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.

Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

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.

Rectangular tunnel heading stability in three dimensions and its predictive machine learning models

Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.

The limit analysis in soil and rock:a mature discipline of geomechanics

The solution of a slope stability problem can be approached by its least upper-bound and maximum lower-bound with high accuracy. The limit equilibrium methods that employ vertical slices imply a lower bound of the factor of safety. It has been successfully extended to the area of active earth pressure analysis that accounts for different input of locations of earth pressure applications. Those methods that employ slices with inclined interfaces give an upper-bound approach to the stability analysis. It enjoys a sound mechanical background and is able to provide accurate solutions of soil plasticity. It has been successfully extended to the area of bearing capacity analysis in which various empirical coefficients are no longer necessary. The 3D upper- and lower-bound methods under this framework have been made possible and show great potential for solving various engineering problems.

Stability Evaluation of Slopes Using Kinematic and Limit Equilibrium Analyses in Seismically Active Balakot, KPK, Pakistan

The Northern segment of Pakistan, especially Balakot city is affected up to large extent by the landslides. Tectonically, it lies in the proximity of Hazara Kashmir Syntaxis and other two active regional faults: Main Boundary and Hazara Frontal Thrusts that traversing right through the Balakot town. This study focuses on the evaluation of slopes near Balakot town in static and pseudo-static condition. A geological map is produced at 1:24,000 scale to separate various rock and soil units. During reconnaissance study, two slopes were selected which seem prone to sliding. The procured data on condition of natural slope, properties of material entailed, structural setting, and vegetation cover distribution was gathered. Discontinuity Surveys of slopes were carried out to collect discontinuity parameters. Kinematic analyses were performed on DIPS v. 7.0 to assess mode of failures based on joints data. Limit equilibrium analyses were carried out at Slide v. 7.0 to check factor of safety at different conditions. The study concluded that the slopes were affected by the plane, wedge and toppling failures, while although in seismically active zone, circular failure is not likely.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-C) strength criterion and the initial normal stress without considering the inter-slice(or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price(M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

A new method for the stability analysis of geosynthetic-reinforced slopes

This paper is concerned with the stability analysis of reinforced slopes.A new approach based on the limit equilibrium principle is proposed to evaluate the stability of the reinforced slopes.The effect of reinforcement is modeled as an equivalent restoring force acting the bottom of the slice and added into the general limit equilibrium(GLE) method.The equations of force and moment equilibrium of the slice are derived and corresponding iterative solution methods are provided.The new method can satisfy both the force and the moment equilibrium and be applicable to the critical failure surface of arbitrary form.Furthermore,the results predicted by the proposed method are compared with the calculation examples of other researchers and the centrifuge model test results to validate its correctness and effectiveness.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead ofthe finite element method is used t perform lower bound limit andshakedown analysis of structures. The self-equilibrium stress fieldsare constructed by a linear combination of several basicself-equilibrium stress fields with parameters to be determined.These basic self-equilibrium stress fields are expressed as elasticresponses of the body to im- posed permanent strains and obtainedthrough elastic-plastic incremental analysis.

Engineering Geological and Geotechnical Studies of Taprang Landslide, West-central Nepal: An Approach for Slope Stability Analysis

Detailed investigation of Taprang landslide was carried out in order tounderstand the surface, subsurface lithological information and physicalproperties of soil by using multi-disciplinary methods such as engineeringgeological, geophysical and geotechnical studies for the determinationof factor of safety for slope stability analysis. Geological study wascarried out by detail mapping of surface geology, soil condition, propertiesof bedrock and its discontinuities. The geophysical survey (ElectricalResistivity Tomography-ERT) were carried out to know the electricalresistivity of soil for identifying the groundwater table and slip surface ofthe landslide. Geotechnical analysis such as grain size analysis, liquid limitand direct shear test were carried out in order to evaluate soil classification,moisture content, cohesion and the angle of internal friction of soil forknowing the strength the soil. These soil parameters indicate the soil is verylow strength. The combination of these results were used for calculatingthe factor of safety (FoS) by Limit Equilibrium Method (LEM) proposedby Bishop and Janbu methods. The result of factor of safety in the Tapranglandslide demonstrates that the slope become stable in drained (dry)condition, remain ultimate stage in undrained (wet) condition and finallyfailure occurs if applied the seismic load in both drained and undrainedconditions.

Probabilistic approach for open pit bench slope stability analysis——A mine case study

The geotechnical slope design of an open pit wall starts at the bench scale configuration.At this scale,the rock slope stability is governed primarily by the geological discontinuities within the rock mass and as a result,structurally-controlled failures(e.g.planar,wedge or toppling)are most likely to occur.The probabilistic approach offers a major advantage over the traditional deterministic method in that it accounts for the different degrees of variability and uncertainty often encountered in rock properties.This paper presents a bench slope stability assessment for an open pit mine in Peru using a probabilistic-based approach by coupling a kinematic analysis based on stereographic projection techniques followed by a kinetic analysis by means of the limit equilibrium method.Finally,these two probabilities are combined to provide an overall measure of the probability of failure(PoF)of the bench slope system.The case study is characterized by significant scatter in the geometrical and mechanical properties of the joints.Extensive surface mapping was conducted at 36 different sites following the ISRM suggested procedures.Several direct shear tests were carried out.It is shown that by combining field and laboratory measurements and engineering judgment,the probability density functions(PDF)of the discontinuity parameters can be obtained.These are then used in a Monte Carlo simulation process to compute both kinematic and kinetic probabilities of failure.The overall probability of failure aims to provide the design engineer with a tool to critically evaluate the bench performance from a geotechnical risk perspective and to provide a basis for future bench design optimization.

An Improved Particle Swarm Optimization Algorithm with Harmony Strategy for the Location of Critical Slip Surface of Slopes

The determination of optimal values for three parameters required in the original particle swarm optimization algorithm is very difficult. It is proposed that two new parameters simulating the harmony search strategy can be adopted instead of the three parameters which are required in the original particle swarm optimization algorithm to update the positions of all the particles. The improved particle swarm optimization is used in the location of the critical slip surface of soil slope, and it is found that the improved particle swarm optimization algorithm is insensitive to the two parameters while the original particle swarm optimization algorithm can be sensitive to its three parameters.

What is the role of tensile cracks in cohesive slopes?

The traditional limit equilibrium method(LEM) is often used to search for the failure surface with a minimum safety factor of slope. In this method, the failure surface is considered as a shear surface,irrespective of its form. However, tensile cracks are frequently found at the outcrops of landslides. In this study, three sets of tests on small-scale landslides with different inclination angles were conducted. The test results demonstrated that tensile cracks could arise in the slope sliding process and the failure surface is composed of both a shear and a tensile fracture surface. Based on the test results, we used the improved LEM, and replaced the traditional shear failure surface by a tensile-shear coupling one, thus new tensile failure modes for slope stability analysis can be established. The safety factors of slope in different failure modes were compared, which show that when considering soil tensile failure and tensile strength less than a certain value(e.g. 15 kPa, 44 kPa and 55 kPa for linear, circular and logarithmic spiral failure surfaces, respectively), the safety factors of slope with three different failure surfaces are less than the one that did not consider the tensile failure. The most critical failure surfaces of the slope may be composed of shear and tensile damages because the tensile strength of the soil cannot be generally greater than its cohesion.

A New Approach to the Determination of the Critical Slip Surfaces of Slopes

A new method for the determination of the critical slip surfaces of slopes is proposed in this paper. In this paper, the original critical slip field method is extended in terms of the total residual moment, values of residual work as well as the unbalanced thrust force at the exit point for a given non-circular slip surface. The most critical slip surface with the maximum representative value for a prescribed factor of safety will be optimized and located using the harmony search algorithm. The prescribed factor of safety is modified with certain tiny interval in order to find the critical slip surface where the maximum representative value is zero. The aforementioned approach to the location of the critical slip surface is greatly different from the traditional limit equilibrium procedure. Three typical soil slopes are evaluated by use of the proposed method, and the comparisons with the classical approaches have illustrated the applicability of the proposed method.

Simplified Calculation Method and 3D Numerical Analysis for Pile Group Under Uplift Loading

Pile foundations of ports, mooring systems for ocean surface or submerged platforms are subjected to amount of uplift loading, and prediction of the uplift capacity is one of the most important subjects in structure designs. The paper pertains to the development of a simplified theoretical method on prediction of the uplift capacity of pile group embedded in clay assuming a composite failure surface （inverted and tnmcated circular pyramidal and cylindrical sttrface）. Various pile and soil parameters such as the arrangement of pile group, pile spacing, length, diameter of the pile and the soil properties such as unit weight, angle of internal friction and the pile-soil interface friction angle, which have direct influence on the uplift capacity of the pile group, are incorporated in the analysis. A 3D numerical model is built by FLAC3D to analyze the pile group under uplift loading for comparison, and various effect factors, such as length to diameter ratio, pile spacing and pile numbers are considered. The predicted values of uplift capacity and failure surface of pile group with different length to diameter ratio, pile spacing and soil properties are then compared with numerical analysis results and tleld test results. The predictions are found to be in good agreement with numerical analysis and measured values, which validate the correctness of the developed method. It is also found that the uplift capacity is significantly influenced by the pile-soil friction coefficient, soil shear strength, etc.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Determination of Optimum Slope Design for Northern Boxcut in Zone 5 KhoeMacao Copper Mine, Botswana

An optimum design of box cuts in soil formations is very crucial in order to obviate the major risk factors originating from the collapse of sidewalls and flooding of excavations during storm rainfall. The present paper aims to present a holistic classification of the Kalahari Formation stratigraphy in Zone 5 and define engineering properties of each lithological unit, in order to establish a safe working design. For the present objectives, collection of data was carried out through logging core from selected geotechnical boreholes drilled within vicinity of the proposed Northern mine box cut. Hydrogeological assessments and feasibility studies within the purview of study region were also considered. Geotechnical logging parameters gathered on site were derived from the Rock Mass Rating system (RMR) for design requirements [1]. Input parameters and material characteristics taken from laboratory test results provided by KCM were incorporated in the analysis. The box cut slopes were modelled in “Rocscience software” for evaluation of safety factor using “limit equilibrium method”. Slope optimization required the slope surface to be as steep as possible while maintaining an adequate factor of safety ranging from 1.5 - 1.8. For the box cut design with optimum safety, the recommended parameters are: stable slope angle—35° - 40°;ramp angle—8°, depth of pit—60 meters;bench width—4.9 meters and the bench length—13.25 meters.

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。

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。