Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

Lateral Bearing Capacity of Modified Suction Caissons Determined by Using the Limit Equilibrium Method

The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.

Comprehensive analysis of slope stability and determination of stable slopes in the Chador-Malu iron ore mine using numerical and limit equilibrium methods

One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

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.

LOWER BOUND LIMIT ANALYSIS OF THREE-DIMENSIONAL ELASTOPLASTIC STRUCTURES BY BOUNDARY ELEMENT METHOD

Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.

基于极限平衡法的危岩倾覆稳定性三维计算方法

目前危岩防治工作中,危岩稳定性评价主要以简化后的二维剖面作为计算模型。由于自然界中的危岩形态极不规则,采用二维剖面计算模型并不能真实反映危岩受力情况。为了研究危岩稳定性三维计算方法,在前人研究基础上,基于极限平衡理论,提出了由后缘裂缝抗拉强度控制的危岩倾覆稳定性三维计算公式,采用数值积分和空间几何方法给出了在危岩单体三维模型基础上求解危岩后缘岩体抗拉力、水压力及其力矩计算公式和实现流程。以三峡库区瞿塘峡吊嘴危岩为实例开展了应用,并通过数值分析进行了验证。通过不同形态危岩的三维稳定性分析,讨论了三维与二维稳定性计算结果的关系,对比发现危岩形态对稳定性计算结果有明显影响,三维计算较二维计算更准确和实用。

广义对数螺旋型滑面模型的构建与验证

临界滑动面的合理确定是边坡稳定性分析的关键问题之一。传统的边坡滑动面假设方法构造生成的潜在滑动面形式单一,且无法考虑复杂边坡中土层强度参数变化对临界滑动面形状的影响,从而降低了边坡稳定性分析结果的可靠性。基于此,提出一种新的广义对数螺旋型滑面模型,该模型可生成包含传统圆弧滑动面和对数螺旋滑动面在内的多种形式的潜在滑动面;并针对非均质边坡中各土层抗剪强度不同的特点,采用多中心分段构造策略,将该滑面模型应用于非均质边坡稳定性分析中。基于极限平衡理论计算滑动面安全系数并搜索临界滑动面,对边坡进行稳定性评估。选取多个均质边坡及多种型式的非均质边坡(水平分层、倾斜分层和斜折线分层)经典算例与现有研究成果以及数值模拟软件获得的结果进行对比分析,验证该滑面模型的合理性与优势性。研究结果表明:文中方法计算所得安全系数与其他方法相比更小,相对误差在5%以内。能够得到传统滑动面假设方法下难以搜索到的临界滑动面,并与数值模拟结果吻合度较好,稳定性分析结果更接近实际情况。由此说明,此方法用于均质边坡及非均质边坡稳定性分析是合理可行的,有望为工程实践提供更优的临界滑动面解决方案。

石灰石露天矿高陡边坡稳定性计算分析

以西南某石灰石矿高陡边坡为研究对象,根据矿山边坡现状、边坡岩体结构和结构面发育特征因素对“现状边坡”和“终了边坡”进行地质分区,通过岩石室内物理力学试验获得坡体岩石物理力学参数,采用GSI法计算边坡岩体内摩擦角、粘聚力、变形模量和泊松比等参数,评估边坡地质强度特性,采用Morgenstern-Price极限平衡法分三种荷载工况分别计算“现状边坡”和“终了边坡”各分区稳定性系数。经分析,该石灰石矿各地质分区“现状边坡”和“终了边坡”稳定性好,采场边坡参数设计合理,可为矿山扩产安全设施设计和安全生产提供参考。

超深基坑吊脚桩局部稳定性分析

目前基坑设计中对于吊脚桩预留岩肩的宽度和支护桩的嵌固深度取值大多从对上部支护结构内力及变形的影响角度出发,往往忽略了支护结构底部附近的局部稳定性问题。依托珠江三角洲水资源配置工程超深竖井项目,提出了外倾结构面下或破碎岩体吊脚桩基坑可能存在的3种破坏模式,采用极限平衡法分别给出了不同破坏模式下稳定安全系数的计算方法。同时针对不同破坏模式下,影响稳定安全系数的参数如岩层的埋深、结构面的倾角和力学参数、岩肩宽度、岩肩深度等进行了分析,结果表明外倾结构面倾角、结构面或岩体的力学参数对稳定安全系数影响较大。研究成果可为类似工程提供参考。

基于双折减系数法与极限平衡法的顺层滑坡稳定性分析

以四川省布拖县龙潭乡冯家坪滑坡为例,利用FLAC3D软件设计了基于双折减系数法的滑坡稳定性分析程序,应用“GIS-Rhino-FLAC3D”耦合技术建立三维地质体模型。考虑黏聚力和内摩擦角在滑坡失稳过程中衰减速度和弱化程度的不同,以及非饱和土中基质吸力对土体抗剪强度的影响,提出一种以黏聚力和摩擦力的衰减权重定义综合安全系数的双折减系数法,并采用极限平衡法作对比计算,研究分析了顺层滑坡的稳定性。结果表明:设计的抗剪强度参数双折减程序可以得出安全系数云图,直观地反映滑坡安全系数的空间分布特征;与传统强度折减法相比,所提出的双折减系数法计算的滑动面分布范围和综合安全系数更精确,较极限平衡法误差更小,可以准确地反映滑坡的稳定状态。研究结果可为双折减系数法应用于滑坡灾害的防治提供参考。

冻融作用对露天矿山边坡稳定性的影响分析研究

为研究冻融作用对不同倾角层状岩质边坡稳定性的影响,以西藏墨竹工卡县高寒地区某露天矿山为研究对象,利用极限平衡法,通过岩土工程仿真分析软件GEO-Studio计算获得边坡的稳定安全系数,对冻融前后不同倾角层状岩质边坡的安全系数进行对比分析,研究了冻融和倾角对层状岩质边坡稳定性的影响。结果表明:(1)随着设计边坡角度逐步增加,冻融前后的边坡安全系数逐渐降低,冻融前下降幅度16.2%~32.6%,冻融后下降幅度15.2%~28.2%;(2)冻融作用后,边坡岩体黏聚力及内摩擦角有所下降,冻融后边坡整体安全系数较冻融前下降0.86%~3.32%,冻融对边坡整体稳定性有一定的影响。本研究成果对冻土地区边坡的损坏及防控具有一定的指导及参考价值。

Stability analysis of tunnel face reinforced with face bolts

Face bolting has been widely utilized to enhance the stability of tunnel face,particularly in soft soil tunnels.However,the influence of bolt reinforcement and its layout on tunnel face stability has not been systematically studied.Based on the theory of linear elastic mechanics,this study delved into the specific mechanisms of bolt reinforcement on the tunnel face in both horizontal and vertical dimensions.It also identified the primary failure types of bolts.Additionally,a design approach for tunnel face bolts that incorporates spatial layout was established using the limit equilibrium method to enhance the conventional wedge-prism model.The proposed model was subsequently validated through various means,and the specific influence of relevant bolt design parameters on tunnel face stability was analyzed.Furthermore,design principles for tunnel face bolts under different geological conditions were presented.The findings indicate that bolt failure can be categorized into three stages:tensile failure,pullout failure,and comprehensive failure.Increasing cohesion,internal friction angle,bolt density,and overlap length can effectively enhance tunnel face stability.Due to significant variations in stratum conditions,tailored design approaches based on specific failure stages are necessary for bolt design.

含软弱夹层顺层岩质边坡开挖稳定性分析

以都安高速公路某段含软弱夹层顺层岩质边坡为例,采用极限平衡法对开挖后的边坡进行稳定性分析,基于FLAC3D软件模拟分析边坡分级开挖、分级支护过程中的位移、最大剪切应变增量、应力特征及抗滑桩的承载性能。结果表明:严格条分法的安全系数为1.011,强度折减法安全系数为条分法的97.13%,当考虑岩土体变形时,传统计算方法可能会高估边坡自身的稳定性;边坡采用抗滑桩+框架锚索+框架锚杆的联合支护方式,并进行分步开挖及分级支护,对坡体扰动小,支护效果良好,能很好地控制坡体变形,避免边坡因软弱夹层塑性区贯通而发生失稳破坏。

Classification and rating of disintegrated dolomite strata for slope stability analysis

Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gaining increasing prominence.This is primarily due to their unique properties,including low strength and loose structure.Current methods for evaluating slope stability,such as basic quality(BQ)and slope stability probability classification(SSPC),do not adequately account for the poor integrity and structural fragmentation characteristic of disintegrated dolomite.To address this challenge,an analysis of the applicability of the limit equilibrium method(LEM),BQ,and SSPC methods was conducted on eight disintegrated dolomite slopes located in Baoshan,Southwest China.However,conflicting results were obtained.Therefore,this paper introduces a novel method,SMRDDS,to provide rapid and accurate assessment of disintegrated dolomite slope stability.This method incorporates parameters such as disintegrated grade,joint state,groundwater conditions,and excavation methods.The findings reveal that six slopes exhibit stability,while two are considered partially unstable.Notably,the proposed method demonstrates a closer match with the actual conditions and is more time-efficient compared with the BQ and SSPC methods.However,due to the limited research on disintegrated dolomite slopes,the results of the SMRDDS method tend to be conservative as a safety precaution.In conclusion,the SMRDDS method can quickly evaluate the current situation of disintegrated dolomite slopes in the field.This contributes significantly to disaster risk reduction for disintegrated dolomite slopes.

基于水流牵引力的河道岸坡稳定性分析

基于极限平衡理论,结合水平条分法,将Bishop法的竖直条间力关系转换到水平土条上,推导出水流牵引力作用下均质岸坡稳定安全系数的理论计算公式,将其结果与ABAQUS有限元软件的强度折减法模拟的计算结果进行对比分析。结合工程实际,分析水流牵引力对不同坡比河流岸坡的稳定性影响规律。结果表明,理论计算公式与软件模拟的结果基本吻合,误差不超过2.1%。河流中水流牵引力会增大岸坡土体的下滑力矩,降低河流岸坡土体稳定安全系数;当岸坡土体遭受降雨、坡脚土体劣化作用等多因素作用下而处于临界稳定状态时,水流牵引力可能成为滑坡启动的关键因素;在河流岸坡失稳滑动时,水流牵引力将导致滑体向河道方向滑移更远距离,加重滑坡对河流航道安全的危害;坡度越陡,岸坡稳定安全系数受水流牵引力的影响越大。在进行高陡河流岸坡稳定性分析时,水流牵引力是与强降雨、泥石流等因素同样重要且不可忽视的导致岸坡灾变失稳的外部荷载作用。

非线性M-C强度准则下预应力锚索加固边坡时效稳定性分析M-P法

拓展传统极限平衡方法在复杂条件下边坡稳定性分析中的适用性一直是岩土工程界的研究热点。众所周知,边坡岩土体剪切失效一般服从于非线性强度准则,而传统极限平衡方法仅适用于线性强度准则下边坡稳定性分析。此外,预应力锚索作为一种主动防护措施,可极大地即时提高边坡稳定性而被广泛应用于中、大型边坡工程加固。然而,在应力松弛、蠕变效应以及腐蚀环境影响下预应力锚索加固边坡稳定性时效特征往往被忽视。由此,基于Morgenstern-Price(M-P)法,嵌入非线性Mohr-Coulomb(M-C)强度准则,并融入应力松弛与蠕变效应下锚索预应力损失模型以及腐蚀环境下锚索性能劣化模型,从而,建立非线性强度准则下预应力锚索加固边坡安全系数时程表达式。进一步,为了解决非线性强度准则下隐式嵌套公式难以求解的问题,归零化条间法向力初始值,并应用迭代循环求解策略,在引入循环终止允许误差判别条件后,可实现边坡稳定性理论真实结果的逼近求解。经过后续算例对比分析,验证了所提方法的可行性和合理性,与此同时,还研究了不同预应力损失速率和不同锈蚀环境下预应力锚索加固边坡稳定性的时效变化规律。

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。