Analysis of random anisotropic damage mechanics problems of rock mass

Summary Probabilistic analysis of random anisotropic damage mechanics problems is proposed in Parts of I and II. In Part I, based on the measured characteristics of random crack distribution on the surface of a rock specimen, a probabilistic law of damage variables for rock mass was presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Two stability problems involving randomly damaged rock mass have been analyzed using the finite element method, to illustrate the statistical estimation method.     

Probabilistic key block analysis of a mine ventilation shaft stability – a case study

In this study, the probabilistic key block analysis was applied to evaluate the stability of a mine ventilation shaft developed in a rock mass of granite. The key blocks were identified based on the block theory. The variations of discontinuity orientations were fitted with the Beta distribution and taken into consideration. The key block forming probabilities were analyzed. For simplification of calculations the first-order second-moment (FOSM) approximation was employed for probability estimation. With the considerations of the rock properties as random variables and applications of several statistical analysis tools, the key block failure probabilities, the probabilistic distribution of safety factors, and the probabilistic distribution of potential maximum key block volumes were analyzed. The analysis indicated that although the safety factor calculated based on the mean values of the variables was above 1.0 for the stability of the most critical key block, the block had a considerable probability of failure with a significant rock volume due to variations in discontinuity orientations and rock properties. Without promptly applying supports to the rock excavation, the shaft had a significant likelihood of failure.     

Rock Slope Stability Assessment Using Geomechanical Classification and its Application for Specific Slopes along Kodaikkanal-Palani Hill Road,Western Ghats,India

Linear infrastructure networks like roads play a vital role in the socio-economic development of hill towns centered on tourism. Stability of the slopes along the hill roads are therefore a major concern and slope failures lead to disruption of traffic and loss of property/life or both. This study analyses the stability of cut-slopes along the Kodaikkanal – Palani hill road in the Western Ghats, India using rock mass classification systems like rock mass rating (RMR), slope mass rating (SMR) and continuous slope mass rating (CSMR). These geomechanical classifications provide a preliminary assessment of rock quality based on rock strength, discontinuity properties, hydrogeological condition of the slopes and slope stability based on the inherent rock strength parameters, discontinuity orientation and method of excavation. The results showed that both rock quality and discontinuity orientation contribute to type of failure in rock slopes with RMR > 40. SMR results are conservative while CSMR classification is matches more closely to the failures obtained from the field survey. CSMR classification represents continuous slope stability conditions and hence are more suitable for development of spatial database. Cutting of roads, thereby, steepening slopes has a definite influence on the stability of slopes.     

Probabilistic assessment of rock slope stability using response surfaces determined from finite element models of geometric realizations

A methodology is developed for probabilistic rock slope stability assessment using numerical modelling that incorporates statistical analysis of the variability of joint set geometric parameters. Each probabilistic input parameter is substituted by its two point estimates. Half-factorial and central composite designs are implemented to obtain a minimum number of representative slope realizations to model. The output from the numerical models is used to construct mathematical prediction models or response surfaces. A response surface can be used to predict the factor of safety of arbitrary realizations without further numerical modelling and can be used to determine the probability of slope failure.     

Probabilistic and sensitivity analyses of effective geotechnical parameters on rock slope stability: a case study of an urban area in northeast Iran

Despite the development of cities, risk assessment of rock slope stability in urban areas seems not to be growing at the same time. Mashhad is a developed city in northeast of Iran with a population of over 2.4 million. Given the closeness of the southern part of Mashhad to the Binaloud mountain ridge, the stability of the residential complexes that are being constructed in this area is a critical issue. Based on the fundamental roles of discontinuity properties and geo-mechanical parameters of rock mass, in this study we evaluated the most influential parameters of the rock slope stability and the failure probability of the slope near the Negin residential complex built on this ridge. According to the deterministic and probabilistic analyses, the north trench that was excavated for this residential complex could potentially cause plane failure. Moreover, the relationship between effective parameters on instability and their impact on safety factors were determined by sensitivity analysis. Therefore, slope dip, pore water pressure, and joint set dip were highly influential on the safety factor. There was also a nonlinear relationship between different parameters and safety in the studied area. This study presents an approach for risk assessment of rock slope stability in urban areas.     

Discontinuity controlled probabilistic slope failure risk maps of the Altindag (settlement) region in Turkey

The evaluation of potential rock slope problems using stereographic projection techniques known as kinematic analysis is one of the most important parts of a slope stability investigation to be carried out in jointed rock media. In conventional stereoprojection techniques for the assessment of possible rock slope failures, the peak orientations of joints together with the slope geometry and the friction angle of the weakness planes are used. Other possible joint orientations which may be encountered in the rock media are ignored, although they belong to the group of joint peak orientations. In this study, nearly vertical jointed andesites cropped out at the Altindag settlement region in Ankara were studied in order to evaluate the relevance of this ignored discontinuity orientation data on slope stability. As a result, probabilistic risk maps for planar, toppling and wedge failures were produced using the kinematic rules and digital elevation model of the study area. The comparison of the distribution of the actual failures in the area and the probabilistic risk maps prepared for the study area revealed that all of the identified failures are found to be located in the higher risk zones on the probabilistic risk maps.     

Probabilistic Stability Evaluation of Oppstadhornet Rock Slope,Norway

Probabilistic analyses provide rational means to treat the uncertainties associated with underlying parameters in a systematic manner. The stability of a 734-m-high jointed rock slope in the west of Norway, the Oppstadhornet rock slope, is investigated by using a probabilistic method. The first-order reliability method (FORM) is used for probabilistic modeling of the plane failure problem in the rock slope. The Barton–Bandis (BB) shear strength criterion is used for the limit state equation. The statistical distributions of the BB criterion parameters, for which comprehensive data were collected and statistically analyzed, are determined by using distribution fitting algorithms. The sensitivity of the FORM model for the BB criterion is also investigated. It is found that the model is most sensitive to the mean value of the residual friction angle (ϕ _r) and least sensitive to the mean value of the slope angle (β _f). It is also found that the standard deviation of joint compressive strength (JCS) causes the greatest difference in the reliability index, which has the least sensitivity to the change in the mean and standard deviation of joint roughness coefficient (JRC).     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

Development of a probabilistic approach for rock wedge failure

For rock slope engineering, uncertainty and variability are inherent in data collected on orientation and strength of discontinuities, yielding a range of results. Unfortunately, conventional deterministic analysis based on the factor of safety concept, requires a fixed representative value for each parameter without regard to the degree of uncertainty involved. Therefore, the deterministic analysis fails to properly represent uncertainty and variability, so common in engineering geology studies. To overcome this shortcoming, the probabilistic analysis method was proposed and used for more than a decade in rock slope stability analysis. However, most probabilistic analyses included a deterministic model as part of the analysis procedure causing subsequent problems, which went uncorrected. The objectives of this paper are to develop a solution for these difficulties in probabilistic analyses and to propose an appropriate simulation procedure for the probabilistic analysis of rock wedge failures. As part of the solution, probability of kinematic instability and probability of kinetic instability are evaluated separately to provide a proper, combined evaluation for failure probability. To evaluate the feasibility of this new probabilistic approach, the procedure is applied to a practical example, a major, highway rock cut in North Carolina, USA. Results of the probabilistic approach are compared to those of the deterministic analysis; findings are significantly different, indicating that the deterministic analysis does not depict rock slope variations, particularly where significant scatter in parameter data occurs.     

Embankment reliability versus factor of safety: Before and after slide repair

Probabilistic slope stability analyses incorporate more information regarding the input variables than do traditional deterministic analyses. Consequently, more information is contained in the results. A probabilistic method for slope stability analysis for very general problems was presented by Wolff and Harr.¹ The method allows analysis of a broad range of slope stability problems. In this Application Brief, the method is reviewed and used to illustrate the significant change in reliability of a dam slope from the time of an actual slide to the time the slide was repaired by the construction of a rock toe berm.     

边坡模糊随机可靠性分析的模糊点估计法

在统计矩点估计法和模糊随机理论的基础之上,提出边坡工程模糊随机可靠性分析的模糊点估计法,将边坡稳定性极限状态方程由模糊随机集向普通随机集转化,然后利用点估计法求解边坡的可靠度指标。鉴于岩土体物理力学参数的近似分布类型,采用区别于梯形模糊数的正态模糊数对随机变量进行模糊随机化处理,使其更趋近于物理力学参数的近似分布类型。该方法考虑了各个力学参数的模糊性,计算结果更能反映边坡的真实工作状态。算例分析结果表明,该法使用简便,计算效率高,结果可靠,避免了传统分析方法的缺点,对复杂边坡或者功能函数为隐式表达的边坡工程可靠性分析具有很大的潜力,为边坡可靠性分析提供了一条新的途径,具有广泛的应用前景。     

Parametric Monte Carlo studies of rock slopes based on the Hoek–Brown failure criterion

Probabilistic evaluation of slope failures is increasingly seen as the most appropriate framework for accounting for uncertainties in design. This paper performs reliability assessments for rock slopes based on the latest version of the Hoek–Brown failure criterion. The purpose of this study is to demonstrate the use of a new form of stability number for rock slope designs that has been recently developed from finite element upper and lower bound limit analysis methods, and to provide guidance for its use in probabilistic assessments. The analyses show that by using this newly proposed stability number, the probability of failure (P_f) obtained from case studies agrees well with the true state of the slope. In addition, this paper details a procedure to determine the magnitude of safety factor required for rock slope design.     

Probabilistic block theory analysis for a rock slope at an open pit mine in USA

A new formulation is given to conduct a probabilistic block theory analysis. A new computer code (PBTAC) is developed to perform both deterministic and probabilistic block theory analysis. The variability of the discontinuity orientation and shear strength is incorporated in the probabilistic block theory analysis. Discontinuity orientation is treated as a bivariate random variable including the correlation that exists between the dip angle and dip direction. PBTAC code was applied to perform both deterministic and probabilistic block theory analyses for a part of an open pit mine in USA. Needed geological and geotechnical data for the analyses were obtained from field and laboratory investigations. The variability of the discontinuity orientations resulted in important differences between the probabilistic and deterministic block theory analyses results. The results confirmed that the design value selected for the maximum safe slope angle (MSSA) for a particular region in the open pit mine based on the deterministic block theory analysis can be on the unsafe side. In summary, the results showed clearly the superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtaining additional important information with respect to designing rock slopes. The calculated values agree very well with the existing almost stable bench face angles reported by the mining company.     

基于参数反演的边坡地下水渗流数值模拟

渗流是影响岩土工程边坡稳定性的重要因素,对不同工况下岩土体边坡地下水渗流规律进行数值模拟,弄清其动态变化规律,对于边坡稳定性分析、支护设计、工程防排水措施的制定等都有重要的意义。以龙滩水电站左岸进水口边坡为研究对象,通过免疫进化规划算法,得到了边坡岩体渗流场参数。在此基础上,对洪水期、枯水期情况下地下水渗流状态进行了数值模拟,通过对比分析,研究了不同河床水位情况下地下水渗流变化规律,从而为边坡稳定性预测奠定了理论基础。     

砾岩边坡稳定性分析与防治工程

沪蓉国道主干线宜昌至恩施段高速公路,是国家“五纵七横“交通网的重要组成部分,其砾岩边坡稳定性分析与防治工程是重要的研究课题。本文以砾岩岩体结构面模拟研究,岩体力学参数估算为基础,结合砾岩特征及边坡地质环境条件,提出砾岩边坡稳定性评价的地质模型,并采用数值模拟与计算,得出砾岩边坡稳定性分析的确切结果。砾岩边坡岩土工程加固设计是关系到该高速公路安全、经济、适用的重要内容,紧密结合砾岩边坡的地质环境和砾岩岩体特征,采用信息化设计,运用生态化设计理念,充分发挥岩土工程技术优势,保护环境,提出合理的岩土工程加固设计方案。本研究成果对砾岩边坡防治工程提出了系统的研究思路,对沪蓉国道主干线宜昌至恩施段高速公路砾岩边坡的设计与施工具重要意义。     

黄河小浪底水库风雨沟西侧边坡稳定性研究

运用结构分析法、关键块体分析法和工程地质类比法定性评价边坡稳定性,抽取边坡岩体破坏模式。根据自制简易纵剖面仪现场绘制了结构面表面轮廓曲线,运用修正直边法和JRC—JCS模型定向统计估算结构面抗剪强度。通过对比验证定向统计估算结果与试验结果,确定计算参数取值标准。在以上两方面研究的基础上,建立边坡极限平衡计算模型,进行边坡破坏概率计算。最后,对边坡稳定性进行了综合评价。     

基于A^＊算法的边坡稳定分析方法

岩质边坡的失稳大都是沿各软弱结构面而发生的,其滑动面往往是软弱结构面的组合,呈阶梯状.岩石边坡中存在大量的随机结构面,从中找出抗剪力最小的滑裂面是边坡工程中的一个研究方向.在岩体结构面调查统计的基础上,用随机网络模拟再现结构面的空间分布,在此基础上应用A*算法,搜索出岩石边坡的临界滑裂面,并对临界滑裂面上的边坡体任意斜条分,与Sarma分析方法相结合,形成一种改进的分析岩石边坡稳定性的方法—— Sarma-A*分析法,通过工程实例验证该方法的合理性.     

建筑边坡岩体分类及其应用合理性研究

当前的建筑边坡岩体分类不含外倾软弱结构面控制的边坡和倾倒崩塌型破坏的边坡,把岩体完整程度、结构面结合程度、结构面产状、岩石坚硬程度和地下水发育程度作为分类因素。对这种分类及其应用存在的问题进行了分析。研究表明,这个分类在分类规律、分类对象、分类因素等方面均不合理,也没有实际意义,已有的关于岩体性状的通用分类和专用于边坡的单因素分类对于边坡工程已经够用。提出了取消专用于边坡的岩体综合分类的建议。     

岩质边坡复合型破坏机制的改进运动单元法研究

目前运动单元法的研究主要集中于土质边坡,未涉及到岩质边坡稳定性分析问题;而岩体中孕育有不同特性的结构面,控制着岩质边坡的力学行为。为求解结构面控制作用下岩质边坡“结构面滑移-岩桥剪断”复合型破坏问题,研究了塑性滑移区节点在岩桥内和结构面上的运动约束条件,推导了含结构面的运动单元计算公式,提出了改进运动单元法。通过经典算例的对比分析,验证了改进运动单元法计算结果的准确性。研究结果表明：岩桥位置、结构面贯通度和结构面倾角是控制岩质边坡力学行为的3个主要影响因素。岩桥越接近坡顶,改进运动单元法所得安全系数越大,而Jennings法无法反映岩桥位置的影响效应。高贯通度的结构面导致岩质边坡发生“结构面滑移-岩桥剪断”复合型破坏模式,安全系数较小;而低贯通度的结构面导致完整岩石发生破坏,安全系数较大。水平或陡倾角结构面导致滑裂面穿切结构面,安全系数较大;而对于其它倾角情况下的结构面,岩质边坡发生“结构面滑移-岩桥剪断”复合型破坏模式,安全系数较小。实例应用结果说明该方法可以有效评价岩质边坡的稳定状态,可在类似工程中应用推广。     

基于蚁群聚类算法的岩石边坡稳定性分析

由于岩石边坡影响因素众多且关系复杂,不能用简单的方法进行分析和判断。在工程类比的基础上,一般采用聚类的方法。但由于边坡工程问题环境的复杂性,岩石边坡稳定分析的聚类问题是一个复杂的模糊、随机优化问题,采用传统方法难免带来很多局限性。为了更好地解决这类问题,首次把蚁群聚类算法这种新近提出的仿生聚类算法引入岩石边坡工程领域,以解决其稳定分析问题,提出一种分析岩石边坡稳定问题的新方法。该方法在分析岩石边坡工程实例资料的基础上,采用蚁群聚类算法,以工程类比的思想判断岩石边坡的稳定状态。工程应用证明,该算法可以自动把岩石边坡分成几种类似的状态,判断准确率较高、计算速度较快,是一种比较实用的岩石边坡稳定分析方法,值得在岩石边坡分析领域推广应用。