Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

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.

Rapid and robust slope failure appraisal using aerial photogrammetry and 3D slope stability models

Slope failures are an inevitable aspect of economic pit slope designs in the mining industry.Large open pit guidelines and industry standards accept up to 30%of benches in open pits to collapse provided that they are controlled and that no personnel are at risk.Rigorous ground control measures including real time monitoring systems at TARP(trigger-action-response-plan)protocols are widely utilized to prevent personnel from being exposed to slope failure risks.Technology and computing capability are rapidly evolving.Aerial photogrammetry techniques using UAV(unmanned aerial vehicle)enable geotechnical engineers and engineering geologists to work faster and more safely by removing themselves from potential line-of-fire near unstable slopes.Slope stability modelling software using limit equilibrium(LE)and finite element(FE)methods in three dimensions(3D)is also becoming more accessible,user-friendly and faster to operate.These key components enable geotechnical engineers to undertake site investigations,develop geotechnical models and assess slope stability faster and in more detail with less exposure to fall of ground hazards in the field.This paper describes the rapid and robust process utilized at BHP Limited for appraising a slope failure at an iron ore mine site in the Pilbara region of Western Australia using a combination of UAV photogrammetry and 3D slope stability models in less than a shift(i.e.less than 12 h).

Determination of Optimum Slope Design for Northern Boxcut in Zone 5 KhoeMacao Copper Mine, Botswana

An optimum design of box cuts in soil formations is very crucial in order to obviate the major risk factors originating from the collapse of sidewalls and flooding of excavations during storm rainfall. The present paper aims to present a holistic classification of the Kalahari Formation stratigraphy in Zone 5 and define engineering properties of each lithological unit, in order to establish a safe working design. For the present objectives, collection of data was carried out through logging core from selected geotechnical boreholes drilled within vicinity of the proposed Northern mine box cut. Hydrogeological assessments and feasibility studies within the purview of study region were also considered. Geotechnical logging parameters gathered on site were derived from the Rock Mass Rating system (RMR) for design requirements [1]. Input parameters and material characteristics taken from laboratory test results provided by KCM were incorporated in the analysis. The box cut slopes were modelled in “Rocscience software” for evaluation of safety factor using “limit equilibrium method”. Slope optimization required the slope surface to be as steep as possible while maintaining an adequate factor of safety ranging from 1.5 - 1.8. For the box cut design with optimum safety, the recommended parameters are: stable slope angle—35° - 40°;ramp angle—8°, depth of pit—60 meters;bench width—4.9 meters and the bench length—13.25 meters.

Improved Statically Solvable Slice Method for Slope Stability Analysis

Although slice methods are simple and effective slope stability analysis approaches,they are statically indeterminate.Several modifications of the slice method,such as the Spencer,MorgensternPrice,and Chen-Morgenstern methods,are statically determinate and solvable as they assume the inter-slice force inclination angle;however,there is a small gap between the assumptions and actual landslide stability analysis.Through reasonable theoretical analysis,the Su slice method provides a reliable approach for determining the inter-slice force inclination angle that can be used in slice analysis to accurately analyse,calculate,and evaluate the stability of landslides.However,the Su slice method requires further research and analysis,especially in terms of the parameter values sinλbiandρ.In this study,we investigated more accurate methods for calculating the parameters sinλbiandρ.In addition,an adjustment coefficient(μ)was introduced to improve the solution method for the inter-slice force inclination angle.The inter-slice force inclination and safety factors of three landslides with arc-shaped slip surfaces and one landslide with a polyline-shaped slip surface were analysed and compared using the different slice methods.The improved inter-slice force inclination not only satisfies the calculation of static force equilibrium condition but also satisfies the calculation of both the force and moment equilibrium conditions.The improved method for calculating inter-slice force inclination presented the best correlation.The safety factors calculated using the improved Su slice method were close to those obtained using numerical simulations and the Morgenstern-Price method.Despite negligible differences among the safety factors calculated using the Su slice,improved Su slice,and M-P methods,the accuracy of the improved Su slice method was better than the M-P method in terms of inter-slice force inclination angles which can be useful to improve protection engineering design.

A Model of Debris Flow Forecast Based on the Water-Soil Coupling Mechanism

Debris flow forecast is an important means of disaster mitigation. However, the accuracy of the statistics-based debris flow forecast is unsatisfied while the mechanism-based forecast is unavailable at the watershed scale because most of existing researches on the initiation mechanism of debris flow took a single slope as the main object. In order to solve this problem, this paper developed a model of debris flow forecast based on the water-soil coupling mechanism at the watershed scale. In this model, the runoff and the instable soil caused by the rainfall in a watershed is estimated by the distrib- uted hydrological model （GBHM） and an instable identification model of the unsaturated soil. Because the debris flow is a special fluid composed of soil and water and has a bigger density, the density esti- mated by the runoff and instable soil mass in a watershed under the action of a rainfall is employed as a key factor to identify the formation probability of debris flow in the forecast model. The Jiangjia Gulley, a typical debris flow valley with a several debris flow events each year, is selected as a case study watershed to test this forecast model of debris flow. According the observation data of Dongchuan Debris Flow Observation and Research Station, CAS located in Jiangjia Gulley, there were 4 debris flow events in 2006. The test results show that the accuracy of the model is satisfied.