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.     

Analysis on velocity distribution and displacement along the profile of a slope using both empirical and analytical methods

Assessing the slope deformation is significant for landslide prediction. Many researchers have studied the slope displacement based on field data from the inclinometer in combination with complicated numerical analysis. They found that there was a shear zone above the slip surface, and they usually focused on the distribution of velocity and displacement within the shear zone. In this paper, two simple methods are proposed to analyze the distribution of displacement and velocity along the whole profile of a slope from the slip surface to the slope surface during slow movement. In the empirical method, the slope soil above the shear zone is assumed as a rigid body. Dual or triple piecewise fitting functions are empirically proposed for the distribution of velocity along the profile of a slope. In the analytical method, the slope soil is not assumed as a rigid body but as a deformable material. Continuous functions of the velocity and displacement along the profile of a slope are directly obtained by solving the Newton's equation of motion associated with the Bingham model. Using the two proposed methods respectively, the displacement and velocity along the slope profiles of three slopes are determined. A reasonable agreement between the measured data and the calculated results of the two proposed methods has been reached. In comparison with the empirical method, the analytical method would be more beneficial for slope deformation analysis in slope engineering, because the parameters are material constants in the analytical solution independent of time t, and the nonlinear viscosity of the soil can be considered.     

平面剪切岩质边坡滑裂面的确定及稳定性分析

由于传统搜索方法对岩质边坡滑裂面的确定无法兼顾效率与精度, 如何迅速准确确定潜在滑裂面仍然是个难题。极限平衡法在岩质边坡稳定性分析中备受认可, 采用岩质边坡平面剪切滑动模型, 以滑裂面的倾角来表征潜在滑裂面的位置; 基于极值法, 推导了极限平衡条件下平面剪切破坏型岩质边坡潜在滑裂面的解析解, 并结合香港秀茂坪路边坡对其准确性进行了验证, 进一步对四川宜宾打营盘山公路多级边坡进行了整体稳定性分析。结果表明: 香港秀茂坪边坡采用本文方法确定的边坡潜在滑裂面倾角与实际滑坡倾角基本一致。实际工程应用中, 采用Slide软件中布谷鸟搜索法和模拟退火法两种搜索方法得到的滑裂面倾角分别为38.0°和37.0°, 本解析法所得倾角为34.8°; 选用Janbu法、Morgenstern-Price法和Sarma法分别计算对应的稳定系数, 结果均为1.04左右, 本文所得稳定系数为1.15, 可见本文方法所得结果基本准确。通过参数敏感性分析发现, 随着黏聚力的增加, 边坡滑裂面倾角越来越小, 稳定系数也随之增加; 而当内摩擦角增大时, 边坡滑裂面倾角和稳定系数也随之增大。      

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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 log-spiral 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.     

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.     

远场GPS同震位移的变形特征分析——以2011年日本东北大地震为例

利用2011日本东北大地震的亚洲东部GPS远场水平位移数据,通过计算及比较分析4个独立震源解和倾/滑角效应,研究了远场地震变形的空间分布特征和规律。结果表明,对于低角度逆冲型地震来说,水平位移格林函数在远场位移场中占主导作用。基于此确定了远场GPS水平位移场能在反演中有效利用的空间范围,为联合远场GPS数据和近场GPS数据反演断层滑动分布作理论准备,并为远场数据反演位错Love数（h、l）提供理论依据。     

基于GNSS观测研究2015年尼泊尔MW7.8地震震后地壳形变特征及其机制

收集及处理尼泊尔境内的GPS连续观测站和中国藏南地区的GPS基准站数据,获得2015年尼泊尔MW7.8地震震后3 a的GPS水平形变场。结果显示,尼泊尔地震的震后形变主要分布于尼泊尔北部及中尼边境区域,且东西方向形变较小,南北方向形变较大,整体继续向南运动,最大震后位移约为10.93 cm。采用孔隙弹性回弹模型计算的理论地表位移远小于GPS观测值,无法解释GPS观测到的震后形变。采用震后余滑模型反演的结果表明,震后余滑主要集中在断层的下倾延伸部分,且空间分布较广,余滑释放的地震矩为1.09×1020 Nm。采用PSGRN/PSCMP程序计算粘弹性引起的理论地表形变结果显示,粘弹性松弛模型不能解释近场GPS观测值,但在远场区域的运动方向与GPS观测值一致。采用粘弹性松弛和震后余滑组合机制模型进行反演,余滑释放的地震矩降为1.08×1020 Nm,且空间分布更加集中。研究结果表明,组合机制模型在保证了模型拟合精度的基础上,反演结果与应力驱动模型反演结果更接近。     

断层破碎带条件下组合式圆截面抗滑桩加固边坡效果研究

随着我国公路建设不断向山区深入, 在地质构造复杂区公路边坡遇到断层破碎带的情况日渐增多, 亟需开展阻滑能力强的抗滑桩结构加固边坡研究。传统的人工挖孔桩施工模式存在高风险、低效率等缺点, 而组合式圆截面抗滑桩具有施工效率高、安全便捷等特点, 为此, 探究其对含断层破碎带边坡的加固效果具有现实意义。采用自主设计的边坡物理试验系统, 设计了5种不同破碎带厚度与组合式圆截面抗滑桩组合的物理模型, 采用坡顶逐级加载的方式模拟加载, 监测桩身应变、桩顶位移和桩后土压力, 采用高速相机捕捉滑体变形破坏图像, 并使用粒子图像测速(PIV)技术对图像进行处理。研究结果表明: 组合式圆截面抗滑桩通过限制桩后滑体水平位移, 并将滑体限制在前、后排桩间来达到加固边坡的效果; 滑体演化分为变形压密、加速变形和破坏滑移3个阶段; 前、后排桩桩后土压力比值介于1/3~1/2之间; 随断层破碎带厚度增加, 滑体水平滑移速率增大, 组合式圆截面抗滑桩的桩顶位移增大, 桩身最大正弯矩减小。模型试验与数值模拟计算的弯矩及桩顶位移较为吻合, 研究成果可为边坡工程组合式圆截面抗滑桩设计提供一定借鉴与参考。      

黑河山区流域平均坡长的计算与径流模拟

 流域平均坡长是侧向流和汇流时间计算的重要参数,其会影响地表径流的计算。应用SWAT 2005和ArcView GIS 3.2集成的AVSWAT模型,对黑河干流上游山区流域莺落峡出山口径流进行模拟,发现其计算的流域平均坡长存在较大误差,进而影响到模拟结果。利用子流域内已知的平均坡度和平均坡长建立回归方程,计算各子流域的平均坡长,替换AVSWAT计算的不合理值,在保持其他参数不变的情况下,模拟的月径流纳什系数从0.60提高到0.75,模拟结果得到显著提高。敏感性分析结果和径流曲线数(CN2)的分析也间接验证了流域平均坡长修正方法的可行性。在修正流域平均坡长后,对AVSWAT模型的其他参数CN2等进行优化,模拟的月径流的纳什系数达到0.81,表明本文建议的流域平均坡长计算方法是可以应用到实际的干旱区黑河流域并取得较好模拟效果。     

土质边坡空间临界滑动面搜索的优化算法

将二维均质土坡作为平面应变问题,假定滑动面是一个圆弧,将滑弧圆心与半径转变为后缘剪入点、坡脚剪出点和过后缘点滑弧切线与x轴的交点等3个点的横坐标,然后以这3个参数为变量,给定合理的取值区间,应用黄金分割法搜索二维边坡的最小稳定系数及相应的临界滑动面。进一步假定均质土坡的三维空间滑动面为一旋转椭球体,旋转椭球体的竖向中轴面和二维的圆弧面一致,给定椭球体不同的水平轴半径值,采用以上二维滑动面搜索方法可求出不同水平半径所对应的三维最小稳定系数及相应的椭球面。结果表明:边坡的三维稳定系数没有极小值,但有极限值;对于横向延伸长的无限边坡,三维稳定系数逼近二维稳定系数,当旋转椭球长轴与短轴之比大于3时,二者很接近,边坡稳定性可简化为二维来分析;对于受地形、地下水等条件约束的短边坡,三维效应明显,在考虑实际边界条件的情况下按三维来分析。     

Analytical expressions for determining the stability of cohesionless soil slope under generalized seismic conditions

In recent major earthquakes, the researchers have found the need for consideration of vertical seismic acceleration for the stability analysis of the man-made and natural slopes. However, in most past studies, the performance of slopes has been assessed by accounting only the horizontal seismic component of the ground motion, without giving due weightage to the effect of vertical component. In the present study, analytical expressions are derived to determine the factor of safety, yield seismic coefficient and consequently the seismic displacement of cohesionless soil slope under combined horizontal and vertical components of the ground motion. The derivation uses the Newmark’s sliding block approach, in which the soil slope with a planar failure surface within the framework of conventional pseudo-static analysis is assumed to follow the Mohr-Coulomb failure criterion. The effects of vertical seismic coefficient on the stability of cohesionless slope have been studied through a set of graphical presentations for a specific range of soil parameters. It is observed that overlooking the effect of the vertical component of the ground motion on factor of safety and the displacement while designing the slope may be detrimental, resulting in the slope failure. The general expressions presented in this paper may be highly useful in the field of earthquake geotechnical engineering practice for designing the cohesionless soil slopes under combined horizontal and vertical seismic loads.     

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Influence of non-dimensional strength parameters on the seismic stability of cracked slopes

Cracks in rock or soil slopes influence the stability and durability of the slopes. Seismic forces can trigger slope disasters, particularly in the cracked slopes. Considering the nonlinear characteristics of materials, the more generalized nonlinear failure criterion proposed by Baker is adopted. The influence of non-dimensional strength parameters on the stability of cracked slopes under earthquakes is performed using the upper bound limit analysis. The seismic displacement is calculated by adopting the logarithmic spiral failure surface according to the sliding rigid block model. Based on the existing studies, two methods for the stability analysis of cracked slopes under earthquakes are introduced: the pseudo-static method(with the factor of safety(Fs) as an evaluation index), and the displacement-based method(with the seismic displacement as an evaluation index). The pseudo-static method can only determine the instantaneous stability state of the cracked slope, yet the displacement-based methodreflects the stability variation of cracked slopes during earthquakes. The results indicate that the nondimensional strength parameters affect the factor of safety and seismic displacement of slopes significantly. The non-dimensional strength parameter(n) controlling the curvature of strength function shapes on the slope stability is affected by other parameters. Owing to cracks, the effect of non-dimensional strength parameters on seismic displacement becomes more significant.     

GIS COMPONENT BASED 3D LANDSLIDE HAZARD ASSESSMENT SYSTEM：3DSLOPEGIS

In this paper ,based on a new Geographic Information System(GIS) grid-based three-dimensional (3D) deterministic model and taken the slope unit as the study object ,the landslide hazard is mapped by the index of the 3D safety factor ,Compared with the one-dimensional(1D) model of infinite slope,which is now widely used for deterministic model based landslide hazard assessment in GIS,the GIS grid-based 3D model is more acceptable and is more adapt-able for three-dimensional landslide.Assuming the initial slip as the lower part of an ellipsoid ,the 3D critical slip surface in the 3D slper stability analysis is obtained by means of a minimization of the 3D safety factor using the Monte Carlo random simulation.Using a hydraulic model tool for the watershed analysis in GIS,an automatic process has been devel-oped for identifying the slope unit from digital elevation model(DEM)data,Compared with the grid-based landslide hazard mapping method ,the slope unit possesses clear topograhical meaning,so its results are more credible,All the calcula-tions are implemented by a computational program,3DSlopeGIS,in which a GIS component s used for fulfilling the GIS spatial analysis function.and all the data for the 3D slope safety factor calculation are in the from of GIS data (the vector and the grid layers).Because of all these merits of the GIS-based 3D landslide hazard mapping method,the complex algo-rithms and iteration procedures of the 3D problem can also be perfectly implemented.     

E24 profile slope stability analysis in Haizhou Opencast Coal Mine of Fuxin

The E24 profile slope analyzed belongs to a series of excavated slopes of the Haizhou Opencast Coal Mine. It seems to be divided into Downslope Part and Upslope Part. Its profile comprises two noticeable coal seams, called the 8# and 9# weak layers, considered as the potential failure surfaces. In consideration of the actual configuration as in the perspective of any modification, assessing the stability of this slope with various profile forms under given conditions, and assessing the risk of instability and quantifying the influence of earthworks or other modifications to the stability of this slope, have constituted the primordial objectives carried out. From assumed potential failure surfaces, any specific profiles and specified slip surfaces are defined. A factor of safety (FoS) is computed for each specified slip surface; the smallest FoS found corresponds to the least favorable slip surface. The safety factor values obtained are compared to the suggested safety factor. Limit equilibrium methods of vertical slices implemented in Slope/W, computer program for slope stability analyses, have been adopted to perform the E24 slope stability analysis. The safety factor values computed with 9# weak layer are lower than for 8#; the factors of safety obtained with Sarma's method are the smallest; more, without groundwater (long term) overall values are greater than those determined under groundwater condition (short term). The lowest safety factor value is found for a profile depending on an adopted earthwork sequence. The E24 profile slope stability analysis shows the instability risk for the deepest weak layer, and also shows the short and long term stability of this slope for the envisaged earth movements. However it demonstrates the existence of instability risk for any earthwork firstly affecting the downslope part.     

E24 profile slope stability analysis in Haizhou Opencast Coal Mine of Fuxin

The E24 profile slope analyzed belongs to a series of excavated slopes of the Haizhou Opencast Coal Mine. It seems to be divided into Downslope Part and Upslope Part. Its profile comprises two noticeable coal seams, called the 8# and 9# weak layers, considered as the potential failure surfaces. In consideration of the actual configuration as in the perspective of any modification, assessing the stability of this slope with various profile forms under given conditions, and assessing the risk of instability and quantifying the influence of earthworks or other modifications to the stability of this slope, have constituted the primordial objectives carried out. From assumed potential failure surfaces, any specific profiles and specified slip surfaces are defined. A factor of safety (FoS) is computed for each specified slip surface; the smallest FoS found corresponds to the least favorable slip surface. The safety factor values obtained are compared to the suggested safety factor. Limit equilibrium methods of vertical slices implemented in Slope/W, computer program for slope stability analyses, have been adopted to perform the E24 slope stability analysis. The safety factor values computed with 9# weak layer are lower than for 8#; the factors of safety obtained with Sarma's method are the smallest; more, without groundwater (long term) overall values are greater than those determined under groundwater condition (short term). The lowest safety factor value is found for a profile depending on an adopted earthwork sequence. The E24 profile slope stability analysis shows the instability risk for the deepest weak layer, and also shows the short and long term stability of this slope for the envisaged earth movements. However it demonstrates the existence of instability risk for any earthwork firstly affecting the downslope part.     

Failure behavior of soil-rock mixture slopes based on centrifuge model test

The stability of soil-rock mixtures(SRMs) that widely distributed in slopes is of significant concern for slope safety evaluation and disaster prevention. The failure behavior of SRM slopes under surface loading conditions was investigated through a series of centrifuge model tests considering various volumetric gravel contents. The displacement field of the slope was determined with image-based displacement system to observe the deformation of the soil and the movement of the block during loading in the tests. The test results showed that the ultimate bearing capacity and the stiffness of SRM slopes increased evidently when the volumetric block content exceeded a threshold value. Moreover, there were more evident slips around the blocks in the SRM slope. The microscopic analysis of the block motion showed that the rotation of the blocks could aggravate the deformation localization to facilitate the development of the slip surface. The high correlation between the rotation of the key blocks and the slope failure indicated that the blocks became the dominant load-bearing medium that influenced the slope failure. The blocks in the sliding body formed a chain to bear the load and change the displacement distribution of the adjacent matrix sand through the block rotation.     

含优势渗流层边坡降雨入渗下的可靠度分析

含优势渗流层边坡在降雨入渗的作用下其渗流场往往具有较高的不确定性,这给边坡的稳定性评价带来困难,通常采用概率的方法解决此类问题。针对含优势渗流层边坡降雨入渗下的可靠度问题,通过将应力分析中的点估计-有限元法引入到边坡渗流-稳定性分析,提出了考虑优势渗流层渗透特性不确定性的渗流概率分析和边坡可靠度分析方法;其次以广西某含碎石夹层土坡为例,分析了降雨入渗下碎石夹层的优势渗流效应及渗流概率,并基于此开展了该边坡降雨入渗下的可靠度分析。结果表明:①含优势渗流层边坡雨水沿优势渗流层渗入坡体内部的深度显著高于沿坡面渗入的深度;优势渗流层渗透特性的不确定性对渗流结果的影响较大,使得边坡稳定性分析具有较强的不确定性;②随着雨水入渗持时的增加,含优势渗流层边坡不同滑动面的失效概率总体呈现增加趋势,最危险滑动面的位置不断向边坡下部演化;依托工程滑动面位置的预测结果与工程实际吻合;③提出的概率分析方法适用于分析含优势渗流层边坡降雨入渗影响下的稳定性问题,而且具有计算量小的优势,可作这类边坡可靠度分析的一种新方法。      

基于等分圆弧滑面土质边坡的稳定性极限分析方法

基于等分圆弧滑面的简化条件,采用土塑性极限分析理论,建立了土质边坡极限分析模型,并推导得到了土质边坡稳定系数计算公式。该方法考虑了圆弧滑面的内能耗散率作用和边坡土体自重荷载、地震惯性力及孔隙水压力所做的外功率作用,可以解决土质边坡稳定性分析问题,是一种改进的土质边坡稳定性评价极限分析方法。