水泥土支护体稳定的可靠度分析

以土层剪切强度指标为基本变量, 对水泥土支护体稳定性设计内容建立了可靠度分析方法, 依据上海软土地区 21 例地质资料, 利用一次二阶矩验算点法( JC 法)对有关的失效模式进行了可靠度指标的核算与分析, 探讨了基本变量的敏感性。     

相关变量生成算法及边坡可靠度Monte Carlo模拟

描述变量相关性的多元分布模型有着广泛的工程应用。利用多元线性自回归模型和排序算法,研究了具有指定边缘分布和指定相关结构的多维随机变量的生成算法。基于MATLAB语言编程实现了该算法。将该算法应用于结构可靠度和边坡可靠度直接抽样Monte Carlo模拟计算问题中,解决了传统Monte Carlo模拟难以考虑变量互相关性的难题。数值实验表明,该方法计算结果精确,可以放松理论模型的理想化要求,能更真实的反映问题实际。将该方法与一次二阶矩方法计算结果对比发现,一次二阶矩方法往往对可靠度有过高的估计。此外失效概率对变量分布类型比较敏感,相同的安全系数可能对应不同的失效概率。提出的方法可以应用于复杂结构系统的可靠度计算问题,并可推广应用于其他领域的相依变量的仿真问题。     

重力式基坑支护系统的可靠性分析

本文分析了重力式基坑支护系统可能包含的多重破坏模式后,在考虑土性参数不确定性的情况下,运用系统可靠度理论对基坑支护系统的失效概率进行分析和计算。结果表明该方法能对基坑系统的稳定性作出较全面的评价。     

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。     

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。     

相关情况下Hasofer_Lind可靠度指标的求解

岩土工程的可靠度计算中, 基本变量之间往往存在着较强的相关性。 阐述了相关情况下 Hasofer-Lind 可靠度指标计算的几种方法: 正交变换法; 改进的验算点一次二阶矩法; Monte-Carlo 模拟法; 优化求解法。 在用优化方法求解可靠度指标 β 时, 利用 Microsoft Excel 中的规划求解器来进行优化求解, 避免了相关变量的独立变换以及求极限状态函数对基本变量的偏导数这两个问题。 实例比较了不同方法的求解结果。     

重力坝层间抗滑稳定体系的动力可靠度分析方法

受明显的层状结构影响,加之材料参数和动荷载的双重随机性,动力条件下碾压混凝土重力坝的层间抗滑稳定可靠度问题值得关注。考虑地震波频谱特性、峰值加速度、坝体材料参数的随机性,统计概化出地震作用下坝体的潜在滑动失效路径;在特定地震动作用下,基于随机有限元分析结果,采用刚体极限状态判断准则和响应面法构建失效路径的动力抗滑稳定功能函数,进而求得其抗滑稳定可靠指标;接着考虑不同失效路径的相关性,用Ditlevsen窄界限公式估算体系的可靠度;最后,考虑地震动荷载的随机性,采用基于全概率公式的数值拟合积分方法求解大坝抗滑稳定体系的动力可靠度。研究结果表明,动力条件下,当水平地震系数大于0.2时,重力坝层间抗滑体系可靠度不再由建基面失效路径决定,而是由下游折坡处层面的失效路径决定。该方法数学意义明确,实用性强。     

岩土工程可靠度分析的改进四阶矩方法

岩土工程可靠度分析中,功能函数往往呈隐式且具有强非线性性质,而目前最为实用的矩方法,如JC法、二次二阶矩法,主要适用于显式功能函数情形。为此,将高效的统计矩估计方法和可靠度分析的高阶矩法相结合,提出了一种岩土工程可靠度分析的改进四阶矩方法。首先,通过引入变量的独立化变换和线性变换将功能函数转换为参考变量的函数,并结合多变量函数的单变量降维近似方法和参考变量计算节点与权系数的确定方法,建立了功能函数前四阶矩的高效点估计法。然后,将上述统计矩与立方正态变换假设相结合,提出了易于实现的岩土工程可靠度分析的改进四阶矩方法。最后,由数学算例验证了统计矩估计方法的效率和精度,并通过经典的岩土工程算例验证了建议的改进四阶矩方法具有高效率、高精度且操作简单等特点。     

边坡可靠度分析的一种新的优化求解方法

介绍了Low & Tang提出的一种新的可靠度优化求解方法,并将之用于边坡可靠度分析中：该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,直接在变量的原始空间内搜索边坡的最小可靠指标和概率临界滑面,可采用任何合适的约束优化方法进行求解,方法清晰简洁。边坡可靠度分析常用的滑面有2个：最小安全系数（变量均值处）对应的确定性临界滑面和最小可靠指标对应的概率临界滑面,但这2个滑面在有些情况下差别较大,Hassan & Wolff提出了一种简化方法可以方便地获得概率临界滑面,但由于方法简单,受到质疑。通过一系列算例分析,优化求解方法得到的概率临界滑面和Hassan & Wolff的简化方法滑面非常接近,显示了简化方法的有效性,值得在工程实践中推广。     

岩质边坡平面滑动的模糊可靠度分析

综合考虑了边坡平边滑动的随机性和模糊性。根据工程实际确定结构功能函数的概率密度函数及表征边坡稳定性的隶属函数,提出了边坡失稳的模糊概率和边坡稳定性模糊可靠度的计算方法,并计算了模糊可靠度的置信区间,具有一定的实际意义。     

Bayesian approach for calibrating transformation model from spatially varied CPT data to regular geotechnical parameter

Cone Penetration Test (CPT) is widely utilized to gain regular geotechnical parameters such as compression modulus, cohesion coefficient and internal friction angle by transformation model in the site investigation. However, it is challenging to obtain simultaneously the unknown coefficients and error of a transformation model, given the intrinsic uncertainty (i.e., spatial variability) of geomaterial and the epistemic uncertainty of geotechnical investigation. A Bayesian approach is therefore proposed calibrating the transformation model based on spatial random field theory. The approach consists of three key elements: (1) three-dimensional anisotropic spatial random field theory; (2) classifications of measurement and error, and the uncertainty propagation diagram of geotechnical investigation; and (3) the unknown coefficients and error calibration of the transformation model given Bayesian inverse modeling method. The massive penetration resistance data from CPT, which is denoted as a spatial random field variable to account for the spatial variability of soil, are classified as type A data. Meanwhile, a few laboratory test data such as the compression modulus are defined as type B data. Based on the above two types of data, the unknown coefficients and error of the transformation model are inversely calibrated with consideration of intrinsic uncertainty of geomaterial, epistemic uncertainties such as measurement errors, prior knowledge uncertainty of transformation model itself, and computing uncertainties of statistical parameters as well as Bayesian method. Baseline studying indicates the proposed approach is applicable to calibrate the transformation model between CPT data and regular geotechnical parameter within spatial random field theory. Next, the calibrated transformation model was compared with classical linear regression in cross-validation, and then it was implemented at three-dimensional site characterization of the background project.     

土体参数不确定性对软土隧洞掌子面稳定影响分析

岩土体参数取值对于工程设计意义较大,为更好地评估土体参数不确定性对软土隧洞掌子面稳定的影响,采用Monte-Carlo随机模拟方法,分析了土体参数变异性及样本容量水平对掌子面稳定特性的影响,提出了掌子面设计安全系数的确定方法.结合工程实例评估了设计安全系数的合理性,分析结果表明,样本容量较大时,土体参数的不确定性对软土...     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

岩土参数的空间变异性分析

岩土参数具有空间变异性和不确定性,本文将岩土参数视为具有随机性和结构性的区域化变量,利用区域化变量理论和地质统计方法分析上海地基土有代表性的抗剪强度指标的空间变异特性。结果表明该方法是可行的。     

柱下独立基础稳健性设计与分析

岩土工程随机参数统计特征的不确定性,使得岩土工程可靠度设计存在一定风险。岩土工程稳健性设计能够充分考虑随机参数的不确定性结合结构安全性、稳健性和经济性实现最优设计。针对随机参数统计特征的不确定性对柱下独立基础设计的影响,基于可靠度理论和岩土工程稳健性设计方法,考虑岩土参数、混凝土和钢筋材料力学参数统计特征不确定性的影响,以独立基础几何尺寸作为可控设计参数进行设计分析。将独立基础地基承载力、地基变形、基础结构冲切破坏和基础弯曲破坏4种失效模式视为串联系统,进行多失效模式下的结构体系稳健性设计,分析了多失效模式下结构几何参数与结构体系可靠度的关系。结合稳健性和经济性,进行了独立基础多目标优化设计,确定柱下独立基础设计的最优解。     

Probabilistical distribution statistical analysis of Tianjin soft soil indices

In the design of soft ground treatment, the soft soil indices are the basic design parameter, and their changes have a strong geographical feature and significant uncertainty. Today, the soft soil indices statistical analysis content is mainly in the correlation and distribution regularity of physico-mechanical indices, which lack systematic study in different regions for different types of soft soils, and the statistical samples are from indoor tests and in-situ tests, without considering the impact of different test methods. In this paper, taking the soft soil in Tianjin as an independent statistical unit body, based on studying the change confines, variability, correlation, probabilistical distribution model of soil indices, some statistical relationship empirical formulas and probabilistical distribution models for physical indices, compression index, strength index were obtained; moreover, the correlation of shear strength results by straight shear test, triaxial test, vane shear test are analyzed; and a method for using random factor to evaluate the uncertainty involved in different test methods of soft soil parameters is proposed. The study results provide a basis and reference for defining the values of geotechnical parameters for soft soil.     

天津软土土性指标概率分布统计分析

软土土性指标作为软基处理设计的基本参数,其变化具有很强的地域特征和显著的不确定性。目前,对软土土性指标统计分析集中在软土物理力学指标的相互关系和分布规律等方面,采用的样本为室内试验和原位测试数据,没有考虑不同试验方法对土性指标不确定性分析的影响。将天津软土作为一个独立的统计单元体,研究了该地区软土物理力学指标的变化范围、变异性、指标间的相互关系和各指标的概率分布模型,得到了天津软土物理指标与压缩指标、强度指标间的统计关系经验公式以及土性指标的概率分布模型;并分析了直剪试验、三轴试验、十字板剪切试验3种不同方法抗剪强度试验结果的相互关系,提出了利用随机因子分析法对试验方法不确定性进行概率评定。研究成果为软土地区工程土工参数的取值提供了依据和参考。     

Effect of 2D spatial variability on slope reliability: A simplified FORM analysis

To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.     

Risk analysis of landslides – A case study

The effects of uncertainty due to the variability of soil parameters on the risk of landsliding in the Himalayan region are investigated using a random field model combined with slope stability analyses. Effects of spatial variability both in horizontal and vertical directions, number of test samples, variations in piezometric level and the influence of earthquake on the reliability of a typical slope in a slide area are investigated. The results show that the reliability of slopes in the slide area is significantly affected by the coefficients of variation of soil parameters, spatial variations of soil parameters, number of test samples and piezometric variations. The results also show that the assumption of isotropic variations to assess slope reliability isconservative. The results of the study are useful in providing guidelines and pointing to remedial measures in the form of sub-surface drainage to improve slope reliability in the area.     

Characterising geotechnical model uncertainty by hybrid Markov Chain Monte Carlo simulation

Geotechnical models are usually associated with considerable amounts of model uncertainty. In this study, the model uncertainty of a geotechnical model is characterised through a systematic comparison between model predictions and past performance data. During such a comparison, model input parameters (such as soil properties) may also be uncertain, and the observed performance may be subjected to measurement errors. To consider these uncertainties, the model uncertainty parameters, uncertain model input parameters and actual performance variables are modelled as random variables, and their distributions are updated simultaneously using Bayes’ theorem. When the number of variables to update is large, solving the Bayesian updating problem is computationally challenging. A hybrid Markov Chain Monte Carlo simulation is employed in this paper to decompose the high-dimensional Bayesian updating problem into a series of updating problems in lower dimensions. To increase the efficiency of the Markov chain, the model uncertainty is first characterised with a first order second moment method approximately, and the knowledge learned from the approximate solution is then used to design key parameters in the Markov chain. Two examples are used to illustrate the proposed methodology for model uncertainty characterisation, with insights, discussions, and comparison with previous methods.