Rock slope reliability analysis based on distinct element method and random set theory

Quantifying coal rib stability and support requirements using bonded block modeling and reliability analysis based on the random set theory

The intermediate principal stress (σ2 ) effect is a mechanical property inherent in many rock and soil materials. However, the effect of σ2 is often ignored in slope stability analyses, and its impact on slope stability is seldom investigated. The primary purpose of this study is to thoroughly investigate the impact of the σ2 effect on slope stability via numerical method. A detailed numerical analysis using the Finite Difference Code Fast Lagrangian Analysis of Continua (FLAC) and Unified Strength Theory (UST) is conducted. The numerical analysis evaluates the values of the Factor of Safety (FOS) for two types of slopes (plane strain and axisymmetric) using the Strength Reduction Method (SRM), and the impact of the σ2 effect on slope stability is analysed. The study found that the influence of the σ2 effect on slope stability is not sensitive to the values of friction angle φ, cohesion c, and slope height H, but increases with increasing slope angle σ values. Furthermore, the stability of the plane strain slope is more affected by the σ2 effect than the axisymmetric slope. The impact of the σ2 effect on the footing capacity and slope stability were compared, and the impact of the σ2 effect on slope stability is significantly lower than its effect on the bearing capacity of footings. The innovation of this paper is to systematically analyse the effect of σ2 on slope with different geometric shapes and soil parameters and reveal the inherent characteristics of σ2 effect on the stability of soil slope.

Application of distinct element method in dynamic analysis of high rock slopes and blocky structures

In order to fully understand the different effect of strength reduction method on slope stability analysis in different instability criterion, and solve the problems related to the instability of slope, this paper uses the platform of the finite element software ABAQUS to carry out the research that finite element strength reduction method analyzes the stability of homogeneous soil slope in different instability criterion. Moreover, in detail, this paper analyzes the difference between slope safety factor and the soil strength parameters change on the effect by using strength reduction method in different instability criterion. The research shows that by using the strength reduction method, the safety factor has been affected by different instability criteria, but its influence affected by the soil strength in a certain range of the parameters are decided, at the same time, soil cohesion, internal friction angle, Poisson ratio and other parameters for the development of the plastic zone and the shape of the sliding surface also have some influence on the critical state of the slope.

Recently, the stability of slopes during earthquakes has become to be an important engineering problem, especially in case of the earthquake-proof design of nuclear power plants. But, for fissured rock slopes, some problems are remained unresolved, because they can not be treated as continua. The authors have been investigating toppling failure of slopes, from a point of view which regards a fissured rock mass as an assemblage of rigid blocks. DEM (Distinct Element Method) proposed by Cundall (1974) seems to be very helpful to such a investigation. So, in this paper, the applicability of DEM to toppling failure of slopes is examined through the comparison between DEM results and theoretical or experimental results using 3 simple models.

Stability analysis of steep rock bedding slope with weak structure planes using strength reduction method was simulated in this paper. The post processing function can display the development condition of the plastic zone, which is the criterion for instability of the slope. Analysis with working conditions of natural circumstance, after excavation, and the slope reinforced by anchor shank after excavation were put forward. Failure modes and safety coefficients of the slope proved that weak plane is the main factor controlling slope failure. Simulation results shown that strength reduction method is appropriate in predict the shape and position of the potential failure surface of steep rock bedding slope.

Road construction is accompanied with the occurrence of the cut slopes. Therefore, when the roads are constructed in mountainous terrain, the number of slopes is increased and the slopes are widely scattered in the regional area. In addition, the stability of rock cut slope is mainly dependent upon geological characteristics such as discontinuities in rock mass. In this study, the regional stability analysis technique based on Geographical Information System (GIS) was developed and applied to practical case, in which the road construction was planned and the planned cut slopes were widely scattered. GIS is the effective tool to deal with the widely scattered and the enormous number of data. Various factors affecting on the slope stability analysis, such as the structural domain, the orientation and dip angle of the cut slopes, and the friction angle of discontinuities, were considered as the input parameters for GIS. By overlaying input data layers and using the developed computer algorithm, the factor of safety (F.S.) values, as an index of slope stability were calculated for each failure mode, which considered for stereographic analysis and limit equilibrium analysis simultaneously. In this research, the factors of safety for each failure mode are evaluated and the minimum factor of safety is also evaluated in the divided small area. In order to verify the developed analysis method, the results of the cut rock slope stability were compared with actual failure modes and locations in the study area. Finally, the stable and economically appropriate cut angle for the planned rock slopes were suggested by using the developed algorithm and applying allowable F.S. value.

Stability analysis of rock slopes is a complex problem because of uncertainties involved in the rock mass properties. The probabilistic approach is a rational way to deal with these uncertainties. This article investigates the stability of a rock slope by deterministic and probabilistic approaches by considering uncertainty in peak and residual strength parameters and strength-drop in stress-strain behavior of the rock mass. A Geological Strength Index (GSI) based on a quantitative approach was used to estimate the statistical parameters of peak and residual strength parameters. Reliability index of the slope was then estimated using Hong’s Point Estimate Method coupled with the finite element method. The approach is demonstrated using an important case study of a Himalayan rock slope supporting the piers of the world’s highest railway bridge. It was observed that the factor of safety and reliability index for the slope was highly sensitive to residual strength parameters, and; hence, ignoring strength-drop from the rock mass behavior and uncertainty in residual strength parameters can overestimate the factor of safety and the reliability index of rock slopes. A parametric study is carried out to evaluate the influence of the coefficient of variation of uniaxial compressive strength of intact rock, the Hoek-Brown strength parameter of intact rock, roughness and alteration parameters of the joints on the probability of failure and the reliability index. The approach is verified by comparing the estimated displacements along the slope with in-situ measured displacements observed during field monitoring over the years. The approach used can be extended to the rock slopes or rock slides where high displacements in the slopes are expected due to triggering forces like seismic forces, excavation or structural loads.

Discontinuous deformation analysis (DDA) and the distinct element method (DEM) are discrete element methods for solving the same class of problems: the elements are rigid or homogenously deformable, and contacts form and break as the system evolves in time. Both methods were originally developed algorithmically, DDA using the principle of virtual work and DEM from the balance equations. Differences between the two methods are algorithmic: coupled contacts (DDA) versus uncoupled contacts (DEM), and right Riemann time integration in accelerations (DDA) versus central difference time integration in velocities (DEM). Here a theory for discrete element methods is developed based on Cosserat points, taking an algorithmically neutral point of view. Changing the point of view away from algorithmic details exposes the mechanics underlying discrete element technology. Application of Hamilton’s principle of least action applied to the resulting lagrangian induces the balance equations, which are discretized using generalized Newmark schemes. Notational conventions useful for specific numerical implementations (DDA or DEM) may then be chosen by practitioners according to taste and utility.

A chart-based seismic stability analysis method for rock slopes using Hoek-Brown failure criterion

This paper proposes the coupling of reliability analysis methods with various mechanical approaches, for a slope stability assessment. Probabilistic strategies include Monte Carlo Simulation method (MCS), First and Second Order Reliability Methods (FORM, SORM), Mean-Value First-Order Second-Moment method (MFOSM) and Quadrature method (QM). Three mechanical models are considered: a Caquot-Taylor formula, a limit equilibrium method of Bishop and a finite element (FE) model based on the strength reduction method (SRM). The present study assumes both the cohesion and friction angle of the soil as uncertain input parameters, to be modelled as correlated random variables. The dependence of the slope reliability on the mechanical modelling and used probabilistic strategies is highlighted.

The rapid development in the construction of infrastructure on the hilly terrain has led to excavation of large bodies of rock mass to form cut slopes, resulting in the deformation and reduction in the stability of the rock material. As the slopes were cut more than 10 years ago, it is worried that there should be strength deterioration of the rock slope that could affect the stability of the slope. A study should be carried out to evaluate the recent condition of the slope in terms of its stability and safety after a long period of the exposure. A field study was conducted to collect the discontinuity data and laboratory test for the purpose of stability analysis using the existing stability analysis scheme of Rock Mass Rating (RMR) and Slope Mass Rating (SMR). The study was taken place at an exposed cut slope of a highway in Sri Jaya, Pahang. The objective of this study is to determine and evaluate the stability of the rock cut slope. A classification of the discontinuity parameters such as the strength, Rock Quality Designation (RQD), spacing, aperture, infilling, persistence, weathering, and groundwater have been used to determine the rock mass condition. The classification also need laboratory test for the point load strength (PLT) parameter. The RMR classification showed the rock to be very good condition, while the SMR showed the slope to be completely stable to stable. This study provide a good database in assessing the rock slope condition from time to time for the slope authority management.

Previous laboratory studies and Distinct Element Method (DEM) simulations have shown that the preparation method used to create samples for testing can affect the sample fabric and hence the mechanical response observed. The specimen preparation methods traditionally used in the laboratory were developed to recreate a given depositional pattern or in-situ soil fabric. Differences in soil response have been attributed to variations in the initial fabric of the sample even when the samples are created at the same densities. If DEM simulations are to provide meaningful insight into soil response observed in element tests, it is important for the initial state (packing density and stress level) and fabric anisotropy of the computer generated sample to closely match the physical reality. This is particularly true where element tests are used to validate DEM models. A key challenge is the lack of quantitative data on the fabric of real physical test specimens. Several approaches have been documented in the literature for generating the initial configuration of specimens for DEM simulations, i.e. artificially creating a percolating (stress transmitting) granular material. Approaches that are commonly used include radius expansion, compression using rigid boundaries, and pluviation under gravity loading. This paper examines the influence of the method chosen on the macro- and micro-scale properties of the material generated. The methods considered involved generating particles as a diffuse cloud at their target size, followed by pluviation under gravity loading with and without a mesh that modeled a sieve. The study fits within a broader research project in which multidirectional simple shear tests on steel spheres will be replicated in DEM simulations. © 2012 American Society of Civil Engineers.

A comparison between the distinct element method and the finite element method for analysis of the stability of an excavation in jointed rock

This paper is an inquiry into the suspected relationship between toppling and large deep-seated landslides along the Beaver Valley, Glacier National Park, British Columbia. The study area includes the Heather Hill landslide, one of several in the valley, and adjacent slopes that show varying degrees of toppling disturbance. The development of the Heather Hill landslide is simulated using the distinct element method of numerical analysis. The rock mass is modelled using deformable columns whose boundaries represent a coarse approximation of in situ discontinuity patterns. An intercalated change in the predominant lithologies and a concomitant change in discontinuity spacings are modelled by varying column thickness and material properties. The analysis confirms that a deep-seated failure surface can develop as a result of the toppling process. The intercalated change in lithologies and the related change in discontinuity spacings account for the curvilinear failure surface and the headscarp position of the Heather Hill landslide. These variables are believed to also control the overall distribution of landslides in the Beaver Valley. The paper demonstrates that the distinct element method provides an effective basis for quantitative analysis of large scale toppling. Many more applications will be needed to refine the geometric and material property generalizations used in this study. Nevertheless, the method appears to offer considerable promise for elucidating problems of rock slope behaviour in both slope engineering and geomorphology. Key words: toppling, landslide, British Columbia, mountains, numerical modelling, distinct element method.