculation. Some analyses under plane-strain (2D) conditions reveal a significant effect of tension cutoff on slope displacement. This paper aims to carry out a three-dimensional (3D) analysis to investigate the seismic displacement of slopes affected by tension cutoff. Within the framework of limit analysis, a 3D rotational failure mechanism is adopted here for homogeneous slopes consisting of c–φ soils. A series of parametric analyses are conducted to explore the influence of the reduction coefficient on the yield acceleration coefficient, displacement coefficient, and seismic displacement. The results are more comprehensive and accurate compared with 2D analysis. [ABSTRACT FROM AUTHOR]

Most slope collapses have three-dimensional (3D) characteristics due to the uniform soil. The traditional plane-strain analyses neglect the 3D effects and could yield an overestimation or underestimation of the slope stability. The present study analyzes the stability of 3D slopes characterized by spatially variable undrained shear strength. A 3D slope reliability analysis approach that can fully consider the spatial variability of soil properties is proposed based on the plastic limit analysis upper-bound theorem. Within the framework of Monte Carlo simulation, the effects of strength gradient, the coefficient of variation, and the scale of fluctuation of soil undrained shear strength on the slope reliability index are examined. The length of the 3D failure surface is highlighted as an essential characteristic in 3D slope analysis. The slope failure mechanisms are classified, and the occurrence probability of each type is quantified. The obtained results indicate that the degree of nonstationarity and the coefficient of variation of undrained shear strength have significant impacts on the slope failure width, and the variation of failure mechanism highly depends on the combined effect of slope inclination and soil strength. The findings could guide slope reinforcement and facilitate a more efficient and accurate risk evaluation of slopes. [ABSTRACT FROM AUTHOR]

The pore-water pressure is a vital factor in determining the slope stability. To deal with the stability of slopes undergoing pore-water pressures, this paper used the pore-water pressure coefficient to develop the three-dimensional limit analysis method for slope stability evaluation with a nonlinear strength envelope. For numerical slope examples, the critical heights and corresponding critical slip surfaces associated with linear and nonlinear envelopes were derived by using a numerical optimization procedure. The influences of pore-water pressures on the slope stability were addressed by comparing the upper-bound solutions derived by linear and nonlinear strength envelopes (the linear and nonlinear results for short). The obtained two critical inclinations between the linear and nonlinear results both decrease and gradually approach with increasing pore-water pressure coefficient. For most slopes subjected to pore-water pressures, using the linear Mohr–Coulomb envelope will obviously overestimate the slope critical height. The overestimation resulted from the linear criterion will become more distinct for slopes with smaller widths. Besides, the presented results showed that the equivalent internal friction angle tends to have a weaker increasing trend for steeper slopes as pore-water pressure coefficient increases. Hence, when pore-water pressure coefficient increases, the critical slip surfaces of gentle slopes with nonlinear strength criteria become shallower, but the critical slip surfaces of steep slopes seem to have no consistent change law. These results and analyses can illustrate the significance of the application of nonlinear strength envelopes in slope stability evaluation considering pore-water pressures and provide certain reference advice in slope engineering design and landslide prevention. [ABSTRACT FROM AUTHOR]

Bentonite-water slurry trenches are utilised not only in underground excavations, but also in geo-environmental protections. Slurry trench can be used to prevent leaks and spills of the contaminant from landfills. This paper presented a procedure for evaluation of the impact of possible tension crack on stability of slurry trench in clay. The procedure is based on variational limiting equilibrium approach to slope stability. A straight extension was made to assess the safety of slurry trenches with cracks. Closed-form solutions were derived for the factor of safety and the potential crack depth for undrained total stress and drained effective stress conditions. Using normalisation presented the derived results in the form of stability chart. These charts provide a convenient tool for selection of the preliminary parameters for the slurry trench and determination of the potential crack depth. The results demonstrate the overestimation on the stability of slurry trenches when neglecting the tension crack, especially for undrained conditions. As the groundwater level increases or slurry level decreases, the depth of tension crack increases. To avoid the water-filled crack occurred, the groundwater level is suggested to be decreased by 10% of the trench depth below the ground surface. [ABSTRACT FROM AUTHOR]

Abstract This paper develops an analysis procedure for turning corner in Geosynthetic-Reinforced Soil Structures (GRSS's). The procedure includes the calculations of the required strength and length of the reinforcement for internal stability. The calculations are based on the variational limit equilibrium analysis of three-dimensional (3D) stability of slopes. Seismic effects are also considered using the pseudo-static method. Results are presented in a condensed form of design charts, providing a simple tool to determine the required tensile strength and embedment length of the reinforcement. Two examples are given to demonstrate the use of the design charts. Compared with the conventional design based on plane-strain analysis, the presented design procedure yields longer reinforcement for the 3D internal stability of the corners. Generally, 3D design requires longer reinforcement than 2D as the seismic acceleration increases. The trend of obtained result is in good agreement with performance observations related to corners reported in commentary of AASHTO. [ABSTRACT FROM AUTHOR]

Current design procedures of Geosynthetic-Reinforced Soil Structures (GRSS's) are for walls/slopes with long straight alignments. When two GRSS segments intersect, an abrupt change in the alignment forms a turning corner. Experience indicate potential instability problems occurring at corners. The purpose of this study is to explore the effects of turning corner on the stability of reinforced slopes. Three-dimensional (3D) slope stability analysis, based on limit equilibrium, resulted in the maximum tensile force of reinforcement. Parametric studies required numerous computations considering various geometrical parameters and material properties. The computed results produced efficient practical format of stability charts. For long-term stability of reinforced slopes with turning corner, the influences of pore water pressure and seismic loading are also considered. Turning corner can improve the stability of reinforced slopes by virtue of inclusion of end effects. However, localized increase of pore water pressure or directional seismic amplification may decrease locally thus stability requiring strength of reinforcement larger than in two-dimensional (2D) plane-strain. While using 2D analysis for non-localized conditions may require stronger reinforcement, it also requires shorter reinforcement than in 3D analysis; i.e., 2D analysis may be unconservative in terms of reinforcement length. [ABSTRACT FROM AUTHOR]

This paper presents a procedure for assessment of the impact of tension crack on stability of slope in clays with linearly increasing undrained strength. The procedure is based on the limit equilibrium method with variational extremization. The distribution of the normal stress over slip surface is mathematically obtained for slopes in clays with the linearly increasing undrained strength and then used to determine the tension crack for clays with zero tensile strength. The seismic effect is also included using the pseudostatic approach. Closed-form solutions to the minimum safety factor and the maximum crack depth can be derived and given in the form of chart for convenient use. The results demonstrate a significant effect of the tension crack on the stability of steep slopes, especially for strong seismic conditions. In this situation, neglecting the impact of tension crack in traditional ϕ=0 analyses may overestimate the slope safety. The most adverse location of the tension crack can be also determined and presented in the charts, which may be useful in designing reinforcements and remedial measures for slope stabilization. [ABSTRACT FROM AUTHOR]

This paper revisits the variational limit equilibrium (LE) analysis of three-dimensional (3D) slope stability in the context of limit analysis (LA). It proves the kinematic admissibility of the 3D mechanism in LA, although it was derived from LE variational extremization. It also includes algorithms in the realm of LA that are associated with the variational mechanism. A comparison between the variational results and reported LA upper-bound or LE closed-form results is conducted. It demonstrates that the variationally derived mechanism consistently yields upper-bound solutions for 3D symmetrical slopes that are as accurate as those produced by postulated mechanisms in LA. However, the results are more critical than those derived from spherical failure mechanism in LE. The generalized log spiral 3D mechanism rigorously legitimizes the variational slope stability analysis in both frameworks of mechanics LE and LA. Stability charts were produced where the 3D factor of safety can be assessed for a constrained length of failure, while including factors like pore water pressure and seismic loading. The results presented within this study demonstrate the capabilities of the variational 3D solution and can be used to evaluate approximate methods, numerical or closed-form, developed in 3D slope stability analyses. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The design of reinforced earth structures uses idealized two-dimensional (2D) geometry – classifying as a plane-strain analysis. This 2D idealization greatly simplifies design by ignoring stabilizing effects posed by three-dimensional (3D) characteristics. While the outcome of this 2D idealization is conservative in terms of required reinforcement strength, ignoring 3D end effects in back-calculations of experimental and field data may overestimate the contribution of the reinforcement to stability thus possibly leading to unconservative learned lessons related to design. The objective of this study is to explore 3D effects on the required strength of reinforcement in geosynthetic-reinforced earth structures (GRESs) using a modified 3D limit equilibrium (LE) slope stability analysis. To determine the stability of GRESs, a rotational, 3D failure mechanism, derived from variational LE analysis, is applied using a log-spiral surface generalized to 3D conditions. In order to determine the long-term strength of geosynthetics required to ensure sufficient internal stability, the moment equilibrium approach is applied and its respective equations solved. In order to conveniently assess the end effects on the required total strength of reinforcement and the volume of failing mass considering the feasible length of potential failure, a series of design charts are presented. These charts can also be useful in forensic studies when back-calculating the in-situ mobilized strength of the geosynthetic for 3D failures. The impact of seismicity and the assumed function of forces distributed amongst the reinforcement layers were investigated to highlight their importance. To keep this study focused on 3D end effects, this study is limited to a simple 3D GRES problem; however, extending the present framework to deal with complex homogenous problems is straightforward. [ABSTRACT FROM AUTHOR]

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A three-dimensional (3D) kinematically admissible rotational failure mechanism is extended from toe failure to include face failure and base failure for homogeneous slopes in both purely cohesive and frictional/cohesive soils. In the strict framework of limit analysis, an analytical approach is derived to obtain the upper bounds on slope stability and the corresponding type of the critical failure mechanism. Compared with the available results from the finite-element limit-analysis method, the 3D rotational failure mechanisms give the best estimate on the upper bound. A set of stability charts is presented in a wide range of parameters for 3D homogeneous slopes under both static and pseudostatic seismic loading conditions. This set is useful in assessing the safety of the 3D homogeneous slopes in practical applications. [ABSTRACT FROM AUTHOR]

Little insight exists into the stability of reinforced slopes supporting spread footings. Existing research is largely focused on idealized, plane strain analyses that do not account for three-dimensional conditions. These conditions are significant because the geometries of both reinforced slopes and footings are three-dimensional in nature. In this study, the stability of reinforced slopes supporting spread footings is analyzed in three dimensions using a limit analysis approach and presented in a series of design charts. To better understand the impact of three-dimensional conditions, a parametric study is conducted to evaluate effects of various design parameters on required reinforcement strength. [ABSTRACT FROM AUTHOR]

Based on the Spencer's method, this paper presents a simplified approach to assess the stability of three-dimensional (3D) asymmetrical slopes. The approach allows for satisfaction of the force equilibrium in all three directions and the moment equilibrium about two co-ordinate axes. A unique direction of sliding is involved here to calculate the factor of safety. The direction of sliding (DOS) is always parallel to the plane of symmetry for symmetrical slopes. However, the DOS in asymmetrical slopes could deviate from the symmetrical plane and affect the stability assessments. Through two simple asymmetrical examples, the calculated results demonstrate that the deviation of the sliding from the symmetry could destabilize the slopes and cause failures. Neglecting the DOS in 3D asymmetrical slopes will overestimate their stability. Application of the presented approach into complex asymmetrical problems is straightforward. [ABSTRACT FROM AUTHOR]

This paper presents a kinematic approach of limit analysis to evaluate the effects of nonlinear failure criterion on the three-dimensional (3D) stability analysis of uniform slopes. For slopes in various clays, the upper bounds on the critical heights associated with the linear and nonlinear failure criteria are obtained and comparisons of the linear and nonlinear results are made to investigate their differences. The differences between the linear and nonlinear solutions change with varying slope inclination, resulting in two critical values on the slope inclination angle. In the intermediate range of slope inclinations, the critical heights associated with the linear failure criterion are smaller than the nonlinear results, and the underestimation by using the linear failure criterion cannot be neglected. For other cases, the analyses based on the linear failure criterion will overestimate the stability of actual slopes obeying the nonlinear failure criterion. Meanwhile, the 3D effects have insignificant influences on the two critical slope inclination angles. However, the sensitivity of the critical heights to the nonlinearity of soil strength envelope appears to be more pronounced for slopes with a smaller width. [ABSTRACT FROM AUTHOR]

Assessing the seismic stability of earth slopes has long been a challenging task in geotechnical engineering mainly because of two reasons: (1) the mechanism of slope movement triggered by an earthquake is not fully understood, and (2) the criteria of seismic performance or failure state are hard to specify. As an attempt to address these concerns, this paper examines the seismic slope failure mechanism of rotational sliding mass. Permanent displacement is analyzed based on Newmark's sliding block theory, with extension to compute the rotational displacement in the presence of horizontal ground acceleration history. A simplified relationship between the rotational and horizontal motions of a circular failure mass is also obtained. By comparing case studies, the possible reasons whether and how the seismic slip surface differs from the static one are explained. In addition, we discuss the allowable displacement when a quantitative judgment of the slope performance is required. In this regard, the underlying uncertainties of the soil properties are introduced to probabilistically relate this threshold value to the reliability index, a substitute for the probability of failure or risk acceptance level. The results from the parametric studies indicate the reliability-based design of the allowable displacement is a promising approach for seismic slope analysis. [ABSTRACT FROM AUTHOR]

The seismic internal stability analysis of geosynthetic-reinforced earth structures (GRESs) is typically conducted under idealized two-dimensional conditions. Though this assumption simplifies the analysis and design procedure, GRESs are three-dimensional in nature. In addition, existing seismic internal stability analyses of three-dimensional GRESs focus on the required strength of reinforcement, ignoring potential pullout failure of reinforcement. This may result in potentially underconservative design as the required length of reinforcement is a vital part of the internal stability analysis of GRESs. In this study, both the required strength and length of reinforcement of three-dimensional GRESs are calculated considering pseudostatic seismic loading. The results are compared with idealized two-dimensional solutions and presented in the form of stability charts for illustrative purposes and ease of application. It shows that seismic loads amplify the effects stemming from consideration of three-dimensional conditions. • A complete, three-dimensional internal stability analysis of GRESs under seismic loads is conducted. • The 2D solutions serve as benchmark and effects of various parameters on the 3D results are investigated. • The 3D solutions under different seismic loads are presented in dimensionless stability charts for ease of application. • Considering seismic loads amplify the effects stemming from 3D conditions, especially for the required reinforcement length. [ABSTRACT FROM AUTHOR]