Shear Strength Reduction Method Research Articles

Study on Stability Reduction Characteristics of Earth and Rockfill Dams under Rapid Drawdown Using Fully Coupled Seepage-Stress Analysis

It can be a great expense to examine individually the stability of earth and rockfill dams on rapid drawdown in civil engineering practice. The aim of this present work is to clarify the safe type on the rapid drawdown among the most common types of earth and rockfill dams and to introduce cheaply the types in dam design. First, a transient analysis of saturated-unsaturated seepage coupled with stress is carried out in the cross sections of typical earth and rockfill dams the during rapid drawdown, and the safety factors of the upstream slopes are determined by the shear strength reduction method. Then, the typical dams are compared for the stability characteristics so that designers can select the safe type of earth and rockfill dams on rapid drawdown. The obtained results show that the decreasing rate of safety factor in a central core dam is 0.72–0.85 times than one of the homogeneous dams and 0.17–0.40 times than one of the sloping upstream core dams so that it is more stable than other earth and rockfill dams during rapid drawdown.

Optimization and variational principles for the shear strength reduction method

AbstractIn this paper, a modified shear strength reduction method (MSSR) and its optimization variant (OPT‐MSSR) are suggested. The idea of MSSR is to approximate the standard shear strength reduction to be more stable and rigorous from the numerical point of view. The MSSR method consists of a simplified associated elasto‐plastic model completed by the strength reduction depending on the dilatancy angle. Three Davis' modifications suggested by Tschuchnigg et al. (2015) are interpreted as special cases of MSSR and their factors of safety are compared. The OPT‐MSSR method is derived from MSSR on the basis of rigid plastic assumption, similarly as in limit analysis. Using the variational approach, the duality between the static and kinematic principles of OPT‐MSSR is shown. The numerical solution of OPT‐MSRR is obtained by performing a regularization method in combination with the finite element method, mesh adaptivity and a damped Newton method. In‐house codes (Matlab) are used for the implementation of this solution concept. Finally, two slope stability problems are considered, one of which follows from analysis of a real slope. The softwares packages Plaxis and Comsol Multiphysics are used for comparison of the results.

Finite element analysis of a slope stability by incrementally increasing the mobilised principal stress deviator

ABSTRACT The assessment of slope stability factor by a FE analysis using the shear strength reduction method (SRM) enjoys several advantages and owns many shortcomings. As an alternative, a new FE approach called stress deviator increasing method (SDIM) is proposed. By means of a factor termed Mohr’s circle expansion factor, the new approach assesses the slope stability by incrementally increasing the mobilised principal stress deviator until the soil failure is reached. The numerical procedure is based then on a rigorous formulation as it preserves the definition of the safety factor consistent with that of LEM and maintains the progressive development of the shear stress on same plane on which the shear strength will occur at failure. The proposed method deals with the actual material by using the real strength parameters and rather than those reduced by a factor. The results of SDIM encoded in a computer code called were thoroughly assessed against those of both SRM and LEM using several slope examples involving and purely cohesive soils. Results of comparison encompassing factor of safety along with plastic strain distributions showed the reliability and the strength of the present method.

The role of joint spacing on the stability analysis of wedge failures

Kinematic analyses of wedge failures in rock slopes are usually carried out based on stereographic techniques. Nevertheless, this methodology presents several limitations that could lead to poorly accurate conclusions. In line with this idea, the main objective of this work is to evaluate the effect of joint spacing in the estimation of the factor of safety of rock slopes affected by potential wedge failures. For this purpose, a 3D numerical distinct-element code (3DEC) was selected to carry out a good number of simulations in which the factor of safety a slope, affected by different discontinuity sets, was studied by using the Shear Strength Reduction (SSR) method. Different values of joint spacing, cohesion and friction angles were considered, combined with two angles of the slope face under study. The joint spacing has been found to relevantly affect the values of the factor of safety, which showed variations of up to 40% in comparison with those obtained from limit-equilibrium methods for rock slopes with similar structural features. This work provides an insight into a more realistic interpretation of rock slope analyses against wedge failures, and particularly to more accurate estimations of the factor of safety.

Probability Methods for Stability Design of Open Pit Rock Slopes: An Overview

The rock slope stability analysis can be performed using deterministic and probabilistic approaches. The deterministic analysis based on the safety concept factor uses fixed representative values for each input parameter involved without considering the variability and uncertainty of the rock mass properties. Probabilistic analysis with the calculation of probability of failure instead of the factor of safety against failure is emerging in practice. Such analyses offer a more rational approach to quantify risk by incorporating uncertainty in the input variables and evaluating the probability of the failure of a system. In rock slope engineering, uncertainty and variability involve a large scatter of geo-structural data and varied geomechanical test results. There has been extensive reliability analysis of rock slope stability in the literature, and different methods of reliability are being employed for assessment of the probability of failure and the reliability of a slope. Probabilistic approaches include Monte Carlo simulation (MCS), the point estimate method (PEM), the response surface method (RSM), first- and second-order reliability methods (FORMs and SORMs), and the first-order second-moment method (FOSM). Although these methods may be complicated, they provide a more complete definition of risk. Probabilistic slope stability analysis is an option in most commercial software; however, the use of this method is not common in practice. This paper provides an overview of the literature on some of the main probabilistic reliability-based methods available for the design of the rock slope in open pit mining. To demonstrate its applicability, the paper investigates the stability of a rock slope in an open pit mine in the Goldfields region, Western Australia. Two different approaches were adopted: deterministic stability analysis using two-dimensional limit equilibrium and finite element shear strength reduction methods using SLIDE and RS2 software, respectively, and probabilistic analysis by applying the MCS and RSM methods in the limit equilibrium method. In this example, the slope stability analysis was performed using the Spencer method with Cuckoo search optimization to locate the critical slip surface. The results obtained were compared and commented on.

Stability of the foundation trench of the immersed tunnel subjected to combined wave and current loading

The determination of stability for the submarine artificial slope is important in the construction of offshore structures such as immersed tunnels and embedded pipelines. Aimed at this issue, a two-dimensional (2D) integrated model is proposed to investigate the slope stability of the foundation trench for the immersed tunnel under the combined wave and current loading, as in the real marine environment. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved to simulate the wave field, meanwhile the current is realized by setting boundary inlet and outlet velocity at both sides. The interface between water and air is tracked by conservative Level Set Method (LSM). The wave-current induced pore pressure in seabed is calculated by Darcy's law, and the shear strength reduction method is adopted to judge the damage of the elastic-plastic seabed slope which is described through Mohr-Coulomb constitutive model. The wave-current model is validated through comparing with experimental data and analytical solution. The consolidation status of foundation trench after excavation is obtained and set as the initial condition for analysis. The factor of stability (FOS) for the slope is demonstrated to depend on the relative distance between wave crest and slope. The minimum of FOS corresponding to the most dangerous situation is regarded as the stability index for the slope with specific slope ratio in the whole process of dynamic wave-current loading. Through the parametric analysis based on this new evaluation method, the effects of soil strength parameters, slope ratio and current direction on the slope stability are discussed in detail.

A multiparameter non-proportional shear strength reduction method for slope stability analysis based on energy evolution theory

A multiparameter non-proportional shear strength reduction method for slope stability analysis based on energy evolution theory

Reliability Assessment of an Open Pit Slope on Bong Iron Ore Mine

Slope stability on Bong mine is crucial for securing a balance in the gross national product of Liberia. The mine is being operated using conventional open pit methods with slope angles optimally designed to maximize ore stripping quantity. However, a working slope has displayed signs of uncertainty. The overall inclination of the slope is 56°, and the proposed maximal excavation is 315.42 m, but current depth in ore is approximately 50%. Based on the study of slope geological characteristics, the physical and mechanical parameters of rock mass and the geometrical calculation of stoping, the study is tailored on the mechanism of inspecting stress-strain behavior in response to seasonal variation of rock moisturization as a more suitable means of stope slope stability analysis in this case. This study took full account of local rainfall and other meteorological conditions. Slope stability is investigated via stereographic projections and stability assessment using the Shear Strength Reduction (SSR) method based on FLAC (Fast Lagrangian Analysis of Continua) numerical modeling technique in three dimensions to predict the stress-strain behavior of the open-pit slope and evaluate its stability state. Global stability has been analyzed under natural and saturated conditions and it is found that the slope is critically stable and needs proper attention.

Analysis of Clay Slopes with Piles Using 2D and 3D FEM

The aim of this paper is to compare between results of the 2D finite element method (FEM) and results of the 3D (FEM) when they are used to assess the factor of safety of clay slopes stabilized with vertical piles. It is expected that this comparison will aid engineers to judge and convert the results of the simplified 2D analysis to the more realistic results of the sophisticated 3D analysis that simulates the real behavior of slopes having infinite length. Extensive numerical modelling of homogeneous clay slopes stabilized with a row of piles and underlined by a bed of rock are carried out using the PLAXIS 2D program (version 8.2) and the PLAXIS 3D program (version 2010), which are both based on the shear strength reduction method to evaluate the factor of safety of the slope. The increase in factor of safety (FSI) of the stabilized clay slope is investigated considering many parameters, which include, the slope width, location of the piles, piles diameter, piles spacing and shear strength of the clay. Results of both PLAXIS programs are presented and compared in terms of increase in the FSI % relative to cases of slopes without stabilizing piles.

Evaluation of geometrical parameters affecting on the optimal slope design of Shadan Gold-Copper Open Pit Mine

The main objective of this research is to present a stable and optimal design of the ultimate slope of the eastern wall of Shadan Gold-Copper open pit mine based on the calculation of minimum factor of safety (1.20) by numerical modeling method under different conditions of slope geometry. Numerical modeling was performed using finite difference method (FDM) and FLAC3D software which is capable of calculating the factor of safety (FOS) by shear strength reduction method. Therefore, a set of 3D numerical models in different scenarios were investigated by varying the geometrical properties of the pit slope (width, height and face angle of bench, pit depth and overall slope angle). Based on the analysis carried out during the different scenarios, finally the fifth scenario with minimum safety factor of 1.20 was introduced as the proposed pattern. According to the initial design (first scenario) with a safety factor of 1.39, in the fifth scenario by decreasing the benches width from 6.8 m to 5 m and increasing their height from 10 m to 12 m which increases the slope angle of the bench face (from 70 degrees to 73 degrees) and overall slope angle (from 43 degrees to 52 degrees), safety factor of the ultimate slope was reduced to a minimum of 1.20. The maximum impact of the change in the safety factor is related to shear strain and horizontal displacement in the model such that the maximum shear strain (1.12 e-2 m) and the maximum horizontal displacement (-25.75 cm) are related to the fifth scenario with minimum safety factor (1.20). Whereas, the maximum vertical displacement (29.63 cm) is related to the first scenario model (FOS = 1.39) with the maximum slope height (pit height) of about 219 m, which shows the least influence on the value of the safety factor.

System reliability analysis of soil slopes through constrained optimization

As a slope may have numerous potential slip surfaces, its failure probability as a system is usually different from that of a single slip surface. Nevertheless, the system failure probability of a slope is often governed by several representative slip surfaces. How to identify the representative slip surfaces is important for system reliability analysis of soil slopes. Previous studies on representative slip surface identification mainly focus on circular slip surfaces within the framework of limit equilibrium methods; there are also relevant researches, albeit limited, within the framework of finite element/finite difference analyses based on the shear strength reduction method. By viewing the task of representative slip surface identification as a multidesign point identification problem, a barrier-based optimization method is suggested in this paper to identify representative slip surfaces of arbitrary shape based on the shear strength reduction method. A multiple starting point strategy is suggested to enhance its efficiency. For the three slopes examined in this paper, the method suggested is capable of identifying representative slip surfaces efficiently without prior assumption on their shapes.

Importance sampling for system reliability analysis of soil slopes based on shear strength reduction

ABSTRACT Probabilistic methods are increasingly used to quantify the effect of uncertainties on slope stability assessment. The shear strength reduction method can be used for slope stability analysis without prior assumption on the shape of the failure surfaces, and hence is an attractive method for slope stability analysis. Since it is computationally more demanding than limit equilibrium methods, reliability analysis based on the shear strength reduction method is often considered as computationally challenging. In this paper, an importance sampling method is suggested to conduct system reliability analysis of soil slopes based on the shear strength reduction method. In the suggested method, the design points are first identified using a response surface method. Then, a sampling function is constructed centred at the design points. An efficient method is used to identify the failure samples based on the shear strength reduction method. Results from two illustrative examples show that the suggested importance sampling method is an effective and robust tool for system reliability analysis of soil slopes.

Stability analysis of twin circular tunnels using shear strength reduction method

This paper investigates the face stability of twin circular tunnels horizontally aligned in cohesive undrained soil under plane strain conditions. The shear strength reduction method in the two-dimensional finite-element limit analysis programme is used to obtain rigorous upper and lower bounds of the factor of safety (FoS) for various depth ratios (C/D) and centre-to-centre spacing ratios (S/D) between the tunnels. Since the undrained shear strength is not a function of the mean normal stress, stability results are independent of loading directions. Therefore, the stability (in collapse or blowout) for this problem is well expressed by using Broms and Bennermarks’ original stability number N = (σs + γH − σt)/Su. The variations of the FoS have been presented for different combinations of stability numbers (N) and geometries (C/D and S/D). The FoS and the stability number results are compared and validated by using the finite-difference method as well as other existing solutions available in the literature. The results from this study are summarised in stability charts for use by designers and practising engineers.

Factor of safety of strain-softening slopes

Abstract Stability analysis of strain-softening slopes is carried out using the shear strength reduction method and Mohr-Coulomb model with degrading cohesion and friction angle. The effect of strain-softening behavior on the slope factor of safety is investigated by performing a series of analyses for various slope geometries and strength properties. Stability charts and equations are developed to estimate the factor of safety of strain-softening slopes from the results of traditional stability analysis based on perfectly-plastic behavior. Two example applications including an open pit mine in weak rock and clay shale slope with daylighting bedding planes are presented. The results of limit equilibrium analysis and shear strength reduction method with perfectly-plastic models were in close agreement. Using perfectly-plastic models with peak strength properties led to overly optimistic results while adopting residual strength properties gave excessively conservative outcomes. The shear strength reduction method with a strain-softening model gave realistic factors of safety while accounting for the process of strength degradation.

Slope Stability Analysis Using Genetic Simulated Annealing Algorithm in Conjunction with Finite Element Method

The calculation of factor of safety and the determination of the critical slip surface (a slip surface with the minimal factor of safety) are essential steps in stability analysis of soil slopes. In this study, a genetic simulated annealing algorithm (GSA), which combines the genetic algorithm and the simulated annealing algorithm, is proposed to quickly and accurately locate the critical slip surface of soil slopes. The corresponding factors of safety of slip surfaces are calculated based on the stress field of soil slopes that are computed by finite element method (FEM). The search ability of GSA for the critical slip surface of an earth-rock dam slope is proved to be more accurate and efficient compared with the golden-section method based on the same stress field calculated by FEM. In addition, a practical slope with complex soil layering is presented to further illustrate the reasonability of the calculation results of GSA in conjunction with FEM. The numerical simulations shows that the factor of safety and the critical slip surface determined using GSA with FEM is in good agreement with that using the shear strength reduction method.

A statistics-based discrete element modeling method coupled with the strength reduction method for the stability analysis of jointed rock slopes

The stability of jointed rock slopes can be effectively analyzed using the discrete element method (DEM). However, the criteria for terminating the DEM iterative calculation process and determining the factor of safety (FOS) are not well defined. In this paper, a displacement-statistics-based discrete element modeling method (DSDM) is proposed to analyze the stability of jointed rock slopes by coupling with the shear strength reduction method (SRM). In the presented DSDM, two important criteria are defined: (1) a statistics-based criterion for terminating the iterative calculation process of the DEM modeling in the stability analysis of jointed rock slopes, and (2) a statistics-based criterion for determining the FOS of a jointed rock slope when coupling DEM and SRM. The novelty of the proposed DSDM is that statistical information of the global displacements around the potential slip surface of the jointed slope, rather than the local displacements of several characteristic points, are utilized to define the criteria for terminating the DEM iterative calculation process and determining the FOS. To verify the effectiveness of the proposed DSDM, the FOS of a simplified jointed rock slope is first calculated using the proposed DSDM, and then compared with the FOS obtained using the finite difference method (FDM). Moreover, the proposed DSDM is applied to analyze the stability of a real high-steep bedding rock slope. The numerical simulation results for the real rock slope are consistent with the in-situ observations. The proposed DSDM is thus capable of effectively analyzing the stability of jointed slopes with potential slip surfaces.

On the Computational Precision of Finite Element Algorithms in Slope Stability Problems

Although the finite element method (FEM) has been used extensively to analyse the slope stability problems, the computational precision and definition of failure are still two main key concepts of finite element algorithms that attract the attention of researchers. In this paper, the modified Euler algorithm and the explicit modified Euler algorithm with stress corrections are used to analyse two dimensional (2D) slope stability problems with the associated flow rule, based on the shear strength reduction method. The rounded hyperbolic Mohr-Coulomb (M-C) yield surface is applied. Effects of the element type and various definitions of failure on the computational precision of 2D slope stability problems are evaluated. Conclusions can be drawn that the modified Euler scheme is applicable when the factor of safety (FOS) is small; however, the explicit modified Euler algorithm with stress corrections is more precise if the factor of safety is relatively large. The fully integrated quadrilateral isoparametric element is better than the triangular element in terms of the precision. With respect to the definition of failure, the displacement mutation of the characteristic point combining with the continuums of the plastic zone can be regarded as a reliable definition of failure and can be widely used to perform and analyse numerical simulations of slope stability problems.

Practical Use of Modified Hoek–Brown Criterion for Soil Slope Stability Analysis

Many slopes are comprised of soils that exhibit a nonlinear shear strength or failure envelope, and multiple mathematical relationships have been developed to account for this nonlinearity. At the same time, the numerical shear strength reduction (SSR) method has become a common method for analyzing the stability of slopes. Despite these developments, a practical, commercially available method to include nonlinear shear strength in numerical analysis has not been established for soil. The Generalized Hoek–Brown (GHB) model provides a nonlinear failure criterion, but is formulated for use with rock. This paper proposes a Modified Hoek–Brown (MHB) criterion to make the model applicable to soil and leverage the GHB criterion present in many numerical analysis packages. Past applications of SSR to the GHB are discussed and a numerical method for reduction of the parameters in the context of soil slopes is proposed. A simple wedge analysis validates the MHB method for a linear envelope. Three examples of increasing complexity compare results of limit equilibrium with both finite element and finite difference SSR analyses. In general, the different numerical methods yield very similar results. The SSR method using MHB predicts critical strength reduction factors 2–5% lower than the limit equilibrium factors of safety. The approach presented in this paper allows practitioners to model nonlinear shear strength in finite element strength reduction analysis for cases where this nonlinearity is judged to be an important factor.

Selected components of geological structures and numerical modelling of slope stability

Abstract This paper presents the impact of selected essential aspects of geological structure on the state of slope stability as assessed by changes in the safety factor (SF). The engineering geological slope features that were analysed include: (i) changes in soil cohesion and internal friction angle, (ii) presence of a weak soil layer and its span, (iii) structural discontinuity (i.e. fault), (iv) soil permeability properties and water conditions (i.e. groundwater level, long and heavy rainfall). A certain scheme of slope stability calculations has been proposed for a case involving complex geological conditions. The numerical modelling of a hypothetic slope was performed using the shear strength reduction method based on the finite element method.

Stability of Irrigation Canal Slopes Considering the Sea Level Rise and Dynamic Changes: Case Study El-Salam Canal, Egypt

Stability of canals slopes are of paramount importance in engineering works due to its interaction with the infrastructure including roads networks and buildings. The failure of these slopes could cause human disaster, catastrophic environmental, and economic losses. The present study aims to investigate the stability of canals slopes considering the climate changes through sea level rise, fluctuation of groundwater level and the seismic actions. The study was simulated on the North Eastern part of Nile Delta aquifer, Egypt using the finite difference code of Visual MODFLOW. Moreover, the groundwater flow under the effect of sea level rise was investigated to study its effect on slope stability of El-Salam Canal, Egypt. Furthermore, the finite element program of Phase 2 was implemented, and safety factors were calculated using the shear strength reduction method (SSRM). The models are calibrated and verified through experimental work using permeability and seepage model. Moreover, the two models were applied on El-Salam Canal considering three scenarios to identify the safety factors including the effect of sea level rise (SLR), earthquake acceleration and a combination of the two scenarios. The results indicated that dynamic response values of the canal slope have different variation rules under near and far field earthquakes. Finally, the damage location and pattern of the slope failure are different in varying groundwater conditions.