可靠性数学在斜坡稳定性分析中的应用

本文将可靠性数学的相关理论引入斜坡稳定分析中，结合斜坡在变形破坏中的各影响因素均具有一定随机性的实际情况，提出了基于概率方法的斜坡稳定性可靠性计算公式，具有一定的现实意义。     

边坡稳定模糊随机可靠度分析

考虑边坡稳定评价中存在的两种不确定性--模糊性和随机性,以模糊随机变量为基本变量,建立模糊随机功能函数和模糊随机极限方程,得到模糊可靠指标和模糊可靠度。本文给出模糊随机可靠度的计算方法,给出实例并与经典随机可靠度比较,得到更合理的结果。     

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.     

基于可靠度的黄土斜坡稳定性分析

以延安市宝塔区虎头峁黄土斜坡为研究对象,在野外详细调查和勘查的基础上,分析确定斜坡可靠度的随机变量为滑带土土体容重r、内聚力c和内摩擦角φ。分别用统计矩法、一次二阶矩法、几何法和蒙特卡洛模拟法计算斜坡的可靠度和破坏概率,得出安全系数为1.00~1.15,可靠度指标为0.35~0.45,破坏概率为32%~37%,说明斜坡具有较大的失稳可能性。计算过程表明,用几何法计算所得的可靠度指标精度最高,一次二阶矩法次之,统计矩法计算精度最低,蒙特卡洛模拟法可作为一种校验方法,对其他方法进行校验和对比。在不需要获取传统的定值安全系数的情况下,可用几何法计算斜坡的可靠度指标,方法较为简便。当需要同时获取安全系数时,应使用统计矩法或一次二阶矩法计算。     

Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces

This paper develops a risk de-aggregation and system reliability approach to evaluate the slope failure probability, p_f, using representative slip surfaces together with MCS. An efficient procedure is developed to strategically select the candidate representative slip surfaces, and a risk de-aggregation approach is proposed to quantify contribution of each candidate representative slip surface to the p_f, identify the representative slip surfaces, and determine how many representative slip surfaces are needed for estimating the p_f with reasonable accuracy. Risk de-aggregation is performed by collecting the failure samples generated in MCS and analyzing them statistically. The proposed methodology is illustrated through a cohesive soil slope example and validated against results from previous studies. When compared with the previous studies, the proposed approach substantially improves the computational efficiency in probabilistic slope stability analysis. The proposed approach is used to explore the effect of spatial variability on the p_f. It is found that, when spatial variability is ignored or perfect correlation assumed, the p_f of the whole slope system can be solely attributed to a single representative slip surface. In this case, it is theoretically appropriate to use only one slip surface in the reliability analysis. As the spatial variability becomes growingly significant, the number of representative slip surfaces increases, and all representative slip surfaces (i.e., failure modes) contribute more equally to the overall system risk. The variation of failure modes has substantial effect on the p_f, and all representative surfaces have to be incorporated properly in the reliability analysis. The risk de-aggregation and system reliability approach developed in this paper provides a practical and efficient means to incorporate such a variation of failure modes in probabilistic slope stability analysis.     

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.     

先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估

受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明:参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然...     

基于认知聚类分区方法的边坡可靠度分析

提出了边坡可靠度分析的一种新的全局优化方法--认知聚类分区方法。该方法主要包括5个步骤：分区、随机抽样、计算极径L、回代、计算可靠指标及验算点。给出了相应的计算流程图,并编写了基于C语言的计算程序KCPREL。最后,以岩质边坡稳定可靠度问题为例证明了所提方法的有效性。结果表明,认知聚类分区方法能同时计算出可靠指标和验算点,并能获得全局最优解。该方法的计算精度和蒙特卡洛模拟方法相当,计算效率远远高于传统的蒙特卡洛模拟方法。此外,该方法在分析含有复杂的隐式及非线性功能函数的边坡稳定可靠度问题方面体现出明显的优越性。等步长认知聚类分区方法能全面且均匀地搜索角度,从而得到更准确的验算点。为了保证足够的计算精度及减小计算量,建议步长取10º以内。     

考虑能量-时间分布的边坡动力可靠性分析新方法

提出一种考虑能量-时间分布的边坡动力可靠性分析方法。该方法将动态最危险滑动面及其稳定系数以时间序列加以刻画,并根据边坡动力反应的能量分布特征,提取持续时间统计窗,用于对上述时间序列的统计分析,以获取边坡动力模糊失效概率、边坡动力可靠度指标和基于保证率的边坡动力稳定系数。以澳大利亚计算机应用协会边坡稳定考核题为例,应用上述新方法考察其在芦山7.0级主震波形条件下的稳定性,研究了在不同统计窗下的边坡动力可靠性。案例分析表明： （1）新方法能够抓住影响边坡动力稳定的主要时间段,使分析结果更为凝练、可信。（2）通过引入边坡失效状态的模糊判别,使得可靠性评价中能够考虑模糊性,解决了以往常规方法区分度不够的问题。（3）基于保证率的边坡动力稳定系数具有很好的应用前景,它在内涵上体现了可靠性分析,在形式上与静力稳定系数的定义兼容,在数值上反映了边坡瞬时动力稳定系数的保守估计值,在实践上与现行规范的拟静力法具有良好的可比性,因而具有多方面的优势。（4）就本案例而言,动力条件下最危险滑动面的发育位置趋向于静力条件下的最危险滑动面,体现了依据静力和拟静力理论框架所进行的防护工程设计,在动力条件下仍然具有积极的意义。（5）新方法对定量研究现行边坡规范的抗震设计冗余提供了一条途径。提出的新方法为边坡抗震研究提供了新的思路、方法和可供参考的实例。     

FLAC-3D在边坡岩体稳定性分析中的应用

采用三维显式差分法（FLAC-3D）对彭水水电站一边坡岩体进行三维弹塑性数值分析,模拟了边坡开挖对其整体稳定性的影响,从而分析了边坡的稳定性,依此为设计提供依据。     

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.     

抗剪强度参数概率分布的最大熵估计及边坡可靠度分析

提出了基于最大熵原理的抗剪强度参数概率分布估计方法。首先简要介绍了最大熵原理估计抗剪强度参数概率分布的基本步骤。其次,基于模拟数据分别验证了最大熵原理估计抗剪强度参数概率分布和边坡失效概率的有效性,并比较了最大熵原理、选优识别和核密度估计方法的不确定性建模精度和稳健性。最后,以一组残积土抗剪强度参数试验数据并结合无限边坡稳定分析为例研究了最大熵原理在抗剪强度参数概率分布和边坡失效概率估计中的应用。结果表明：最大熵原理能够有效地估计抗剪强度参数的概率分布和边坡失效概率。与传统的选优识别和核密度估计相比,最大熵原理估计抗剪强度参数概率分布和边坡失效概率的精度和稳健性都更高。最大熵原理避免了核密度估计过分依赖有限样本数据的缺点,又克服了选优识别可能未将真实分布包括在备选概率分布集合中的缺陷。此外,基于有限数据估计的抗剪强度参数概率分布和边坡失效概率具有较大的离散性。     

岩层倾角影响顺层岩石边坡稳定性的模型试验研究

根据相似理论建立地质力学模型,介绍了模型试验的设计和过程。通过4组对比试验,研究了原型边坡的变形破坏机制以及改变边坡岩体的岩层倾角对边坡稳定性的影响。试验结果表明,顺层边坡的主要变形方式均为滑动变形,破坏模式为滑移-拉裂破坏,滑动过程为分级滑动,越往后拉裂面倾角越小。边坡的变形破坏首先发生在临空面靠近地表部位。层面强度越大,边坡越稳定;岩层倾角越小,边坡越稳定。     

层状岩质边坡遍布节理模型的三维稳定性分析

采用遍布节理模型（ubiquitous-joint模型）描述层状岩体的各向异性特征,并探讨ubiquitous-joint准则中安全系数的计算方法,利用FLAC3D分析层理倾角、倾向与边坡稳定性之间的关系,结果表明：（1）对于顺层边坡,当岩层倾向与坡面倾向的夹角 较小时,边坡的安全系数随层理倾角 的增大呈现先减小后增大再减小的趋势; 20°～30°时,安全系数得到最小值, 60°时安全系数得到最大值;不同破坏型式导致安全系数变化规律之间的差异;当 较大时,曲线从先减小后增大的趋势转变为不断增大的趋势;根据 的大小将顺层边坡分为两类：当 45°时,为严格顺层边坡;当45° 90°时,为斜向层状边坡。（2）对于逆层边坡,当 45°时,曲线呈现先增大再减小然后又增大的趋势,各曲线随 的变化程度基本相同;但减小过程中,随着 的增大,曲线的斜率逐渐减小,边坡稳定性的各向异性程度减小;当 45°时,曲线随 的增大呈现非线性单调递增的趋势。（3）安全系数与 之间的关系表明,对于顺层坡,随着 的增大,边坡安全系数逐渐增大;对于逆层坡,当 较小时( 150°),边坡安全系数随 的增大而逐渐减小;随着 的增大( 120°),边坡安全系数与 呈现递增关系。     

顺层岩质路堑边坡稳定性的敏感性因素分析

运用弹塑性理论和有限元法,建立了顺层岩质路堑边坡稳定性的模拟分析模型。结合沪蓉国道主干线湖北宜昌至恩施高速公路的顺层岩质路堑高边坡工程,分析了结构面强度、岩层厚度、岩层倾角等各项因素对顺层岩质路堑边坡稳定性的影响,探讨了顺层岩质路堑边坡稳定性的规律。结果表明：软弱结构面的强度参数对顺层岩质路堑边坡稳定性起主要控制作用,岩层倾角对顺层岩质路堑边坡的稳定性也有明显的影响。在该工程的地质条件下,当岩层倾角为38°左右时,顺层路堑边坡的稳定性最差。     

Seismic stability analysis of a layered rock slope

In general, the determination of the factor of safety and the location of the critical slip surface are two major challenges in seismic slope stability analysis. In this paper, a new approach for determining the factor of safety and the corresponding critical slip surface of a layered rock slope subjected to seismic excitations is presented, through a case study based on the combination of the shear strength reduction technique and distinct element method. According to this proposed method, the seismic factor of safety and the critical slip surface of the slope are estimated and compared with those obtained by the pseudo-static approach, combined with the limit equilibrium method. It is found that the factor of safety obtained from the proposed method is slightly greater than that computed by the pseudo-static analysis, with a difference of 4.2%, and that the critical slip surface obtained from the two methods is identical, which confirms the reasonability and feasibility of the proposed method.     

基于模拟退火算法的边坡稳定分析方法

岩石边坡开挖中存在大量的随机结构面,结构面与岩桥的组合破坏是边坡破坏的一种重要形式。如何确定抗剪强度最小的滑裂面是边坡工程中的重要研究方向。在岩体结构面调查统计基础上,运用随机网络模拟的方法得到边坡的裂隙网络图像,在此基础上应用模拟退火算法,搜索出边坡由结构面与岩桥组合形成的潜在最危险滑裂面的位置,将结构面组合滑动面与Sarma分析方法结合,形成一种改进的分析岩石边坡稳定性的方法--Sarma-SA分析法,通过一工程实例验证了该方法的合理性。     

Efficient system reliability analysis of rock slopes based on Subset simulation

How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the “max” and “min” functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.     

节理岩体边坡稳定性分析新方法

节理岩体边坡失稳破坏同时受控于节理与岩体抗剪强度。在对具有2组平行节理的岩体坡边失稳破坏机制研究基础上,研究了具有2组平行节理岩体边坡的极限平衡分析方法,并推导了相应的边坡稳定性分析计算公式,编制了基于潜在滑动面自动搜索的边坡稳定性研究程序。通过与文献中算例的对比研究,证明了所提出的节理岩体边坡稳定性分析方法的正确性,为具有2组平行节理岩体边坡的稳定性分析提供一条新的有效途径。     

含断层高陡岩石边坡稳定性的弹塑性分析

根据我国西部山区某露天矿工程实际,通过现场工程地质调查及室内外试验,在分析了该矿北部高陡边坡岩体分布特征、断层等具体地质条件之后,选择最具代表性的主剖面,建立弹塑性力学模型,采用Drucker-Prager屈服条件,利用有限单元法模拟在爆破动力和地下水作用下高陡岩石边坡开挖的动态过程,计算了边坡安全系数。最后,针对边坡在开采后期的整体稳定性提出了安全技术措施。