Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.     

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su~zestions for future study are also oresented.     

Parametric Analysis of the Stability of Degraded Railroad Platforms

The current study is developed based on one of the types of subgrade rupture risk suggested by Selig and Waters （1994）. It aims to evaluate subgrade stability railroad, which consists of the slope stability analysis of a railway yard embankment subjected to a wagon load type gondola parked on this track. This proposed analysis was taken into consideration because there are Brazilian railroads in high deterioration level. In some of these lines the tracks are submitted to increasing amount of load every year. The adopted model slope stability to the studied railroad embankments considers the rupture on circular line. It was applied the Geoslope-Slope/W software, version 6, to the evaluation of the platform-slope system. Several situations are adopted to reach the minimum safety slope, permitting to analyze the platform stability to keep railroad traffic under adequate safety level.     

A comprehensive testing method for global stability analysis of high arch dams

Hydropower projects are rapidly developing in China at present,and a number of high dams and large reservoirs are currently under construction or will soon be built.These large projects are mainly located on the great rivers in West China with complicated topographical and geological conditions.Evaluation of stability and safety of these high dam projects is an important topic.Geomechanical model test is one of the main methods to study the global stability of high dam and foundation.In this paper,a comprehensive testing method that combines overloading and strength reduction in a model is proposed.In this method,both the influence of excessive flooding and the effects of strength reduction of rock masses and weak structural planes on dam stability are considered.Thus,the comprehensive testing method can accurately incorporate multiple factors that affect the global stability of high dam and its foundation.Based on the failure testing principle and model similarity theory,a similarity relation formula for safety evaluation through comprehensive test is established.A new model material,temperature-dependent analogous material,is also developed.By rising the temperature and reducing the strength of the model material,the mechanical behaviors resulting from gradual strength reduction can be simulated.Thus,the comprehensive testing method is realized in a single model.For case studies,the comprehensive geomechanical model test is conducted for Jinping I and Xiaowan high arch dam projects.     

Polyaxial strength criterion and closed-form solution for squeezing rock conditions

In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ_2) and minor(σ_3) principal stresses in place of σ_3 in Ramamurthy(1994)'s strength criterion.The proposed criterion has the main advantages of negligible variation of strength parameters with confining stress and ability to link with conventional strength parameters.Additionally,a new closed-form solution based on the proposed criterion is derived and validated for Chhibro Khodri tunnel.Further,analytical solutions including Singh's elastoplastic theory,Scussel's approach,and closed-form solutions based on conventional and modified Ramamurthy(2007) criteria are compared with the results of proposed approach.It is shown that the in situ squeezing pressure predictions made by the proposed approach are more accurate.Also,a parametric study of the present analytical solution is carried out,which displays explicit dependency of tunnel stability on internal support pressure and tunnel depth.The influence of tunnel geometry is observed to be dependent on the applied support pressure.     

Bayesian data analysis to quantify the uncertainty of intact rock strength

One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σ_(ci) and m_i used in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student's t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.     

Improvement parameters in dynamic compaction adjacent to the slopes

Dynamic compaction is a cost-effective method commonly used for improvement of sandy soils.A number of researchers have investigated experimentally and numerically the improvement parameters of soils using dynamic compaction,such as crater depth,improvement depth,and radial improvement,however,these parameters are not studied for improvement adjacent to the slopes or trenches.In this research,four different slopes with different inclinations are modeled numerically using the fi nite element code ABAQUS,and impact loads of dynamic compaction are applied.The static factors of safety are kept similar for all trenches and determined numerically by application of gravity loads to the slope using strength reduction method(SRM).The analysis focuses on crater depth and improvement region which are compared to the state of fl at ground.It can be observed that compacted area adjacent to the slopes is narrower and slightly away from the slope compared to the fl at state.Moreover,crater depth increases with increase in slope inclination.     

A generalized three-dimensional failure criterion for rock masses

The smooth convex generalized failure function, which represents 1/6 part of envelope in the deviatoric plane, is proposed. The proposed function relies on four shape parameters (Ls, a, b and c), in which two parameters (a and b) are dependent on the others. The parameter L s is called extension ratio. The proposed failure function could be incorporated with any two-dimensional (2D) failure criteria to make it a three-dimensional (3D) version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion for geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering (1) constant extension ratio and (2) variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio (Ls) that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters (σc and m) are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameter fis introduced. The modified extension ratio is related to f and extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range of f varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression between f and Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.     

Discussion on “A generalized three-dimensional failure criterion for rock masses”

There are many methods to construct true triaxial strength criteria for rocks.Jaiswal and Shrivastva(2012)proposed a strength criterion,named J–S criterion,in the deviatoric plane,which provides nearly the same misfts for true triaxial test data as the exponential criterion.It is diffcult to calculate the strength at given2and3using the J–S criterion,and the multiple solutions to the nonlinear equation may induce confusion and mistake.Strength envelopes in deviatoric planes are not geometric similar;therefore,true triaxial test data cannot be grouped in the mean stress to check strength criteria in the deviatoric plane.     

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects.Several step-by-step analytical solutions have been developed for analyzing these types of slope failures.However,manual application of these analytical solutions for real case studies can be time-consuming,complicated,and in certain cases even impossible.This study will first examine existing methods for toppling failure analyses that are reviewed,modified and generalized to consider the effects of a wide range of external and dead loads on slope stability.Next,based on the generalized presented formulae,a Windows form computer code is programmed using Visual C#for analysis of common types of toppling failures.Input parameters,including slope geometry,joint sets parameters,rock and soil properties,ground water level,dynamic loads,support anchor loads as well as magnitudes and forms of external forces,are first loaded into the code.The input data are then saved and used to graphically draw the slope model.This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode.The results are presented using a graphical approach.The developed code allows probabilistic introduction of the input parameters via probability distribution functions(PDFs)and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique.This allows calculation of the probability of slope failure.Finally,several published case studies and typical examples are analyzed with the developed code.The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code.The comparisons demonstrate good agreement between the results.     

非线性强度参数对高土石坝坝坡稳定性的影响

堆石料在高应力状态下，其抗剪强度具有明显的非线性。使用对数形式的非线性强度准则得到的坝坡计算安全系数要高于按线性强度准则得到的计算安全系数。现行规范所规定的许可安全系数，是与多年来大量使用偏低的线性强度指标所作的稳定计算相适应的，偏于保守：改用非线性强度后应作适当的提高。对采用非线性强度计算的安全系数比采用线性强度计算的安全系数提高程度进行了统计分析，给出了用非线性强度指标进行稳定分析的安全系数取值标准的建议值。     

块碎石强度非线性对山区高填方边坡稳定性的影响

边坡稳定分析结果的可靠性很大程度上取决于抗剪强度指标的正确选择,这一点对山区高填方边坡的稳定分析尤为重要。广泛应用于山区高边坡的块碎石填料,其强度具有明显的非线性,只有采用非线性指标进行分析才能较好反映边坡真实的安全状态。通过对数形式的非线性强度准则在极限平衡条分法中的应用,讨论线性强度与非线性强度指标对应的计算结果差异,指出采用线性强度指标计算高边坡稳定时,强度指标的选取应当考虑边坡的应力水平,且不应采用无黏聚力的线性强度。     

顺层滑坡弹塑性接触有限元稳定性分析

有限元强度折减法可以作为极限平衡分析方法的一种逆过程。根据已有文献报道和工程实践,建立有限元强度折减法与极限平衡法计算稳定性系数的数理统计相关式,为充分利用极限平衡法计算滑坡稳定性系数的优点、发挥有限元强度折减法计算滑坡稳定性系数的优势和保证滑坡稳定性系数计算及分析的可靠性提供更加充分的依据。确定有限元强度折减法中滑体(包括滑带)的强度参数和重度、精确划分网格和收敛准则等原则。通过工程实例分析认为,这些原则的确定在风化岩质顺层滑坡稳定性系数计算及稳定性分析中是正确的,可作为该类型滑坡稳定性分析和计算的参考。采用不分离接触弹塑性有限元强度折减法分析高度非线性问题的风化岩质顺层滑坡稳定性,可以更加逼真地反映滑坡变形、破坏的实际情况。     

关于有限元边坡稳定性分析中安全系数的定义问题

在边坡稳定性分析的极限平衡法中存在3种安全系数的定义:定义1将安全系数定义为剪切强度比剪应力;定义2将安全系数定义为强度储备系数,当土体抗剪强度除以安全系数后,边坡将处于临界平衡状态;定义3将安全系数定义为沿某一特定滑面的抗滑力比滑动力。讨论了定义3与定义1之间的关系,给出了在进行有限元边坡稳定性分析时确定对应于定义3和定义2的临界滑面的统一算法,最后通过算例证明了一般情况下基于定义3所求得的安全系数和临界滑面不同于基于定义2所求得的结果,同时指出基于定义3的计算结果会表现出一些不合理的现象。     

基于强度折减法的边坡稳定性三维有限元分析

将强度折减法应用于边坡稳定性分析中，折减土体强度，代入有限元程序进行计算，直至计算不收敛，此时的折减系数即为安全系数。将强度折减法应用于边坡稳定性的三维分析，结合工程实例，基于强度折减法的边坡稳定性有限元法和传统极限平衡法的计算结果，对边坡稳定性二维分析和三维分析的结果进行了对比，表明基于强度折减法的边坡稳定性三维有限元分析是可行的。在边坡稳定性分析中，为得到更符合实际情况的结果，在有条件的前提下宜补充进行边坡稳定性三维分析。     

一种边坡稳定性分析的三维极限平衡法及应用

将离散后的条柱间作用力等效成滑面正应力,依据整个滑体的平衡条件,提出一种适用一般空间形态滑面的边坡三维极限平衡法。首先通过类比经典土压力理论和Spencer的条间力假定,提出了条柱间作用力假设模型,由典型条柱的平衡条件得到滑面正应力的分布函数(含3个待定参数),再根据整个滑体的4个主要平衡条件建立平衡方程,采用数值方法和解析法求解平衡方程组获得三维安全系数。算例验证研究结果表明：该方法计算结果与已有方法相印证,其精度与严格三维极限平衡法相当,适用于任意空间滑面形态。最后,应用该方法初步评价金坪子II区边坡的整体稳定性,取得较理想的效果。该方法理论严谨,结果可靠,计算过程简单且易于编程,可在边坡工程设计及滑坡治理中推广应用。     

强度折减法在强夯边坡稳定性评价中的应用

基于强度折减原理的有限元法不但满足力的平衡条件,而且考虑了材料的应力应变关系,使得计算结果更加精确合理。文章采用强度折减法对某电厂地基处理中所涉及的髙填方夯填边坡进行了稳定性评价。计算结果表明,该边坡工程安全系数较大,工程设计较为安全。通过与传统极限平衡法结果对比,表明强度折减法用于夯填边坡稳定性分析的适宜性。同时在边坡高度不变的情况下变化坡率进行稳定性分析,结果表明坡率为1:1.5左右时较为合适。     

LSSVM-based approach for refining soil failure criteria and calculating safety factor of slopes

The failure criteria of practical soil mass are very complex, and have significant influence on the safety factor of slope stability. The Coulomb strength criterion and the power-law failure criterion are classically simplified. Each one has limited applicability owing to the noticeable difference between calculated predictions and actual results in some cases. In the work reported here, an analysis method based on the least square support vector machine (LSSVM), a machine learning model, is purposefully provided to establish a complex nonlinear failure criterion via iteration computation based on strength test data of the soil, which is of more extensive applicability to many problems of slope stability. In particular, three evaluation indexes including coefficient of determination, mean absolute percentage error, and mean square error indicate that fitting precision of the machine learning-based failure criterion is better than those of the linear Coulomb criterion and nonlinear power-law criterion. Based on the proposed LSSVM approach to determine the failure criterion, the limit equilibrium method can be used to calculate the safety factor of three-dimensional slope stability. Analysis of results of the safety factor of two three-dimensional homogeneous slopes shows that the maximum relative errors between the proposed approach and the linear failure criterion-based method and the power-law failure criterion-based method are about 12% and 7%, respectively.     

龙滩水电站航道失稳边坡加固有限元模拟分析

通过用非线性有限元模拟分析边坡开挖支护过程,探讨不同情形下失稳边坡在加固治理过程中的应力、变形演变特征及塑性区的分布和扩展状态,采用有限元强度系数折减法推求边坡安全系数,并据此对边坡的稳定性进行分析和评价,为设计和施工提供科学依据。     

基于三维非线性有限元的拱坝坝肩稳定分析

 刚体极限平衡法不能反映岩体中实际的应力分布,而基于有限元的强度折减系数法在判断收敛性方面也存在一些问题。为了解决这些问题,采用多重网格法,分别建立用于有限元计算的结构网格和用于计算滑面稳定安全系数的滑面网格。基于有限元计算的应力结果,通过插值获得滑面的受力分布情况,然后可以方便地计算得到任意滑面或滑块的稳定安全系数,从而将非线性有限元和刚体极限平衡分析方法结合起来。为了改善计算的收敛性和提高非线性求解的精度,非线性有限元计算采用一种基于Drucker-Prager准则的理想弹塑性增量分析方法,无论是对于小荷载步长还是大荷载步长,弹塑性计算均具有很好的收敛性。该方法已经集成到三维非线性有限元分析程序TFINE中,在分析了插值方法和网格密度对计算结果精度的影响基础上,将该方法应用于某水电站高拱坝坝肩的稳定分析中。计算结果分析以及与刚体极限平衡法结果的对比表明,由于考虑了计算过程中的非线性应力调整,所提出方法的计算结果虽然比刚体极限平衡法偏大,但更符合实际情况。