Deterministic and Probabilistic Stability Analysis of Soil Slope — A Case Study

In this paper, stability analysis of dry cohesion-less soil slope of height 6m with buried pipeline with effect of blasting is carried out by using numerical method. Stage wise construction of soil slope and installation of concrete pipeline of 0.5m thickness and of 2m diameter is considered while doing numerical modeling using finite difference based geotechnical software FLAC 3D (Fast Lagrangian Analysis of Continua in 3 dimension). Soil in free-field condition for blasting is calibrated and the radial velocities obtained from FLAC 3D model are compared with empirical values from CONWEP program as well as velocities using scalar wave equation. Restricted zone for slope is defined as the area surrounding the slope where pipeline should not be installed to avoid the slope instability due to blasting. To propose this restricted zone, blasting in pipeline is carried out at 30 different locations in the foundation soil. It has been noticed that restricted zone for soil slope is up to the depth of 8.5m with respect to allowable peak particle velocity (PPV) and from depth of 4m to 9.5m with respect to allowable peak particle displacement (PPD) from the face of soil slope. The effects of lateral and longitudinal position of pipeline in foundation soil, property of foundation soil, location of blasting in pipeline on the slope stability are also evaluated which can provide a guideline for design of pipeline in soil slope where blasting can be expected.

The performance of the stability chart (SC), limit equilibrium (LE), and finite element (FE) methods for stability analysis of weathered volcanic rock slopes under static and earthquake loads is not fully understood. This research aimed to evaluate the performance of the SC, LE, and FE methods for slope stability analyses by studying a case of a weathered volcanic rock slope at the Leuwikeris Dam diversion tunnel in Indonesia. Site characterisations were carried out to obtain the input parameters for the static and pseudostatic slope stability analyses. The results showed that using various search methods of failure surface and the suggested optimum number of finite elements, multiple non-circular failure surfaces were predicted from the LE and FE methods that were not anticipated in the initial slope design based on the SC method. The location and shape of the failure surfaces from the LE method agreed with those from the FE method. The difference between the Fs values from the static LE analysis and those from the static FE analyses was less than 14%, but the discrepancy increased up to 78% in the pseudostatic analyses. This study highlights the importance of validating the results from one method with the other methods to prevent slope failures.

The stability analysis of slopes is crucial for designing appropriate slope stabilisation methods based on the physical and engineering properties of the soil in the slope area. Slope stability is typically evaluated using the factor of safety (FOS) determined through the Limit Equilibrium Method (LEM). However, the Finite Element Method (FEM) has gained significant attention in geotechnical engineering for conducting comprehensive numerical slope stability analyses. By employing mathematical models and computational algorithms, engineers can simulate slope behaviour and predict stability more accurately and efficiently than traditional methods. Thus, this paper aims to analyse the FOS of slopes and identify the critical slip surface using the LEM and FEM performed by computer software. Two slope profiles were analysed using GEO5 for LEM and PLAXIS 2D for FEM. The findings were compared and discussed. The results show that the FEM generally yields higher FOS values, while the LEM provides slightly lower values. The shapes and locations of the critical slip circles are almost identical for each analysis and method. Overall, this comparative study is crucial in ensuring the validity of the performed analysis by utilising computer software to expedite the analysis and design of the suitable slope stabilisation method.

From the examples of several past worldwide disasters caused by earthquakes, scientists and researchers realized the requirement for incorporation of vertical earthquake loading in the dynamic stability analysis of soil slopes. However, in earlier studies, the vertical component of the ground motion has been neglected, and the importance has been given to only horizontal seismic acceleration for the assessment of the stability under seismic loading conditions. In this paper, a finite element method based pseudo-static stability analysis was carried out by taking horizontal and vertical seismic acceleration together. A two-dimensional hypothetical slope model was developed by using the finite elements under plain-strain conditions. The seismic behavior of the slope under joint earthquake loading was described by means of the safety factor, displacement, and yield acceleration. The results showed that the slope which was found stable after applying the horizontal seismic loading that fails due to combined seismic loadings. Further, the impacts of vertical seismic acceleration on the slope stability were examined by means of parametric studies. Finally, the validity of the numerical analysis was established by comparing the result with that obtained from analytical analysis based on the sliding block mechanism. The study recommends that for comprehensive stability estimation of slopes under seismic loads, the combined seismic loading should be considered in order to achieve a safe design.KeywordsVertical seismic accelerationFinite elementPseudo-static stability analysisFactor of safetyYield acceleration

The design of slopes in open pit mines requires an in-depth understanding of the ground behavior to predict the potential failure mechanism and to better determine the stabilization measures. This study compares the critical slip surface defined by the limit equilibrium method (LEM), the limit analysis (LA), and the finite elements method (FEM) for the stability analysis to better approach the stability on a multi-layered slope. The safety factor, the size, and the location of the critical slip surface obtained from the applied methods are considered in the comparisons. This study highlights some features that affect the slope stability and presents a procedure for addressing the evaluation challenges in a multi-layered formation. Moreover, it presents some aspects of the upper-bound computation on the safety factor of a layered slope subjected to the effects of pore water pressures. Based on the obtained results, the critical slip surface defined by the limit equilibrium method compares well with the slip mechanism suggested by the limit analysis and the finite element approach. In view of the differences in the shape and location of the critical slip surface, as well as the values obtained for the safety factor, it is recommended that an engineer should analyze critical slopes using the finite element method in combination with the limit equilibrium or limit analysis method as a cross reference. The authors propose that in defining the potential failure mass, consideration must be given to the conducted field research and monitoring.

A rain-induced landslide has occured in Guyon Village, Tengklik Tawangmangu District Karanganyar Regency, Central Java Province, Indonesia on February 2009. The movement was initiated by crack occurrence, 30 cm in depth and 2 meter in length. Such crack continuously developed in depth, extention and numbers, until then it resulted in land subsidence up to 260 cm in depth. Accordingly, ten houses were damaged and ten of families must be evacuated. This subsidence is very potential to further grow and create more consequences for human life and houses / land damage. Therefore, this research is carried out to understand the influence of geological factors and rainfall to the landslide phenomena. This research conducted engineering geology investigation such as mapping, drilling, insitu test, XRD test, soil mechanic test and slope stability analysis by limit equilibrium method i.e. Seep/W and Slope/W. By those research activities, the cause and mechanism of landslide can be understood. Rainfall characteristics which triggered such landslide can also be identified.
 
 Based on those investigations, it is found that the landslide occurred in slow rate sliding (creep) due to the control of slope stratigraphy conditions and gentle slope inclination, which is induced by rainfall. Stratigraphy condition that plays important role in landslide mechanism are the permeable layers consisted of sandy silt (shear strength 12 kPa) and silty sandstone (shear strength 18 kPa) overlaid above impermeable andesite breccia (shear strength 104 kPa). Undulating slope may induce landslide in creep rotational type. Based on slope stability simulation, it is known that rainfall triggered landslide is rainfall 20 mm/ day average precipitation in 55 days and rainfall 20 mm/ day average precipitation in 49 days followed by one day with 178 mm/ day average precipitation.
 
 Keywords: Landslides, slope stability

Shallow failures occur frequently in both engineered and natural slopes in expansive soils. Rainfall infiltration is the most predominant triggering factor that contributes to slope failures in both expansive soils and clayey soils. However, slope failures in expansive soils have some distinct characteristics in comparison to slopes in conventional clayey soils. They typically undergo shallow failures with gentle sliding retrogression characteristics. The shallow sliding mass near the slope surface is typically in a state of unsaturated condition and will exhibit significant volume changes with increasing water content during rainfall periods. Many other properties or characteristics change such as the shear strength, matric suction including stress distribution change with respect to depth and time. All these parameters have a significant contribution to the expansive soil slopes instability and are difficult to take into consideration in slope stability analysis using traditional slope stability analysis methods based on principles of saturated soil mechanics. In this paper, commercial software VADOSE/W that can account for climatic factors is used to predict variation of matric suction with respect to time for an expansive soil cut slope in China, which is reported in the literature. The variation of factor of safety with respect to time for this slope is computed using SLOPE/W by taking account of shear strength reduction associated with loss of matric suction extending state-of-the art understanding of the mechanics of unsaturated soils.

Failure of soil slopes is observed under static loading, dynamic loading, and rapid drawdown conditions. In the present study, soil nails are installed at an inclination of 10°,15°, and 30°with the horizontal and subjected to tensile stresses. Nailing is carried out in homogeneous soil slope subjected to dynamic loading and assuming a planar failure surface passing through the toe of the slope. The global factor of safety is calculated analytically considering both resisting forces and driving forces. The influence of various factors like inclination angle of the nails with the horizontal, combinations of horizontal and vertical seismic acceleration coefficients, along with soil friction angle on the factor of safety is studied. It is observed that factor of safety reduces with increase in seismic acceleration coefficients and inclinations angle of soil nails. Design charts obtained using the proposed method can be used for analysis of reinforced soil slopes under seismic conditions.

Slope stability has been a long-standing problem in geotechnical practice. The difficulty in analyzing slope stability may be attributed to geological complexity and versatile environments, but the limitations of analysis methods should not be ignored. In this work, the conventional limit equilibrium methods and the FE stress-based limit equilibrium methods with special emphasis on their limitations are reviewed, and the advantages of the finite element method with the capability of strength reduction are pointed out and illustrated by using some slope examples. Particularly, a flowchart of decision tree on selecting single-grid or two-grid search scheme is proposed for the shear strength reduction finite element method of slope stability analysis. Based on some slope examples, it is demonstrated that the automatic selection or switch between the single-grid scheme and the two-grid scheme can be remarkably superior to the single mesh scheme from the perspectives of computational cost and software development.

The limit equilibrium analysis through the horizontal slice method is used to study the seismic stability of reinforced soil slopes by satisfying the equilibrium of the horizontal and vertical forces as well as moments. Unlike the pseudo-static (PS) method, the pseudo-dynamic method consideres the effects of time and phase difference of the P and S waves propagation inside the soil mass. In this paper, the PS, the conventional pseudo-dynamic (CPD), and the modified pseudo-dynamic (MPD) methods are used to study the seismic stability of reinforced soil slopes. In addition, the equivalent linear method is implemented to analyze the site response for the purpose of calculating the soil dynamics parameters required for the seismic stability analysis of soil slopes via the MPD method. A MATLAB code is developed to calculate via the abovementioned methods. Using the log-spiral slip surface, this code considers the distribution of reinforcements as uniform and variable spacing. In addition, the effect of surcharge pressure on the seismic stability of the slope is included in this study. The obtained results showed that, in general, the MPD method combined with the equivalent linear analysis would produce more critical results than other methods.

Physics-guided neural network-based framework for 3D modeling of slope stability

The stability evaluation of the slope commonly uses limit equilibrium methods, for example, Fellenius’ method in Japan. The limit equilibrium methods have two limitations. (1) It is necessary to divide the sliding mass into slices, and to set up some additional equations to make the problem statically determinate. (2) It is necessary to search sliding surface with a minimum safety factor. Shear strength reduction finite element method (SSR-FEM) can solve the limitations of the limit equilibrium methods. This paper inspects superiority of the slope stability analysis by SSR-FEM. And, as a model case, the failure of base ground of the embankment is considered. Comparing the calculated results of SSR-FEM with limit equilibrium method, we point out the problems inherent in limit equilibrium method for the model case when the slip surface is assumed to be circle. We propose an approach to use SSR-FEM for slope stability analysis in practical design. ) ' tan ( tan ' , ' ' 1 F F c c F F φ φ − = = (4) In SSRFEM, firstly, the initial stresses in slope are computed using the elastic finite element analysis. The vector of externally nodal forces consists of three parts: (1) surface force; (2) body force(total unit weight of soils); and (3) pore water pressure. Secondly, stresses and strains are calculated by the elasto-plastic finite element analysis, where the reduced shear strength criterion. The shear strength reduction factor F is initially selected to be so small, for example 0.01, that the shear strength is large enough to keep the slope in elastic stage. Stresses at some Gaussian points reach the yielding condition with the shear strength reduction factor F in Equation 3 increased gradually. When the stress at anyone Gaussian point reaches the yielding condition, the increment of the shear strength reduction factor will make stresses at more Gaussian points reach the yielding condition because of the residual force induced by the decrease in the shear strength soils.

Static and quasi-static stability analysis of embankment dams is of vital importance in different stages of dam’s design, construction and operation. The stability can be studied using different techniques which are generally analyzed through Limit Equilibrium Method. Base on this main method, the critical slip surface is selected and the shear strength required to counter the slip at the selected surface is obtained and compared with shear strength of the soil at that surface in order to obtain confidence coefficient. In the present research, the Geo-studio Slope/w software that is a geotechnical software based on finite element method and is widely used in geotechnical field, is employed in order to analyze the stability of the body and foundation of Narmab dam in Golestan province. Narmab dam is a homogeneous embankment dam with a height of 60 m, crest length of 807 m and reservoir volume of 115 million cubic meters. The confidence coefficients provided by the software are compared to the permissible confidence coefficients. Moreover, the sensitivity of the confidence coefficients values to the changes in the effective factors, adhesion and internal friction coefficient, is analyzed. The analyses were performed on 8 values (±5, ±10, ±15, ±20) of c and φ and the obtained values of confidence coefficients were compared. In addition, a comparison was made between different methods of stability analysis. According to the static and quasi-static conditions, Narmab dam is stable in all loading stages (End of Construction, First Impounding and Steady State Seepage and In general, only for the static conditions of the end of construction stage, the sensitivity of adhesion is greater than the angle of internal friction, but, in other conditions and stages, the sensitivity of friction angle has more effects.

A Limit Equilibrium Method Based on Geostress Calculated by Implicit Stabilized Node-Based Smoothed Finite Element Method for Stability Analysis of Soil Slopes

Slope stability represents an area of geotechnical analysis in which finite element method provides a lot of benefits over limit equilibrium. In this paper, the authors apply a finite element code, PLAXIS, on slope stability analysis with various conditions to state out sensitivities of not only the soil parameters, slope configuration and groundwater condition but also numerical condition that one would encounter when making a FE slope design. It demonstrates that slightly conservative safety factor is obtained using FEM over the ones from limit equilibrium method. Intensity of mesh for simulation domain shall be selected as a fine level for an acceptable accuracy and economical computation time. Element nodes slightly affect the result of safety factor and final deformation of the slope.