多失效模式下基于区间非概率的岩质隧道稳定可靠度分析

对于岩质隧道工程的稳定可靠度分析,一方面由于岩体参数的统计数据获取困难使得概率可靠度方法难以适用,另一方面其工程稳定与多种失效模式密切相关,须考虑隧道结构体系的可靠度问题。首先,基于区间理论,通过区间变量形式表征不确定性参数;然后,针对岩质隧道工程中多种失效模式并存的情况,引入结构体系可靠度理念,建立基于区间非概率的岩质隧道结构体系可靠度指标计算及其稳定性评价方法;在此基础上,通过工程实例验证了该方法的合理性;最后,定义不确定性参数的波动幅度,进一步分析各失效模式中不同参数对相应可靠度指标以及结构体系可靠度指标的影响。分析结果表明,各失效模式相应的非概率可靠度指标均随区间变量范围的增大而降低,且同一参数在不同失效模式中表现出不同的影响;另外,不确定性参数的变化还将导致影响岩质隧道结构体系稳定的主要失效模式发生相应的变化。     

土坡稳定可靠度分析中若干规律的探讨

采用可靠度分析的JC法,对土坡稳定可靠度分析中的若干规律进行了探讨。指出了土的抗剪强度指标的均值及变异系数对可靠指标的不同影响,并对可靠指标和安全系数二者之间的关系进行了讨论绘制了可靠指标与安全系数的关系曲线。     

考虑参数和模型不确定性的基桩正常使用极限状态可靠度分析

考虑承载力计算模型和荷载不确定性,利用可靠度分析方法和概率统计理论,推导出承载能力极限状态（ULS）和正常使用极限状态（SLS）下可靠度指标的计算公式,给出了两种极限状态下可靠度指标间的线性关系式,研究了桩顶容许沉降 随机性对正常使用极限状态可靠度分析结果的影响。研究结果表明,土体类别和桩型对正常使用极限状态模型因子影响很小;正常使用极限状态下基桩可靠度指标随承载力计算模型和荷载不确定性的增大而减小,但减小幅度逐渐降低,且可靠度指标总变化量不大,工程应用中可忽略承载力计算模型和荷载不确定性在可靠度分析中的影响; 随机性对正常使用极限状态可靠性分析结果的影响很大,随 的增加,正常使用极限状态模型因子和可靠度指标逐渐增大,而模型因子变异性逐渐减小,但桩本身性质并没有任何改变,只是所允许的沉降条件不同。研究结果可为规范修订和工程应用提供参考。     

按单桩极限承载力设计复合桩基方法的可靠度分析

从按单桩极限承载力设计复合桩基的总安全度方法出发，运用可靠度理论，结合工程实例，建立了用该法确定的承载力极限状态方程，进行了可靠度分析与验证。对抗力及各基本变量的敏感性、设计参数不同组合时的安全系数与可靠度指标的关系进行了全面的分析，研究了天然地基承载力满足率ψ的合理取值范围，证实了天然地基满足率ψ≥0.5的必要性。     

CFG桩复合地基承载力可靠度分析

利用可靠度理论对从国内收集到的25组CFG桩复合地基承载力试验数据进行了概率统计处理。借助无量纲计算模式,计算不同载荷组合下CFG桩复合地基承载力的可靠度指标,并分析了各随机变量对可靠度指标的影响程度。为评价常 用经验公式 的可靠性提供一定的参考。     

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。     

填土边坡稳定性的可靠度分析

为了系统地建立填土边坡稳定性的可靠度分析方法, 首先, 在可靠度分析原理的基础上, 对填土边坡的不确定性进行了讨论; 然后, 建立了多变量影响下填土边坡可靠度分析的基本流程; 最后, 以广西平乐县二塘锰矿区典型填土边坡为例, 基于GeoStudio软件, 应用所提出的分析流程对典型填土边坡的可靠度指标进行了计算, 通过"安全概率"对边坡的安全性进行了评价.研究结果表明: (1)填土边坡的不确定性包括内部结构和环境因素两方面, 前者不确定因素来自于填土土体不确定性和边坡的几何特征不确定性, 后者不确定性因素来自于降雨、地震和人工加载等; (2)可靠度分析的基本流程为填土边坡系统不确定性分析、建立可靠度极限状态方程、求解可靠度指标和边坡安全性评价; (3)广西平乐二塘锰矿填土边坡敏感性因素排序为: 内摩擦角Φ＞黏聚力C＞车辆荷载F; (4)考虑50年一遇极值降雨过程, 稳定性系数在降雨12 h达到最小, 其可靠度指标(β)为8.79, 破坏概率为0.根据《滑坡防治工程设计与施工技术规范》所规定的安全系数, 填土边坡的安全概率为69.84%.      

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。     

采用不同失效准则的桩基可靠度分析

桩基的极限承载力通常是根据失效准则来确定的。由于各国采用的失效准则不同,得到的极限承载力也不同,从而获得的可靠指标也不同。因此,有必要分析和比较不同失效准则对桩基可靠性的影响,以及根据桩基技术规范采用的S-lgt失效准则确定可靠指标的状况。为此,以S-lgt失效准则为基准,引进了失效准则的偏差系数的概念,根据一组实测钻孔桩数据对另外6种失效准则的偏差系数进行了评估,进而进行了可靠度分析。结果表明,不同失效准则具有不同的偏差系数,桩基可靠度明显地受失效准则的影响。根据S-lgt失效准则确定的可靠度在7种失效准则中是偏大的,不同失效准则确定的相同名义可靠指标的桩基的实际可靠性是不一样的。     

LHS方法在边坡可靠度分析中的应用

Monte Carlo（MC）法在目前边坡可靠度分析中是一种相对精确的方法,应用广泛,受问题限制的影响较小,适应性很强,其误差仅与标准差和样本容量有关。但其精度受随机抽样的可靠性和模拟次数制约,收敛速度慢,影响了实际使用。在极限平衡方法的基础上,用拉丁超立方抽样（Latin hypercube sampling,LHS）方法代替MC法的随机抽样,考虑边坡参数的变异性和相关性进行边坡可靠度分析。讨论了LHS法、MC法中可靠指标的各种计算方法,建议以破坏概率、安全系数均值和标准差作为评价指标。算例显示LHS法较MC法效率上有很大改善：较少的抽样样本就能反映参数的概率分布,可靠度分析收敛快,不需要大量的模拟,因此,值得在边坡可靠度分析中推广应用。也将工程上常用的均匀设计和正交设计用于边坡可靠度分析,结果表明,正交设计结果和中心点法比较接近,而均匀设计得到的结果则是不可靠的。     

土钉支护结构可靠度分析的电子表格法

岩土工程中存在大量的不确定性,因此,进行土钉支护结构的可靠度分析是十分必要的。利用Excel的规划求解及VB编程功能,采用电子表格法,建立了适用于分层土体的电子表格计算模型,进行了土钉支护结构内部稳定的可靠度分析,得出了最小可靠指标及其相应的临界滑面位置。建立的电子表格模型由数据输入模块、土钉计算模块、土层计算模块、可靠指标计算模块及优化求解模块5部分组成。模型建立之后,只需改变电子表格中的输入数据,即可适用于不同土钉支护结构的可靠度分析。算例分析表明：方法正确,计算过程简单直观。它既可用于不同工况下土钉支护结构内部稳定的可靠度分析,也可简化为相应情况下的定值法分析。     

Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations

ABSTRACT

Field data is commonly used to determine soil parameters for geotechnical analysis. Bayesian analysis allows combining field data with other information on soil parameters in a consistent manner. We show that the spatial variability of the soil properties and the associated measurements can be captured through two different modelling approaches. In the first approach, a single random variable (RV) represents the soil property within the area of interest, while the second approach models the spatial variability explicitly with a random field (RF). We apply the Bayesian concept exemplarily to the reliability assessment of a shallow foundation in a silty soil with spatially variable data. We show that the simpler RV approach is applicable in cases where the measurements do not influence the correlation structure of the soil property at the vicinity of the foundation. In other cases, it is expected to underestimate the reliability, and a RF model is required to obtain accurate results.     

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.     

System reliability-based analysis of cantilever retaining walls embedded in granular soils

Reliability-based analysis of cantilever retaining walls requires consideration of different failure mechanisms. In this paper, the reliability of soil-wall system is assessed considering two failure modes: rotational and structural stability, and the system reliability is assumed as a series system. The methodology is based on Monte Carlo Simulation (MCS), and it deals with the variability of the design parameters in the limit equilibrium analysis of a wall embedded in granular soil. Results of the MCS indicate that the reliability of the failure components increases exponentially by increasing the variability of design parameters. The results of the system reliability indicate how the system reliability is different from the component reliabilities. The strength of the weakest component influences the reliability of the system. The system reliability index increases with the wall section gradually. However it remains constant for the rotational failure mode.     

Reliability and redundancy of the internal stability of reinforced soil walls

In the present study, a new methodology for reliability assessment of the internal stability of reinforced soil walls, taking into account the highly strength-redundant character of these structures, is suggested. Internal stability is probabilistically modeled as a series configuration and as an r-out-of-m configuration. Consideration of redundancy is formulated based on transitional probabilities and Markov stochastic processes. Following the suggested framework, the updated reliability of the structure, as failure propagates among the different layers of reinforcement, can be quantified. As an illustration of the developed methodology, an example of a reinforced soil wall is analyzed and results are discussed.     

沟灌土壤湿润体空间矩特征参数估算模型

为进一步增加矩分析理论在研究沟灌土壤湿润体运移特性方面的实用性,采用数值模拟和理论分析相结合的方法,定量分析了土壤初始含水率、入渗水深、沟底宽和边坡系数等因素对沟灌自由入渗条件下土壤湿润体空间矩特征参数的影响,并建立了其与主要影响因素间的函数关系式。结果表明,土壤初始含水率、入渗水深和沟底宽对垂直向土壤水分分布的质量重心影响较大;水平向湿润锋的平均离散度主要受土壤初始含水率、入渗水深、沟底宽和边坡系数的影响,而垂直向对土壤初始含水率和入渗水深变化的敏感性较高;选取不同土壤质地对所建模型的可靠性进行了验证,结果表明所建模型估算不同入渗时刻的空间矩特征参数值与根据HYDRUS软件模拟结果所得计算值具有高度一致性,所有验证组合条件下两者相对误差绝对值均值均低于8.5%,且无显著性差异,说明所建模型估算沟灌土壤湿润体空间矩特征参数具有高度可靠性。研究结果可为沟灌灌水方案设计和管理提供理论基础和技术支撑。     

考虑土性参数空间变异性的边坡可靠度分析

采用基于Morgenstern-Price法的Monte-Carlo模拟对黄河大堤开封段边坡进行了可靠度分析,并用抽样法进行了考虑土性参数空间变异性的可靠度分析,讨论了土性参数互相关性对可靠指标的影响,得到了一些有益的结论。对边坡工程安全度评价研究有一定的理论意义和实际应用价值。     

Reliability analysis of shallow foundation in the vicinity of the existing buried conduit

ABSTRACT

The present study proposes reliability-based approach for assessing the performance of shallow foundation placed in the vicinity of an existing buried flexible pipe or utility tunnel. Performance function for the reliability analysis is defined in terms of % bearing capacity loss in the load carrying capacity of the shallow foundation due to the presence of buried flexible pipe or utility tunnel, and, allowable bearing capacity loss in load carrying capacity that can be tolerated. For the reliability analysis, an explicit functional relationship between input variables, such as geotechnical parameters of in situ soil as well as material properties of pipe, and, output response, i.e. % bearing capacity loss in load carrying capacity of foundation soil is needed. Using concept of response surface methodology (RSM) combined with the results of the numerical analysis; such an explicit functional relationship is easily established. Thereafter, reliability analysis can be performed, conveniently, using standard First Order Second Moment (FOSM) approach and performance of the foundation soil system with buried flexible pipe, present in the vicinity, can be assessed in terms of an index, popularly known as ‘reliability index (β)’.     

Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method

ABSTRACT

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.