Three-dimensional Slope Stability Research Articles

Three-dimensional (3D) slope stability analysis using stability charts

Stability of slopes is a very serious issue in the field of geotechnical engineering. The analysis and design of failing slopes requires a thorough knowledge of the failure mechanism in order to choose the right slope stability analysis method. The two-dimensional (2D) slope stability methods are very common to the engineers because of the simplicity in their assumptions. As a result the analysis results vary greatly between the different analysis methods. The importance of three-dimensional (3D) slope stability analysis greatly increased where the geometry of the problem becomes complex which makes it very difficult to solve using 2D analysis. A lot many 2D slope stability methods were extended to 3D methods since 1970s based on limit equilibrium (LE) and finite element approaches. In this paper, slopes were analysed using 3D limit equilibrium method (LEM) using SLIDE3 software having different geometry and soil parameters and finally stability charts were prepared to calculate the FOS of the slopes. It is found that the slope stability factor can be read from the stability charts without the need for iterations.

Three-Dimensional Slope Stability Analysis of Convex Turning Corners

AbstractSlopes forming convex corners are often constructed in practice. Observed failures of such corners possess three-dimensional (3D) characteristics. Hence, assessing corner stability requires...

Combined methodology for three-dimensional slope stability analysis coupled with time effect: a case study in Germany

High-steep slopes in open pit mines are much more likely to collapse due to mining operations. Challenges such as data acquisition, precise numerical models and adaptable methodologies have impeded more reliable results of slope stability analysis based on the current methods. Within this context, this paper proposes a combined methodology using light detection and ranging technology to capture high-resolution slope geometry, three-dimensional geological and geotechnical modeling technologies for creating high-quality numerical simulation models and finite-element slope stability analyses combined with a new automatic strength reduction technique to analyze complex geotechnical problems. At the end, the methodology introduces a time series analysis to improve the reliability of the calculated factor of safety. A case study in the deepest open pit mine in Hambach, Germany, was conducted to test and demonstrate the effectiveness and applicability of the proposed methodology.

3D effects of turning corner on stability of geosynthetic-reinforced soil structures

Current design procedures of Geosynthetic-Reinforced Soil Structures (GRSS's) are for walls/slopes with long straight alignments. When two GRSS segments intersect, an abrupt change in the alignment forms a turning corner. Experience indicate potential instability problems occurring at corners. The purpose of this study is to explore the effects of turning corner on the stability of reinforced slopes. Three-dimensional (3D) slope stability analysis, based on limit equilibrium, resulted in the maximum tensile force of reinforcement. Parametric studies required numerous computations considering various geometrical parameters and material properties. The computed results produced efficient practical format of stability charts. For long-term stability of reinforced slopes with turning corner, the influences of pore water pressure and seismic loading are also considered. Turning corner can improve the stability of reinforced slopes by virtue of inclusion of end effects. However, localized increase of pore water pressure or directional seismic amplification may decrease locally thus stability requiring strength of reinforcement larger than in two-dimensional (2D) plane-strain. While using 2D analysis for non-localized conditions may require stronger reinforcement, it also requires shorter reinforcement than in 3D analysis; i.e., 2D analysis may be unconservative in terms of reinforcement length.

Research on limit equilibrium method of three-dimensional slope stability

The limit state design method for slope stability has many assumptions which are approximate solution and analyzing the safety state of soil. Thus, this method is not a strict calculation method satisfying all the static equilibrium conditions of a three-dimensional sliding body. Based on the stress analysis of a point on a space curved surface, the fundamental equation for slope stability analysis without any assumption was established. Actual engineering cases confirm that the results obtained using the method reported in the paper are reasonable and significant for broad applications.

Three-dimensional slope stability analysis of block sliding slope failure at the Pikeview Quarry, El Paso County, Colorado

Three-dimensional slope stability analysis of block sliding slope failure at the Pikeview Quarry, El Paso County, Colorado

Three-dimensional simplified slope stability analysis by hybrid-type penalty method

In this study, we propose a three-dimensional simplified slope stability analysis using a hybrid-type penalty method (HPM). In this method, a solid element obtained by the HPM is applied to a column that divides the slope into a lattice. Therefore, it can obtain a safety factor in the same way as simplified methods on the slip surface. Furthermore, it can obtain results (displacement and strain) that cannot be obtained by conventional limit equilibrium methods such as the Hovland method. The continuity condition of displacement between adjacent columns and between elements for each depth is considered to incorporate a penalty function and the relative displacement. For a slip surface between the bottom surface and the boundary condition to express the slip of slope, we introduce a penalty function based on the Mohr-Coulomb failure criterion. To compute the state of the slip surface, an r-min method is used in the load incremental method. Using the result of the simple three-dimensional slope stability analysis, we obtain a safety factor that is the same as the conventional method. Furthermore, the movement of the slope was calculated quantitatively and qualitatively because the displacement and strain of each element are obtained.

Reliability analysis of three-dimensional rock slope

Reliability analysis is generally regarded as the most appropriate method when uncertainties are taken into account in slope designs. With the help of limit analysis, probability evaluation for three-dimensional rock slope stability was conducted based upon the Mote Carlo method. The nonlinear Hoek-Brown failure criterion was employed to reflect the practical strength characteristics of rock mass. A form of stability factor is used to perform reliability analysis for rock slopes. Results show that the variation of strength uncertainties has significant influence on probability of failure for rock slopes, as well as strength constants. It is found that the relationship between probability of failure and mean safety factor is independent of the magnitudes of input parameters but relative to the variability of variables. Due to the phenomenon, curves displaying this relationship can provide guidance for designers to obtain factor of safety according to required failure probability.

Study on the theory of three-dimensional limit analysis of soil and practical calculation

Based on the stress analysis of a point in space, the stress analysis of a point on a surface is performed, and then the relationship among the normal stress, the shear stress, and the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established, which include differential equilibrium equation of force, equilibrium equation of force, and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method, a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is reasonable and applicable.

Reply to “Discussion of ‘Numerical limit analysis of three-dimensional slope stability problems in catchment areas’ by Camargo et al. (DOI:10.1007/s11440-016-0459-3)” by Ukritchon et al. (DOI:10.1007/s11440-017-0589-2)

Reply to “Discussion of ‘Numerical limit analysis of three-dimensional slope stability problems in catchment areas’ by Camargo et al. (DOI:10.1007/s11440-016-0459-3)” by Ukritchon et al. (DOI:10.1007/s11440-017-0589-2)

Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method

A three-dimensional (3D) slope stability analysis method is presented in this paper based on three-dimensional independent cover based manifold method (ICMM3D) and vector sum method (VSM). ICMM3D is proposed in the framework of independent cover, which avoid the time-consuming and error-prone cover system generation of convention numerical manifold method (NMM). It is very suitable for the continuous/discontinuous deformation analysis in slope engineering. Then, with the stress field obtained by ICMM3D, VSM is employed to calculate the factor of safety, which is effective in computation and clear in physical meaning. In addition, a new strategy of discretization of the slip surface is proposed, which discretizes the slip surface into a set of calculating points in order to avoid errors caused by the special handling in the boundary columns in limit equilibrium method (LEM) and the tedious triangulation of the slip surface in VSM. Finally, genetic algorithm is employed to search for the critical slip surface. Numerical examples demonstrate the efficiency, accuracy and robustness of the proposed method.

Three-dimensional slope stability analysis using laser scanning and numerical simulation

ABSTRACTDetailed surface topography is important when analyzing the stability of slopes. Recent advances in new technologies such as interferometric synthetic aperture radar and light detection and ranging have allowed us to obtain high-precision profiles of distant landscapes and objects including detailed slope information for three-dimensional (3D) slope stability analysis. However, techniques of reconstructing 3D numerical models from scanned data of slope geometry have not been well investigated or tested. This paper proposes a comprehensive approach that integrates laser scanning and finite element method for slope stability analysis, particularly failure prediction under precipitation scenarios. The methodology is applied to a slope in the Wenchuan earthquake-stricken mountainous region that failed in 2013, triggered by severe rainfall. The modelling results show that the surface sampling resolution can affect the prediction accuracy of the potential failure zones. When constructing the slope model, the selected surface grid should be fine enough to capture the important topographic features of the slope while minimizing computation demand. This paper confirms that the proposed method can be successfully used to identify the potential failure zones of the investigated slope under severe rainfall conditions.

Limit analysis approach for accessing stability of three-dimensional (3-D) slopes reinforced with piles

ABSTRACTThe stabilization of slopes by placing piles is one of the most innovative and effective slope reinforcement techniques in the coastal engineering in recent years. Due to the simplicity and efficiency, limit analysis method is the most common approach for assessing the stability of slopes. However, the majority of existing limit analysis methods is limited to slope without the presence of piles. In this technical note, a novel upper-bound limit analysis method was proposed to access the stability of three-dimensional slopes reinforced with piles incorporating the admissible rotational failure mechanism where toe failure, face failure, and base failure were taken into account. The effects of key designing parameters, e.g., pile location, pile spacing, slope angle, slope width on the stability of earth slopes, and geometry of critical slip surface were presented and discussed. The results demonstrate that the proposed approach is more appropriate for assessing the stability of slopes reinforced with piles and can be also utilized in the design of piles stabilizing the unstable slopes.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

Numerical limit analysis of three-dimensional slope stability problems in catchment areas

Risk analysis of existing slopes in catchment areas requires quantification of their stability. This quantification becomes particularly difficult when dealing with larger areas under 3D conditions and including saturated and unsaturated water flow. This paper proposes the use of an effective numerical procedure to solve three-dimensional slope stability problems in large areas subjected to pore pressure effects. This numerical approach, numerical limit analysis, utilizes the finite element method and mathematical programming techniques. Mathematical programming is needed because the basic plasticity theorems for limit analysis can be cast as optimization problems. The generated optimization problem is formulated under a second-order cone programming framework, which is known to solve large-scale problems with great computational efficiency. The main objective of this work was to determine the slope safety factor and the collapse mechanism of soils governed by the Drucker–Prager yield criterion for large-scale 3D problems including pore pressure effects. This approach is applied to an experimental catchment in the Oregon Coast Range that failed after an intense rainfall. The results were compared with a previous stability analysis of the area available in the literature that used a novel 3D limit equilibrium method.

Three-dimensional slope stability problem with a surcharge load

Abstract. A semi-analytical solution for the three-dimensional stability analysis of the ultimate uniform patched load on top of a slope is developed by the limit analysis using kinematically admissible failure mechanisms. The failure mechanism which is assumed in the analytical solution is verified by three-dimensional strength reduction analyses and laboratory model test. Furthermore, the proposed method and the results are further compared with some published results for illustrating the applicability of the proposed failure mechanism.

Two and three-dimensional slope stability analyses of final wall for Miduk mine

In this research, Two and three-dimensional slope stability analyses of final slope for Miduk copper mine is investigated by using distinct element code. These analyses were repeated in three positions (dry- drained- wet) and were done for four walls of the mine; including eastern wall, northern wall, western wall and southern wall. The stability of Miduk copper mine walls were accomplished by distinct element code (UDEC&3DEC). Both 2D and 3D slope stability analyses were performed to establish the representative shear strength parameters to use in the analyses and to examine the differences in the results. The extended Mohr–Coulomb failure criterion was used for analyses. The rock mass was assumed to be permeable and also by the obtained data from surveying, laboratory tests and field observations. The results are as follows: - Water and pore pressure in the faults and main joints were the most important destabilizer factors in these analyses. - The factor of safety after the drainage improved (27–34) % and (20–28) % based on the 3D and 2D slope stability analyses, respectively. - The difference in factors of safety between the 2D and 3D slope stability analyses for the deeper groundwater table (water level in the elevation 2540 on the walls) is less than 7 %. The factors of safety obtained from 2D slope stability analyses are not necessarily more conservative than 3D slope stability analyses. Analyses of the slope after lowering of groundwater table by horizontal drains showed that the factor of safety of the slope has improved tremendously. The differences in factors of safety for 2D and 3D slope stability analyses are greater for low groundwater table as compared with those for high groundwater table. The results illustrated how 3D slope stability analyses have become less daunting to perform and can be incorporated into routine slope designs.

Three-dimensional rock slope stability analysis considering the surface load distribution

Previous studies on slope stability mainly focused on conditions under gravity load in which the slope tends to slide down along the potential slip surface. However, the existence of a horizontal load on the slope surface can restrain the slope-slipping trend and improve the stability of the slope, similar to the effect of a retaining wall. The slope failure mode can be altered by a sufficiently large horizontal surface load. In this case, the slope stability problem will be converted to a rock foundation stability problem. However, the reciprocal transformation of slope stability and rock foundation stability has been rarely studied. This study considers the Ice and Snow World project in Changsha, China, as the engineering background. This project is located at an abandoned mine pit, the structural load of which mainly acts on the top of the pit. To study the three-dimensional (3D) slope stability under the slope surface load, a 3D slope model is established using the numerical commercial code. The mechanical parameters of the rock mass, as well as the value and the distribution areas of the surface load, are changed to identify the corresponding safety factor of rock mass, deformation and failure mode.

Determination of three-dimensional shape of failure in soil slopes

This paper presents the application of particle swarm optimization (PSO) in three-dimensional (3D) slope stability analysis to determine the shape and direction of failure as the critical slip surface. A detailed description of adopted PSO is presented and a rotating ellipsoidal shape is introduced as the possible failure surface in the analysis. Based on the limit equilibrium method, an equation of factor of safety (FoS) was developed with the ability to calculate the direction of sliding (DoS) in its internal process. A computer code was developed in Matlab to determine the 3D shape of the failure surface and calculate its FoS and DoS. Then, two example problems were used to verify the applicability of the presented code, the first by conducting a comparison between the results of the code and PLAXIS-3D finite element software and the second by re-analyzing an example from the literature to find the 3D failure surface. In addition, a hypothetical 3D asymmetric slope was introduced and analyzed to demonstrate the ability of the presented method to determine the shape and DOS of failure in 3D slope stability problems. Finally, a small-scale physical model of a 3D slope under vertical load was constructed and tested in the laboratory and the results were re-analyzed and compared with the code results. The results demonstrate the efficiency and effectiveness of the presented code in determining the 3D shape of the failure surface in soil slopes.

Three-dimensional slope stability assessment of two-layered undrained clay

This paper uses the finite element upper and lower bound limit analysis methods to investigate the three-dimensional (3D) slope stability of two-layered undrained clay slopes. The solutions obtained from the slope stability analyses are bracketed to within ±10% or better. For comparison purposes, results from two-dimensional (2D) analyses based on the numerical limit analysis methods and the conventional limit equilibrium method (LEM) are also discussed. This study shows that 3D boundary of a slope can have significant effects on the slope stability. In addition, the results are presented in the form of stability charts which can be convenient tools for practicing engineers.