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Detection of critical failure surface and associated minimum factor of safety ( F ) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count ( k max ) range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best F b , worst F w , mean F ¯ , standard deviation (SD) and % error (% E ) of the optimum solutions i.e. factor of safety ( F ) from 10 independent runs. The effect of GWO parameters such as NP and k max to obtain optimum solution are also presented. The F b , F w , F ¯ and SD for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (% E ) in best F b from optimum ( F ) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.

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

The identification of ideal values for algorithm-specific parameters required for the functioning of metaheuristic approaches at their optimum performance is a difficult task. This paper presents the application of a recently proposed teaching–learning-based optimisation (TLBO) algorithm to determine the lowest factor of safety (FS) along a critical slip surface for soil slope. TLBO is a nature-inspired search algorithm based on the teaching–learning phenomenon of a classroom. Four benchmark slopes are reanalysed to test the performance of the TLBO approach. The results indicate that the present technique can detect the critical failure surface and can be easily implemented by practitioners without fine-tuning the parameters that affect the convergence of results. Statistical analyses indicate a drastic decrease in uncertainty and the number of function evaluations in the estimation of the FS over previous approaches.

Determination of the critical failure surface is performed in stability evaluation process for road cut slope, embankments, dam, excavations, retaining walls and many more. Finding the critical failure surface in a rock or soil slope is very cumbersome and becomes a difficult constrained global optimization problem. Due to existence of discontinuous function and strong multiple local minima points, researchers are facing difficulties to employ trial-and-error methods in a large search space. Thus, classical optimization techniques fail to converge to a valid solution. In this study a stochastic method called biogeography-based optimization algorithm was adopted for analyzing the factor of safety. Based on the finding from the implementation and quantitative evaluation, it was found that the proposed method for locating critical failure surface in homogeneous soil slope acquires more efficient results over other implemented methods such as grid search and genetic algorithm. The validation and effectiveness of the proposed method are investigated by solving two benchmark case studies from the literature, while the simulation design for slip surfaces is carried out using ‘Rocscience slide’ software tool for comparing the results.

In rock slopes where sedimentary rock masses dip into the face of the slope, failure may occur by block toppling. In traditional analytical models, the failure surface is assumed to be a single plane running from the upper columns to the toe of the slopes, which may be inconsistent with the physical situation, where the weak plane has undergone counter-tilting within the rock slope due to variations of lithology and weak plane characteristics. To better reflect the physical situations, the failure surfaces ought to be determined instead of basing it on assumptions and incorporated in the existing analytical methods for stability analyses. Therefore, a searching technique for determining the counter-tilted failure surface angle has been proposed and traditional analytical models for evaluating the stability of rock slopes subjected to block toppling failure mechanisms have been modified by incorporating the counter-tilted weak plane angle. The physical slope with counter-tilted failure surface was comprehensively analyzed using the modified analytical model and the results were validated using numerical simulation models. The simulated failure mode zones are consistent with the failure mode zones obtained by the modified analytical method. The influence of relative angles of the counter-tilted failure surface on the slope stability has been studied and the results show that progressive increase of the counter-tilted failure surface angles lead to a gradual increase in slope instability. The proposed analytical method could provide precise applications to evaluate the slope instability in rock slopes with counter-tilted failure surface.

There appears to be a clear general consensus in the literature regarding four critical issues that define the problem of the October 1963 Vaiont landslide and its behaviour that are central to the disaster: (1) the 1963 failure was a reactivation of an ancient landslide; (2) failure took place along thin clay seams (already at residual strength); (3) the sliding surface had a ‘chair’ shape with a (sub)horizontal base; and (4) failure was triggered by inundation of the toe of the slide mass by rising reservoir levels. The key to understanding the Vaiont landslide is the failure surface geometry, which was controlled by the structural geology. It now appears that the so-called chair structure (that was assumed to define the shape of the failure surface) does not exist, and without it, the first consensual point is untenable, and the fourth may not contain the whole truth. We have systematically re-examined the published evidence and undertaken our own new research in order to test the logical and geotechnical validity of the four elements of the consensus. Glacial processes can account for the pre-failure morphology of the landslide site; the clay seams must therefore have been at peak shear strength as there was no ancient landslide. Tectonic processes can account for the failure surface geometry, which does not have a ‘chair’ shape, as well as small-scale structures; and rainfall appears to have been an essential element in the initiation and development of the landslide. Our findings largely contradict the consensus position and thus form the basis of a new overarching hypothesis for the landslide that should account for all of the observed and known features, events and data.

Natural and man-made slopes can undergo a retrogressive landslide when subjected to seepage. Studying the mechanism of retrogressive landslides contributes greatly to the employment of effective mitigation approaches. A multi-stage limit equilibrium-based study was performed to explore how the geometry of initial failure affects the progress of a retrogressive, multiple-rotational landslide caused by seepage flow. Seepage-stability analyses were carried out on two silty sand slopes which were previously found to experience successive rotational failures upon raising the water table in centrifuge tests. Analyzed in prototype dimensions were the slope models with the height of 24 cm and inclinations of 45° (1V:1H) and 63.4° (2V:1H) tested at different centrifugal accelerations. According to the tests, the initial shallow failures were assumed to be circular initiating from the face and emerging from the toe of the slopes in the stability analyses. The impact of curvature and length of the initial failure surface (referred to as IFS) as well as the height of the scarp shaped at each failure episode were investigated. The results show that the landslide continues until the slope profile finds a stable curvature. For the landslides that occur in the 45° inclined slope, when the initial failure initiates at a higher elevation on the slope face, the landslide retrogresses further. In addition, with an increase in the length or curvature of IFS, the final retrogression distance decreases. Further, it was observed that the progress of landslides depends on the height of the scarp exposed at each failure episode.

Searching for critical failure surface (CFS) with minimum factor of safety (FOS) of any slope require application of optimization. A particle swarm optimization (PSO) based MATLAB code is developed to search for CFS and associated minimum FOS of slopes by minimizing the objective function. The FOS against slope failure is determined by Bishop’s method based on limit equilibrium technique, which also serves as the objective function. With this goal, another computer code is developed in MATLAB to solve non-linear nature of equation of FOS. The effectiveness of developed code is investigated through study of different parameters such as swarm size, iteration count and slice numbers etc. The applicability of PSO is evaluated for homogeneous and layered slopes considering the effect of seepage and seismic loading.

The solution of slope stability problems requires determination of critical failure surface and associated optimum/minimum factor of safety (FOS) value. Investigation of critical failure surface in any soil slope can be posed as a constrained global optimization problem. In this article, a simplified technique of generation of segmented non-circular failure surface is proposed. Unified particle swarm optimization (UPSO) method is utilized to search for the critical failure surface and associated minimum FOS of the slope. Limit equilibrium technique-based Morgenstern–Price method is used to evaluate the FOS value of the potential failure mass which satisfy both force as well as moment equilibrium. To demonstrate the performance of UPSO and its competence in yielding critical failure surface along with minimum FOS value, three benchmark problems with differing complexities are chosen from existing literatures. The results obtained are compared and are found to be in accord with the published literatures. The performance of UPSO as a solution algorithm for slope problems are established through convergence studies of various related parameters.

One of the most crucial geotechnical engineering problems is the stability of slopes that are still attracting scientists and engineers. In this study, five recently developed meta-heuristic methods are utilized to determine the Critical Failure Surface (CFS) and its corresponding Factor of Safety (FOS). Through the FOS calculations, the Finite Element Method (FEM) is employed to convert the strong form of the main differential equation to a weak form. Additional to the general loading, seismic forces and seepage effect are considered, as well. Finally, the proposed optimization procedure is applied to numerical benchmark examples, and results are compared with other methods.