The Ellipsoidal Surface Method Solving by Integration for Slope Stability Analysis

Landslide is common phenomena in construction field. Nowadays the cylindrical surface method has been used widely to analyze slope stability. However, this method contains two main disadvantages： firstly, the slip surface is assumed to be in circular shape while in fact it is ellipsoid commonly; and secondly, resolve by difference method causing immensely complicated process due to statically indeterminate equations. In this paper, the authors have presented a method that allows transferring of ellipsoid slip surface to cylindrical shape and carries out a single variable equation （by applying integration method）. Also thanks to this method, the current cylindrical surface method has been proved that its application is proper for man-made slopes but usually inappropriate for natural ones. Those results help analysis of slope stability reaching closer to reality.

Application of artificial slope stability evaluation of improved response surface method in Donggang Power Plant

The study of artificial slope stability has been a key item of geological engineering projects. Though more evaluation methods are available,result of stability evaluation simulation does not explain the actual problem owing to the diversified geological engineering factors and complexity. The author made a detailed study based on surveys of large amount of geological engineering research on Donggang Power Plant slope project,discussed the comprehensive factors influencing the project,and gave analytical calculation and evaluation to the improved response surface of the slope project. The study result shows that the slope is stable,which can provide scientific basis for designing the slope.

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.

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.

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.

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.

Comprehensive Analysis Method of Slope Stability Based on the Limit Equilibrium and Finite Element Methods and Its Application

To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case.

Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis

In many construction projects,a proactive slope stability evaluation is a prerequisite.Although many deterministic or non-deterministic approaches have been commonly used,metaheuristic approaches have resulted in high precision and significant outcomes for slope stability analysis problems.The current work focuses on the reliable assessment of critical failure surfaces associated with the least factor of safety value in both homogeneous and non-homogeneous slopes using a new simplified meta-heuristic approach called optics-inspired optimization(OIO).The algorithm utilizes six different LEM methods as a fitness function for deriving the factor of safety.Experimental analysis over three benchmark studies has been performed to demonstrate the algorithm's robustness and effectiveness.The implementation found more robust results as compared to previous studies.Meanwhile,the algorithm's statistical implication is conducted using the ANOVA test,which inferred better outcomes.With this interpretation,the approach claims to be suitable and efficient for slope stability analysis.

Probabilistic assessment of rock slopes stability using the response surface approach——A case study

This paper examines the stability condition of a jointed rock slope in the south western region of Saudi Arabia using deterministic and probabilistic approaches,under both dry and wet conditions.The study area is characterized by complex geology in rugged terrains.The stability analysis is carried out using the code FLAC3D to generate a 3-dimensional,ubiquitous joint model,to determine the influence of the dominant,unfavourable discontinuity orientation with respect to the slope face.The deterministic analysis is first implemented using the mean values of the selected random variables,namely the dip,dip direction and friction angle of the dominant discontinuity set,and the stability condition is assessed with a factor of safety based on the classical frictional joint constitutive model.A Box-Behnken design(BBD)approach is then adopted to create the surface response function as a second order polynomial for the factor of safety.To do so,fifteen FLAC3D models are generated in accordance with the BBD.Based on this,10,000 simulations of different slope realizations are carried out using Monte-Carlo simulation technique,and the probability of unsatisfactory of performance of the rock slope is assessed.It is shown that the probabilistic approach provides more insight and confidence in the stability condition of the rock slope,both under dry and steady state heavy rainfall conditions.A discussion is presented on the significance of accepting lower safety factors when heavy rainfall conditions are encountered.

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.

3D Identification and Stability Analysis of Key Surface Blocks of Rock Slope

Complicated geological structures make it difficult to analyze the stability of rock slopes, such as faults, weak intercalated layers or joint fissures. Based on 3D geological modeling and surface block identifying methods, an integrated methodology framework was proposed and realized to analyze the stability of surface blocks in rock slopes. The surface blocks cut by geological structures, fissures or free faces could be identified subjected to the four principles of closure, completeness, uniqueness and validity. The factor of safety(FOS)of single key block was calculated by the limit equilibrium method. If there were two or more connected blocks, they were defined as a block-group. The FOS of a block-group was computed by the Sarma method. The proposed approach was applied to an actual rock slope of a hydropower project, and some possible instable blocks were demonstrated and analyzed visually. The obtained results on the key blocks or block-groups provide essential information for determining potential instable region of rock slopes and designing effective support scheme in advance.

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.

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.

Comparative Study on Response Surfaces for Reliability Analysis of Spatially Variable Soil Slope

This paper focuses on the performance of the second-order polynomial-based response surfaces on the reliability of spatially variable soil slope. A single response surface constructed to approximate the slope system failure performance function G（X） （called single RS） and multiple response surfaces constructed on finite number of slip surfaces （called multiple RS） are developed, respectively. Single RS and multiple RS are applied to evaluate the system failure probability pf for a cohesive soil slope together with Monte Carlo simulation （MCS）. It is found thatpe calculated by single RS deviates significantly from that obtained by searching a large number of potential slip surfaces, and this deviation becomes insignificant with the decrease of the number of random variables or the increase of the scale of fluctuation. In other words, single RS cannot approximate G（X） with reasonable accuracy. The value of pc from multiple response surfaces fits well with that obtained by searching a large number of potential slip surfaces. That is, multiple RS can estimate G（X） with reasonable accuracy.

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.

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.

Comparative study of material point method and upper bound limit analysis in slope stability analysis

The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.

基于折线形滑动和SLOPE/W模拟的滑坡稳定性对比分析

为提高滑坡稳定性分析的准确性,首先采用折线形滑动面稳定性计算方法对某滑坡进行了稳定性分析,再利用SLOPE/W程序对某滑坡进行了计算机模拟,并采用Bishop法和Janbu法在考虑地下水与未考虑地下水的情况下对该滑坡进行了计算,并将计算结果与折线性滑动的稳定性进行了比较和分析,给出了该滑坡的稳定性评价.

基于Geo-Slope的南芬露天铁矿A区滑坡体稳定性分析

以南芬露天铁矿A区滑坡体为研究对象,利用Geo-Slope软件从理论解析和定量的角度,计算出边坡体的稳定性系数,并搜索出最危险滑动面,以及滑动面在外界影响作用下的变化特征。对边坡的稳定性状况进行深入分析研究后发现:开挖到334~328 m平台后,边坡块体基本处于极限平衡状态,此时应停止开挖,时刻密切观察边坡体的稳定状况,并做好人员、设备的撤场准备,待采取爆破或者降雨之后,边坡体产生滑动后再进场开挖。事实表明,在10月5日开挖到340 m平台时,遇上强降雨,370 m平台局部发生平面滑动,由于提前撤场,避免了较大的人员伤亡及经济损失。

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.