3D Safety Factor Research Articles

Simulation analysis on three-dimensional slope failure under different conditions

The failure mechanism of two-dimensional (2D) and three-dimensional (3D) slopes were investigated by using the strength reduction method. An extensive study of 3D effect was conducted with respect to boundary conditions, shear strength and concentrated surcharge load. The results obtained by 2D and 3D analyses were compared and the applicable scope of 2D and 3D method was analyzed. The results of the numerical simulation show that 3D effect is sensitive to the width of slip surface. As for slopes with specific geometry, 3D effect is influenced by dimensionless parameter c/( γHtanø). For those infinite slopes with local loading, external load has the major impact on failure mode. For those slopes with local loading and geometric constraints, the failure mode is influenced by both factors. With the increase of loading length, boundary condition exerts a more significant impact on the failure mode, and then 2D and 3D stability charts are developed, which provides a rapid and reliable way to calculate 2D and 3D factor of safety without iteration. Finally, a simple and practical calculation procedure based on the study of 3D effect and stability charts is proposed to recognize the right time to apply 2D or 3D method.

Limit Analysis and Stability Charts for 3D Slope Failures

The kinematic approach of limit analysis is explored in three-dimensional (3D) stability analysis of slopes. A formal derivation is first shown indicating that, in a general case, the approach yields an upper bound to the critical height of the slope or an upper bound on the safety factor. A 3D failure mechanism is used to produce stability charts for slopes. The slope safety factor can be read from the charts without the need for iterations. While two-dimensional (2D) analyses of uniform slopes lead to lower safety factors than 3D analyses do, a 3D calculation is justified in cases where the width of the collapse mechanism has physical limitations, for instance, in the case of excavation slopes, or when the analysis is carried out to back-calculate the properties of the soil from 3D failure case histories. Also, a 3D failure can be triggered by a load on a portion of the surface area of the slope. Calculations indicate that for the 3D safety factor of the loaded slope to become lower than the 2D factor f...

A preliminary method for the evaluation of the landslides volume at a regional scale

Dealing with the evaluation of the risk connected to the formation of landslide dams at regional scale, it is important to estimate the volume of the depleted material that can reach the riverbed. This information, combined with other elements (river dimensions, valley width, landslide velocity, etc.) allows making predictions on the possibility of river blockage. One of the problems of this approach is the lack of data concerning the shape and position of the sliding surface; this does not permit us to estimate the volume of the landslide material. The IFFI (Inventario dei Fenomeni Franosi in Italia, i.e. Landslide Inventory in Italy) project furnishes information, at different levels of precision, on nearly totality of the landslides existing in Italy. The first level of the IFFI (compiled for all slides) does not contain information on the depth of the sliding surface but contains data regarding the type and the activity of the slope movement. Along with this information the IFFI project also furnishes vector maps containing the boundary of each landslide and the main sliding direction. This paper describes the implementation of an algorithm aimed to define, with an adequate approximation, the 3D geometry of the sliding surface of rotational slides for which, on the basis of geologic maps available at regional scale, some geotechnical parameters can be known or estimated. The work also required the creation of a computer code useful for the 3D analysis of slope stability (3D safety factor) using the simplified Janbu method. All computer code has been created on a GNU-Linux OS and using shell scripting, based on GRASS GIS and R statistical software.

Three-dimensional slope stability analysis by elasto-plastic finite elements

Slope stability analysis is one of the oldest applications in geotechnical engineering, yet it remains one of the most active areas of study in both research and practice. The vast majority of slope stability analyses are performed in two dimensions under the assumption of plane strain conditions. Even when two-dimensional (2D) conditions are not appropriate, three-dimensional (3D) analysis is rarely performed. There are a number of reasons for this. The majority of work on this subject strongly suggests that the 2D factor of safety is conservative (i.e. lower than the ‘true’ 3D factor of safety). Even when 3D may be justified on geometric grounds, the available methods, being often based on extrapolations of 2D ‘methods of slices’ to 3D ‘methods of columns’, are complex, involve numerous assumptions, and are not readily modified to account for realistic boundary conditions in the third dimension such as sloping abutments. The power and versatility of the elasto-plastic finite element approach to slope stability analysis in 2D are well known, and these advantages are even more attractive in 3D. The paper demonstrates some 3D slope stability analyses by finite elements, placing the results in context with 2D solutions and validating the results where possible against alternative methods.

GIS-based 3D limit equilibrium analysis for design optimization of a 600 m high slope in an open pit mine

Combining the GIS (geographic information systems) grid-based data with four proposed column-based 3D slope stability analysis models, a comprehensive solution of a high-steep open-pit slope has been obtained. For six searching ranges, 19 critical slip surfaces of different sizes have been studied, in which the minimum 3D safety factor is 1.33. Comparison of 3D safety factors of designed and proposed slope plans shows for all the critical slip surfaces for the proposed plan, the smallest 3D safety factor is 1.33 under the most unfavorable condition. This means that the proposed plan of the high slopes, about 600 m, of an open pit (2–5° steeper than designed plan) is feasible.

Stability of earth–rockfill dams: Influence of geometry on the three-dimensional effect

A series of parametric studies were performed to investigate the three-dimensional (3D) effect on the stability of an earth–rockfill dam, with respect to some major factors, such as geometrical characteristics of the dam and topography of the canyon. The length–height ratio of the earth–rockfill dam clearly influences the 3D safety factor. A power function suitably expresses the relationship between the increment ratio for the safety factor and the length–height ratio. The canyon shape, gradient of dam slope and height of the dam significantly influence the 3D effect. The results may be used as a blueprint by combining the two-dimensional (2D) safety factor in common use, and the relationship between 2D and 3D safety factors established in this study.

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.

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.

Reliability analysis of three-dimensional dynamic slope stability and earthquake-induced permanent displacement

Different models were developed for evaluating the probabilistic three-dimensional (3D) stability analysis of earth slopes and embankments under earthquake loading using both the safety factor and the displacement criteria of slope failure. In the 3D analysis, the critical and total slope widths become two new and important parameters. The probabilistic models evaluate the probability of failure under seismic loading considering the different sources of uncertainties involved in the problem, i.e. uncertainties stemming from the discrepancies between laboratory-measured and in-situ values of shear strength parameters, randomness of earthquake occurrence, and earthquake-induced acceleration. The models also takes into consideration the spatial variabilities and correlations of soil properties. Five probabilistic models of earthquake-induced displacement were developed based on the non-exceedance of a limited value criterion. Moreover, a probabilistic model for dynamic slope stability analysis was developed based on 3D dynamic safety factor. These models are formulated and incorporated within a computer program (PTDDSSA). A sensitivity analysis was conducted on the different parameters involved in the developed models by applying those models to a well-known landslides (Selset landslide) under different levels of seismic hazard. The parametric study was conducted to evaluate the effect of different input parameters on the resulting critical failure width, 3D dynamic safety factor, earthquake-induced displacement and the probability of failure. Input parameters include: average values and coefficients of variations of water table, cohesion and angle of friction for effective stress analysis, scales of fluctuations in both distance and time, hypocentral distance, earthquake magnitude, earthquake strong shaking period, etc. The hypocentral distance and earthquake magnitude were found to have major influence on the earthquake-induced displacement, probability of failure (i.e. probability of allowable displacement exceedance), and dynamic 2D and 3D safety factors.