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.     

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。     

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。      

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.     

Evaluation of the possible slip surface of a highly heterogeneous rock slope using dynamic reduction method

A new method, the dynamic reduction method (DRM) combined with the strain-softening method, was applied to evaluate the possible slip surface of a highly heterogeneous rock slope of the Dagangshan hydropower station in Southwest China. In DRM, only the strength of the failure elements is reduced and the softening reduction factor K is adopted to calculate the strength parameters. The simulation results calculated by DRM show that the further slip surface on the right slope of the Dagangshan hydropower station is limited in the middle part of the slope, while both SRM (strength reduction method) and LEM (limit equilibrium method) predict a failure surface which extends upper and longer. The observations and analysis from the three recorded sliding events indicate that the failure mode predicted by DRM is more likely the scenario. The results in this study illustrate that for highly heterogeneous slopes with geological discontinuities in different length scales, the proposed DRM can provide a reliable prediction of the location of the slip surface.     

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.     

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.     

基于内外功率比的非直线坡面型边坡的稳定系数研究

在边坡稳定性上极限分析中,由于考虑了材料的理想弹塑性本构关系与相关流动法则,相比极限平衡法更符合岩土材料的特征。在以往的二维边坡极限分析上限法中,要求坡面形态为规则的直线,而无论是天然边坡还是人工边坡,边坡的坡面形态往往并非规则的直线。此外,以往的边坡极限上限分析中得到的稳定数N_s=c/γH主要针对土坡的临界高度计算,且未考虑孔压等外力对边坡施加的外功率。不同于传统极限平衡法采用静力学的平衡条件,本研究针对非直线型坡面边坡稳定性问题,假定滑动面为对数螺旋线,基于极限分析上限定理和虚功原理,提出了一种边坡发生旋转破坏时旋转中心的确定方法,推导出了非直线型坡面边坡的重力虚功功率和能量平衡方程的解析解,并提出了基于内、外功率之比的稳定系数K用以评价边坡的稳定性。通过算例比较了不同形态天然边坡的稳定性和人工削坡对边坡稳定性的影响,并分析了边坡的坡度(β)、土体的内摩擦角(φ)、黏聚力(c)以及孔压系数(r_u)对稳定系数K的影响规律。对于坡度较大的边坡,通过削坡改变坡面形态提高了边坡的稳定系数K。稳定系数K随黏聚力的增加而非线性增大,随孔压系数的增加而...     

Effect of lithology and structure on seismic response of steep slope in a shaking table test

Studies on landslides by the 2008 Wenchuan earthquake showed that topography was of great importance in amplifying the seismic shaking, and among other factors, lithology and slope structure controlled the spatial occurrence of slope failures. The present study carried out experiments on four rock slopes with steep angle of 60° by means of a shaking table. The recorded Wenchuan earthquake waves were scaled to excite the model slopes. Measurements from accelerometers installed on free surface of the model slope were analyzed, with much effort on timedomain acceleration responses to horizontal components of seismic shaking. It was found that the amplification factor of peak horizontal acceleration, RPHA, was increasing with elevation of each model slope, though the upper and lower halves of the slope exhibited different increasing patterns. As excitation intensity was increased, the drastic deterioration of the inner structure of each slope caused the sudden increase of RPHA in the upper slope part. In addition, the model simulating the soft rock slope produced the larger RPHA than the model simulating the hard rock slope by a maximum factor of 2.6. The layered model slope also produced the larger RPHA than the homogeneous model slope by a maximum factor of 2.7. The upper half of a slope was influenced more seriously by the effect of lithology, while the lower half was influenced more seriously by the effect of slope structure.     

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.     

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。     

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.     

Theoretical Analysis of Coral Reef Stability in South Sea

In this paper, we utilize the variational limiting equilibrium (LE) procedure to theoretically determine the slope stability of homogeneous coral sand in the South China Sea. By establishing a reasonable functional and calculating its extremum, we can deduce the stability factor of a coral reef identical to that obtained by upper bound analysis. To determine the accuracy of the results obtained using the variational LE procedure, we present some classical examples of homogeneous sand slopes without a hard shell and compare our results with those obtained by the upper bound theorem of plasticity. A series of extensive calculations and comparisons reveal that the results obtained by our proposed analysis method and those obtained using classical methods are slightly different, but the variational results are believable. On the other hand, our method solves some stability factors for reef slopes covered with a hard shell, which indicates that the existence of a hard reef shell may significantly enhance the stability of a reef slope, and that there is strong nonlinear relationship between reef stability and the mechanical characteristics of the reef shell, such as its thickness and strength. Finally, based on the variational results presented in this paper, we present a useful chart that offers a convenient and straightforward way to determine the maximum stability factor of reef slopes. Taking into account the influence of the hard reef shell, we found that, in some limit equilibrium cases, the limit stability factor and critical height of a coral slope could be improved significantly. Therefore, this issue deserves careful attention in engineering practice.     

Permanent displacement models of earthquake-induced landslides considering near-fault pulse-like ground motions

The permanent displacement of seismic slopes can be regarded as an effective criterion for stability estimation. This paper studied the characteristics of permanent displacements induced by velocity pulse-like ground motions and developed an empirical model to readily evaluate the stability of seismic slopes in a near-fault region. We identified 264 velocity pulse-like ground motions from the Next Generation Attenuation(NGA) database using the latest improved energy-based approach. All selected ground motions were rotated to the orientation of the strongest observed pulse for considering the directivity of the pulse effect, so that the most dangerous condition for slopes was considered. The results show the velocity pulse-like ground motions have a much more significant effect on permanent displacement of slopes than non-pulse-like ground motions. A regression model based on a function of peak ground velocity(PGV), peak ground acceleration(PGA) and critical acceleration(ac), was generated. A significant difference was found by comparing the presented model with classical models from literatures. This model can be used to evaluate the seismic slope stability considering the effects of nearfault pulse-like characteristics.     

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。      

Experimental study of motion characteristics of rock slopes with weak intercalation under seismic excitation

In order to investigate the effect of a weak intercalation on slope stability, a large-scale shaking table model test was conducted to study the dynamic response of rock slope models with weak intercalation. The dynamic response of the prototype slopes were studied in laboratory with the consideration of law of similitude. The initiation failure was observed in the rock slope model with a counter-tilt thin-weak intercalation firstly, not in the slope model with a horizontal thin-weak intercalation. Furthermore, it was interesting that the fracture site is shifted from crest top to the slope surface near the weak intercalation, which is different with the location of failure position in a normal layered slope. We also discussed the effect of the dip angle and the thickness of weak intercalation on the failure mechanism and instability mode of the layered rock slope. From the experimental result, it was noted that the stability of the slope with a counter-tilt weak intercalation could be worse than that of the other slopes under seismic excitation. The findings showed the difference of failure in slopes with a horizontal and counter weak intercalation, and implicated the further evaluation of failure of layered slopes caused by seismic loads.     

Effect of the inclined weak interlayers on the rainfall response of a bedded rock slope

Engineering experience shows that outward dipping bedded rock slopes, especially including weak interlayers, are prone to slide under rainfall conditions. To investigate the effect of inclined weak interlayers at various levels of depth below the surface on the variation of displacements and stresses in bedded rock slopes, four geo-mechanical model tests with artificial rainfall have been conducted. Displacements, water content as well as earth pressure in the model were monitored by means of various FBG (Fiber Bragg Grating) sensors. The results showed that the amount of displacement of a slope with a weak interlayer is 2.8 to 6.2 times larger than that of a slope without a weak interlayer during one rainfall event. Furthermore, the position of the weak interlayer in terms of depth below the surface has a significant effect on the zone of deformation in the model. In the slope with a high position weak interlayer, the recorded deformation was larger in the superficial layer of the model and smaller in the frontal portion than in the slope with a low position weak interlayer. The slope with two weak interlayers has the largest deformation at all locations of all test slopes. The slope without a weak interlayer was only saturated in its superficial layer, while the displacement decreased with depth. That was different from all slopes with a weak interlayer in which the largest displacement shifted from the superficial layer to the weak interlayer when rainfall persisted. Plastic deformation of the weak interlayer promoted the formation of cracks which caused more water to flow into the slope, thus causing larger deformation in the slope with weak interlayers. In addition, the slide thrust pressure showed a vibration phenomenon 0.5 to 1 hour ahead of an abrupt increase of the deformation, which was interpreted as a predictor for rainfall-induced failure of bedded rock slopes.     

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。      

Rock slope stability evaluation using kinematic and kinetic methods along the Kamyaran-Marivan road,west of Iran

Interest in rock slope stability in mountainous regions has increased greatly in recent years.This issue has become a topic of major interest for geoscientists and engineering professionals,as well as for private citizens and local administrators,in many parts of the world.This paper evaluates the stability of seven rock slopes along the KamyaranMarivan tourist road,Kurdistan province,Iran,using various methods.The two main reasons for performing this research were to determine whether different methods of stability analysis provide the same results,and to determine how different factors such as the presence of water,tension cracks,and seismic forces affect the stability of these rock slopes.Firstly,field investigations were performed to obtain the engineering characteristics of the rock masses,discontinuities,and intact rocks of the slopes.Secondly,laboratory tests were carried out on rock samples obtained from the slopes,to determine the engineering properties of the intact rocks.Then for each rock slope,the contour diagram of discontinuities and slope face was drawn in the Dips v.5.1 software environment,and the failure mechanism was determined based on the kinematic or stereographic method.Next,the factors of safety of the rock slopes were calculated using the limit equilibrium method,based on the failure mechanisms resulting from the kinematic method.The accuracy of the results obtained by these two methods was investigated using SWedge v.4.0 software.The results indicated that four rock slopes have a potential for plane,wedge,and toppling failure,and three others are stable.Also,it was found that the stability of the studied rock slopes decreases greatly in the presence of water,tension cracks,and seismic forces.