苏中腹地湖相沉积土层相关距离的统计分析

相关距离是用随机场理论建模土层剖面的一个非常重要的参数,也是利用随机场理论进行岩土工程可靠性分析的关键所在。基于苏中地区某建筑工程原位静力触探测试数据中的锥尖阻力指标,针对粉质黏土层,利用不同取样间距对相关距离进行了统计计算,分析了取样间距对相关距离计算结果的影响及原因,提出了实际应用中基于尺度匹配原则的取样间距确定方法;随后,基于江苏中部某高速公路工程地质勘察所提供的大量原位静力触探测试数据,结合相关距离计算的平均零跨距法、递推空间法和相关函数法,对该区湖相沉积土层土性参数的竖直向和水平向相关距离进行了系统地统计分析。研究成果不仅提供了土性参数相关距离计算过程中取样间距的确定原则,而且获得了相关距离的区域性代表值,为区域性土性参数随机场模型的建立打下坚实的基础,能对苏中地区岩土工程可靠性分析提供参考。     

相关函数法求解土性参数相关距离

介绍了相关距离在岩土工程应用中的实际物理意义,探讨了相关函数法计算相关距离的基本思路、标准相关函数型式的选择标准以及一些典型土层的标准相关函数类型。计算中发现,当土性参数的标准相关函数符合指数函数,尤其是单指数时,相关函数法能较合理地确定相关距离值。通过大量计算,得出了石家庄市桥东区3种典型土层的相关距离的分布范围,对于指导岩土工程勘测中的钻孔布置和取样间距具有一定的实际应用价值。同时得到相关距离具有区域性的特点,分区域研究具有重要的实际意义。     

空间递推平均法在估计土性指标自相关距离中的应用

像许多土层一样,黏性土层的土性参数也具有空间变异性。土性参数的空间变异性主要是由沉积和成岩等地质作用和环境因素导致的,而相关距离的确定是分析土性参数空间变异性的关键。为了分析天津南疆港地区土层参数的空间变异性,对确定土性参数相关距离的空间递推平均法及其改进方法进行了汇总分析,并结合地质勘查资料,运用改进的空间递推平均法对天津港地区典型土层的垂直相关距离进行了统计分析,得到了典型土层地区性代表值,对该地区岩土工程的可靠度分析及勘探点位的选取具有重要的指导意义。此外,还结合工程实例讨论了相关距离的贝叶斯估值法,贝叶斯估值法比直接取平均值确定自相关距离的方法更为可靠、合理,应用贝叶斯定理对天津港南疆石化码头淤泥及淤泥质黏土层的自相关距离进行估值,为今后该地区的取样间距选择提供参考,也为可靠度理论在该地区岩土工程中的应用提供有价值的参数。     

静力触探参数自相关距离确定方法与影响因素分析

在岩土工程可靠性分析中,土性参数空间变异性的分析至关重要,其中土体的固有变异性可以通过随机场理论获取方差折减函数和自相关距离值进行分析。基于天津临港静力触探试验(CPT)得到的锥尖阻力,对波动函数法确定自相关距离过程中所遇到的问题进行深入研究,并分析了去趋势化方法、取样间距、取样范围等影响自相关距离的因素。结合空间递推平均法的改进方法,首次对应用波动函数法确定自相关距离时出现的多个峰值的选择开展分析,结果表明对于所分析场地的地层静力触探数据而言,应选取波动函数曲线中第一个峰值作为该土层的自相关距离值。通过去趋势化后的随机分量统计特性及对应自相关距离计算结果的对比发现,去趋势化方法要依实际情况而定,并不是所有情况都可以使用线性去趋势化方法,建议最高选用二次非线性拟合结果对原始数据去趋势化;当取样范围较大,即触探孔数量较多时自相关距离随取样间距的增大而增大。分析还表明,对于同样的样本间距,随着触探孔数量的增加,自相关距离是逐渐减小的,但这种差距随着取样间距的增大而逐渐缩小。     

西安黄土土性相关距离的统计分布特性研究

土性指标概率模型参数的确定是进行岩土工程可靠度分析和设计的基础。为了更好地推行岩土工程可靠度设计,应该首先建立地区土性参数的概率模型。作为反映土性指标自相关特性的相关距离,研究其区域分布特性,建立其概率分布模型是必要的。本文收集了西安黄土的176个钻孔CPT数据,利用其端阻值qc作为样本,采用递推空间法计算了各层西安黄土的相关距离。研究了计算结果的统计特性,并对其均值进行了单侧置信区间估计,提出了各层西安黄土相关距离的代表值。建立了西安各层黄土相关距离的概率模型,对模型参数进行了估计,采用皮尔逊-卡方检验法对模型进行了拟合优度检验,检验结果认为其符合Beta分布。     

西安黄土土性相关距离的统计分布特性研究

土性指标概率模型参数的确定是进行岩土工程可靠度分析和设计的基础。为了更好地推行岩土工程可靠度设计,应该首先建立地区土性参数的概率模型。作为反映土性指标自相关特性的相关距离,研究其区域分布特性,建立其概率分布模型是必要的。本文收集了西安黄土的176个钻孔CPT数据,利用其端阻值q c作为样本,采用递推空间法计算了各层西安黄土的相关距离。研究了计算结果的统计特性,并对其均值进行了单侧置信区间估计,提出了各层西安黄土相关距离的代表值。建立了西安各层黄土相关距离的概率模型,对模型参数进行了估计,采用皮尔逊-卡方检验法对模型进行了拟合优度检验,检验结果认为其符合Beta分布。     

岩土工程可靠度分析中方差折减函数确定的一般规律

将可靠度理论应用于岩土工程稳定性分析过程中,即使是已证明安全的工程所得到的边坡或地基的失效概率通常较大,导致这一现象的原因是估算的方差偏大。计算土性指标的试验数据仅表征了该试验点的特征,而不是空间平均特征。在随机场理论应用于岩土工程可靠度分析的过程中,方差折减函数是将点特性过渡为空间平均特性的必要参数。首次对闫澍旺等提出的完全不相关距离理论中完全不相关距离的确定方法进行改进,不但理论上有所突破,而且计算方法更为简洁。对折减函数值的确定过程进行了分析,得到了用完全不相关距离方法确定折减函数的一般规律。     

相关函数法计算相关距离的分析探讨

根据数百个土层土性参数相关距离的计算, 对相关函数法计算相关距离的方法、相关函数型式选择、拟合范围等问题进行了分析探讨。     

关于土层相关距离计算方法的研究

根据随机场理论,对求解土层相关距离的递推空间法和相关函数法进行比较和探讨,指出两种方法所求得的相关距离值存在偏差的原因,并从理论上证明当样本容量足够大时两种方法的计算结果可以得到统一。对相关函数法作出改进,使其更易于曲线的拟合和参数的确定,最后采用实际工程的勘察测试资料进行了分析计算,验证了由计算公式推导所得的结论在实际工程中也是成立的。     

天津港地区土层剖面随机场特征参数的估计

天然地基或人工地基在形成过程中,不同位置的土由于成因相似,其物理力学特性指标具有空间自相关性,这种空间自相关性可以用随机场理论进行研究。为估计天津港地区土体物理力学性质的空间随机场特性,采用了现场钻孔取样、静力触探等方法获取了大量的描述土体物理力学性质的参数。由于静力触探试验能够连续取样以获得足够多的数据来进行随机场分析,文章主要应用静探数据检验了该地区土性指标的平稳性和各态历经性,指出应用Vanmarcke的随机场模型对土性指标进行分析具有可行性。本文的创新点在于探讨了天津港地区随机场模型的建立方法并应用改进的完全不相关距离方法估计了天津港地区典型土层剖面的随机场特征参数。为随机场理论应用于天津港地区岩土工程可靠度分析打下了坚实的基础。相同的方法可用于其他地区土层随机场特征参数的估计。     

基于CPT资料的土性参数随机场特性研究

通过CPT资料研究土性参数随机场特性是一种比较理想的方法。土性参数随机场的平稳性是后续研究的先决条件之一,可以通过Bartlett统计量进行检验,但采用不同的模型拒绝域相差比较大,这样给实际应用造成困难,新模型LGS由于适应范围广可以解决这一问题。从随机场的基本理论出发,介绍了新相关模型LGS的数值模拟方法。基于LGS相关模型,采用修正的Bartlett统计量对随机场平稳性进行检验,统一了拒绝标准。用两组数据进行了实例分析,通过编制的程序进行计算,结果表明,这种相关模型对不同形式的相关函数有较好的适应性,可以解决拒绝域不统一的问题。     

Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing

Geotechnical engineering problems are 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 a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.     

Conditional random field reliability analysis of a cohesion-frictional slope

Discarding known data from cored samples in the reliability analysis of a slope in spatially variable soils is a waste of site investigation effort. The traditional unconditional random field simulation, which neglects these known data, may overestimate the simulation variance of the underlying random fields of the soil properties. This paper attempts to evaluate the reliability of a slope in spatially variable soils while considering the known data at particular locations. Conditional random fields are simulated based on the Kriging method and the Cholesky decomposition technique to match the known data at measured locations. Subset simulation (SS) is then performed to calculate the probability of slope failure. A hypothetical homogeneous cohesion-frictional slope is taken as an example to investigate its reliability conditioned on several virtual samples. Various parametric studies are performed to explore the effect of different layouts of the virtual samples on the factor of safety (FS), the spatial variation of the critical slip surface and the probability of slope failure. The results suggest that whether the conditional random fields can be accurately simulated depends highly on the ratio of the sample distance and the autocorrelation distance. Better simulation results are obtained with smaller ratios. Additionally, compared with unconditional random field simulations, conditional random field simulations can significantly reduce the simulation variance, which leads to a narrower variation range of the FS and its location and a much lower probability of failure. The results also highlight the great significance of the conditional random field simulation at relatively large autocorrelation distances.     

苏中腹地湖相软土土性参数变异性统计描述

基于江苏中部某高速公路工程地质勘察所提供的大量室内试验测试数据,运用随机场理论,将土层剖面模拟为随机场而非传统意义上的随机变量,提出了基于随机场理论、考虑空间趋势分量的土性参数变异性统计方法,系统地统计分析了苏中腹地湖相软土土性参数的变异特性,对比了实验室物理性质指标参数、变形参数和强度参数变异性特征。统计结果表明,该地区软土实验室物理性质指标参数变异性较小,不存在明显的趋势分量,可用传统方法进行统计估计;实验室变形和强度参数存在明显的趋势分量,统计前需对数据进行回归分析和去趋势化处理,从而基于随机场理论进行统计分析。研究不仅提供了土性参数变异性统计的新方法,而且能对苏中地区工程建设提供必要的参考,为区域性软土土性参数随机场模型的建立打下了坚实的基础。     

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.     

Response of Vertically Loaded Pile in Clay: A Probabilistic Study

This study presents the response of a vertically loaded pile in undrained clay considering spatially distributed undrained shear strength. The probabilistic study is performed considering undrained shear strength as random variable and the analysis is conducted using random field theory. The inherent soil variability is considered as source of variability and the field is modeled as two dimensional non-Gaussian homogeneous random field. Random field is simulated using Cholesky decomposition technique within the finite difference program and Monte Carlo simulation approach is considered for the probabilistic analysis. The influence of variance and spatial correlation of undrained shear strength on the ultimate capacity as summation of ultimate skin friction and end bearing resistance of pile are examined. It is observed that the coefficient of variation and spatial correlation distance are the most important parameters that affect the pile ultimate capacity.