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。     

基于可靠度理论的滑坡稳定性及其影响因素分析

基于可靠度理论,利用Morgenstern-Price法、Ordinary法、Bishop法和Janbu法等4类极限平衡方法对台州市北水南调工程朱溪引水段Ⅷ号滑坡的稳定性进行了分析,设计了最不利组合、最有利组合、平均值组合的确定性分析方案,目的是为可靠度计算结果提供对比基准;设计了Monte-Carlo循环次数为5 000,50 000,500 000,5 000 000次等4种计算工况,岩土参数的概率分布函数为正态分布、三角形分布和均匀分布等3种情况,方差等于0.5,1.0,2.0,3.0,4.0,5.0倍初始实验方差等6种计算方案,岩土参数间相关性在-1.0～1.0间按0.25等幅变化的9种情况。研究发现,循环次数仅对安全系极值有较大影响,对可靠度指标影响不大;分布函数和数据离散性均会对结果精度造成影响;参数相关性仅对失效概率造成较大影响。     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

A FORM-based approach for probabilistic analysis in geotechnics: Application to a reinforced concrete drainage culvert

As numerical models are increasingly used as a design tool in geotechnical engineering, it is highly desirable if geotechnical reliability analysis can be conducted based on numeral models. Currently, the practical use of geotechnical reliability analysis-based numerical models is still quite limited. In this study, an easy to access method is derived to conduct geotechnical reliability analysis based on numerical models. To facilitate its application, a procedure is outlined to implement the suggested method such that geotechnical reliability analysis can be automated using existing geotechnical numerical packages. The procedure is illustrated in detail with an example, and the source codes provided can be easily adapted to analyze other similar problems. The method described in this paper is used to study the reliability of a deteriorating reinforced concrete drainage culvert in Shanghai, China. The suggested method provides a convenient means for reliability analysis of complex geotechnical problems.     

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。     

对岩土工程有限元强度折减法的几点思考

有限元强度折减法是岩土工程极限分析有限元法中研究和应用较多的一种。近年来获得了快速发展,且成果丰硕,初步显示出在岩土工程中的可行性、优越性和实用性。在充分肯定其优势及特点的同时,从安全系数定义、摩尔-库仑准则的应用条件、计算参数选取等方面,探讨了有限元强度折减法的若干问题。认为应注意该方法的使用条件和计算参数选取;研究以变形控制设计为主的岩土结构安全系数及稳定性,与传统极限平衡方法结合互补,研发多种方法和用途的专业计算软件是较好的发展方向。     

岩土工程可靠度分析的改进响应面法研究

为了提高响应面法的计算效率和精度,对现有的全局响应面法进行了改进。采用径向基函数（RBF）神经网络,代替目前常用的BP网络,迭代过程中在超锥体的范围内构造响应面,逼近隐式的非线性功能函数。数值算例分析表明,与通常的响应面法相比,改进全局响应面法的迭代次数和有限元分析次数均大幅减少,节省机时,有利于提高计算精度。同时,以浅基础和挡土墙为工程背景进行可靠度分析,表明该方法能以较快的收敛速度和较少的有限元分析次数,获得较高精度的可靠度指标,适用于岩土工程的可靠度分析。     

岩土工程可靠度分析的神经网络四阶矩法

针对岩土工程的功能函数强非线性且难以显式表达的特点,提出了基于人工神经网络的四阶矩法,充分利用了基本随机变量的统计信息。首先利用神经网络对结构的隐式功能函数进行拟合,求得基本随机变量在均值点处的功能函数值及其偏导数,然后利用泰勒级数展开的方法由基本随机变量的前四阶矩求得功能函数的前四阶矩,并借助于Pearson系统获得功能函数的更高阶矩。在此基础上,通过最大熵原理确定以功能函数各阶矩为约束的功能函数的概率密度函数,最后由一次积分得到结构的失效概率。通过数值算例和工程实例不同方法的对比分析,表明基于神经网络的结构可靠度分析四阶矩方法是可行的,有效的,能够满足岩土工程可靠度分析的要求。     

An approximation to the reliability of series geotechnical systems using a linearization approach

A method based on the linearization of the limit state functions (LSFs) is applied to evaluate the reliability of series geotechnical systems. The approach only needs information provided by first order reliability method (FORM) results: the vector of reliability indices, β, of the LSFs composing the system; and their correlation matrix, R. Two common geotechnical problems—the stability of a slope in layered soil and a circular tunnel in rock—are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure, and advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, the second order reliability method (SORM)—that approximates the true LSF better than FORM—can be employed to compute better estimations of the system’s reliability.     

Role of reliability calculations in geotechnical design

ABSTRACT

This paper adds to the ongoing discussion on the role of reliability calculations in geotechnical design. It situates design calculations, be it verified by a global factor of safety, partial factors, or reliability-based design (RBD), in a larger context of quality management over the life cycle of the structure. It clarifies that uncertainties amenable to probabilistic treatment typically fall under the category of “known unknowns” where some measured data and/or past experience exist for limited site-specific data to be supplemented by both objective regional data and subjective judgement derived from comparable sites elsewhere. Within this category, reliability is very useful in handling complex real-world information (multivariate correlated data) and information imperfections (scarcity of information or incomplete information). It is also very useful in handling real-world design aspects such as spatial variability that cannot be easily treated using deterministic means. Examples are presented to illustrate how reliability calculations could relieve engineering judgement from the unsuitable task of performance verification in the presence of uncertainties so that the engineer can focus on setting up the right lines of scientific investigation, selecting the appropriate models and parameters for calculations, and verifying the reasonableness of the results.     

An adaptive high-dimensional model representation method for reliability analysis of geotechnical engineering problems

In this study, a new reliability analysis method was developed based on the adaptive high-dimensional model representation (HDMR) and applied to geotechnical engineering problems. For practical problems requiring finite element (FE) analysis or other numerical methods to evaluate system responses such as stresses and deformations, an efficient and accurate metamodeling technique is needed because it is not efficient or straightforward to directly adopt the conventional sampling-based or gradient-based reliability analysis approaches. In this work, an adaptive metamodeling approach was created and studied based on the HDMR framework and augmented radial basis functions (ARBFs). In this adaptive ARBF-HDMR technique, a simple and inexpensive first-order ARBF-HDMR metamodel was first constructed to explicitly express a performance function, and an alternate first-order reliability method (FORM) was applied to locate the design point and compute the reliability index. A local window was then defined such that additional sample points were generated and a higher-order HDMR component function was created using ARBF and added to the existing ARBF-HDMR metamodel. The accuracy of the ARBF-HDMR metamodel was improved through this adaptive process, especially in the region surrounding the design point. One mathematical and four geotechnical engineering problems were studied and solved using the proposed adaptive ARBF-HDMR approach. The proposed method was found to be capable of obtaining accurate reliability indices within a few iterations in all test problems.     

双滑块边坡锚固系统时变可靠性分析

考虑锚杆锚固段从岩体中拔出、拉杆拉断、拉杆从注浆体中拔出等失效模式,利用系统可靠性原理和极限平衡分析方法,并基于Monte-Carlo抽样原理提出双滑块岩质边坡锚固系统破坏概率的直接求解方法。同时考虑锚杆钢筋的腐蚀与软弱滑动面抗剪强度c、? 的时变性,建立了考虑锚杆多失效模式双滑块岩质边坡锚固系统的时变可靠性模型。算例计算结果表明：软弱滑动面上的强度参数c、? 的时变性和注浆体与围岩之间的抗力时变性对锚固系统的破坏概率的影响较大,而锚杆的腐蚀对锚固系统破坏概率的影响不明显。     

The geological and geotechnical design model in tunnel design: estimation of its reliability through the R-Index

ABSTRACT

In this paper recent improvements of the R-Index method are presented, based on its application on several projects in various geological and geotechnical contexts. The R-Index derives from a probabilistic procedure conceived for estimating the reliability level of the Geological and Geotechnical Design Model used to design underground structures, especially tunnels. The R-Index takes into account the geological complexity of a site and recommended empirical scores (based on expert judgement) for different quality levels of geological surveys and geotechnical and geophysical investigations.     

System reliability analysis for near-surface radioactive waste disposal facilities

The low- and intermediate-level radioactive wastes are generally disposed in near-surface disposal facility (NSDF). The NSDF is composed of engineered barriers. The probabilistic safety assessment model has been developed to analyse the performance of NSDF. The endpoints of the assessment are the concentration of the radionuclide in the groundwater and the corresponding dose rate of the radionuclide. The barrier system can have multiple failure modes but practically the possible failure modes are failure of top cover, failure of waste container, degradation of waste form and failure of bottom cover, which are usually considered as independent failure events. Through a sensitivity analysis, the most critical parameters affecting the design reliability for failure criteria are identified as the groundwater velocity and distribution coefficient. The study shows that for the NSDF considered, there is a high degree of dependence between the failure modes, and demonstrates the probability of the simultaneous occurrence of failures. Thus, the need to consider the system reliability in the NSDF is highlighted. The study also advocates the use of optimisation techniques to evaluate the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulations.     

Reliability analysis of strength of cement treated soils

The design strength of cement treated soils and its variability are influenced by various contributing factors such as inherent variability of the soft ground as well as variations in the quantities of the additives used for improvement. To consider these variations, geotechnical designs use the factor of safety approach. This paper shows that the reliability-based analysis enables a rational choice of a design strength value for the cement-stabilised soft soil, considering the variations in the influencing input parameters in an appropriate manner. An approach for identifying the important variables governing the strength behaviour of improved soft soils is also illustrated.     

基于系统评价的块体可靠度指标分析及应用

利用条件概率评价及系统工程理论,将关键块体作为块体系统一个重要组成部分,分析了关键块体可靠度指标评价办法,探讨了关键块体与次生关键块可靠度内在关系,由此类推,提出块体系统评价方法,推导出块体系统可靠度计算公式,实现对块体系统的失稳概率的评价计算。并选择一工程实例,对评价方法予以验证。结果表明：传统关键块体可靠度评价办法忽略块体间内在影响,结果偏向风险;而文中方法综合考虑块体之间影响,并建立了系统评价模型,对块体系统评价更接近实际情况,对块体系统理论的研究有一定借鉴意义。     

基于不平衡推力法的边坡可靠度分析

Rosenblueth方法是一种简单实用的可靠度指标计算方法,不需要了解各状态变量分布函数,只要利用它们的均值和方差,就可求得边坡的可靠指标。推导了下滑力超载储备安全系数的显式表达式,以此式作为边坡可靠度分析的状态函数,结合Rosenblueth方法的优点,给出了一种边坡稳定可靠度分析的实用方法。     

On the use of pore pressure measurements in safety reassessments of concrete dams founded on rock

In probabilistic stability analyses of concrete dams founded on rock, the uplift pressure is often a parameter of major importance. In previous literature, it has been suggested that assessing uplift with pore pressure measurements, instead of using empirical assumptions, could improve the calculated dam safety. This paper presents a coherent methodology to investigate whether incorporating pore pressure measurements has any impact on the calculated dam safety, based on Bayesian linear regression of pore pressure data in combination with series-system and the first-order reliability method. The study concludes that the probability of sliding failure is closely related to the probability of an extreme increase in uplift. Hence, measured uplift should only be incorporated while this probability remains sufficiently small, which requires proper programs both for uplift monitoring and for maintenance of drains and grout curtains.     

甘肃黄土高边坡可靠度研究

以甘肃省266个黄土自然极限状态坡为研究对象,将其按地形地貌、地层岩性等特征划分为4个亚区,对每个亚区的极限状态坡高与坡宽进行双对数线性模型回归和不同置信度下的统计分析,给出4个亚区不同置信度下坡高与坡宽的相关关系。以1 024组黄土物理力学指标统计结果作为计算参数,用Bishop法的稳定系数计算公式建立极限状态方程,利用 Monte Carlo法对各亚区不同置信度下的边坡进行可靠度模拟,系统分析了坡高、坡度、参数变异性对失效概率的影响,以及失效概率与稳定系数的关系。结果表明,临洮-永靖亚区边坡坡度低于31.5?,失效概率可控制在10%以下;陇东亚区、兰州-定西-会宁亚区和天水-秦安-通渭亚区在强度参数变异系数取当地平均水平,稳定系数为1.3情况下失效概率在10%以内,稳定系数为1.2情况下,失效概率多在20%以内。