节理岩体的块体尺寸特征分析及其可靠度评价

通过对块体形成机制的讨论,根据岩体内节理面间距分布的随机性,分析了不同尺寸块体的出现概率。在计算块体的可靠度时,考虑了结构面的产状,粘结系数,磨擦系数等多个随机因素的影响。     

基于随机响应面法的边坡系统可靠度分析

提出了一套基于随机响应面法的边坡系统可靠度分析方法。该方法首先从大量潜在滑动面中筛选出代表性滑动面。针对每条代表性滑动面,采用Hermite多项式展开建立其安全系数与土体参数间的非线性显式函数关系（即随机响应面）。然后,采用直接蒙特卡洛模拟计算边坡系统失效概率。在蒙特卡罗模拟中,采用所有代表性滑动面的随机响应面计算每一组样本所对应的边坡最小安全系数。最后,以两个典型多层边坡系统可靠度问题为例验证了该方法的有效性。结果表明：文中提出的边坡系统可靠度分析方法能够有效地识别边坡代表性滑动面,具有较高的计算精度和效率,并且确定代表性滑动面时无需计算滑动面间的相关系数。同时该方法可以有效地计算低失效概率水平的边坡系统可靠度,为含相关非正态参数的边坡系统可靠度问题提供了一条有效的分析途径。此外,多层边坡可能同时存在多条潜在滑动面,基于单一滑动面（如临界确定性滑动面）或者部分代表性滑动面进行边坡系统可靠度分析均会低估边坡失效概率。     

岩体节理模型的节点偶对分析

本文提出一种节点偶对分析用以解决岩体节理模型的数学模拟问题。为改善Goodman单元,M. Katona提出了不考虑刚度系数的摩擦-滑动节理模型。但是,由于缺乏可行的分析方法,因而得不到真实可信的结果,特别是出现块体相互嵌入问题,影响了它的实际应用。本文提出的节点偶对分析建立在几何-力学约束边界的序列矢量判定的基础上,计算结果完全合理。利用这一方法还可顺利地解决节理交汇组合等复杂的岩体力学问题,是一个有前景的方向。     

裂隙岩体抗滑稳定分析的概率方法

本文应用概率论和数理统计理论,探讨了裂隙岩体抗滑稳定分析方法。根据裂隙产状服从半球法线分布的假设,求得裂隙组集中产状的均值、方差和均值的可信区间。根据剪断试验资料,尝试用两点法确定抗剪参数的分布。采用极限平衡理论,应用蒙特卡洛法,计算坝肩岩体中可能滑动的块体的安全特征β和块体的稳定安全可靠度Pr,以此来评价该块体的稳定性。为了研究单个参数对稳定性的影响,在稳定性可靠度分析的程序中考虑了参数的灵敏度分析。最后给出了块体失稳的破坏概率Pf和安全系统Kc之间的关系,以便与常规的确定性分析加以比较。     

基于广义子集模拟的土坡系统可靠度分析

如何有效地评价边坡的系统可靠度并识别出对边坡稳定性具有重要影响的关键滑面一直是边坡稳定性分析的关键问题。提出了基于广义子集模拟的边坡系统可靠度分析方法及代表性滑面识别方法,并推导了基于广义子集模拟的边坡系统可靠度计算公式及边坡中滑面对边坡系统失效的相对贡献量化公式。基于广义子集模拟计算结果,采用概率网络评价方法识别边坡代表性滑面。以一个双层黏性土坡和芝加哥国会切坡算例验证了所提方法的有效性。结果表明：提出的基于广义子集模拟的边坡系统可靠度分析方法可有效地估计边坡系统及其单一滑面的失效概率,对于具有低失效概率水平边坡可靠度的求解,其计算效率明显优于传统蒙特卡洛模拟方法。此外,对于单个失效模式而言,广义子集模拟与子集模拟计算效率相当。对于多个失效模式的失效概率计算问题,广义子集模拟不需要重复对每个失效模式失效概率进行计算,计算效率明显优于子集模拟。提出的代表性滑面选择方法是在系统失效概率及单滑面失效概率的高效计算基础上实现的,代表性滑动面能够较好地代表边坡系统失效,从而有效地降低了边坡系统失效概率对代表性滑面数目及代表性滑面失效概率估计准确性的依赖性。     

基坑体系可靠度的条件概率计算方法

基坑存在多种失效模式,考虑失效模式之间的相关性,双界限法计算体系失效概率存在计算结果区间范围较大的弊端。利用均匀试验和非参数回归方法建立响应面,在响应面的基础上,对Monte Carlo模拟生成的随机参数进行插值,得到各个失效模式指标,结合Pearson相关系数检验两两失效模式之间的相关性,用条件概率方法计算基坑体系失效概率,提出了基于条件概率考虑多失效模式相关的基坑体系可靠度分析方法。在此基础上,通过1个典型算例进行对比分析,计算结果表明,该方法不仅计算简便,而且结果可靠,其结果可为基坑体系可靠度分析理论提供一条新的途径。     

基于岩体三轴压缩试验的节理力学参数确定方法

岩体节理面的刚度系数、黏结力和内摩擦角是反映节理面力学特性的重要参数。基于含不同倾角节理岩样的三轴压缩试验,通过对标准岩样的应力-位移分析,由互等功原理,建立节理岩样应变与位移新的几何关系,推导出弹性状态下节理刚度系数解析解,根据摩尔-库仑强度理论得出节理面的黏结力和内摩擦角。为了检验方法的正确性,对含节理面的同类岩体进行直接剪切试验,测出节理面的法向刚度、切向刚度、黏结力和内摩擦角。结果表明,两种方法所得结果基本吻合,说明所提出的方法可以通过节理岩样三轴压缩试验及理论分析间接得到岩体节理面的刚度系数、黏结力和内摩擦角,实现了节理岩体力学参数的简捷、快速测定。     

某水电站地下洞室随机块体稳定性评价及系统锚固设计

地下洞室中的随机块体是指由岩体中的随机节理或者基体裂隙构成的不确定性块体 ,在已建的地下厂房中 ,这类块体大量存在 ,这类块体的稳定性会对洞室的施工安全造成较大的影响。在设计中这类块体常常是通过系统锚杆进行加固 ,但由于块体位置随机性和几何特征的不确定性 ,使得系统锚杆的长度和间距很难确定。本文以某水电站的地下洞室为研究对象 ,在深入了解地质条件、岩体结构特点的基础上 ,找出可能构成随机节理的分布规律 ,再分析节理与节理、节理和Ⅰ、Ⅱ类确定性结构面可能的组合 ,得到可能的随机块体 ,然后采用块体理论评价其稳定性 ,得到随机块体的几何特征和稳定状况 ,总结出最优的锚杆长度 ,为地下洞室的系统锚杆长度的确定提供了理论依据     

块体理论赤平解析法在锦屏二级水电站皮带机隧洞稳定分析中的应用

块体理论是适用于分析节理发育破碎刚性岩体稳定性的有效方法。锦屏二级水电站皮带机隧洞岩体不连续面发育,隧洞开挖面是否产生可动块体影响着皮带机隧洞的稳定性。在对皮带机隧洞详细的地质调查和研究基础上,运用块体理论赤平解析法分析皮带机隧洞的稳定性,对各不连续面和开挖面构成的可动块体滑动形式进行判断,得出了块体的失稳形式以单面滑动为主,双面滑动和垂直掉块相对较少的结论;同时得出皮带机隧洞各部分可动块体分布的直观统计结果,即皮带机隧洞左侧墙,左、右顶拱失稳块体较多,右侧墙较少。     

颗粒流离散元在滑坡运动过程模拟中的应用

介绍了颗粒流离散元的分析原理,以某岩质边坡为实例,构建了计算模型。根据实际资料,在计算模型中加了节理,节理的力学参数弱于岩体。在下方的抗滑挡土墙完全失去作用的情况下,用此模型对该滑坡的运动过程进行了计算预测,分析了整体的变形、不同部位的位移和应力等运动特点,上部粉质粘土区系拉裂引起的下滑,下部碎石土区因挡墙损坏而产生沿节理面的滑动,但拉应力变化不大。指出了在该滑坡存在2个滑动面,并针对2个滑动面提供了相应的治理建议。     

开挖边坡随机楔体稳定分析与加锚优化方法

随机楔体的破坏是岩石开挖边坡中常见的破坏类型之一，在对组成楔体的结构而调查统计的基础上，应用随机模拟的方法，生成开挖边坡的三维裂隙网络，进一步运用随机搜索方法与块体理论，搜索出边坡面上的随机楔体，进行楔体的稳定分析，采用风险设计的理论，建立系统锚杆的优化设计方法，将研究结果应用于小湾水电站进水口开挖边坡的稳定分析与锚固优化设计中，得到了较为可信的结果。     

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.     

A system reliability approach for evaluating stability of rock wedges with correlated failure modes

This paper proposes a system reliability approach for evaluating the stabilities of rock wedges considering multiple correlated failure modes. A probabilistic fault tree is employed to model the system aspects of the problem. The system reliability analysis is performed using an N-dimensional equivalent method taking into account correlations between different failure modes. Reliability sensitivity analyses at three different levels, namely, single limit state function level, single failure mode level, and system reliability level, were carried out to study the effect of changes in variables on the stability of the wedge. An example case was analysed to illustrate the proposed approach. The stability of the wedge can be evaluated efficiently using the proposed system reliability approach in a more systematic and quantitative way. The probabilities of failure of the wedge from the N-dimensional equivalent method are fairly consistent with those from the Monte Carlo simulation method. The results demonstrate that the probability of failure will be overestimated if the correlations between different failure modes of the wedge are not taken into account. They also demonstrate that the relative importance of different failure modes to the system reliability of the wedge can differ considerably and be treated systematically and quantitatively by the proposed approach. The sensitivity results are highly dependent on the selected sensitivity analysis level.     

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.     

The Time-Dependent Reduction of Sliding Cohesion due to Rock Bridges Along Discontinuities: A Fracture Mechanics Approach

Summary In this paper, a fracture mechanics model is developed to illustrate the importance of time-dependence for brittle fractured rock. In particular a model is developed for the time-dependent degradation of rock joint cohesion. Degradation of joint cohesion is modeled as the time-dependent breaking of intact patches or rock bridges along the joint surface. A fracture mechanics model is developed utilizing subcritical crack growth, which results in a closed-form solution for joint cohesion as a function of time. As an example, a rock block containing rock bridges subjected to plane sliding is analyzed. The cohesion is found to continually decrease, at first slowly and then more rapidly. At a particular value of time the cohesion reduces to value that results in slope instability. A second example is given where variations in some of the material parameters are assumed. A probabilistic slope analysis is conducted, and the probability of failure as a function of time is predicted. The probability of failure is found to increase with time, from an initial value of 5% to a value at 100 years of over 40%. These examples show the importance of being able to predict the time-dependent behavior of a rock mass containing discontinuities, even for relatively short-term rock structures. Received November 5, 2001; accepted July 24, 2002; Published online November 19, 2002     

Statistical Analysis of Anisotropic Damage of the Bukit Timah Granite

Summary This paper presents a method to analyze probabilistic anisotropic initial damage of a rock mass. A three-dimensional geometric model of cracks in a rock mass is established in terms of several parameters, such as orientations, spacing and normalized sizes of cracks in the rock mass. The dip, dip direction, spacing, and normalized size of cracks of the Bukit Timah granite in Singapore were obtained from visual inspection of rock cores, color TV imaging, and impression packer tests in the boreholes at a site of geological investigation. Using the measured data, probabilistic distribution laws of geometric parameters of cracks on the surface of the boreholes are derived. Based on these statistical distributions and using Monte-Carlo simulation method, the distribution of anisotropic initial damage of the Bukit Timah granite is derived and found to have a beta distribution. This anisotropic initial damage distribution of a rock mass can be used in probabilistic analysis of rock mass responses to both static and dynamic loads.     

一种新型粗糙节理面随机强度模型及其应用

天然岩体在长期地质作用下会生成各种节理裂隙等不连续面,而地下工程结构的稳定性一般取决于这些不连续面的强度。在众多因素中,表面形态对岩石节理面剪切强度具有决定性影响。为了系统研究岩石节理面剪切强度的确定方法,把岩石节理面概化为一系列高度不同的微长方体凸起组成的粗糙表面结构,且微长方体凸起有剪胀破坏和非剪胀破坏两种模式。综合微长方体凸起破坏规律,应用概率密度函数描述节理面表面起伏分布的影响,建立了粗糙节理面随机强度模型,推导了节理面剪切强度理论公式,提出了节理面强度的随机评价方法。基于随机强度模型和评价方法编制Matlab计算程序计算自然粗糙节理面的剪切强度,并将计算结果与试验结果进行比较分析。研究表明:粗糙节理面随机强度模型综合了粗糙节理面表面形态和法向应力对节理剪切强度的影响机制,理论计算值与试验数据吻合良好,可以较好的评价粗糙节理的峰值剪切强度和残余剪切强度。该随机模型可作为进一步深入研究的重要基础,分析结构面的连续剪切过程,建立更完善的节理面强度模型。     

System probabilistic model of rock slope stability considering correlated failure modes

In this paper, a system reliability analysis of rock slope stability with considering all input parameters as stochastic parameter is presented. To perform reliability analysis a cut-set system has been used. For this purpose, Sequential Compounding Method (SCM) as a powerful method for reducing the computational time and accurate evaluation is employed to determine the reliability indices with considering correlations between failure modes which are calculated by defining equivalent linear safety margin for each failure mode. Furthermore, the 3-D system probability of failure surface is presented and the probabilistic model is developed to evaluate the rock slope probability of failure.     

动载下节理岩体破坏过程的数值试验研究

节理岩体是工程中最常见的一类岩体,其在地震、爆炸等动载下的力学响应及破坏过程对相关工程安全性的影响至关重要。采用基于有限元应力分析和统计损伤理论开发的动态版RFPA2D数值模拟软件,对动载下节理岩体的动态破坏过程进行了模拟,重点讨论了节理条数、节理贯通度、节理倾角及应力波峰值对岩体动态破坏过程的影响规律。计算结果表明,断续节理岩体动态破坏过程及破坏强度与节理构造形态、应力波峰值密切相关。相同动载下,随着节理条数的增加,岩体破坏程度以及应力波能量损失增强,但当节理条数数超过一定值后,岩体破坏程度及应力波能量损失逐渐趋于稳定;节理贯通度较小时,岩体破坏程度较低且破坏单元自上而下均匀分布。随着节理贯通度的增加,岩体破坏增强,且破坏主要出现于节理上部岩体;节理倾角较小时,节理上部岩体破坏严重,易形成次生贯通裂纹。随着节理倾角增加,破坏范围逐渐变大,不易形成次生贯通裂纹;倾角为45°～60°时,岩体破坏效果最佳;动载荷的峰值越大,试样的破坏越严重。当峰值达到一定值时,节理附近发育出多条裂隙并向上下方不断发展而导致岩体完全破坏。在不同节理贯通度工况下与岩石霍布金森压杆（SHPB）试验结果进行比较,结论吻合,证明该数值模拟的合可行性和结论的可靠性。