Three-dimensional Slope Stability Research Articles

Three-dimensional critical slip surface locating and slope stability assessment for lava lobe of Unzen volcano

Even Unzen volcano has been declared to be in a state of relative dormancy, the latest formed lava lobe No.11 now represents a potential slope failure mass based on the latest research. This paper concentrates on the stability of the lava lobe No.11 and its possible critical sliding mass. It proposes geographic information systems (GIS) based three-dimensional (3D) slope stability analysis models. It uses a 3D locating approach to identify the 3D critical slip surface and to analyze the 3D stability of the lava lobe No.11. At the same time, the new 3D approach shows the effectiveness in selecting the range of the Monte Carlo random variables and locating the critical slip surface in different parts of the lava lobe No.11. The results are very valuable for judging the stability of the lava lobe and assigning the monitoring equipments.

Assessment of 3D Slope Stability Analysis Methods Based on 3D Simplified Janbu and Hovland Methods

AbstractAn assessment of three-dimensional slope stability analysis methods in terms of safety factors using several idealized sliding masses composed of plane sliding surfaces was made. Three-dimensional safety factors were calculated and compared for different study cases considered in this study on the basis of the exact solution methods, the Hovland method, and the 3D simplified Janbu method. Parameters investigated in this study included the effect of water pressure, horizontal seismic force, the changing gradient of a sliding surface, the changing lateral gradient of a sliding surface, and anchor force. Results showed that the Hovland method gives smaller safety factor values compared to the exact solutions, especially in cases of narrow failure width and high water pressure along sliding surfaces whereas the 3D simplified Janbu method gives the same safety factor values as the exact solutions

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm3 potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.

A numerical simulation of landslide-prone slope in Himalayan region—a case study

Stability of slope will always a problem due to its geodynamic nature of Himalayan region. The area investigated belongs to the Lower Siwalik formation, which is prone to failure due to presence of various weak planes or structures present in the rock mass. Frequent landslides causing loss of life, property, disturbance of morphological, surface and subsurface water flow pattern. A huge landslide in the Amiyan area occurred in 1999 and blocked the Gaula River which caused loss of agricultural land and other properties as well as waterlogged upstream side. The debris of Amiyan slope contains soil and sandstones of various types. This article deals with instability analysis of slopes of the Amiyan area, near Kathgodam, Nainital, Uttarakhand. This area experiences a number of local as well as regional slides. Extensive field surveys have been carried out to understand the geological detail. Laboratory experiments have been conducted to determine the various physicomechanical properties of rock mass. These properties have been used as input parameters for the numerical simulation. A number of researchers have used two-dimensional numerical models to simulate the slide area. Three-dimensional slope stability studies provide a better understanding of the mechanism of failure as well as zone of influence. The computed deformations and stress distribution, along the failure surface, have been compared with the field measurements and found to be in good agreement with field observations. In this case, finite difference method has been applied on the stability analysis of Amiyan slope. The study indicates that the slope is vulnerable and needs proper protection.

Three-Dimensional Slope Stability Analysis with Rotational Failure Mechanism

This paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. An upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. The theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads need to be found. According to the upper-bound theorem, for a kinematically admissible velocity field an upper bound of the collapse load can be obtained by equating the power dissipated internally in an increment of displacement to the power expended by the external loads. Such kinematically admissible velocity fields have to comply with the kinematical boundary conditions and compatibility conditions. A rotational mechanism consisting of three slip surfaces is used to determine the factor of safety for a slope or the ultimate limit load of a foundation with eccentric load near a slope. This mechanism includes two lateral surfaces and a surface at bottom. As the soil is assumed to obey the associated flow rule, the angle between the relative velocity vector and velocity discontinuity has to be equal everywhere with soil's friction angle (φ). The geometries of lateral surfaces are represented by a nonlinear differential equation. A surface with log-spiral section is used for bottom surface of the mechanism. To obtain the minimum upper-bound, an algorithm is proposed to optimize the failure mechanism. Results from this algorithm for typical conditions are comparable to those of other existing methods. Dimensionless diagrams for various conditions are presented which can be used to predict the bearing capacity of a foundation with eccentric load located on a slope.

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

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

Three-Dimensional Stability Analysis of Convex Slopes in Plan View

A method of three-dimensional slope stability analysis for convex slopes in plan view is presented here based on the upper-bound theorem of the limit analysis approach. The method can also be used to determine the bearing capacity of foundations adjacent to such slopes. A rigid-block translational collapse mechanism is considered in which energy dissipation takes place along planar velocity discontinuities. Comparing the bearing capacity of foundations, numerical results indicate that the one located near convex slopes has less capacity than the one located near straight slopes. Inversely, slopes not subjected to surcharge loads are more stable when they are convex. Concerning the bearing capacity analyses, consideration of the curvature effect of convex slopes is more significant in frictional soils whereas for slope stability analyses, mentioned effect is of prime importance in cohesive soils. Numerical results of proposed algorithm are presented in the form of nondimensional graphs.

Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods

In this paper, three-dimensional (3D) slope stability analysis is analyzed by the strength reduction method (SRM) and the limit equilibrium method (LEM) for several cases. In general, the factors of safety (FOS) and the failure modes obtained by these two methods are in good agreement. The authors have discovered many interesting results which appear to be surprising, but a more detailed analysis by the SRM and LEM along with some physical insight have suggested that these results may be true for simple slopes. It is also found that the 3D SRM can be very sensitive to the convergence criterion, boundary conditions and the design of the mesh, and that it is more difficult to define the ultimate limit state with the 3D SRM as compared with the corresponding two-dimensional (2D) analysis. It is concluded that a proper 3D analysis requires great care and judgment, and a trial and error analysis may be required for both the SRM and LEM, as the actual failure mode and the solution domain are not known in advance.

Three-Dimensional Asymmetrical Slope Stability Analysis Extension of Bishop’s, Janbu’s, and Morgenstern–Price’s Techniques

Most existing three-dimensional (3D) slope stability analysis methods are based on simple extensions of corresponding two-dimensional (2D) methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. In this paper, 3D asymmetric slope stability models based on extensions of Bishop’s simplified, Janbu’s simplified, and Morgenstern–Price’s methods are developed. Under these new formulations, the direction of slide is unique and is determined from 3D force/moment equilibrium. Results from the new formulations are similar to the classical methods in normal cases but are numerically stable under transverse load. Further, the writers demonstrate that the present formulation is actually equivalent to the axes rotation formulation by Jiang and Yamagami but is much more convenient to be used for general problems. The writers have also discovered some inherent limitations of 3D limit equilibrium analysis which are absent in the corresponding 2D analysis.

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.

Potential role of compressional structures in generating submarine slope failures in the Niger Delta

The study area, offshore Nigeria, is located in one of the compressional zones within the Niger Delta, which is characterized by imbricate thrust structures. Although the low mean slope angle (around 2°), bathymetry data from the study area have shown the existence of several submarine landslides which coincide with known subsurface faulted compressive features. In this paper, we have focused on a submarine slide occurring in water depths ranging between 1690 and 1750 m. Headwall scars, internal architecture and associated deposits have been characterized using a combination of 3D seismic data, near-bottom echosounder seismic profiles, Kullenberg cores and in-situ geotechnical measurements. The slide shows horseshoe shaped headwall scars and depositional lobes with positive relief. Monitoring of excess pore pressure for 12 months indicates the presence of negative hydraulic gradients, which is either an indication of a local present-day mechanical activity of subsurface faults or related to the regional extension of the Niger Delta and the possible creation of a regional depression in the hydraulic regime. In order to identify the triggering mechanism of the observed landslide, a three-dimensional slope stability model (SAMU-3D) based on the upper bound theorem of plasticity was used. Calculation results have shown that the gravity loading generated by the sediment weight alone is not sufficient to explain the observed submarine slide. Cylindrical cavity expansion theory was used to locally simulate the compressional structure movements and to evaluate the strength generated within the upper sediment layers. Slope stability assessment carried out by considering this additional structural strength has shown that regional compressional gravity driven deformation can explain the observed submarine failures.

Spatio-temporal estimation of shallow landslide hazard triggered by rainfall using a three-dimensional model

A shallow landslide triggered by rainfall can be forecast in real-time by modeling the relationship between rainfall infiltration and decrease of slope stability. This paper describes a promising approach that combines an improved three-dimensional slope stability model with an approximate method based on the Green and Ampt model, to estimate the time–space distribution of shallow landslide hazards. Once a forecast of rainfall intensity and slope stability-related data, e.g., terrain and geology data, are acquired, this approach is shown to have the ability to estimate the variation of slope stability of a wide natural area during rainfall and to identify the location of potential failure surfaces. The effectiveness of the estimation procedures described has been tested by comparison with a one-dimensional method and by application to a landslide-prone area in Japan.

Comments on ‘Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis’ by M. Xie, T. Esaki, C. Qiu, C. Wang [Computers and Geotechnics 33 (2006) 260–274

Comments on ‘Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis’ by M. Xie, T. Esaki, C. Qiu, C. Wang [Computers and Geotechnics 33 (2006) 260–274

Reply to “Comments on ‘Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis’ by M. Xie, T. Esaki, C. Qiu, C. Wang,” by R. Baker [Computers and Geotechnics 33 (2006) 260–274

Reply to “Comments on ‘Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis’ by M. Xie, T. Esaki, C. Qiu, C. Wang,” by R. Baker [Computers and Geotechnics 33 (2006) 260–274

Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis

Three-dimensional (3D) evaluation of slope stability is a widely addressed problem in the domain of geotechnical engineering. The growing popularity of the geographical information system (GIS) approach, with capacities ranging from conventional data storage to complex spatial analysis and graphical presentation, means that it is also becoming a powerful tool for geotechnical engineers. In this study, in which we combine GIS grid-based data with four proposed column-based models of 3D slope stability analysis, we have devised new correspondent GIS grid-based 3D deterministic models to calculate the safety factor of the slope. Based on the four GIS-based 3D slope stability analysis models, a GIS-based program, 3DSlopeGIS, has been developed to implement the algorithm where all the input data are in the same format as the GIS dataset. The 3DSlopeGIS system, which is an extension of the widely used GIS software package, represents the combined development of 3D slope stability analysis and GIS-based component object model (COM) skills. Since all related data are supplied in the GIS format, this new database approach will be convenient for the repeated renewal and consulting of data. Certain widely addressed examples are evaluated in this paper and the results show the correction and potential of this GIS-based tool as a means of assessing the 3D stability of a slope. Two practical slope problems have been evaluated using the 3DSlopeGIS system. The results illustrate the convenience of data management as well as the effective range selection of Monte-Carlo random variables and the critical slip surface location in some parts of a lava dome.

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.

WITHDRAWN: Geographical Information System-based computational implementation and application of spatial three-dimensional slope stability analysis

WITHDRAWN: Geographical Information System-based computational implementation and application of spatial three-dimensional slope stability analysis

A three-dimensional slope stability problem in clay

A three-dimensional slope stability problem involving a spherical failure surface in clay is often used in the literature as a benchmark example against which numerical models are validated. The factor of safety, which is used as a reference value, has been found to be inaccurate. This technical note shows how to obtain the correct value for the factor of safety and compares the result with those given by some numerical models used in practice.Key words: three-dimensional slope stability analysis, clay, undrained shear strength, factor of safety, spherical failure surface, comparisons.

Three-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodology

An erosion and force/moment equilibrium based three-dimensional dam breach model is developed for the non-cohesive earthen dam overtopping breach problem. The breach location can be anywhere along the dam. The model considers the topography of the entire dam site. Three-dimensional slope stability along the main direction of flow in the breach channel is checked. A second order hybrid-type of total variation diminishing finite-difference scheme is proposed to simulate the dam breach outflow by solving the two-dimensional shallow water equations. The scheme is shown to accurately reproduce supercritical, subcritical, and transcritical flows for the following analytical or experimental cases: one-dimensional theoretical dam break with initially dry and wet beds, steady flow over a bump, hydraulic jump, one-dimensional dam break with a bottom slope, and two-dimensional dam break with bottom and side slopes. Applications to a simple breach channel show that calculated flows match the broad-crested weir formula and reasonably fit the grids.

A three-dimensional upper-bound approach to slope stability analysis based on RFEM

An upper-bound limit analysis method based on rigid finite elements has been developed recently. Numerical procedures for implementing the three-dimensional upper-bound slope stability analysis using rigid finite elements are presented in the paper. The search for the minimum value of the factor of safety can be set up as a non-linear programming problem. Because of the existence of non-linear equalities, a special sequential quadratic programming (SQP) algorithm, CFSQP, is applied to obtain the optimal solution in the paper. Two test problems are used to examine the validation and capability of the present rigid element upper-bound limit analysis method by comparison with results obtained by other methods. A practical example illustrates the application of the present method in three-dimensional slope stability analysis.