Shear Strength Reduction Method Research Articles

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules

The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used criterion in rock slope stability analysis and is still the base for the shear strength reduction method applied in finite element modelling. Different proposals for estimating the equivalent strength parameters based on confining stress level are evaluated. The limitation of stress-dependent linear Mohr–Coulomb parameters is emphasized by analysing the vertical cut problem, for which, depending on the chosen stress level, different critical heights are obtained for the same material. Sensitivity analysis of geotechnical parameters used as input for failure criterion is performed to determine their influence on slope stability. Probabilistic analysis is conducted to determine the probability of failure when different flow rules are applied. If slope stability analysis is performed with an assumption of associative flow rule, the probability of failure is within the acceptable limits for the considered case study, while employing non-associative flow rule, the probability of failure is rather high. The chart is presented that could be readily used to estimate the combination of σci, GSI, and mi values that produce failure for the analysed case study.

Investigation of Shear Strength Reduction Method in Slope Stability of Reinforced Slopes by Anchor and Nail

Since the stability of slopes in infrastructures such as road and railroad embankments, excavations, and, in general, earthwork is important, analyzing the stability of these slopes has been one of the main focuses of geotechnical engineers. Although analyzing both reinforced and unreinforced slopes is needed, reinforced slopes require special attention as the reinforcement elements significantly affect the calculations. Hence, the current study’s aim is to find out the differences between obtained safety factors using the Limit Equilibrium Method (LEM) and Shear Strength Reduction Method (SSRM). For this purpose, first, the origin differences in terms of Safety Factor (SF) are theoretically determined according to basic formulas for the aforementioned techniques. Then, to verify the formula, several numerical modelings are carried out using in situ measured geotechnical data to better understand the differences in terms of safety factors. The results indicate that for the reinforced slope with an SF value of higher than 1, the SSRM provides a higher SF in comparison with the other techniques, and the origin of this difference is the definitions of the SF in the different methods.

Stability Assessment of the Dam of a Tailings Pond Using Computer Modeling—Case Study: Coroiești, Romania

Anthropogenic activities related to mining generate both progress and a vast amount of waste that is responsible for environmental degradation. The Jiu Valley is one of the areas of Romania where mining has affected large areas of land, used to build mines and tailings ponds. The former Coroiesti coal processing plant (CCPP) is such a location with a total area of 25 ha containing approximately 5.5 million tons of tailings. The assessment of the stability of tailings dams is extremely important from safety and environmental aspects. This study proposes a solution based on numerical methods for determining the stability of a section of the dam of a tailings pond. The model of tailings pond no. 1, compartment B, from the Coroieşti Coal Preparation was built using COMSOL Multiphysics. Two scenarios of stability analysis were conducted on a section of the tailings dam: the FOS was determined using the shear strength reduction (SSR) method for both the initial and the current state of this TP. This method is a modern alternative to the limit equilibrium method, and its implementation by COMSOL is new to our country, thus aligning this methodology with current worldwide trends and developments in the field. The results obtained proved to be in line with those calculated in the past with traditional analytical methods, proving that the safety criteria of the studied TP/TD are being met.

Coupled stability of offshore wind monopile foundations and submarine slopes under periodic loads

Long-term cyclic loading on offshore wind monopiles will lead to a decrease in the mechanical properties of the seabed near the monopile's foundation, therefore, causing instability of the submarine slope and the monopile foundation. To capture the accumulation strain caused by high cycle numbers and plastic deformation of seabed sands, the high cycle accumulation (HCA) model is complied with Mohr-Coulomb constitutive models. The shear strength reduction (SSR) method is used to obtain the safety factor of submarine slopes. The coupled numerical model simulates a 6 MW offshore monopile foundation with a single periodic lateral load applied on the monopile at the sea level, which represents concentrated wind and wave loads in storm conditions. The results show that the plastic zones begin to form at the monopile foundation, then extends towards the slope toe and slope top, and eventually across the entire slope, leading to slope instability. In this process, the safety factor of the slope is significantly reduced with each stage of the process. It was found that both the sharp changes of load amplitude and large average load also decreases the safety factors. Moreover, at the beginning of the monopile installation, the safety factor will increase by nearly 10%, but it will drop by nearly 30% due to long-term periodic lateral loads. Therefore, these have important implications for the installation of monopile foundations for offshore wind turbines (OWTs) since the slopes we consider are within the range of slopes at planned sites for OWTs. An increase in monopile diameter and embedded depth can enhance the overall slope stability. However, an increase in embedded depth could potentially instigate more extensive seabed landslides despite enhancing overall stability.

Stability of slope corners: a displacement-based FEM study

The stability of slopes is typically evaluated by two-dimensional plane strain analysis. However, many slopes exhibit three-dimensional (3D) geometries, including slope corners. Several researchers have studied the stability of slope corners but found that the factor of safety (FS) was close to the FS for the plane strain case. The results of a new series of 3D finite element method (FEM) simulating slope corners, including slope angle, plan view angle, radius of curvature, and slope height are presented. They confirm that the FS does not vary much for corners compared to the plane strain case. However, 220 cases using an elastic-perfectly plastic soil model together with the FEM shear strength reduction method show that the displacement field is very different at the corners compared to plane strain with differences reaching over 100%. The displacement ratio between corners and plane strain is presented as a function of the plan view angle of the corner. Often failure is defined at a chosen large displacement, as in the ultimate load of foundation elements. If this concept is carried over to slope stability, it would indicate that the FS of corners should be very different from the plane strain case. A possible explanation is discussed.

Lateral facing deformation versus factor of safety for geosynthetic-reinforced soil walls in a tiered configuration

Geosynthetic-reinforced soil (GRS) walls in a tiered configuration have been used for high earth retaining structures, especially in mountainous areas. More attention has recently been paid to lateral facing deformations and stability of such walls. A validated numerical model of a GRS wall was utilized to calculate the maximum lateral facing deformations and the maximum tensile forces in reinforcement layers in tiered GRS walls. The same model was used to compute their factors of safety (FS), using the shear strength reduction (SSR) method. A parametric study was carried out to assess the effects of backfill and foundation soil properties, reinforcement layout and stiffness, and tiered wall configuration on the maximum lateral facing deformations at the end of construction (EOC) and the FS values of the tiered GRS walls. Moreover, the relationship between the FS value and the normalized maximum lateral facing deformation at EOC was established. The comparison with the existing numerical results demonstrates that the empirical relationship established in this study can reasonably predict the FS values for tiered GRS walls.

Data augmentation for CNN-based probabilistic slope stability analysis in spatially variable soils

A novel methodology that involves the coupling of Convolutional Neural Networks (CNNs) and a data augmentation technique is proposed for slope reliability calculations. The methodology starts from generating a small set of random field samples, which are then calculated using the shear strength reduction method in the finite-difference scheme to obtain the associated factors of safety. Based on the theoretical relationship between the factor of safety and soil property values derived from the underlying mechanism of the shear strength reduction method, an innovative data augmentation technique is developed to enhance both the quantity and comprehensiveness of the dataset. A CNN model is then trained using the augmented dataset to learn the relationship between the factors of safety and random fields and predict the probability of slope failure. The effectiveness of the methodology is illustrated and validated using a c-φ soil slope and a multi-layered Su slope. The results show that CNNs are effective in interpreting high-dimensional random fields. In addition, through using the data augmentation technique, not only has the predictive capability of the CNN model been effectively boosted, particularly for cases involving low probability levels of failure, but the computational efficiency of the slope reliability analysis has also been improved.

Optimization variant of the shear strength reduction method and its usage for stability of embankments with unconfined seepage

In this paper, an optimization variant of the shear strength reduction method is introduced and used for the solution of embankment stability problems with unconfined seepage. The optimization framework is based on approximations of non-associated Mohr–Coulomb plastic models with associated ones, especially by using various Davis’ approaches. Next, the finite element method is considered and mesh adaptive solution concepts are developed for both the unconfined seepage and stability problems. In-house codes in Matlab are used for their implementation. Finally, two numerical examples inspired by geotechnical practice are investigated in order to demonstrate the accuracy of the optimization framework and to evaluate three different Davis’ approaches. The results are compared with commercial codes in Plaxis and Comsol Multiphysics.

System reliability analysis of landslides involving sliding surfaces using intelligent multiple response surfaces

The shear strength reduction method provides an effective tool of numerical analysis for landslides reliability analysis. However, it ignores the failure probability of the secondary failure surfaces and requires huge computational cost. To avoid these common criticisms, an intelligent multiple response surfaces method for system reliability using multiple response-surface method (MRSM) and least-squares support vector machine (LSSVM) is presented to evaluate the stability of complex multistage historic landslides with multiple sliding surfaces. Deterministic analysis of each sliding surface is first performed using the finite element method of sliding surface stress analysis, which is applied to obtain the safety factors of different sliding surfaces from the stress fields generated by finite element simulations. The LSSVM model with excellent nonlinear fitting ability is then employed to construct the multiple response-surface method (MRSM) of the sliding surfaces and a genetic algorithm (GA) is adopted to optimize the LSSVM. This proposed methodology is finally applied to investigate the probability of system failure of the Zhenggang landslide in southwestern China. The results indicate that the proposed approach can reduce the computational cost of finite element analysis in direct Monte Carlo simulation (MCS) by proper training using a limited of samples, and the calculation accuracy meets the engineering requirements of complex multistage historic landslides.

Earthquake Effects on Slope Stability by Using Finite Element Method. Case Study: Brazzaville City, Republic of Congo

The slopes are affected by the variations of slope gradient combined with the driving forces including external actions such as earthquake forces, producing shear stresses in the slopes, which are opposed to the soil shear resistance. Therefore, landslides are one of the most important worries on the social and economic viewpoint and for the quality of life of a local people. The present study is carried out in Brazzaville City, Republic of Congo where the region in its southern part is recognised to be geologically active, due to its tectonic background which has some influence on surrounding slopes or embankments. Then, it was used the shear strength reduction method to assess the slopes stability by using pseudo-static and static methods. Effects of various parameters on slopes stability are discovered by achievement of numerous analyses. Two magnitudes effects of earthquake on slopes stability for different height, slope gradient and shear resistance parameters were assessed by using the finite element code. Slope stability was evaluated considering its factor of safety from the usage of strength reduction method.

Some considerations on the role of joint spacing in rock slope stability analyses using a 3D discrete element approach

Stability assessment of potential wedge failures in rock slopes is usually carried out based on stereographic projection techniques and limit equilibrium analyses. Nevertheless, this methodology presents several limitations (i.e., lack of information on joint mechanical properties, oversimplification of the structure, etc.) 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 substantial number of simulations in which the factor of safety of two types of slopes, 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. A discrete fracture network (DFN) model was also implemented, with the aim of benchmarking results with those obtained from the original models. The joint spacing has been found to relevantly affect the values of the factor of safety of the slope, which showed variations of up to 40% in comparison with those obtained from limit equilibrium methods. This work provides an insight to a more realistic interpretation of rock slope analyses against wedge failures, particularly to better estimations of the factor of safety.

A combined shear strength reduction and surrogate model method for efficient reliability analysis of slopes

Surrogate models are often used to alleviate extensive computational burden for slope reliability analysis. How to efficiently train a surrogate model with high precision is always a nontrivial task. This paper proposes a novel method, which combines the shear strength reduction (SSR) technique, the surrogate model and the adaptive pool-based sampling strategy for efficient slope reliability analysis. The surrogate model is used to replace the time-consuming slope stability model in simulation-based reliability analysis, while the SSR technique coupled with an adaptive pool-based sampling strategy is innovatively adopted to search for the most informative samples to train the surrogate model, which can improve the computational efficiency significantly. Further, an expanded sampling method is suggested to improve the local prediction of surrogate model in other design space, enabling an efficient evaluation of the slope failure probability corresponding to different threshold safety factors. The main feature of the proposed method is that it takes advantage of SSR technique to efficiently generate training samples in the region of interest. Several slope examples are analyzed to validate the accuracy, computational efficiency as well as the applicability of the proposed method. The results show that proposed method outperforms other approaches in computational efficiency and can give accurate estimation of slope failure probability as well.

Slope stability analysis of deep-seated landslides using limit equilibrium and finite element methods in Debre Sina area, Ethiopia

Slope failure is a recurring natural hazard in the western margin of the Main Ethiopian Rift and especially around the Debre Sina area. To minimize the damage caused by failure events, a detailed investigation of landslide-prone areas identified using numerical modelling plays a crucial role. The main aim of this study is to assess the stability of slopes and to evaluate and compare safety factors calculated by the different available numerical methods. Stability analyses of slopes prone to different types of failures were performed with different techniques. The stability was assessed for slopes of complex geometry composed of aphanitic basalt, porphyritic basalt, tuff, and colluvium (poorly sorted clayey sand to silty sand) using the limit equilibrium method and the shear strength reduction method based on finite elements. Furthermore, numerical analysis was done under static and pseudo-static loading using the horizontal seismic coefficient to model their stability during a seismic event. Satellite images were used to select failure-prone slopes based on slope properties and identified past landslides, as well as to derive structural and geological information for the numerical models. The slope stability analysis indicates that the studied slopes are unstable, and any small-scale disturbance will further reduce the factor of safety and cause failure. The slope stability of landslide prone hills in the study area strongly depends on the saturation conditions and the seismic load.

Effect of Various Rainfall Conditions on the Roadside Stabilisation of Slopes in Gippsland

A distinctive slope stabilisation method that integrates two well-developed methods for slope stabilisation is analysed in this paper. The slope stabilisation method utilises embedded piles and geogrid-reinforced retaining walls with gabion basket wall facing. To study the effect of this integrated slope stabilisation method on the stability of the slope under the negative impacts of rainfall, a three-dimensional finite element model with fluid–solid coupling is adopted to indicate the rainfall infiltration process and investigate the corresponding slope responses. The shear strength reduction method is applied after fluid–solid coupling analysis to investigate the impact of various rainfall intensities and rainfall patterns on the stability of slopes with different configurations. The results from the comparison of slope responses among various configurations indicate that under the highest rainfall intensity, the integrated method improves the stability of the slope up to 41.2% and restrains the displacement increment of the road edge to a maximum of 12.5 mm. The most critical rainfall pattern for the stability of the slope has also been recognised in terms of the factor of safety and the variation in the negative pore-water pressure of the slope. The numerical results indicate that the back-loaded rainfall pattern always yields the lowest factor of safety and induces the highest loss of matric suction, which can be 23 kPa at the toe of the slope. Moreover, a comparison between two construction scenarios under various rainfall intensities was also conducted, which demonstrates that the reinforced filled slope configuration is preferable when the site conditions permit.

Sustainable Slope Stability Analysis: A Critical Study on Methods

When studying the stability of a slope, the first issue that needs to be clarified is the slip surface, which determines the minimum safety factor. The slopes investigated here are homogenous with three distinct gradients (1:1.5; 1:1; 2:1), two defined heights (H-3 m; H-8 m), and four different soil characteristics (S1—clayey silt, S2—sandy clayey silt, S3—sandy silty clay, S4—clay). The purpose of this paper is to develop a new methodology capable of estimating the safety factor and the shape and centre of the critical slip surface, delivering an improved estimate of slope probability of failure, which can represent a significant component in a more precise risk assessment. This paper compares distinct methods used in the slope stability analysis, examining their hypotheses and effects on the estimated safety factor and the centre and shape of the critical slip surface. The study compares the limit equilibrium results with those determined by the shear strength reduction method using an approach based on the upper-bound limit analysis to compare the predictions extracted from these methods with those from the finite element method (FEM) analysis. The finite element method discretizes the soil mass into finite elements. Hence, it establishes a kinematically admissible velocity field searching for the failure mechanism of the slope. Results for FEM show the influence of the slope geometry and the mesh size and density on the safety factor. In the study, plots of the regression curves of five different critical slip surface shapes, including a circular slip surface (benchmark), show that the shape of the failure surface depends on the shape and material of the slope. Furthermore, they show that the critical slip surface layout can approach a logarithmic spiral, damped sinusoid, parabola, etc.; the slip surface is not always circular. The analysis reveals that none of the approaches can consider all uncertainties concerning the factor of safety and the interpretations of critical slip surfaces.

Three-Dimensional Stability of Unsaturated Excavation Slopes Under Different Seepage Conditions: A Case Study

Three-dimensional stability analysis of soil slopes remains a hot topic in the field of geotechnical engineering. Considering the fluid–solid coupling effect, this study performs a number of numerical analyses on the stability of a 3D excavation slope located in the Wuxi Taihu Tunnel, China. Three typical cases of the issued slope are investigated, i.e., the slope at the initial state, with the water-stop curtain, and with both the water-stop curtain and concrete-sprayed layer. The shear strength reduction method was adopted to determine the factor of safety (FOS) of the slope. The distributions of pore pressures and wetting lines, the horizontal and vertical displacements, and the critical slip surface are presented. The results indicate that the water-stop curtain can prevent the groundwater seepage effectively. The water-stop curtain and concrete-sprayed layer are effective in restraining the slope deformation, altering the critical slip surface, and improving the slope safety.

DEM-Based Numerical Investigation of Seismic Stability of Rock Slope in Terms of Rigid Block Displacement

Abstract For the seismic behavior of a rock slope or more specifically a rock wedge, the limit equilibrium method is frequently utilized to determine the static and pseudo-static safety factor, and the Newmark method is usually applied to estimate the permanent dynamic displacement. However, the two methods are relatively complex, which negatively affects their usage in engineering practice. A new idea to analyze the static and dynamic stability of a complex rock slope was provided in this paper by combing the rigid discrete element method (DEM), shear strength reduction (SSR) method, and Newmark method. The research results show that (1) by setting the joint contact stiffness to a very large magnitude, the joint displacement caused by the reduction of joint contact stiffness during the SSR calculation process can be considered ignorable, making the contact behavior between the respective two joints approximately satisfy the rigid-plastic assumption. In this manner, it is feasible to calculate the static and pseudo-static safety factor (SF) and the permanent dynamic displacement of a rock wedge with the rigid DEM. (2) The SF and sliding forces of wedges can be directly calculated by this new method without any auxiliary assumption of motion direction or sliding type. Additionally, the new method is suitable for complex wedges, which is important to practical design. (3) The rigid DEM can be realized in 3DEC, which is testified in this paper by 5 classic static examples and 3 typical dynamic examples. (4) The effect of some important parameters, such as the excitation acceleration amplitude and dip of intersection line between two joints, on the dynamic displacement and SF under dynamic excitation was analyzed. The parameter analysis revealed that evaluating the seismic performance of a rock slope only with the pseudo-static SF would potentially underestimate the seismic displacement, under some special conditions. (5) An example case was presented in this paper that the seismic stability assessment of a block was performed with the proposed approach in terms of seismic displacement. And the slope reinforcement scheme was suggested with respect to exceedance probability. It is noted that the reinforcement scheme obtained from the rigid DEM has a better cost-saving benefit under the same SF. Overall, the knowledge gained in this paper may offer a new idea for the static and dynamic analysis to the rock slope stability.

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.