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.

Seismic stability analysis of slopes with pre-existing slip surfaces

In analyzing seismic stability of a slope with upper bound limit analysis method, the slip surface is often assumed as a log-spiral or plane slip surface. However, due to the presence of a weak layer and unfavorable geological structural surface or a bedrock interface with overlying soft strata, the preexisting slip surface of the slope may be irregular and composed of a series of planes rather than strictly logspiral or plane shape. A computational model is developed for analyzing the seismic stability of slopes with pre-existing slip surfaces. This model is based on the upper bound limit analysis method and can consider the effect of anchor bolts. The soil or rock is deemed to follow the Mohr-Coulomb yield criterion. The slope is divided into multiple block elements along the slip surface. According to the displacement compatibility and the associated flow rule, a kinematic velocity field of the slope can be obtained computationally. The proposed model allows not only calculation of the rate of external work owing to the combined effect of self-weight and seismic loading, but also that of the energy dissipation rate caused by the slip surface, interfaces of block elements and anchorage effect of the anchors. Considering a direct relationship between the rate of external work and the energy dissipation rate, the expressions of yield acceleration and permanent displacement of anchored slopes can be derived. Finally, the validity of this proposed model is illustrated by analysis on three typical slopes. The results showed that the proposed model is more easily formulated and does not need to solve complex equations or time consuming iterations compared with previous methods based on the conditions of force equilibrium.

Shaking table test and numerical simulation on the effect of reinforcement on the seismic safety of dam slopes

The seismic safety of the reinforcement dam slope is studied through shaking table test and numerical simulation.The dynamic characteristics of dam slopes,failure mechanism,seismic stability,as well as the effect of reinforcement during earthquakes are discussed.An elasto-plastic analysis method (FLAC) is used to simulate the dynamic failure process of the reinforcement dam slope.The change law of permanent displacement of dam slope is studied.The effect of the length and the space of reinforcement on the depth of slip surface and the slope stability are investigated.Good agreement is obtained between the numerical results and those from shaking table tests.The results show that the dynamic failure is a gradual process not at a particular time.With the increase of the reinforcement length or the decreasing reinforcement spacing,the slip surface becomes deeper and thus the slope stability is improved.The reinforcement can obviously enhance the overall stability of slope dam.It can also effectively control the shallow sliding of slope.These researches provide basic data for reinforcement measures design of earth-rockfill dam.

A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

Evaluation of mountain slope stability considering the impact of geological interfaces using discrete fractures model

The stability of rock slope is often controlled by the existing discontinuous surfaces, such as discrete fractures, which are ubiquitously distributing in a geological medium. In contrast with the traditional approaches used in soil slope with a continuous assumption, the simulation methods of jointed rock slope are different from that of in soil slope. This paper presents a study on jointed rock slope stability using the proposed discontinuous approach, which considers the effects of discrete fractures. Comparing with traditional methods to model fractures in an implicit way, the presented approach provides a method to simulate fractures in an explicit way, where grids between rock matrix and fractures are independent. To complete geometric components generation and mesh partition for the model, the corresponding algorithms were devised. To evaluate the stability state of rock slope quantitatively, the strength reduction method was integrated into our analysis framework. A benchmark example was used to verify the validation of the approach. A jointed rock slope, which contains natural fractures, was selected as a case study and was simulated regarding the workflow of our framework. It was set up in the light of the geological condition of the site. Slope stability was evaluated under different loading conditions with various fracture patterns. Numerical results show that fractures have significant contributions to slope stability, and different fracture patterns would lead to different shapes of the slip surface. The devised method has the ability to calculate a non-circular slip surface, which is different from a circular slip surface obtained by classical methods.

Development of a preliminary slope stability calculation method based on internal horizontal displacements

This paper proposes a horizontal displacement-based approach to determine the potential slip surface of the slope. Firstly, a group of in-situ inclinometers with an appropriate spacing in the horizontal direction is located in the model slope.The equation of horizontal displacement with time for each in-situ inclinometer is fitted during the whole simulation process. Furthermore, the intersection of each inclinometer with potential slip surface is determined by using an optimization model. The slip surface can be obtained by using least square fitting method. Finally, the feasibility and accuracy of the method are validated by a series of numerical simulations. It is noted that the optimization model taking the maximum value of displacement increment gradient as an objective has higher accuracy when compared with other optimization models. This method employed in this study provides a preliminary approach to determine the real-time slope stability based on displacement, which can also be measured by using conventional instruments on site.

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.

THREE-DIMENSIONAL SLOPE STABILITY ANALYSIS BASED ON NONLINEAR FAILURE ENVELOPE

The effects of nonlinearity of strength envelopes on 3D slope stability analysis are investigated.A power relation for the nonlinear envelope is employed to derive the 3D factor of safety equations of an extended Spencer method hich satisfies boty force equilibrium and moment equilibrium.Then,a search procedure is presented based on dynamic programming to determine the 3D critical slip surface for a general slope,Linear and nonlinear strength envelopes used for slope stability computations are obtained by fitting curves to the 103 strength data of consolidated-undrained(CU)triaxial compression tests for compacted Israeli clay.Results of a typical 3D problem show that a linear approximation of the nonlinear strength envelope may lead to a significant overestimation of calculated safety factors.

Critical Slope and Plasticity

Limit analysis based on upper bound theorem into slope stability is presented. A rotational failure mechanism (log spiral) passing through the toe in an inclined slope is assumed for getting the critical height. The proposed limit analysis, although on the kinematical admissible velocity field, always satisfies the equilibrium of forces acting on sliced rigid blocks. And the most critical slip surface can be searched by random technique. A new solution scheme is also developed for rapid searching critical slip surface. It is also applicable to a variety of slope models. The method is shown having a high accuracy compared with limit solution for simple slope.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

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。

不同降雨强度下离子型稀土矿边坡渗流特性与临界滑移面变化分析

以离子型稀土矿边坡为研究对象,研究了不同降雨强度条件下降雨、停雨阶段离子型稀土矿边坡孔隙水压力变化情况,并利用有限元Morgenstern-Price法研究了各时间段临界滑移面的变化。结果表明,降雨强度是影响离子型稀土矿浅层边坡孔隙水压力的显著因素;雨水在离子型稀土矿边坡中的传递具有滞后性,是停雨阶段造成离子型稀土矿边坡不稳定隐患的内在原因;降雨强度越大,进入289滑移面的时间越快,安全系数变化的“加速度”波峰越高,影响时间越长。首次提出降雨条件下离子型稀土矿边坡发展可能历经的4个阶段为:较为安全阶段、内部剧烈变化阶段、极易滑坡阶段及相对安全阶段。

红沙泉露天矿地表筛分厂对西端帮边坡稳定性影响

为了研究红沙泉露天矿地表筛分厂对西端帮边坡稳定性影响,采用Bishop边坡稳定性计算方法,分别以施加地表载荷和无地表载荷为对比,探索了地表筛分厂对西端帮边坡上部、下部影响的局部稳定性规律及对西端帮边坡整体稳定性影响规律。结果表明:当上部局部边坡地表荷载增大时,边坡受到的影响较小,所以更应关注地表荷载对下部局部边坡及整体边坡稳定性的影响。在地表筛分厂的设备重量、储煤量以及设备运输等总重量不超过500 t并位于距离坡顶55 m的条件下,整体边坡的稳定性未受到地表荷载的影响,但下部局部边坡的稳定性略有降低。

Study on embedded length of piles for slope reinforced with one row of piles

The embedded length of anti-slide piles for slope is analyzed by three-dimensional elastoplastic shear strength reduction method. The effect of embedded pile length on the factor of safety and pile behavior is analyzed. Furthermore, the effects of pile spacing, pile head conditions, pile bending stiffness and soil properties on length and behavior of pile are also analyzed. The results show that the pile spacing and the pile head conditions have significant influences on the critical embedded length of pile. It is found that the critical embedded length of pile, beyond which the factor of safety does not increase, increases with the decrease in pile spacing. The smaller the pile spacing is, the larger the integrity of the reinforced slope will be. A theoretical analysis of the slip surface is also conducted, and the slip surface determined by the pressure on piles, considering the influences of both soil and piles for slope, is in agreement with the ones in previous studies.

基于GEO-Slope/W的土质高边坡稳定性分析

GEO-Slope/W软件可综合考虑地下水、土体裂缝、坡顶堆载等因素,能够对复杂土层、任意滑动面形状及多种孔隙水压力状况建立二维计算模型分析边坡的稳定性.本文以河南航空港区某一老旧办公区域的土质高边坡为例,通过对任意形状滑动面的计算假设,设定滑动坡面为自由边界、底部为固定约束边界、四周为自由边界来建立滑坡计算模型,选取两个典型边坡剖面,分析其在自然状态和饱和状态下的最危险滑动面、对应滑动圆心以及相应的最小稳定安全系数.结果表明：边坡在饱和状态下的稳定系数比自然状态下的降低了0.10～0.11,验证了含水量的增加对土质边坡的稳定性影响较大的结论;模拟分析得典型坡面的最大稳定系数为0.84,远小于滑坡允许稳定系数1.2～1.3,说明该边坡处于极不稳定状态,与现场勘查情况相吻合.另外,提出采用混凝土挡墙加喷锚支护提高土体抗滑力,防止雨水对坡体的浸润破坏;或用削坡、人工植草、浆砌石防护坡脚等措施来减轻坡体荷载,保持边坡稳定。

复合地基对临近基坑稳定性影响的数值模拟研究

目的 基于已有基坑稳定性分析的建模方法,开展邻近复合地基深基坑变形与稳定性问题的精细化研究。方法 结合某基坑工程实例利用PLAXIS 3D软件建立三维数值计算模型,分析支护桩水平位移、基坑稳定性系数、基坑滑裂面位置与状态等不同变形特征参数对基坑性状的影响,进而研究既有建筑复合地基桩体条件变化对基坑稳定性的影响。结果 邻近复合地基的基坑稳定性系数均大于桩基础和天然地基,且支护桩水平位移峰值较天然地基减小40%;复合地基和桩基下的基坑滑裂面形态大致相近,均从基础中部向基坑底部延伸;CFG桩桩长在超过1倍开挖深度、桩径超过0.7 m及桩体刚度达到500 kPa后,滑裂面与地表的交点位置不再变化,复合地基与临近基坑距离超过1倍开挖深度后,对基坑影响可以忽略不计。结论 提出邻近复合地基的基坑整体稳定性系数优于桩基础和天然地基,CFG桩桩长、桩径、桩体模量和临近基坑距离的变化均对基坑开挖呈有利作用等影响规律,结果可供工程实际应用参考。

地震作用下分层土边坡多滑面变形破坏的数值模拟研究

地震引起的滑坡对生命、环境和经济造成了巨大的威胁。目前,对于地震作用下边坡稳定性的研究主要集中在单一滑动面破坏模式,对于具有多个潜在滑动面边坡的地震稳定性研究比较欠缺。基于此,利用有限差分软件FLAC对不同边坡进行地震稳定性数值模拟,对比分析不同强度地震动作用下均质土体、分层土体和含软弱夹层土体边坡的滑动面演化过程和永久变形分布特征。结果表明:对于均质边坡,地震引起的滑动面为单一的整体滑动面,地震动强度的增加仅导致沿滑动面的永久变形量增大;对于非均质边坡,在地震作用下还可能形成通过土层交界面的局部滑动变形,且地震作用下最先形成和发生变形的滑动面与静力条件下得到的最小安全系数对应的最危险滑动面一致;同时,地震引起的边坡浅层和深层变形破坏存在复杂的相互影响,当局部浅层滑动先发生时,地震动的进一步增大很容易诱发更深层的坡体滑动,而当深层滑动先发生时,由于塑性变形影响地震惯性力向上部坡体的传播,浅层坡体的进一步滑动变形相对较难被触发。

某砂岩顺层挖方高边坡治理工程施工期变形特征与工程效果评价

为了研究砂岩顺层挖方高边坡支护工程施工期间及施工后的边坡变形规律和治理工程效果,文章依托北京某边坡支护项目,对边坡在施工过程中的锚索轴力及边坡位移进行监测分析,结果表明:锚索轴力变化主要分为加速损失阶段、波动阶段以及持续稳定趋变阶段;锚索轴力变化可以很好地反映坡体内力的变化情况;坡顶水平位移和竖向沉降的变化,可以反映边坡深层位移的变化规律和边坡的稳定性;框架预应力锚索抗滑桩组合支护体系应用于砂岩顺层挖方高边坡的支护时,具有较好的支护效果。采用有限元分析软件,模拟该砂岩顺层挖方高边坡的开挖支护过程发现:随着边坡的开挖,坡体位移沿着软弱滑动面向坡角发展,边坡稳定性降低。将监测结果与模拟结果对比分析,发现二者的变化趋势基本一致,证明了该边坡的支护体系能有效地控制边坡的变形。研究成果能为以后类似边坡的设计施工提供参考。

含多层泥化夹层边坡的抗滑桩支护优化设计

泥化夹层在城市建设、公路的边坡中分布广泛,为了研究抗滑桩对含多层泥化夹层边坡稳定性的影响,通过建立有限元三维数值模型,基于强度折减法研究了抗滑桩分布位置和间距对边坡稳定性的影响。结果表明:含多夹层的边坡破坏面呈折线形,抗滑桩能有效阻止边坡失稳;在L_(x)/L=0.375、桩间距为2倍桩径时,安全系数最大,支护效果最佳。