Application of kriging method to structural reliability problems

Approximation methods are widely used to alleviate the computational burden of engineering analyses. For structural reliability analyses, the common approach is to use the response surface method (RSM) based on the least square regression. However, another approximation method based on kriging has gained popularity especially in the field of deterministic optimization. However, the application of the kriging method to structural reliability problems has not been realized until recently. Therefore, this paper investigates the use of the kriging method for structural reliability problems by comparing it with the most common RSM. The effects of the kriging parameters are also examined on the basis of the β computation and fitting behavior. It can be deduced from the results given in this paper that using the most common approach in the literature to find the kriging parameters does not guarantee a good result for the structural reliability problems. As a result, some advantages as well as disadvantages of the kriging method are reported, based on the results obtained from the application of the kriging method to the examples from the literature. Finally, this paper suggests the points for which the kriging model could be improved to get better results for structural reliability problems.     

Spatial-temporal prediction of secondary compression using random field theory

A methodology is presented for observation-based settlement predictions by considering the spatial correlation structure of soil. The spatial correlation is introduced among the settlement model parameters, and the settlements at various points are spatially correlated through these geotechnical parameters, which naturally describe the phenomenon. The method is based on Bayesian estimations, considering both prior information, including spatial correlation, and observed settlements, to search for the best estimates of the parameters. Within the Bayesian framework, the optimized selection of the auto-correlation distance, by Akaike’s Bayesian Information Criterion (ABIC), and the spatial interpolation of the model parameters, by the kriging method, are also proposed. The application of the proposed approach in secondary compression settlement predictions, based on the linear relationship between settlement and the logarithm of time, is presented in this paper. Several case studies are carried out using both simulated settlement data and actual field observation data. It is concluded that the accuracy of settlement predictions can be improved by taking into account the spatial correlation structure, especially when the spacing of the observation points is shorter than half of the auto-correlation distance, and that the proposed approach produces rational predictions of settlements at any location and at any time with quantified errors.     

考虑地层变异性和土体参数空间变异性的边坡可靠度全概率设计方法

目前边坡稳定设计研究中大多数考虑了土体参数的空间变异性,但忽略了地层变异性的影响。为此,提出了一种同时考虑这两类变异性的边坡可靠度全概率设计方法。在全概率设计框架内,将广义耦合马尔可夫链模型与随机场模型相耦合用于同时表征地层变异性和土体参数空间变异性,给出了所提方法的计算流程。利用澳大利亚珀斯市钻孔资料,以某边坡为例进行可靠度设计,为说明在边坡可靠度设计中同时考虑地层变异性和土体参数空间变异性的重要性,分析了仅考虑土体参数空间变异的情况,进一步分析了同时考虑两类变异性的情况,并对二者进行了比较。结果表明:所提出的边坡可靠度设计方法能够有效地考虑边坡中存在的地层变异性和土体参数空间变异性。当仅考虑土体参数空间变异性时,边坡可靠度设计结果很大程度上取决于所采用地层的分布情况,特别是地层分布中抗剪强度较强土体类型占比高于真实情况时,将导致得到的最优设计方案偏于危险。反之,若地层分布中抗剪强度较弱的土体类型占比高于真实情况,得到的最优设计方案偏于保守。因此,为准确地得到最优设计方案,在边坡可靠度设计中应同时考虑地层变异性和土体参数空间变异性的影响。     

箱形基础的空间分析及其结构优化设计

采用能量变分原理与多重子结构技术相结合的方法,建立了考虑上部结构与箱基、地基土共同工作的箱基内力空间分析模型.特别提出了上部结构为框架-剪力墙体系时箱基内力的实用算法.在空间内力分析的基础上,建立了箱形基础造价优化的数学模型,并采用子空间组合可行方向法求优.所提出的优化方法应用于工程实例,取得了明显的经济效益.     

考虑地质成因的土坡可靠度分析

 不同地质成因的边坡在土体参数统计变异性相同的情况下,由于空间变异性不同,其稳定状态并不一定相同,传统的边坡稳定性确定性分析和基于随机变量模型的边坡可靠度分析方法无法考虑坡体的特定地质成因。由地质成因估计土体参数的波动范围,从而通过土体参数波动范围这一指标把地质成因纳入边坡稳定性分析框架,提出考虑地质成因的边坡可靠度分析方法,介绍具体的分析流程,采用一维随机场模拟和验算点法完成边坡可靠度分析。算例计算结果显示岩土参数空间变异性对边坡稳定性的影响很大,由地质成因估计土体参数的波动范围,为在边坡可靠度分析中合理考虑土体参数空间变异性提供一条现实的解决途径,值得在工程应用中推广。     

考虑岩土参数空间变异性的盾构隧道地表沉降分析

现有随机场理论能够较好地描述单一岩土参数的天然随机性、空间结构性和局部奇异性。当前面临的挑战是如何考虑多个土层、多元及统计相关的岩土参数空间变异性对岩土工程的影响。考虑岩土参数如黏聚力、内摩擦角和压缩模量等具有明显的空间变异性,将随机场理论引入盾构隧道地表沉降可靠指标分析。主要研究工作包括:(1)采用局部均值方法将多个非平稳土层同一岩土参数转化为平稳各向异性随机场变量,并给出随机场的统计特征;(2)简化岩土参数的空间变异性为一般变异性,直接采用响应面方法计算盾构隧道地表沉降可靠指标;(3)提出协同序贯高斯离散算法,在空间网格上实现多元岩土参数随机场的同步离散化,并基于经典Monte-Carlo随机模拟原理和盾构隧道数值计算,直接统计地表沉降的可靠指标;(4)引入子集Monte-Carlo随机模拟加速算法。将以上方法应用于天津~#5、~#6地铁环湖西路站—宾馆西路站区间盾构隧道四线交叠工程,结果表明,采用经典随机理论描述岩土参数的变异性,所得到的盾构隧道地表沉降可靠指标小于基于随机场理论的对应值。该结论为复杂盾构隧道的施工控制与设计优化提供了理论依据。     

基于单元重构的岩土工程复杂地质断层建模方法

 针对岩土工程数值分析中地质断层建模困难的问题,提出基于单元重构的岩土工程复杂地质断层建模方法。该方法首先对分析对象进行独立离散,建立不考虑地质断层的模型。再通过单元重构,可将地质断层嵌入已建模型,实现复杂地质断层的自动建模。所谓单元重构,是首先使用八节点六面体单元,建立不考虑断层的分析模型,再借助四节点四面体,五节点四棱锥和六节点三棱柱等单元形态,对地质断层穿过的网格进行处理,重构为由多种单元形态构成的模型。然后结合岩土工程断层建模实例,将该方法应用于复杂地下岔管、重力坝坝肩和坝基以及大型地下洞室群的断层建模,可证明其有效性。进一步以大型地下洞室群为例,将考虑地质断层的洞室群模型导入通用软件,采用实体单元模拟地质断层进行开挖计算,并与不考虑断层的情形对比分析发现,考虑地质断层后,围岩位移和应力分布都呈现出不连续性,被断层切割部位的围岩变形增大,应力出现松弛。这表明含有地质断层的重构模型可以用于数值计算,且能有效反映出地质断层对洞室围岩稳定的影响,从而可证明该建模方法的可靠性,为岩土工程的复杂地质断层建模提供便捷的实现途径。     

基于截尾概率分布的基坑突涌模糊可靠度分析

岩土工程可靠度分析中,计算参数具有随机性,稳定性评价具有模糊性。传统的Monte Carlo模拟方法计算可靠度时,往往假定参数概率分布在正负无穷之间分布,与真实情况不符,而且其计算效率也往往较低。规范推荐的基坑突涌验算公式,计算结果往往偏于保守。引入截尾概率分布的确定方法,对参数概率分布进行截尾处理;提出拉丁超立方抽样与最大熵原理结合来确定结构响应概率分布的方法,并将其与模糊可靠度原理结合,构建了基于抽样模拟的模糊可靠度计算模型;推荐了考虑土体抗剪强度的突涌验算公式。将所提方法应用于某深基坑工程突涌分析中,其结果表明,基于截尾分布的抽样可以有效避免参数抽样值为负数的情况,所提计算模型效率明显优于传统的Monte Carlo模拟方法,模糊可靠度的计算结果比经典可靠度更符合工程实际情况。     

不排水强度的空间变异性及单桩承载力可靠性分析

对于土性随深度变化的情况,讨论了不排水剪切强度cu空间变异性的随机场概率统计模型.由于现有的土层随机场模型都是针对平稳随机场,即土性的随机分量的,所以首先要用回归的方法分离出趋势分量来,然后才能对随机分量进行模拟.认为在进行岩土工程可靠度分析时,不仅要考虑抽样所带来的误差,还要考虑土性本身的空间变异性.并用不排水剪强度cu的变异性来计算粘性土中单桩承载力的方差,旨在阐明随机场理论在岩土工程可靠性分析中的应用.最后用一个算例作了具体说明.     

Trivariate analysis of soil ranking-correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems

An important issue in the probabilistic prediction modelling of multivariate soil properties (usually including cohesion, friction angle, and unit weight) is the measurement of dependence structure among these properties. The use of Pearson's correlation as a dependence measure has several pitfalls; therefore, it may not be appropriate to use probabilistic prediction models in geotechnical engineering problems based on this correlation. As an alternative, a copula-based methodology for prediction modelling and an algorithm to simulate multivariate soil data are proposed.In this method, all different random variables are transformed to a rank/uniform domain in order to form a copula function by applying cumulative distribution function transformations. The technique of copulas, representing a promising alternative for solving multivariate problems to describe their dependence structure by a ranked correlation coefficient, is highlighted. Two existing observed soil data sets from river banks are used to fit a trivariate normal copula and a trivariate fully nested Frank copula. The ranking correlation coefficient Kendall's τ and the copula model parameters are estimated. The goodness-of-fit test to choose the best-fitting model is discussed.A series of triplet samples (i.e., cohesion, friction angle, and unit weight) simulated from the trivariate normal copula with flexible marginal distributions are used as input parameters to evaluate the uncertainties of soil properties and to define their correlations. The influence of the cross-correlation of these soil properties on reliability-based geotechnical design is demonstrated with two simple geotechnical problems: (a) the bearing capacity of a shallow foundation resting on a clayey soil and (b) the stability of a cohesive-frictional soil in a planar slope. The sensitivity analysis of their correlations of random variables on the influence of the reliability index provides a better insight into the role of the dependence structure in the reliability assessment of geotechnical engineering problems.     

数值模拟分析基坑开挖空间效应的变化规律

基坑开挖导致墙后土体产生滑裂面,通过MIDAS有限元计算软件对万达广场基坑工程进行数值分析,总结硬化土模型的参数取值规律。结合万达广场深基坑工程实例,计算墙后土体水平位移监测点的变化曲线,对土体水平位移的变形规律加以分析。通过分析数值分析中得到的数据,分析基坑开挖的空间效应,结合工况对比分析SMW支护和双排桩支护下的空间效应比值的规律。     

基于承载力和沉降的条形基础稳定性区间非概率可靠性综合分析方法

 提出采用区间值表示土体力学参数取值,以反映参数取值的不确定性特征,并根据参数取值特性建立出相应参数的区间值确定方法。在研究地基承载力计算方法基础上建立条形基础承载力区间非概率可靠性分析模型,并以沉降计算方法为基础建立条形基础沉降区间非概率可靠性分析模型。运用区间理论与一维优化算法求解非概率可靠性指标,并采用可靠性评价准则对条形基础稳定性进行综合评价,从而建立出基于承载力和沉降的条形基础稳定性区间非概率可靠性综合分析方法,该方法能综合反映承载力和沉降对条形基础稳定性的影响。工程算例分析表明该方法具有一定的合理性,能完善条形基础稳定性的可靠性分析方法与理论。     

考虑参数空间变异性的隧道结构变形分析简化方法

土体参数具有空间变异性是被广泛接受的,而这种变异性对岩土中结构性能有着重要的影响.随机场理论是一种常用的用来模拟土体参数空间变异性的方法.基于随机场理论,以土体弹性模量的空间变异性为切入点,采用蒙特卡罗方法和有限差分模拟计算相结合的方法,开展隧道水平收敛的随机分析.在大量蒙特卡罗计算基础上,提出了3种简单易用的简化考虑...     

Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces

Slope reliability analysis considering inherent spatial variability (ISV) of soil properties is time-consuming when response surface method (RSM) is used, because of the “curse of dimensionality”. This paper proposes an effective method for identification of representative slip surfaces (RSSs) of slopes with spatially varied soils within the framework of limit equilibrium method (LEM), which utilizes an adaptive K-means clustering approach. Then, an improved slope reliability analysis based on the RSSs and RSM considering soil spatial variability, in perspective of computation efficiency, is established. The detailed implementation procedure of the proposed method is well documented, and the ability of the method in identifying RSSs and estimating reliability is investigated via three slope examples. Results show that the proposed method can automatically identify the RSSs of slope with only one evaluation of the conventional deterministic slope stability model. The RSSs are invariant with the statistics of soil properties, which allows parametric studies that are often required in slope reliability analysis to be efficiently achieved with ease. It is also found that the proposed method provides comparable values of factor of safety (FS) and probability of failure (P_f) of slopes with those obtained from direct analysis and literature.     

硬化土本构模型在FLAC3D中的开发及应用

 基于塑性增量理论,推导硬化土本构模型的有限差分格式。在VC++编程环境下,利用FLAC3D提供的二次开发平台,编制硬化土本构模型的有限差分程序,实现硬化土本构模型在FLAC3D中的二次开发,并给出二次开发的步骤、方法和编程要点。通过不同应力路径室内试验结果与采用不同本构模型的FLAC3D数值计算结果进行对比分析,验证硬化土本构模型在FLAC3D中二次开发的正确性和必要性。对比分析表明：采用硬化土本构模型的FLAC3D数值计算结果与试验结果吻合较好,而且硬化土本构模型的模型参数可从常规三轴试验获得,模型参数简单,硬化土本构模型不仅能够反映土体的非线性特性,还能够反映深基坑工程复杂的应力路径,与其他土体本构模型相比,硬化土本构模型更适合用于深基坑工程的计算分析。硬化土本构模型在FLAC3D中二次开发的实现,扩大了FLAC3D的适用范围,在一定程度上弥补FLAC3D在分析岩土工程尤其是深基坑工程方面上的不足。     

考虑岩土材料变形时空非均匀特征的DSCM快速分析方法

岩土材料在外荷载作用下其变形通常表现出时间与空间分布上的非均匀性特征,在应用DSCM(数字散斑相关方法)进行图像像素测点的相关搜索过程中,传统方法通常对于全部试验阶段的图像和同一幅图像上的所有测点均采用相同的搜索范围,显然,这是一个虽然简单但效率很低的图像搜索分析方法。提出一种依据参考网格的测点动态范围搜索方法(简称PDSS),即首先利用常规搜索方法分析获得一个间距较大且覆盖正式分析范围的测点网格的位移,然后以其作为正式图像测点分析的参考网格,最后,对任一测点,以其所在的参考单元节点的最大位移作为该测点的搜索范围值,从而可实现与测点变形大小相适应的动态范围搜索。PDSS方法本质上是通过减少相关分析的像素点数量来大幅提高图像分析速度。试验检验结果表明,PDSS方法相对于普通方法的图像分析速度通常可提高10倍左右。研究成果解决了具有时空非均匀变形特征的岩土材料DSCM的快速优化分析问题,可进一步提高DSCM在岩土材料变形量测中的应用技术水平。     

大型石油储罐复合地基稳定性分析

针对建立在松软地基上的大型石油储罐地基,提出了平面应变条件下复合地基沉降计算的复合本构有限元法,以某炼油厂地基资料为例建立了储罐地基处理的复合力学模型,采用数值仿真计算进行定量分析,得出了处理复合地基的一些规律。工程实例分析表明,该方法是有效的,可为储罐基础的工程设计提供依据。     

Multivariate geostatistical modelling of geotechnical characteristics of the alluvial deposits in West Thessaly,Greece

Land subsidence due to ground-water overexploitation in the Western Thessaly basin resulted in the manifestation of ground deformations. In order to investigate the mechanism of this phenomenon, borehole data regarding geomechanical properties of soil were examined. Based on these data, the spatial variability of soil compression index (Cc) was evaluated in relation to other geotechnical parameters, by means of multivariate geostatistics. Multivariate statistics and geostatistics were combined and compared to evaluate the estimation methods of Cc. Principal component analysis (PCA) was applied in order to highlight the relationships between the geotechnical parameters. Through cross-validation, multiple linear regression, kriging and cokriging were tested as estimators of the Cc. The results show that spatial correlation of the target variable is less important than its correlation to the auxiliary variables. Cross-validation demonstrates that kriging with two PCA factors and application of inverse transform gives the best results for Cc estimates.     

多层地基土坡的随机有限元模型不同参数比较分析

对James Bay堤坝进行了基于随机有限元方法的蒙特卡罗模拟。该法可以给出边坡可靠度（或破坏概率）而不是更加传统的安全系数作为边坡安全评估的度量准则。不同土层的不同的土性参数由随机场产生并且投影到有限元网格的高斯积分点上。研究了非均质各向同性和各向异性的不同的一维和二维随机场模型参数对结果的影响。通过对其结果的比较分析,展示了5种随机场相关结构对边坡可靠度的影响,并强调了选择一个适合模型及其参数的重要性。根据统计分析结果,提出了基于可靠度的土强度特征设计参数,结果显示只有10%～40%（取决于不同的随机有限元模型）的土坡可以达到所期望的确定性分析中的平均结构反应。这是由于随机有限元方法可以更加严格地考虑空间相关性,使得边坡破坏可以更加自然地沿着最小阻力（即最弱材料强度）的路径发展。结果证明水平方向的相关距离在该堤坝的分析中起主导作用,并且指出随机有限元模型中若采用简单公式（不考虑破坏面几何形状）得出的等效各向同性的相关距离,可能导致错误的可靠度评估。