Boundary effect of toppling failure based on three-dimensional mechanical model

Previous researches on the mechanical model of toppling failure mainly concentrated on twodimensional mechanical model(TwDM) analysis. The TwDM analysis assumes the width of the slab beam is unit width without considering the lateral constraint force. The assumed conditions are obviously different from the site conditions, thus there is a certain difference between the calculated results and the field work. A three-dimensional mechanical model(ThDM)of toppling failure was established, considering that the slab beam was mainly subject to self-weight, the frictional resistance of interlayer and lateral constraint force. Due to the progressive characteristics of toppling failure, the concept and the formula of the first fracture depth(FFD) of toppling was raised and constructed. The case study indicates that the ThDM is more effective and can be accurately used to calculate the toppling fracture depth of the slab beam. The FFD decreases proportionally with the increase of slab beam width. FFD grows fast when the slab beam width is less than 2.0 m and it tends to be stable when the slab beam width is above 2.0 m. The FFD decreases with the increase of the lateral constraint coefficient, indicating that the boundary condition of the free space is positively correlated with the stability and depth of toppling. This is a good explanation of the free space effect. This study provides a reference for the stability evaluation and prevention-control design of toppling slope in the future.

Numerical and theoretical study of large-scale failure of strata overlying sublevel caving mines with steeply dipping discontinuities

The deformation and fracture evolution mechanisms of the strata overlying mines mined using sublevel caving were studied via numerical simulations.Moreover,an expression for the normal force acting on the side face of a steeply dipping superimposed cantilever beam in the surrounding rock was deduced based on limit equilibrium theory.The results show the following:(1)surface displacement above metal mines with steeply dipping discontinuities shows significant step characteristics,and(2)the behavior of the strata as they fail exhibits superimposition characteristics.Generally,failure first occurs in certain superimposed strata slightly far from the goaf.Subsequently,with the constant downward excavation of the orebody,the superimposed strata become damaged both upwards away from and downwards toward the goaf.This process continues until the deep part of the steeply dipping superimposed strata forms a large-scale deep fracture plane that connects with the goaf.The deep fracture plane generally makes an angle of 12°-20°with the normal to the steeply dipping discontinuities.The effect of the constant outward transfer of strata movement due to the constant outward failure of the superimposed strata in the metal mines with steeply dipping discontinuities causes the scope of the strata movement in these mines to be larger than expected.The strata in the metal mines with steeply dipping discontinuities mainly show flexural toppling failure.However,the steeply dipping structural strata near the goaf mainly exhibit shear slipping failure,in which case the mechanical model used to describe them can be simplified by treating them as steeply dipping superimposed cantilever beams.By taking the steeply dipping superimposed cantilever beam that first experiences failure as the key stratum,the failure scope of the strata(and criteria for the stability of metal mines with steeply dipping discontinuities mined using sublevel caving)can be obtained via iterative computations from the key stratum,moving downward toward and upwards away from the goaf.

Comparisons between centrifuge and numerical modeling results for slope toppling failure

This paper presents series studies on the toppling mechanism by centrifuge tests and numerical simulations. Two different discrete element methods, i.e., the continuum-based discrete element method(CDEM) and the discontinuous deformation analysis(DDA), are adopted. The modeling results show that both the methods can accurately capture the failure modes of the centrifuge tests, including three distinct zones and two failure surfaces. Comparisons are made between the physical test and numerical simulation results. The critical inclination angle of the tilting table where the slope models are fixed on can be moderately predicted by the two methods, with different degrees of precision. The error between the test results and the simulated results is within 1% for the slope models without rock-bridges by both CDEM and DDA. However, it is amplified for the staggered-joint models that simulate the rock-bridges. With DDA, the average error is about 5%, and the maximum error is up to 17%. While with CDEM, the errors for the aligned-joint models are ranged from 1% to 6%, and it is from 10% to 29% for the staggered-joint models. The two numerical methods show the capability in simulating toppling failure of blocky rock mass with and without rock-bridges. The model with rock-bridges which provides a certain bending resistance is more stable than the one without any rock-bridge. In addition, the two failure surfaces were observed, which is different from the common understanding that only one failure surface appears.

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects.Several step-by-step analytical solutions have been developed for analyzing these types of slope failures.However,manual application of these analytical solutions for real case studies can be time-consuming,complicated,and in certain cases even impossible.This study will first examine existing methods for toppling failure analyses that are reviewed,modified and generalized to consider the effects of a wide range of external and dead loads on slope stability.Next,based on the generalized presented formulae,a Windows form computer code is programmed using Visual C#for analysis of common types of toppling failures.Input parameters,including slope geometry,joint sets parameters,rock and soil properties,ground water level,dynamic loads,support anchor loads as well as magnitudes and forms of external forces,are first loaded into the code.The input data are then saved and used to graphically draw the slope model.This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode.The results are presented using a graphical approach.The developed code allows probabilistic introduction of the input parameters via probability distribution functions(PDFs)and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique.This allows calculation of the probability of slope failure.Finally,several published case studies and typical examples are analyzed with the developed code.The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code.The comparisons demonstrate good agreement between the results.

Integrated simulation and monitoring to analyze failure mechanism of the anti-dip layered slope with soft and hard rock interbedding

The significant difference between the mechanical properties of soft rock and hard rock results in the complexity of the failure mode of the anti-dip layered slope with soft and hard rock interbedding.In order to reveal the landslide mechanism,taking the north slope of Fushun West Open-pit Mine as an example,this paper analyzed the failure mechanism of different landslides with monitoring and field surveys,and simulated the evolution of landslides.The study indicated that when the green mudstone(hard rock)of the anti-dip slope contains siltized intercalations(soft rock),the existence of weak layers not only aggravates the toppling deformation of anti-dip layered slope with high dip,but also causes the shear failure of anti-dip layered slope with stable low dip.The shear failure including subsidence induced sliding and wedge failure mainly exists in the unloading zone of the slope.Its failure depth and failure time were far less than that of toppling failure.In terms of the development characteristics of deformation,toppling deformation has the long-term and progressive characteristics,but shear failure deformation has the abrupt and transient characteristics.This study has deepened the understanding of such slope landslide mechanism,and can provide reference for similar engineering.

Smart and fast reinforcement design for anti-dip bedding rock slopes

Rock slopes are usually reinforced by a number of rock bolts due to the high efficiency and low price.However,where should the rock bolts be installed is still a troublesome issue.For anti-dip bedding rock slopes(ABRSs),the installation position of rock bolts is a controlling factor that determines the reinforcement effect.In this work,a theoretical method is firstly proposed for assessing the stability of ABRSs reinforced by rock bolts using a limit equilibrium model.A comparison of theoretical calculations and numerical results was conducted to test the correctness of the theoretical method.Based on the stability assessment of ABRSs,we introduce adaptive moment estimation method(Adam)to optimize the installation location of rock bolts.Using Adam optimizer,the optimal layout of rock bolts with the maximum factor of safety can be determined,and the factor of safety of the slope increases by about 25%using the same amount of rock bolts but with different installation locations.The proposed method enables the fast stability analysis and supporting design for reinforced ABRSs,which paves the way to smart supporting design of slopes.