Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

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.

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.

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.

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.

Weight Analysis of Impact Factors of Interbedded Anti-Inclined Slopes Block-Flexure Toppling Based on Support Vector Regression

Block-flexure toppling failure is frequently encountered in interbedded anti-inclined rock(IAR)slopes,and seriously threatens the construction of hydropower infrastructure.In this study,we first investigated the Lean Reservoir area’s geological setting and the Linda landslide’s characteristics.Then,uniform design and random design were used to design 110 training datasets and 31 testing datasets,respectively.Afterwards,the toppling response was obtained by using the discrete element code.Finally,support vector regression was used to obtain the influence weights of 21 impact factors.The results show that the influence weight of the slope angle and rock formation dip angle on the toppling deformation among tertiary impact factors is 25.96%and 17.28%,respectively,which are much greater than the other 19 impact factors within the research range.For the primary impact factors,the influence weight is sorted from large to small as slope geometry parameters,joints parameters,and rock mechanics parameters.Joints parameters,especially the geometric parameters,cannot be ignored when evaluating the stability of IAR slopes.Through numerical simulation,it was qualitatively determined that failure surfaces of slopes were controlled by cross joints and that the rocks in the slope toe play a role in preventing slope deformation.

Mechanism of toppling and deformation in hard rock slope: a case of bank slope of Hydropower Station, Qinghai Province, China

Recently, various toppling slopes have emerged with the development of hydropower projects in the western mountainous regions of China. The slope on the right bank of the Laxiwa Hydropower Station, located on the mainstream of the Yellow River in the Qinghai Province of Northwest China, is a typical hard rock slope. Further, its deformation characteristics are different from those of common natural hard rock toppling. Because this slope is located close to the dam of the hydropower station, its deformation mechanism has a practical significance. Based on detailed geological engineering surveys, four stages of deformation have been identified using discrete element numerical software and geological engineering analysis methods, including toppling creep, initial toppling deformation, intensified toppling deformation, and current slope formation. The spatial and time-related deformation of this site also exhibited four stages, including initial toppling, toppling development, intensification of toppling, and disintegration and collapse. Subsequently, the mechanism of toppling and deformation of the bank slope were studied. The results of this study exhibit important reference value for developing the prevention–control design of toppling and for ensuring operational safety in the hydropower reservoir area.

基于离散元的边坡弯曲倾倒渐进破坏特征分析

发生弯曲倾倒的边坡一般存在一组优势的陡倾不连续面,岩层在自重或外力作用下向临空面弯曲变形,表现出明显的柔性特征。基于物理模型试验建立了相应的离散元计算模型,模拟了边坡弯曲倾倒的渐进失稳过程,系统剖析了岩体弯曲倾倒的力学机制和破坏特征。结果显示,塑性区贯通是边坡弯曲倾倒失稳的必要非充分条件,悬臂岩柱在弯折过程中其内部应力表现出明显的不均匀性。进一步探讨了关键力学参数对倾倒破坏面的影响规律,具体表现为破坏面倾角随节理摩擦角的增大而增大,而节理黏聚力和岩体抗拉强度对其影响并不显著。研究成果可为倾倒边坡的分析设计提供科学参考。

Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.

基于FLAC3D的某水电站岩体倾倒变形过程数值模拟研究

我国西南高山峡谷地区地质作用强烈,倾倒变形岩体广泛发育,基于拉格朗日有限差分法的FLAC3D软件可对岩体倾倒变形过程进行数值模拟研究。建立了流变模型对澜沧江上游某在建水电站的一处倾倒变形体进行了研究,结果表明,在岩体自重和卸荷应力的长久作用下,库区陡立岩层会朝向临空位置发生倾倒变形破坏。这是一个长期的流变破坏过程。倾倒变形仅发育在边坡的浅表层,深部的岩体未发生倾倒,浅表层底部的岩层弯曲最为强烈,这些部位的岩层将最先发生折断,若折断面贯通,极有可能导致倾倒体整体垮塌滑动引发滑坡等灾害。在水电站建设中要着重考虑对倾倒变形程度严重的坡体进行支护,防止发生大规模的失稳破坏。

陡倾片麻岩滑坡演化过程研究——以兰陵溪滑坡为例

弯曲-倾倒破坏是陡倾顺层岩质斜坡的一种变形模式,当其折断面贯通形成滑移面时,斜坡演化为滑坡。以三峡库区兰陵溪滑坡为例,引入反转应力法、梁板强度理论对滑坡变形模式与演化过程进行了研究。结果表明:①该岩质斜坡具有典型的陡倾顺层、岩体结构软硬相间的特点,为其发生弯曲-倾倒破坏提供了先天性条件。②差异性风化是兰陵溪滑坡发生弯曲-倾倒变形的主要原因,片状片麻岩抗弯强度变弱,促使片麻岩逐渐发生弯曲,最后产生弯曲折断-倾倒变形破坏。③兰陵溪滑坡演化过程历经差异性风化、岩层弯曲变形、岩层倾倒破坏、折断面贯通等4个阶段,所有折断面贯通形成潜在滑移面时,斜坡演化为滑坡。研究成果可为该滑坡工程治理提供理论依据,也可为同类型岩质斜坡治理提供思路。

边坡倾倒破坏模式的多米诺骨牌模型研究

边坡稳定性分析是边坡安全评估和加固的理论依据,针对多米诺骨牌分析方法只考虑了条块底面滑移剪切破坏的不足,提出了考虑边坡发生倾倒破坏形式的多米诺骨牌分析方法。给出了多米诺骨牌模型在倾倒破坏假设下的计算方法和求解步骤,并提出了边坡发生倾倒破坏、滑移破坏和倾倒与滑移混合破坏的判别方法。通过研究倾倒破坏模式的多米诺骨牌模型,进一步完善和推进了边坡稳定性分析方法的理论及其在边坡工程中的应用。

某水电站2#倾倒体时效变形及失稳模式的离散元分析

为深入研究倾倒体变形破坏全过程特征,以某水电站消力塘左岸2#倾倒体为例,在野外调查基础上,利用离散元模拟,从模型时效变形及变形机理出发,分析该倾倒边坡在现状及地震作用下的失稳模式。结果表明:当边坡变形累积到一定程度,不稳定地质体将发生失稳,其位移表现为宏观的快速增加,若地质体的失稳是强震触发的,其位移还具有一定的“震荡”特征;倾倒边坡前期或前中期的变形破坏以沿结构面的剪切错动为主导,之后,随着拉张效应的逐渐积累,变形转为以沿结构面的拉张破裂为主;地震作用下,边坡中质点的水平速度及加速度均有高程放大效应,其中加速度放大系数大于速度放大系数,边坡破坏时,由于动力波的加速效应及岩体弹性应变能的释放将获得较大的水平加速度,表明岩体中的弱面对于岩质边坡的稳定性起控制作用;现状条件下,2#倾倒体整体稳定,其失稳模式以浅表层岩体的局部垮塌或沿小型山脊的滑塌为主,而遭受地震时则有整体失稳的可能,若整体失稳,其失稳过程应为:表层松动岩体率先垮塌、滚落→坡体震裂松弛→形成“滑移-拉裂”型滑坡。

弯曲型倾倒变形边坡破坏模式研究

为了分析弯曲型倾倒变形边坡破坏模式,以西藏扎拉水电站为研究对象,分析了弯曲型倾倒变形边坡在天然状态、开挖工况下的破坏模式及其控制因素。结果表明:弯曲型倾倒变形边坡的破坏模式主要有表层剥落与崩塌、浅层滑移、深层或大规模失稳。(1)剥落与崩塌发生在坡表,在倾倒变形及卸荷、风化作用下,坡表岩体破碎,在降雨产生的坡面水流作用下易发生剥落、崩塌;(2)浅层滑移发育在强倾倒变形区,倾倒变形过程中产生的倾向坡外的张剪裂隙是边坡失稳的控制性结构面,当路堑边坡开挖或河水冲刷切脚时,边坡产生应力调整,导致倾向坡外的破裂面贯通,进而发生滑坡;(3)边坡发生深层或大规模失稳的控制因素是大断裂或活断裂、软弱夹层等软弱结构面。西藏扎拉水电站弯曲型倾倒变形边坡弯曲界面及深部弱倾倒变形区没有形成贯通性失稳界面,整体处于稳定状态。该工程区弯曲型倾倒变形边坡的发育特征和破坏模式具有典型性,研究成果可供类似工程借鉴。

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.

考虑随机横向节理的反倾层状边坡倾倒破坏分析

实际边坡工程中,横向节理极其发育,且节理位置分布随机,节理长度也各不相同,随机横向节理对反倾向层状边坡倾倒破坏的影响规律尚不清楚。为此,通过计算机随机生成了横向节理的位置系数和长度系数来表征横向节理的随机特性,建立随机横向节理反倾向层状边坡模型。应用该模型探讨边坡发生倾倒破坏的启动条件和破坏机理,并基于极限平衡理论确定岩层的破坏模式和破坏位置。以皖南山区的典型反倾向层状板岩边坡为研究对象,分析横向节理位置和横向节理长度对边坡倾倒破坏的影响规律。结果表明:无论横向节理如何分布,岩层(从坡脚至坡顶)发生破坏所需的层间力总是先增大后减小;当横向节理位置或者横向节理长度发生改变时,潜在破坏岩层的层间力也随之发生改变,且其数值随横向节理长度的增加而明显减小;当横向节理位置和横向节理长度都随机改变时,层间作用力曲线形状变化较大,个别岩层发生破坏时所需的层间力差值较大。研究结论对反倾层状边坡倾倒破坏机理的认识与地质灾害防治有参考价值。

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.

岩质边坡倾倒破坏的稳定分析方法

本文提出了一种边坡倾倒破坏地质力学模型的概化方法，并对Ｇｏｏｄｍａｎ和Ｂｒａｙ的极限平衡分析理论作了改进，改进后的方法考虑了岩体结构面的具体分布特征和岩体结构面连通率即岩桥的作用。该方法已在龙滩工程中实际应用。

陡倾顺层岩质斜坡倾倒变形破坏特征研究

顺层岩质斜坡是常见的斜坡结构类型之一,对该类斜坡的变形破坏特征以及形成机制研究已较深入,一般认为顺层岩质斜坡的变形破坏以滑移–拉裂、滑移–弯曲(或溃曲)模式为特征。通过系统的文献收集及大量现场调查发现,陡倾顺层岩质斜坡还存在一种典型的变形破坏形式,即倾倒变形。结合具体的陡倾顺层岩质斜坡倾倒变形破坏的实例,详细分析、总结该类斜坡发育的地质环境条件及变形破坏特征,在此基础上结合典型斜坡分析陡倾顺层岩质斜坡倾倒变形是在河谷演化、成坡过程中,岩层在平行坡面的最大主应力作用下由坡脚开始从下至上作悬臂梁弯曲,最终导致岩层根部折断,形成倾倒体;当坡体内折断带的剪应力超过其抗剪强度时,坡体将发生滑动形成滑坡。

反倾层状岩质边坡倾倒变形破坏机理综述

倾倒变形破坏常见于层状岩质边坡工程,其机理研究对边坡稳定性分析具有重大意义。在国内外相关研究基础上对弯曲倾倒、块状倾倒及块状-弯曲倾倒3种不同破坏模式进行了分析,就边坡几何形状、岩层强度和长细比、层面力学参数、地下水、开挖作用等因素对倾倒变形的影响进行了阐述,介绍了倾倒变形破坏机理在物理模型试验、极限平衡、数值模拟3种方法中的研究进展,指出了不同方法的适用性和优缺点,说明了研究中需要改进和深化的内容。