Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

Limit equilibrium stability analysis of slopes under external loads

Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.

Limit equilibrium analysis for stability of soil nailed slope and optimum design of soil nailing parameters

Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.

A Method Combining Numerical Analysis and Limit Equilibrium Theory to Determine Potential Slip Surfaces in Soil Slopes

This paper describes a precise method combining numerical analysis and limit equilibrium theory to determine potential slip surfaces in soil slopes. In this method, the direction of the critical slip surface at any point in a slope is determined using the Coulomb’s strength principle and the extremum principle based on the ratio of the shear strength to the shear stress at that point. The ratio, which is considered as an analysis index, can be computed once the stress field of the soil slope is obtained. The critical slip direction at any point in the slope must be the tangential direction of a potential slip surface passing through the point. Therefore, starting from a point on the top of the slope surface or on the horizontal segment outside the slope toe, the increment with a small distance into the slope is used to choose another point and the corresponding slip direction at the point is computed. Connecting all the points used in the computation forms a potential slip surface exiting at the starting point. Then the factor of safety for any potential slip surface can be computed using limit equilibrium method like Spencer method. After factors of safety for all the potential slip surfaces are obtained, the minimum one is the factor of safety for the slope and the corresponding potential slip surface is the critical slip surface of the slope. The proposed method does not need to pre-assume the shape of potential slip surfaces. Thus it is suitable for any shape of slip surfaces. Moreover the method is very simple to be applied. Examples are presented in this paper to illustrate the feasibility of the proposed method programmed in ANSYS software by macro commands.

Engineering Geological and Geotechnical Studies of Taprang Landslide, West-central Nepal: An Approach for Slope Stability Analysis

Detailed investigation of Taprang landslide was carried out in order tounderstand the surface, subsurface lithological information and physicalproperties of soil by using multi-disciplinary methods such as engineeringgeological, geophysical and geotechnical studies for the determinationof factor of safety for slope stability analysis. Geological study wascarried out by detail mapping of surface geology, soil condition, propertiesof bedrock and its discontinuities. The geophysical survey (ElectricalResistivity Tomography-ERT) were carried out to know the electricalresistivity of soil for identifying the groundwater table and slip surface ofthe landslide. Geotechnical analysis such as grain size analysis, liquid limitand direct shear test were carried out in order to evaluate soil classification,moisture content, cohesion and the angle of internal friction of soil forknowing the strength the soil. These soil parameters indicate the soil is verylow strength. The combination of these results were used for calculatingthe factor of safety (FoS) by Limit Equilibrium Method (LEM) proposedby Bishop and Janbu methods. The result of factor of safety in the Tapranglandslide demonstrates that the slope become stable in drained (dry)condition, remain ultimate stage in undrained (wet) condition and finallyfailure occurs if applied the seismic load in both drained and undrainedconditions.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

Discontinuous flying particle swarm optimization algorithm and its application to slope stability analysis

A new version of particle swarm optimization(PSO) called discontinuous flying particle swarm optimization(DFPSO) was proposed,where not all of the particles refreshed their positions and velocities during each iteration step and the probability of each particle in refreshing its position and velocity was dependent on its objective function value.The effect of population size on the results was investigated.The results obtained by DFPSO have an average difference of 6% compared with those by PSO,whereas DFPSO consumes much less evaluations of objective function than PSO does.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

A New Closure to Slice Model for Slope Stability Analysis

This paper presents a new closure to slice models for evaluating slopes. The discussion is based on the minimal inter-slice action (MIA) hypothesis, which results in a new slice model without including artificially adjustable parameters. It has been realized that the new slice model predicts the minimum value of the safety factor, while all other slice models available always overestimate the value of the safety factor. Moreover, the gravity moment of each slice is found to be opposite to the overturning moment, which is different from the existing knowledge. In particular, the new slice model overcomes the situation where different assumptions of the inter-slice force function will give different safety factors to the same slope. The related numerical examples indicate that the new slice model can serve as a reliable tool for investigating geotechnical slope stability.

A New Approach to the Determination of the Critical Slip Surfaces of Slopes

A new method for the determination of the critical slip surfaces of slopes is proposed in this paper. In this paper, the original critical slip field method is extended in terms of the total residual moment, values of residual work as well as the unbalanced thrust force at the exit point for a given non-circular slip surface. The most critical slip surface with the maximum representative value for a prescribed factor of safety will be optimized and located using the harmony search algorithm. The prescribed factor of safety is modified with certain tiny interval in order to find the critical slip surface where the maximum representative value is zero. The aforementioned approach to the location of the critical slip surface is greatly different from the traditional limit equilibrium procedure. Three typical soil slopes are evaluated by use of the proposed method, and the comparisons with the classical approaches have illustrated the applicability of the proposed method.

基于Geo-Slope数值模拟的某石灰石矿边坡稳定性分析

随着露天矿山边坡安全滑坡事件频发,矿山企业对边坡安全越发重视。以某石灰石矿超过100 m的边坡为研究对象,通过分析该矿区的工程地质、水文地质条件,从中选择3个典型剖面,通过赤平投影方式分析其破坏模式,结合室内试验和数值分析的方法进行渗流场分析和安全系数算。结果表明,3个典型剖面最小安全系数均满足规范要求,均达到稳定状态。随着矿山开采深度的延伸,边坡高度越来越高,需要加强对边坡监测及安全管理工作。

某钼(铜)多金属矿排土场边坡稳定性分析

为了研究排土场边坡稳定性,以西藏天仁矿业有限公司邦铺矿区钼(铜)多金属矿排土场为研究对象。通过工程地质条件调研,并考虑自然工况、降雨工况、地震工况三种工况,最后采用极限平衡分析法中的简化Bishop法、Spencer法与Morgenstern-Prince法对该矿排土场边坡稳定性进行分析。结果表明:排土场1-1’剖面在自然工况、降雨工况及地震工况下以极限平衡法计算所得到的安全系数均大于规范值,据此排土场边坡处于稳定状态。研究结果对该矿其他排土场边坡稳定性分析提供一定的参考依据。

三维加筋边坡抗震稳定性的拟动力上限分析

拟动力法可以更好地考虑地震传播的时空变化特性,文章采用拟动力分析方法研究均匀加筋与三角加筋2种不同加筋模式下,加筋土坡的三维地震稳定性问题;基于极限分析上限定理,构建三维加筋土边坡的破坏机构,推导地震边坡三维安全系数的表达式,并考察拟静力与拟动力分析结果之间的差异性;通过参数分析揭示三维加筋边坡的拟动力安全系数变化规律。结果表明:相对于拟动力分析,拟静力分析获得的安全系数解更为保守,特别是对于水平地震力系数k_(h)和坡角β较大的情况,两者差异更加显著;随着水平地震力系数k_(h)、宽高比B/H、放大系数f的增加,加筋土边坡的稳定性明显降低;而随着平均加筋强度k_(0)增加,边坡稳定性显著提高;地震波周期T对边坡稳定性的影响较小;2种加筋模式对边坡稳定性的影响规律一致,且三角加筋模式效果更优。

某露天矿山高边坡稳定性分析研究

为研究露天矿山边坡稳定性,本文以四川某石灰石露天矿山为例,在考虑边坡处于3种不同工况下,如自重+暴雨、自重+暴雨+爆破震动、自重+暴雨+地震,分别采用极限平衡法和数值模拟法对该矿山B区典型特征剖面进行分析研究。研究结果可知,在最不利工况下(自重+暴雨+爆破震动),极限平衡法得到的安全系数为1.181,数值模拟法得到的安全系数为1.150,均大于边坡允许安全系数,说明该露天边坡属于稳定边坡。

基于赤平投影法与极限平衡法的某矿山边坡稳定性研究

露天矿山高陡边坡稳定性已成为人民和国家关注的矿山安全问题之一。该研究根据边坡坡向、边坡岩体结构特征、结构面发育特征和岩体产状对矿山边坡地质工程分区,利用赤平投影法对3个分区进行边坡稳定性研究,选取3个典型剖面基于Slide软件利用极限平衡法对矿山高陡边坡进行稳定性研究。研究结果表明,该矿山边坡发生滑动、楔体破坏的可能性较小,且在3种工况下的安全系数均大于许用安全系数,该矿山边坡处于稳定状态,可保证矿山生产的安全。

西部某露天高陡矿山边坡稳定性分析及影响因素研究

西部地区矿山资源丰富,地质条件复杂,使得该地区的边坡稳定性分析问题备受关注。本文以西部地区某露天金属矿山边坡为研究对象,根据边坡形态、地层岩性、构造、水文和风化程度等工程地质条件,划分3个边坡分区,每个分区选取1~2条代表性剖面。在现场勘察的基础上,采用室内试验和数值模拟方法开展边坡稳定性分析研究工作。对研究区4种主要岩性开展必要的岩石物理力学试验,采用Hoek-Brown强度折减法用于计算岩体的抗剪强度参数;对研究区地下水作用下的渗流场进行分析,在此基础上采用两种不同的极限平衡分析方法计算边坡稳定性。研究结果表明,在3种不同工况下计算的安全系数均满足规范要求。

基于极限平衡法与强度折减法的某高寒高海拔矿山边坡稳定性分析

为验证西部高寒高海拔地区某露天矿山设计边坡稳定性是否满足现行规范要求,并分析露天开采导致的位移变化规律,本文参考矿区终了境界平面图选取具有代表性的典型剖面,结合矿区实际情况、工程地质条件、室内物理力学试验,利用H-B准则等,综合确定矿区边坡的岩土体物理力学参数;采用极限平衡法中的不平衡推力法和M-P法及有限差分强度折减法,以安全系数为指标,验证了设计边坡的稳定性。通过极限平衡与强度折减计算结果的对比,验证了强度折减法计算潜在滑动面形态及安全系数的可靠性。在此基础上,分析强度折减前,在岩体开挖、施加爆破及地震荷载下矿山边坡的位移显现规律。研究结果可为露天矿山设计中的边坡稳定性定量分析提供参考。

某石灰石矿边坡稳定性分析与安全监测等级划分

为了保证某石灰石矿山生产过程中边坡安全,采用极限平衡法中的Morgenstern-Price法和Sarma法对该矿山终了边坡进行稳定性分析,研究了不同荷载条件下边坡稳定性安全系数,结合边坡参数和安全系数,对最终边坡安全监测等级进行划分。结果表明:选取的4个典型剖面经过计算,安全系数均满足规范要求,最终边坡西侧安全监测等级为三级,东侧、北侧、南侧边坡安全监测等级为二级。

考虑参数空间变异性的边坡稳定可靠性有限元极限分析

当土性参数空间变异性较大时,极限平衡法得到的滑移面不尽合理。阐述了基于广义变分原理的有限元极限分析方法,采用混合有限元方法,构筑了线性应力三角形单元与线性速度三角形单元,结合强度折减法与线性规划算法,建立了边坡稳定安全系数上下限分析方法,分析了土的抗剪强度参数空间变异性对边坡稳定性的影响,并与3种典型极限平衡法进行了对比。结果表明,FELA方法可有效搜索边坡临界滑移面,并给出安全系数的严格上下限。对于简单均质边坡,有限元极限分析与极限平衡法结果接近,极限平衡法结果大多位于极限分析的上下限内;对于空间变异性较大的边坡,有限元极限分析法可以有效搜索可能的多种临界滑移面,而极限平衡法则存在显著偏差,且往往高估滑坡风险。强度参数的空间变异性还导致边坡安全系数分布形式变化显著,仅采用安全系数无法反应这一变化。根据安全系数的分布形式,给出了土性参数设计值建议。

基于滑面正应力修正的边坡安全系数解答

首先,对边坡滑动面正应力分布作初始假设;然后,用含有2个待定参数的修正函数对其修正,使滑体整体满足所有力与力矩平衡条件,推导出边坡安全系数计算公式。该法计算过程简单,无需迭代,适合任意形状滑动面,且为严格的极限平衡解,值得在工程中推广应用。