3D Slope Stability Analysis Research Articles

GIS-Based Implementation of Three-Dimensional Limit Equilibrium Approach of Slope Stability

The growing popularity of the geographical information system (GIS), with capacities ranging from conventional data storage to complex spatial analysis and graphical presentation, means it is also becoming a powerful tool for geotechnical engineers. In this technical note, integrating the GIS grid-based data with four proposed column-based limit equilibrium models of three-dimensional (3D) slope stability analysis, new correspondent GIS grid-based 3D deterministic models have been devised in order to calculate the safety factor of the slope. Based on four GIS-based 3D slope stability analysis models, a GIS-based program, 3DSlopeGIS, has been developed to implement the algorithm where the whole of the input data is in the same form as the GIS dataset. Certain widely addressed examples have been evaluated using 3DSlopeGIS and the results show the correction and potential of this GIS-based tool as a means of assessing the 3D stability of a slope. A practical slope problem has also been evaluated using the 3DSlopeGIS system, and the results have illustrated the convenience of data management.

An extension of 2D Janbu’s generalized procedure of slices for 3D slope stability analysis I

Based on 2D Janbu's generalized procedure of slices (GPS), a new three-dimensional slope stability analysis method has been developed, in which all forces acting on the discretized blocks in static equilibrium are taken into account in all three directions. In this method, the potential sliding mass is divided into rigid blocks and each block is analyzed separately by using both geometric relations and static equilibrium formulations. By introducing force boundary conditions, the stability problem is determined statically. The proposed method can be applied to analyze the stability of slopes with various types of potential sliding surfaces, complicated geological boundaries and stratifications, water pressure, and earthquake loading. This method can also be helpful in determining individual factor of safety and local potential sliding direction for each block. As an extension of 2D Janbu's method, the present method has both the advantages and disadvantages of Janbu's generalized procedure of slices.

An extension of 2D Janbu’s generalized procedure of slices for 3D slope stability analysis II

This paper provides a numerical approach on achieving the limit equilibrium method for 3D slope stability analysis proposed in the theoretical part of the previous paper. Some programming techniques are presented to ensure the maneuverability of the method. Three examples are introduced to illustrate the use of this method. The results are given in detail such as the local factor of safety and local potential sliding direction for a slope. As the method is an extension of 2D Janbu’s generalized procedure of slices (GPS), the results obtained by GPS for the longitudinal sections of a slope are also given for comparison with the 3D results. A practical landslide in Yunyang, the Three Gorges, of China, is also analyzed by the present method. Moreover, the proposed method has the advantages and disadvantages of GPS. The problem frequently encountered in calculation process is still about the convergency, especially in analyzing the stability of a cutting corner. Some advice on discretization is given to ensure convergence when the present method is used. However, the problem about convergency still needs to be further explored based on the rigorous theoretical background.

A Simple Monte Carlo Method for Locating the Three‐dimensional Critical Slip Surface of a Slope

Abstract Based on the assumption of the plain‐strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope‐stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column‐based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

A GIS-based method for locating the critical 3D slip surface in a slope

The minimum safety factor and the critical slip surface of a slope can be located using various methods of optimization or random search. However these methods have not been adopted to search for the three-dimensional (3D) critical slip surface. This paper proposes a new Monte Carlo random simulation method to identify the 3D critical slip surface, in which assuming the initial slip as the lower part of an ellipsoid, the 3D critical slip surface in the 3D slope stability analysis is located by means of a minimization of the 3D safety factor. Based on a column-based three-dimensional slope stability analysis model, a new geographic information systems (GIS) grid-based 3D deterministic model has been developed to calculate the 3D safety factor. Several practical cases, of known minimum safety factor and its critical slip surface by using a two-dimensional (2D) optimization or random technique, have been extended to 3D slope problems to locate the 3D critical slip surface and to compare with the 2D results. As another 3D case, a multi-strata slope, considering the effect of a fault and the underground water, is used to demonstrate the efficiency and capability of the proposed method. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference for simple slope geometries, but the associated 3D safety factor is definitely higher.

Geographic Information Systems-Based Three-Dimensional Critical Slope Stability Analysis and Landslide Hazard Assessment

In this paper, by combining the geographic information systems (GIS) spatial analysis function and a hydrologic analysis and modeling tool with a column-based three-dimensional (3D) slope stability analysis model, a new GIS grid-based 3D deterministic model has been developed for slope stability analysis. Assuming the initial slip as the lower half of an ellipsoid, the identification of the 3D critical slip surface in the 3D slope stability analysis is performed by means of a minimization of the 3D safety factor using Monte Carlo random simulation. By using this hydrologic analysis and modeling tool, dividing the whole study area into slope units, and taking each slope unit as a study object, the minimum 3D safety factor for each slope unit can be obtained, and the landslide hazard can then be mapped for the whole study area.

A simplified method for 3D slope stability analysis

This paper presents a simplified three-dimensional (3D) slope stability analysis method based on the limit equilibrium theory. The assumption involved in this method is of a parallel intercolumn force inclination, similar to Spencer's method in the two-dimensional (2D) area. It allows for the satisfaction of complete overall force equilibrium conditions and the moment equilibrium requirement about the main axis of rotation. The method has been proven to be numerically tractable for many practical problems. By combining this method with the 3D upper bound approaches, it is possible to bracket the accurate solution of a 3D slope stability analysis problem into a small range.Key words: slope stability analysis, three-dimensional analysis, limit equilibrium method, upper bound method.

GIS component based 3D landslide hazard assessment system: 3DSlopeGIS

In this paper, based on a new Geographic Information System (GIS) grid-based three-dimensional (3D) deterministic model and taken the slope unit as the study object, the landslide hazard is mapped by the index of the 3D safety factor. Compared with the one-dimensional (1D) model of infinite slope, which is now widely used for deterministic model based landslide hazard assessment in GIS, the GIS grid-based 3D model is more acceptable and is more adaptable for three-dimensional landslide. Assuming the initial slip as the lower part of an ellipsoid, the 3D critical slip surface in the 3D slope stability analysis is obtained by means of a minimization of the 3D safety factor using the Monte Carlo random simulation. Using a hydraulic model tool for the watershed analysis in GIS, an automatic process has been developed for identifying the slope unit from digital elevation model (DEM) data. Compared with the grid-based landslide hazard mapping method, the slope unit possesses clear topographical meaning, so its results are more credible. All the calculations are implemented by a computational program, 3DSlopeGIS, in which a GIS component is used for fulfilling the GIS spatial analysis function, and all the data for the 3D slope safety factor calculation are in the form of GIS data (the vector and the grid layers). Because of all these merits of the GIS-based 3D landslide hazard mapping method, the complex algorithms and iteration procedures of the 3D problem can also be perfectly implemented.

Errata for “Generalized Method for 3D Slope Stability Analysis” by Ching-Chuan Huang, Cheng-Chen Tsai, and Yu-Hong Chen

Errata for “Generalized Method for 3D Slope Stability Analysis” by Ching-Chuan Huang, Cheng-Chen Tsai, and Yu-Hong Chen

A 3D slope stability analysis method assuming parallel lines of intersection and differential straining of block contacts

A three-dimensional (3D) method of analysis of the stability of slopes was developed based on the sliding mechanism observed in the 1988 failure of the Kettleman Hills landfill slope (Kettleman City, California) and the associated model studies. By adopting a limit equilibrium concept, the method assumes the sliding mass as a block system in which the contacts between blocks are inclined. The lines of intersection of the block contacts are assumed to be parallel, which enables the sliding kinematics. In consideration of the differential straining between blocks, the shear stresses on the slip surface and the block contacts are evaluated based on the degree of shear strength mobilization on these contacts. The overall factor of safety is calculated based on the force equilibrium of the individual blocks and the entire block system as well. Based on comparisons with a series of hypothetical 3D and 2D problems with known solutions, the method was generally found to be accurate in predicting the stability of slopes involving a translational type of sliding failure. For rotational sliding failures in clays, however, the method appears to slightly overestimate the calculated factor of safety; up to as much as 10% in a typical problem examined in this study.Key words: slope stability, 3D method, limit equilibrium, block kinematics, strain incompatibility.

A three-dimensional slope stability analysis method using the upper bound theorem

A three-dimensional (3D) slope stability analysis method, based on its two-dimensional approaches proposed by Donald and Chen (Can. Geotech. J. 34 (1997) 853.) is presented in this paper. It starts from establishing a compatible velocity field and obtains the factor of safety by the energy and work balance equation. Optimisation is followed to approach the critical failure mode that offers the minimum factor of safety. The method is demonstrated to be identical to Sarma's limit equilibrium method (1979) that employs inclined slices, if it is extended to the 3D area. However, it has been established on a sound theoretical background supported by the upper bound theorem of plasticity. Test problems have demonstrated its feasibility. A feature of the method is its very simple way to obtain the factor of safety without complicated 3D force equilibrium evaluations. Limited assumptions are involved in this method and their applicability has been justified.

New Method for 3D and Asymmetrical Slope Stability Analysis

A new three-dimensional (3D) slope stability analysis method is developed based on two-directional moment equilibrium. This method calculates not only the safety factor but also the possible direction of sliding for semispherical and composite failure surfaces. As a result, the possible errors associated with assuming a plane of symmetry in 3D stability analyses are eliminated. Another advantage of the new method is to eliminate the tedious work on the coordinate transformation prior to the analysis. Two examples of symmetrical failure surfaces are used to verify the basic formulation in the present study. Three additional examples further demonstrate the applicability of the proposed method in analyzing 3D asymmetrical failure surfaces. An analysis on a slope, subject to asymmetrical excavation unloading and geological conditions, shows that using the method of one-directional moment equilibrium may give an overestimated safety factor of the slope.