Critical Failure Surface Research Articles

Application of sparrow search swarm intelligence optimization algorithm in identifying the critical surface in slope-stability

The use of nature-inspired meta-heuristics to tackle complex optimization problems is steadily gaining popularity within a rapidly evolving world. Swarm intelligence (SI) optimization motivated by behavior of community-based organisms of flocks of birds, schools of fish, colonies of ants and bees performs the search through agents whose trajectories are primarily adjusted stochastically and sporadically deterministically, by golden rules drawn from Mother Nature. Each entity within the swarm is swayed by its individual ‘best’ and group’s ‘best’ position while moving randomly to converge to optimal through competition and cooperation. The sparrow search algorithm (SSA), developed by Xuea and Shen (Xue and Shen in Syst Sci Cont Eng 8:22–34, 2020) is a very recent SI approach that adopts the sparrow producer–scrounger model metaphorically for designing optimum searching strategies, inspired by the foraging, anti-predation behavior, and the overall group wisdom of sparrows. SSA has been experimented on some hard benchmark test functions to test its effectiveness and thereafter, applied in slope-stability problems in searching the critical failure surface. The objective function to be optimized is the factor of safety against failure given by Bishop's (Bishop in Geotechnique 5:7–17, 1955) simplified method. Results show SSA is a strong contender to bio-inspired methods like genetic algorithms, big-bang big-crunch, simulated annealing, and artificial bee colony algorithms. The study illustrates the flexibility, efficiency, and robustness of the methodology in function optimization.

Impact of spatially varying rock disturbance on rock slope stability

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.

MODELACION NUMERICA EN DOS DIMENSIONES PARA ANALISIS DE MUROS MECANICAMENTE ESTABILIZADOS UTILIZANDO MACSTARS

For the modeling of mechanically stabilized walls, it involves performing a two-dimensional analysis through numerical methods, given the complexity of variables for their evaluation. One methodology frequently used in the field of geotechnical engineering is that of limit equilibrium, describing in the article the Macstars computer code, this allows to introduce the geometry of the wall, the main reinforcements, the type of front facing, the geomechanical properties of the different soil layers that make up the area to be evaluated, the phreatic layer, the earthquake and the way in which the voussoirs are divided according to the geometry of the slope. It becomes a complementary computational tool, in the determination of stress-strain values, where the introduction of the collected data is focused on the sequence, selection and iteration, to obtain with it, the safety factor that satisfies the conditions for the evaluation of the critical failure surface.

2D calculation method on global stability safety factor of diaphragm wall slurry trench based on minimum potential energy principle

In order to limit the phenomenon that the global stability safety factor (GSF) of the diaphragm wall slurry trench calculated by the two-dimensional (2D) wedge method is too small, the 2D calculation model on global instability of trench wall is established by assuming the whole critical failure surface (CFS) is a quarter elliptic cylindrical surface, and the determination method of CFS is given too. In view of the successful application of the minimum potential energy principle in slope stability checking calculation and on the basis of the new model established, the 2D minimum potential energy method for calculating the GSF is proposed according to the minimum potential energy principle. The correctness of the 2D calculation model built and the rationality of the 2D calculation method proposed are verified based on ten engineering cases, and the sensitivity of the GSF to various parameters is analyzed on the basis of six design examples. Finally, the new calculation method is applied to the global stability checking calculation of trench wall in practical engineering, and the result shows the new calculation method given in this paper is still conservative, so the result calculated by the new calculation method is advised to be multiplied by a modification factor of 1.67 in practical application.

An improved discretization‐based kinematic approach for stability analyses of nonuniform c‐φ soil slopes

AbstractThis paper proposes an improved discretization‐based kinematic approach (DKA) with an efficient and robust algorithm to investigate slope stability in nonuniform soils. In an effort to ensure rigorous upper‐bound solutions which may be not satisfied by the initial DKA based on a forward difference method (DKA‐FD), a central and backward difference “point‐to‐point” method (DKA‐CD and DKA‐BD) is proposed to generate discretized points to form a velocity discontinuity surface. Varying (including constant) soil frictional angles along depth are discussed, which can be readily considered in the improved DKA‐CD. Work rate calculations are performed to derive upper‐bound formulations of slope stability number, and critical failure surface is correspondingly obtained at limit state. The comparison with forward and backward difference methods clearly reveals that the improved DKA‐CD could significantly reduce the mesh‐dependency issue and enhance efficacy of slope stability analyses in nonuniform soils.

Upper Bound Analysis of Two-Layered Slopes Subjected to Seismic Excitations Using the Layer-Wise Summation Method

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.

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

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

Reservoir Slope Stability Analysis under Dynamic Fluctuating Water Level Using Improved Radial Movement Optimisation (IRMO) Algorithm

External water level fluctuation is the major trigger causing reservoir slope failure, and therefore it is of great significance for the safety assessment and corresponding safety management of reservoir slopes. In this work, the seepage effects stemming from fluctuating external water levels are given special analysis and then incorporated into the rigorous limit equilibrium method for assessing the stability of reservoir slope. An advanced metaheuristic intelligent algorithm, the improved radial movement optimisation (IRMO), is introduced to efficiently locate the critical failure surface and associated minimum factor of safety. Consequently, the effect of water level fluctuation directions, changing rates, and soil permeability coefficient on reservoir stability are investigated by the proposed method in three cases. It is found that the clay slope behaved more sensitively in stability fluctuation compared to the silty slope. With the dropping of external water, the higher dropping speed and lower soil permeability coefficient have worse impacts on the slope stability. The critical pool level during reservoir water dropping could be effectively obtained through the analysis. The results indicate that the IRMO-based method herein could effectively realise the stability analysis of the reservoir slope in a dynamic fluctuating reservoir water level, which could provide applicable technology for following preventions.

Upper bound stability analysis of tiered geosynthetic-reinforced soil wall

The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in practice. This study is aimed at proposing an upper-bound stability analysis method of a tiered GRS wall. The proposed method was firstly validated by the existing results from the centrifuge test and the numerical method, and then a parametric study was performed to investigate the effects of the cohesionless backfill friction angle ϕ1 and the wall geometric parameters including the offset distance, the total wall height, the batter angle δ, the number of tiers n, and wall height ratio of adjacent tiers on the dimensionless equivalent earth pressure coefficient KT. The analysis results demonstrated that as the ϕ1 increases, the shear strength of backfill is enhanced and thus the KT or the total reinforcement tensile force decreases, and the KT decreases with the increase of the offset distance at the initial stage and then becomes stable when it reaches a certain critical value. For a fixed offset distance, the KT or the total reinforcement tensile force decreases with the increase of the δ. For the two-tiered GRS walls having the offset distance less than the critical value, the wall with the smaller wall height ratio has a larger KT. Further, the variation of the location of the critical failure surfaces of tiered GRS walls was presented in this study with the variation of the ϕ1 and the wall geometry.

A novel stability equation for the estimation of the factor of safety for homogeneous dry finite slopes

AbstractThis paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance to the limit state. It can be easily programmed into calculators or computers and accurately determines the minimum factor of safety based on the shear strength parameters and slope geometry—meaning that it is ideally suited for integration into reliability calculations. The equation is determined parametrically for various soil parameters and slope geometry using the Morgenstern–Price method and compares favorably with conventional techniques, such as slope stability charts, limit equilibrium, and strength reduction methods (SRM). From a practical perspective, the proposed equation greatly simplifies the analysis of the slope stability as the creation of a numerical model is not required and is suited to use in the feasibility stage of a project, for example, for large linear infrastructure projects with differing slope geometries or in situations where a quick assessment is desired.

A comparative study of critical failure surface in unsaturated soil slopes

Landslides are rapid downslope movements triggered by factors such as rainfall, earthquakes, or human activity, where factors like relative permeability, air flow, and variations in hydraulic conductivity affect the mechanisms behind rainfall infiltration and landslide occurrence. This study investigates these phenomena using the finite difference method (FDM) and finite element method (FEM) in FLAC and PLAXIS software. These methods account for the coexistence of water and air, including the Two-phase flow option, in evaluating unsaturated slope stability and identifying critical failure surfaces. The efficiency of these approaches is gauged by varying soil parameters and exploring the impact of different values of suction and hydraulic conductivity, as well as soil-water characteristics, on the safety factor. It was observed that there are disparities between both software packages at high suction values, which impact the safety factor. FLAC is noted for its conservative approach and superiority in representing unfavourable conditions.

Identification of arbitrarily shaped critical 3D failure surface of a slope based on the sliding direction

AbstractThe determination of critical failure surface and stability evaluation of 3D slopes have been a hot and difficult problem in geotechnical engineering. The conventional method defines the critical failure surface using the safety factor (SF) whereas it is powerless for some special problems, such as two different failure surfaces with equal SFs. So far, many studies on the critical failure surface of a 3D slope have mainly focused on rotational ellipsoid, while less research has been done on the arbitrary shape. To solve the above problems, we develop a model for constructing a arbitrarily shaped failure surface and ascertain the critical failure surface by the sliding direction (SD). To verify rationality of the introduced theory, the critical failure surfaces of two benchmark symmetric slopes and corresponding SFs are reanalyzed, and the results are compared with the reference solutions. Meanwhile, the results obtained by the proposed method are also consistent with the reference solutions for the complex slope with the asymmetric failure surface. The parametric analysis explores the relationships between the mechanical properties of soil and the SD as well as the SF. Furthermore, influence factors of the spatial characteristics of sliding mass are also revealed. The proposed method is used as a helpful complement to the existing methods.

Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis

In many construction projects, a proactive slope stability evaluation is a prerequisite. Although many deterministic or non-deterministic approaches have been commonly used, metaheuristic approaches have resulted in high precision and significant outcomes for slope stability analysis problems. The current work focuses on the reliable assessment of critical failure surfaces associated with the least factor of safety value in both homogeneous and non-homogeneous slopes using a new simplified meta-heuristic approach called optics-inspired optimization (OIO). The algorithm utilizes six different LEM methods as a fitness function for deriving the factor of safety. Experimental analysis over three benchmark studies has been performed to demonstrate the algorithm's robustness and effectiveness. The implementation found more robust results as compared to previous studies. Meanwhile, the algorithm's statistical implication is conducted using the ANOVA test, which inferred better outcomes. With this interpretation, the approach claims to be suitable and efficient for slope stability analysis.

Slope stability analysis based on improved radial movement optimization considering seepage effect

Among various effecting factors, groundwater is commonly known as one of the major triggers for slope failures. Thus, it is great significant of considering the contribution from groundwater seepage in slope stability analysis. In this study, the effect from groundwater seepage are considered as the interaction force (infiltration force) between water and soil materials for static and moment equilibrium analysis. Based on Rigorous Janbu method, the implicit equations are determined for estimating the minimum factor of safety and locating the non-circular critical failure surface. A new metaheuristic algorithm, Improved Radial Movement Optimization (IRMO), was adopted to figure out such complex, nonlinear and constrained optimization problem due to its high precision and stability. The effectiveness of the proposed methodology is validated by four different cases including homogeneous and inhomogeneous slopes from the literature. Comparative studies in different optimization algorithms have been carried out to validate the stability and efficiency of proposed IRMO algorithm accordingly. The results indicate that proposed approaches could acquire a more acceptable and stable result with more efficient way in slope stability analysis considering seepage effect over several existing methods.

Stability of layered soil slope with tension crack: a closed-form solution

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.

Estimation of seismic passive earth pressure coefficients for caissons in c-φ soils with a 3D log-spiral failure wedge

Passive resistance offered by soil to any embedded structure has been of significant interest to researchers since the inception of the concept. The present study deals with the estimation of passive earth pressure coefficients in seismic conditions that will control the passive resistance offered to a caisson embedded in c (cohesion) – φ (friction) soil in presence of surcharge loading. The three-dimensional (3D) geometry of failure wedge (log-spiral in vertical plane and oval in horizontal plane) has been obtained from the results of numerical analysis and past experimental studies. The critical failure surface has been obtained in the presence of all resisting components [unit weight (γ), cohesion (c) and surcharge (q)] by minimizing the passive resistance. Thereafter, seismic passive earth pressure coefficients for cohesion component (Kspc), surcharge component (Kspq) and unit weight component (Kspγ) have been obtained separately corresponding to the critical failure wedge obtained in the previous analysis. Limit equilibrium method of analysis in conjunction with pseudo-static approach has been used to perform the analyses. Charts for a variety of caisson geometry, soil and site condition and seismic condition have been prepared to facilitate prediction of passive resistance in a more economical and reliable manner since unique failure wedge has been considered for all the components instead of separate failure wedge which would be impractical.

Dynamic stability analysis of jointed rock slopes using the combined finite-discrete element method (FDEM)

The combined finite-discrete element method (FDEM) is an advanced finite element and discrete element coupling method, which is commendably suitable for simulating the slope’s entire evolution process from cracking, expansion, penetration, sliding, collision to deposition under seismic load. The original FDEM has apparent shortcomings in simulating the dynamic instability process of earthquake-induced landslides, and some targeted improvements are made to the original program. Numerical tests are carried out to prove the accuracy and robustness of the improved FDEM, and the influence of the structural plane on the dynamic evolution mechanism and process of the slope is studied. The results show that the improved FDEM can accurately reproduce the entire dynamic evolution processes and failure forms of different jointed rock slopes under seismic load and can quantitatively evaluate the dynamic stability of jointed rock slopes (dynamic safety factor and critical failure surface). In addition, the results also emphasize that the slope failure degree significantly affects the dynamic response of the slope and suggest that the combination of the cut-through of the failure surface and the increase of kinetic energy should be used as the criteria for slope dynamic instability simulation by FDEM. This study provides scientific and technological support for revealing the failure mechanism of jointed rock slopes and disaster reduction and prevention.

Predicting Failure of Additively Manufactured Specimens with Holes

Experimental and computational studies were conducted to predict failure loads of specimens containing different-sized holes made using the additive manufacturing (AM) technique. Two different types of test specimens were prepared. Flat specimens, manufactured from polylactic acid (PLA), were subjected to uniaxial loading. Tubular specimens, made of polycarbonate (PC), were subjected to combined loading that was applied using uniaxial testing equipment. Test specimens were uniquely designed and printed to apply the combined bending and torsional loads to tubular specimens. A newly developed failure theory was applied to predict the loads that would result in the fracture of these test specimens. This theory is composed of two conditions related to stress and the stress gradient to be simultaneously satisfied to predict failure. The failure loads predicted using the new failure criteria were compared closely with the experimental data for all test specimens. In addition, a semi-empirical equation was developed to predict the critical failure surface energy for different printing angles. The critical failure surface energy is a material property and is used for the stress gradient condition. Using the semi-empirically determined values for the failure criterion provided close agreement with experimental results.

Back-analysis of a rainfall-induced landslide case history using deterministic and random limit equilibrium methods

Because recurrent rainfall-induced landslide episodes mimic prior failures, this study builds a back-analysis approach to identify those prior failure events and assess the prospective slope performance going forward. Engineers use the results of this approach to project the slope performance based on the quantity of rainfall accumulation during the anticipated rainfall event. A landslide case that occurred in 2004, as a result of a typhoon event, was selected for the back-analysis procedure. Four typhon events were chosen to simulate the pore water pressure conditions, which may have caused damage of varying severity (including landslide failure) to the slope. The numerical model was initially analyzed via the deterministic limit equilibrium slope stability approach to evaluate the most critical failure surface. By adopting the Monte Carlo simulation approach, the following step assessed the random limit equilibrium slope stability on the most critical failure surfaces. The probabilistic distributions of the safety factor were then generated for each typhoon event. Subsequently, the simulation outcomes provide safety indicator values incorporating the mean safety factor, failure probability, and reliability index. From the failure probability and reliability index, a zonation approach with various site-specific performance levels were established by using the corresponding accumulated rainfall to define the exceedance threshold values for each zone. In order to confirm the site-specific performance, we compared the normalized error values acquired from the analysis technique to those measured under two recent typhoon occurrences. An acceptable consistency was attained, validating the procedure's appropriateness for future rainfall events.

Three-dimensional soil slope dynamic stability assessment using minimum potential energy approach

This study introduces a new stability analysis method of 3D slopes under the earthquake forces by combining the minimum potential energy method with pseudo-dynamic method. A new formulation for 3D slope stability analysis is given by introducing the elastic module and Poisson ratio. The minimum potential energy approach is used to directly obtain the stress state on failure surface, and the displacement direction where the potential energy of slope reaches the minimum is regarded as the movement direction of landslide mass. The determination of critical failure surface under earthquake forces and the associated safety factor (SF) are resolved using the genetic algorithm. The performance of the developed approach for evaluating slope stability is demonstrated with four cases. The influences of seismic forces and Poisson ratio on the slope stability are investigated, and the results show that Poisson ratio is insensitive to the accuracy of the proposed method, while the horizontal earthquake force has a greater impact on slope stability than the vertical earthquake force. The effects of the earthquake forces on the normal stress on failure surface, the sliding direction of landslide mass and the shape of failure surface are also explored. In addition, we discuss the differences between the proposed method and the pseudo-static method.