Reliability analysis of piles in spatially varying soils considering multiple failure modes

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.     

大型地下洞室施工过程中的可靠性分析

通过对Monte-Carlo随机有限元和系统可靠度计算的? 分支法的研究分析,考虑把二者联合起来分析洞室施工过程安全性,提出了一种大型地下洞室开挖过程中可靠度评价的方法。以海南工程为例,对地下洞室开挖过程中的每一步进行可靠性评价,分析比较了多层耦合法与分层逆作法之间洞室施工过程中的稳定性,比较了二者的优缺点。从而对多层耦合法施工有一个全面的了解和比较,为今后的大型洞室快速施工提供科学依据。     

Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations

This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested.     

Practical second‐order reliability analysis applied to foundation engineering

A practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd.     

基于拉丁超立方抽样的有限元可靠度程序开发及应用

在地下工程结构可靠性分析中,岩土体参数离散性大,功能函数非线性程度高,常为隐式函数,因此,对可靠度计算方法提出了很高的要求。针对传统蒙特卡罗抽样方法计算量非常大,难以满足工程要求的问题,基于拉丁超立方抽样技术,结合了Matlab和有限元软件Abaqus各自的优点,编制了Matlab-Abaqus联合计算的有限元可靠度程序,该程序具有节省样本空间、提高抽样效率的显著特点。通过对某圆形隧道的结构可靠性分析,表明该程序能很快达到收敛,能够满足地下工程结构可靠性计算分析的要求。     

地下洞室岩体力学参数反演软件系统开发与应用

岩体力学参数对地下洞室的施工和设计是极其重要的,通过位移反分析确定岩体参数的应用研究很多。为了提高参数反演的效率,采用均匀设计理论设计不同的反演参数组合,用有限元计算组建的样本集训练神经网络,根据洞室开挖过程中实测位移反演地下洞室岩体力学参数。基于面向对象、自适应、可视化三大关键技术,开发了地下洞室岩体力学参数反演有限元软件系统BAFES。该软件可实现地下洞室力学参数反演分析、开挖预报过程的可视化,将地下洞室岩体力学参数反演模式由“数据－有限元分析－数据”转变为“图形－有限元分析－图形”,结合现场监控技术和工程稳定分析,能及时地指导工程设计和施工。以某水电站地下厂房洞室群岩体力学参数反演为例,说明了该软件的实用性。     

大型地下洞室群开挖支护弹塑性损伤优化研究

正在设计施工的某大型水电站地下洞室群地质条件复杂,其开挖支护方案对围岩稳定性非常重要,因此,对支护方案进行优化研究非常必要。为更真实地模拟岩体的力学特性,研究施工过程中岩体的损伤破坏,根据不可逆热力学理论建立了弹塑性损伤模型和损伤演化方程,并编制了三维弹塑性损伤有限元程序D-FEM,具有模拟开挖与支护、计算速度快、群组功能等特点。建立大型地下洞室群三维数值模型,将通过实测地应力反演的应力作为初始地应力。采用D-FEM模拟了不同支护方案洞室群的施工过程,通过分析洞室围岩的应力、位移和破损区,支护方案2的支护效果最好,建议采用此方案。考虑岩体损伤演化后与FLAC3D塑性区相比,洞室群边墙中部的破损区显著增加,因此,程序可应用于地下工程的稳定性分析     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

Probabilistic stability assessment using adaptive limit analysis and random fields

For deterministic scenarios, adaptive finite element limit analysis has been successfully employed to achieve tight bounds on the ultimate load of a geotechnical structure in a much more efficient manner than a dense uniform mesh. However, no probabilistic studies have so far considered finite element limit analysis with adaptive remeshing. Therefore, this research explores the benefits of combining adaptive mesh refinement with finite element limit analysis for probabilistic applications. The outcomes indicate that in order to achieve tight bounds on probabilistic results (such as the probability of failure), the ultimate load in each individual simulation (e.g. factor of safety or bearing capacity) has to be estimated with a very high level of accuracy and this can be achieved more economically using adaptive mesh refinement. The benefits, assessed here for undrained conditions, are expected to be much more pronounced in the case of frictional soils and complex geometries.     

水电站地下洞室群分步开挖的非连续变形分析

利用大岗山水电站的地质勘探资料建立不同贯穿节理组合下地下洞室群的DDA模型,分析了洞室群开挖的破坏模式,并简单阐述其破坏机制。基于Monte-Carlo方法模拟节理的随机分布,结合大岗山水电站的开挖设计方案,对地下洞室群在分步开挖过程中的位移及应力演化进行研究。研究表明：洞室群开挖完成后,洞周块体的位移均指向洞内,尾调室上下游与主厂房上游的变形较大;洞周块体的大主应力均平行于洞室边界线,尾调室的应力释放比较明显,其边墙块体发生了滑移;洞室群在开挖过程中互相影响,其中主变室受主厂房和尾调室的影响比较明显。研究结果指出了洞室群开挖过程中需要关注和加固的具体部位,为工程支护措施的优化提供了依据。     

Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement estimation

This article focuses on the statistical characterisation and stochastic modelling of the load-displacement behaviour of shallow footings on cohesionless soils and on the probabilistic estimation of settlement for serviceability limit state design (LSD). The study relies on a field database of 30 full-scale footings subjected to vertical loading with cone penetration testing data available for each site. The performance of three load-displacement models in replicating field data is assessed comparatively through statistical analysis. Load-displacement uncertainty is subsequently modelled probabilistically to perform Monte Carlo Simulation (MCS)-based estimation of footing settlement using the best-performing power law model. The dependence among load-displacement model parameters is investigated and replicated using copula theory. Samples are generated to account for parametric uncertainties in model inputs. The simulation output samples of settlement are examined statistically in order to assess the relevance of parametric and load-displacement uncertainties in settlement estimation, as well as the importance of accounting for correlation between power law model parameters. A simple analytical model for the estimation of settlement at any target reliability level is obtained on the basis of the outputs of MCS. The model can be practically implemented in geotechnical LSD at serviceability limit states.     

地下洞室动态开挖的三维数值分析及优化研究

针对云南锡业集团公司个旧锡矿地下采场洞室的开挖技术条件,采用非线性三维有限元法,对其动态开挖过程进行了数值模拟分析,并优化选择了地下采场洞室的开挖顺序和开挖跨距,从而得到一些有益的结论。     

海岛环境下地下水封油库海水入侵数值模拟研究

海水入侵是影响海岛地下水封油库施工及运营安全的重要因素。海岛环境下建设地下水封油库,大规模的地下开挖将显著改变海岛天然地下水渗流场,海水入侵地下洞室一方面引发突水风险,另一方面海水中的氯离子将会对地下洞库结构设施造成侵蚀,影响地下油库的使用寿命。因此在海岛环境下建造地下水封油库,除了需要考虑水封可靠性与岩体稳定性外,还需要关注海水入侵等现象。科学设置水幕系统可以有效地减弱海水入侵风险,论文基于污染质运移相关理论,采用有限元数值模拟方法,以拟建浙江省舟山市某海岛大型地下水封油库为例,模拟了地下油库建造及运营期的海水入侵现象,研究表明:若不设置淡水水幕系统,开挖地下洞室会直接导致海水入侵;设置水平水幕后在确保水封可靠性的前提下,能在一定程度上减弱海水入侵;而设置垂直水幕系统则能较为明显地抑制海水入侵的发生。该成果为海岛环境下建造地下水封油库可能遇到的海水入侵问题研究提供了理论依据。     

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.     

向家坝水电站地下厂房围岩稳定的黏弹塑性有限元分析

考虑流变作用,建立三维有限元模型进行数值计算,以洞室变形和点抗滑安全系数为指标,针对向家坝水电站地下厂房围岩的特殊性进行稳定性研究,结果表明,随着围压的增高,流变速率逐渐减小,初始应变逐渐减小;软弱夹层处流变速率较其他岩体减小缓慢,且开挖后流变达到稳态状态时软弱夹层最终流变位移较大;黏弹塑性下围岩位移分布及变化规律与弹塑性一致,但黏弹塑性下计算位移明显要比弹塑性大;流变效应对岩体变形和稳定性,以及对支护结构有重要影响;黏弹塑性情况下,洞室围岩特征点抗滑安全系数比弹塑性条件下小,软弱夹层出露处和拱顶点抗滑安全系数较低,点抗滑安全系数分析还表明,软弱夹层对其稳定性影响明显,验证了位移分析结果。     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

基于Copula函数的基桩荷载-位移双曲线概率分析

提出了基于Copula函数的基桩荷载-位移双曲线概率分析方法。首先将基桩标准化荷载-位移双曲线模型不确定性转化为双曲线参数不确定性,然后在Copula理论框架下建立了双曲线参数的联合分布函数。最后以钻孔现浇灌注桩试验数据为例证明了所提方法的有效性,并进行了基桩正常使用极限状态可靠度分析。结果表明：Copula函数是构造基桩标准化荷载-位移双曲线参数联合分布函数一种有效的方法,它能够更加准确地实现基桩荷载-位移双曲线的随机模拟,从而得到更为合理的可靠度结果。钻孔现浇灌注桩双曲线模型中两个参数间具有较强的负相关关系,忽略了这种负相关性将会高估基桩的失效概率。此外,常用的Gaussian Copula函数并不是拟合双曲线模型中两个参数间相关结构最优的Copula函数,采用Gaussian Copula函数将会明显低估基桩的失效概率。     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

正交各向异性岩体中地下洞室稳定的粘弹-粘塑性三维有限元分析

建立了一种正交各向异性岩体的粘弹－粘塑性模型，推导和描述了相应的数值计算表达式和有限元分析的步骤，并使用所编制的三维有限元程序，以在层状岩体（横观各向同性介质）中的地下洞室开挖为算例，考察了围岩的流变动态，得出了几点结论。     

大型地下洞室不同开挖效应的动态仿真分析

针对云南锡业集团公司个旧锡矿地下采场洞室的开挖技术条件,采用非线性三维有限元法,对其动态开挖过程进行了仿真模拟分析,并优化选择了地下采场洞室的开挖顺序.结果表明,不同的开挖顺序,对围岩的稳定性具有显著的影响.