路堤边坡稳定可靠度计算中的模型不确定性分析

基于均质路堤边坡Monte Carlo法的稳定可靠度计算,分析了临界滑面搜索策略和稳定分析方法两类模型不确定性对边坡可靠度的影响特性,讨论了边坡失效概率随土工参数变异性的变化规律。研究表明,选用不同的临界滑面搜索策略所得可靠度结果差异不大,参数滑面法（overall slope）的失效概率略大于均值滑面法（global minimum）,但差别对边坡稳定性分析没有实质性影响;土性参数变异水平是影响边坡可靠度的最重要因素,边坡在相同设计参数安全系数下的可靠度指标随参数变异性增大而急剧降低;不同稳定性分析方法对应的安全系数概率密度函数曲线形态基本一致,但失效概率差异明显,因此目标可靠度指标取值应与稳定性分析方法相适应。提出的考虑土工参数变异水平的安全系数取值修正原则,对改进确定性设计的边坡稳定分析技术有积极意义。     

Reduction of slope stability uncertainty based on hydraulic measurement via inverse analysis

The determination of slope stability for existing slopes is challenging, partly due to the spatial variability of soils. Reliability-based design can incorporate uncertainties and yield probabilities of slope failure. Field measurements can be utilised to constrain probabilistic analyses, thereby reducing uncertainties and generally reducing the calculated probabilities of failure. A method to utilise pore pressure measurements, to first reduce the spatial uncertainty of hydraulic conductivity, by using inverse analysis linked to the Ensemble Kalman Filter, is presented. Subsequently, the hydraulic conductivity has been utilised to constrain uncertainty in strength parameters, usually leading to an increase in the calculated slope reliability.     

考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例--詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明：在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。     

基于蒙特卡罗边坡稳定二元体系的建立与应用

边坡是一个具有明显不确定性、模糊性和时变性的系统,安全系数及可靠度理论在边坡稳定评价上各有优缺点。二元体系是基于确定性指标（安全系数）和不确定指标（可靠度）建立的边坡稳定综合评价指标体系,兼有二者的优点,具有重要的理论意义和实践价值。考虑到边坡材料指标具有区间分布及稳定边坡的安全系数不能小于其临界值的特点,对纯数学理论模型进行修正,提出了一种更加符合工程实际的边坡稳定二元评价体系,同时选取蒙特卡罗模拟法,将该二元评价体系融入GeoStudio软件,借助GeoStudio软件强大的计算能力,形成一套完整而高效的边坡稳定二元指标分析方法。采用该方法进行了降雨条件下花岗岩残坡积土边坡稳定性分析,得出了有益的结论,验证了该方法的可行和高效。     

Structural stability of gravity dams: a progressive assessment considering uncertainties in shear strength parameters

Structural sliding stability of gravity dams is generally quantified using deterministic factor of safety, FS_det. Large FS_det (e.g. 3 in normal condition), are used in existing guidelines to guard against material and load uncertainties. Some guidelines allow an arbitrary reduction in FS_det (e.g. 2) when the knowledge in strength parameters increases from material test data. Yet, those reduced FS_det are not based on a rational consideration of uncertainties. Propagation of uncertainties could be done using probabilistic analyses, such as Monte-Carlo simulations (MC) which are complex and challenging for practical use. There is thus a need to develop simplified reliability based safety assessment procedures that could rationalise the adjustment of FS_det. This paper presents a progressive analysis methodology using four safety evaluation formats of increasing complexity: (i) deterministic, (ii) semi-probabilistic (partial coefficient), (iii) reliability based Adjustable Factor of Safety (AFS), and (iv) probabilistic. Comprehensive comparisons are made for the sliding safety evaluation of a 80 m gravity dam. Results are presented in terms of sliding factors of safety, allowable water levels, and demand/capacity ratios. It is shown that the AFS formulation, using direct integration, is simple and practical to use in complement to existing dam safety guidelines before undertaking MC simulations.     

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.     

参数变异性对围护结构稳定性影响分析

利用可靠度分析方法代替传统的安全系数法来分析基坑围护结构的整体稳定性,考虑岩土参数的不确定性和空间变异性,对土性参数进行空间折减可显著提高可靠度分析的精度。结合工程实例,分析了参数均值和变异系数对基坑整体稳定性可靠度指标的影响。分析表明,可靠度指标β对土体黏聚力c、内摩擦角φ、地面超载q及支护桩嵌固深度hd的均值变化的敏感性较安全系数K对上述参数的敏感性强;c、φ及hd值的变异性对β值影响较大,地面超载较大时,其变异性对β影响较为显著;采用可靠度指标β评价基坑整体稳定性较安全系数K更加合理。     

Explicit limit equilibrium solution for slope stability

Conventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non‐linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non‐convergence occasionally occurring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed‐form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern–Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley & Sons, Ltd.     

石头坪景区边坡几何形态对稳定可靠度的影响分析

兰州金城公园石头坪景区提升改造工程存在大量的自然边坡和人工边坡。因边坡土体物理力学参数存在变异性,采用了蒙特卡洛随机抽样法和极限平衡法按不同坡高及坡度计算分析了边坡稳定可靠性指标及其变化规律,结果表明在景区实际坡高、坡度范围内边坡是稳定可靠的,适宜景区建设,但当坡高、坡度达到实际范围的最大值或超范围时,边坡处于基本稳定或欠稳定状态,建议采取加固措施。     

降雨条件下考虑饱和渗透系数变异性的边坡可靠度分析

土体饱和渗透系数表现为天然的变异性,为此基于Green-Ampt模型建立了考虑饱和渗透系数变异性的降雨入渗物理模型,并藉此模型确定了坡体湿润锋深度和含水率分布。然后结合无限长非饱和土边坡稳定模型得到解析形式的反映边坡稳定性的极限状态函数。采用Monte Carlo法对饱和渗透系数进行随机抽样并最终建立降雨条件下考虑饱和渗透系数变异性的边坡概率分析框架。针对一假想边坡,探讨了饱和渗透系数的变异系数、降雨持时和降雨强度对边坡破坏概率以及破坏发生时间概率分布的影响,结果表明：在降雨初期,边坡的破坏概率随饱和渗透系数变异性的增强而逐渐增加,但随着降雨的持续,破坏概率开始随变异性的增强而显著降低;滑坡最可能发生时间的大小并不受饱和渗透系数变异性的影响,而是直接取决于降雨强度;滑坡最可能发生时间所对应的概率却随变异性的增强而逐渐减小。     

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。     

最小势能方法在二维边坡稳定分析中的应用

提出了一种新的边坡稳定性评价方法。依据平衡体系势能变化最小的原理，从整个边坡的势能变化求得一个满足势能的最小位移，并直接求出滑面上的法向力分布。均质边坡直接用此分布即可求出合理的安全系数；具有多种土层边坡在保持法向力代数和不变的前提下，按自重应力因子重新分布，也可以求得合理的安全系数。     

禁忌搜索在确定土坡危险滑动面中的应用

在土坡稳定的计算过程中常采用经典的极限平衡法。对每一条可能的圆弧滑动面通过条分法计算其安全系数,最小的安全系数就代表了土坡的实际安全系数。在此过程中,滑动面的圆心坐标和半径可以视为安全系数的函数,滑动面的圆心坐标和半径是自变量,安全系数就是函数值。这样,土坡安全系数的计算过程实际上是对安全系数这个函数求极值的过程。通过将土坡的安全系数视为圆心坐标和滑弧半径的函数,应用连续变量的禁忌搜索技术计算土坡稳定安全系数,提高土坡稳定计算的可靠性。     

重度增加法在某公路边坡稳定性分析中的应用

基于D-P准则,采用关联流动法则,用非线性有限元重度增加法对一非均质不规则公路边坡进行了分析。其原理是保持粘聚力c及内摩擦角φ不变,通过逐步增加土体重度的方法使土体达到临界状态。采用坡顶水平位移随重度增加系数变化的关系曲线上位移陡然增大作为边破的破坏标准。有限元重度增加法事先无须对滑动面的位置和形式做出任何假定,同时考虑了土体的材料非线性和几何非线性,因此利用二维有限元重度法能更好地模拟土坡的破坏,有助于了解土坡的破坏机理。其结果不仅对工程实践具有指导作用,而且对研究土体的破坏机理,探索分析边坡稳定的适用计算方法都有现实意义。用重度增加法得到的安全系数与传统方法的误差在9%左右,因此重度增加法可以用于边坡稳定分析。     

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。     

高填方对红黏土地基力学性质影响及坡体稳定性

以云南安宁市一高填方边坡为例,通过勘察、监测等手段,在查明红黏土分布特征的基础上,对填土前后红黏土的物理力学性质变化进行分析,应用数值模拟软件对坡体稳定性进行研究。结果表明,填方工程施工前后,红黏土地基物理力学指标呈现出先降低后增强的特征,致使填土边坡的稳定性呈现出先降低后提高的趋势;坡体上部的地裂缝是在地基土、原地形、填土厚度不均的不利组合下,由于填方体、地基土固结引起坡体的不均匀变形所致,坡体整体稳定。研究成果对于红黏土地基的高填方边坡工程设计、红黏土地基土物理力学指标对坡体稳定性的影响、施工过程中不均匀变形量控制、坡体上部裂缝病害研究具有一定的参考价值和指导意义。     

随机地震作用下滑坡稳定性可靠度分析

应用边坡可靠性分析中常用的蒙特卡罗法,并结合稳定性计算的剩余推力法和Sarma法,研究随机地震作用下边坡的可靠性。以三峡库区黄土坡滑坡为例,分析了地震效应对边坡稳定性的影响。计算结果表明：地震加速度对滑坡稳定性影响显著;竖向地震加速度小于水平地震加速度2/3时,对滑坡稳定性影响较小,大于水平加速度时,对滑坡稳定性影响明显。因此在一般工程设计中,可以只考虑水平向的地震作用,而对于设计烈度较大的大型工程,则应同时考虑水平向和垂直向的地震作用。     

考虑计算参数不确定性的边坡稳定分析

岩土体当中存在大量的不确定因素,给边坡的稳定性分析判断带来了困难。在分析了计算参数的不确定性是影响分析可靠性的主要原因的基础上,运用模糊集理论考虑计算参数的不确定性,提出了模糊参数的具体构造方法和边坡稳定的不确定性分析思路。该方法可以根据不同隶属度下的参数截集区间,计算出相应隶属度下的安全系数区间,并可由此得到边坡的可靠性指标和安全系数建议值。通过不同算例研究表明,使用此方法能充分考虑计算参数的不确定性,得到的安全系数更加科学可靠。     

Determination of stability of slope using Minimax Probability Machine

This article examines the capability of Minimax Probability Machine (MPM) for the determination of stability of slope. MPM is constructed within a probabilistic framework. This study uses MPM as classification and regression tools. Unit weight (γ), cohesion (c), angle of internal friction (φ), slope angle (β), height (H) and pore water pressure coefficient (r_u) have been used as inputs of the MPM model. The outputs of MPM are stability status of slope and factor of safety (F). The results of MPM have been compared with the artificial neural network models. The experimental results demonstrate that the developed MPM is a promising tool for the determination of stability of slope.     

二维随机场下边坡稳定性的径向基函数神经网络分析法

岩土参数的随机性会直接影响边坡稳定性评价结果的精度。首先,依据边坡参数的常用分布特征,利用拉丁超立方抽样法生成若干组边坡土性参数和几何参数的随机样本,用有限元强度折减法求解各组样本对应的边坡安全系数。再考虑土性参数的空间变异性,在二维随机场模型下将蒙特卡罗模拟和有限元强度折减法相结合求解各组样本对应的边坡失效概率。然后,利用样本数据及其安全系数和失效概率对径向基函数（RBF）神经网络进行训练和测试,从而建立边坡安全系数和失效概率的预测模型。算例表明,二维随机场模型能相对精确地考虑参数的空间变异性;在此基础上建立的神经网络模型对边坡的安全系数和失效概率具有较高的预测精度,且能极大地节省边坡稳定性分析的时间。