非均质地基上条形基础沉降的随机有限元分析

针对非均质地基土上条形基础弹性沉降计算的复杂性,建立了无量纲化有限元模型,处理了边界距离和弹性模量变异性问题。在确定性分析基础上,分别运用一阶Taylor展开式随机有限元(简称SFEM)和Monte-Carlo数值模拟随机有限元(简称RFEM)分析了土体弹性模量变异性对基础沉降的影响。结果表明,SFEM低估了基础沉降特征值受弹性模量变异性的影响程度。弹性模量变异系数越大,SFEM对基础沉降均值和标准差低估程度越显著,基础沉降均值随弹性模量空间相关距离逐渐减小。RFEM分析结果则呈现波动性但整体有不断增大趋势,因而基础沉降计算结果更为合理。     

考虑不排水抗剪强度空间变异性的条形基础极限承载力随机分析

目前有关抗剪强度参数随深度变化对地基稳定性影响的研究还不深入。为此,提出了考虑土体不排水抗剪强度均值和标准差随深度变化的地基稳定性随机分析方法。建立了表征不排水抗剪强度空间变异性的不平稳随机场模型,采用Karhunen-Loeve（KL）展开离散随机场。探讨了土体不排水抗剪强度参数空间变异性对地基极限承载力的影响规律,并比较了不排水抗剪强度参数平稳和不平稳随机场模型对地基稳定的影响。以不排水黏性地基稳定随机分析问题为例验证了所提方法的有效性。结果表明：考虑不排水抗剪强度参数空间变异性时,地基极限承载力均值和标准差随相关距离的增大而增大,地基极限承载力对竖直向相关距离更为敏感。地基极限承载力均值随不排水抗剪强度变异系数的增加而减小,标准差随变异系数的增加而增加。不排水抗剪强度变异性对地基失效概率有明显的影响,安全系数较大时,不排水抗剪强度相关距离越小,地基失效概率越小。与不排水抗剪强度参数的不平稳随机场相比,不排水抗剪强度的平稳随机场模型会高估地基极限承载力的变异性,在相同的安全度水平下,当地基的安全系数较低时,平稳随机场模型会导致对地基失效概率的低估;当地基安全系数较高时,平稳随机场模型会导致对地基失效概率的高估。     

软黏土双层地基堆载预压固结空间概率分析

根据工程地质资料,分析固结系数的概率统计值;以双层地基为对象,研究堆载预压固结的概率分析方法和空间概率特性;采用正交试验方法,分析固结参数的不确定性及其分布对固结概率特性的影响;推导固结度均值和方差的解析计算公式,据此分析固结的空间概率特性与自相关距离的相关性;探讨方差折减系数的相关函数选取问题。研究表明,在固结后期双层软黏土地基固结系数的不确定性和概率分布对固结概率特性的影响比较显著,而压缩模量的影响不显著;固结度的均值随着固结系数的变异系数增大而减小,而它的方差则随着固结系数的变异系数增大而增大;固结系数的自相关性对固结概率特性具有一定程度的影响;方差折减系数对于自相关函数形式的选取不敏感。     

基于随机场理论的盾构隧道地表变形分析

采用随机场理论和数值分析相结合的方法,研究土性参数的空间变异性对盾构隧道施工地表变形的影响。利用协方差矩阵分解法建立描述土性参数空间变异性特征的随机场模型,结合Monte-Carlo策略,采用FLAC3D软件分析弹性模量的变异系数、相关距离对地表变形的影响。研究结果表明:土体弹性模量的空间变异性对地表变形规律有着重要的影响,在变形形态和量值上均有不同程度的体现;根据土体弹性模量的相关距离与隧道直径之间比值的大小关系,总结提出3种地表变形模式;最大地表沉降近似服从对数正态分布,且随着土体弹性模量的变异系数和相关距离的增大,最大地表沉降的概率分布越分散,超出沉降监测控制值的概率逐渐增加。     

任意荷载下连续排水边界分数阶黏弹性地基一维固结模型

以基于Caputo分数阶导数的弹壶元件修正Kelvin模型来描述饱和土体一维固结的力学行为,并引入连续排水边界条件,通过Laplace变换,联立求解得到任意荷载下连续排水边界分数阶黏弹性地基有效应力及固结沉降的解析解。采用Laplace逆变换,获得了其时域内的理论解,并分析了梯形循环荷载及施工荷载作用下相关参数对固结沉降的影响。研究结果表明:循环荷载作用下,黏土地基的沉降变化呈振荡增长,且振荡幅值随着边界透水性的增大而增大;分数阶次α增大,使固结前期沉降速率减慢,而在固结后期,α值对沉降的影响正好相反;循环荷载下沉降变化曲线的振荡幅值随着分数阶次α的增大而减小。此外,一维固结沉降的发展还与土体力学参数及荷载参数相关,弹性模量E越大,最终沉降量越小;黏弹性体的延迟时间F越大,固结沉降变化越慢。     

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。     

土工离心模型的空间变异性研究

土工离心模型的试验结果主要由模型箱内空间平均的土性指标影响。基于随机场的原理,研究了土工离心模型中土性指标的空间变异性。根据实测土密度和孔隙率数据,采用相关函数法计算相关距离,并讨论了模型与原型的空间变异性的相似关系。结果表明,离心模型中土性指标的点变异系数相比原位测试值偏小,相关距离则远小于原位土的相关距离。即使点变异系数和相关距离一致,不同比尺的模型对应原型的空间均值变异系数也不相等。给出了空间均值变异系数云图,可用来调整离心模型以满足原型空间均值变异系数的要求。     

连续排水边界条件下土体一维非线性固结解析解

基于Davis和Raymond土体一维非线性固结的假设,通过引入连续排水边界条件研究瞬时荷载下的土体一维非线性固结问题。利用变量代换、分离变量法及Laplace变换得到连续排水边界下土体一维非线性固结问题的解析解,通过退化为Davis双面排水解答初步验证本文解析解的正确性。基于所得解析解,对不同界面参数以及非线性参数对土体固结特性的影响进行分析。结果表明:基于连续排水边界条件的土体一维非线性固结理论的边界条件能严格满足其初始条件,并且其退化结果表明固结方程是适定的,且所得解是连续的。连续排水边界条件下按沉降定义的平均固结度Us随非线性参数Nσ值的增大而增大,而按孔压定义的平均固结度Up随Nσ值的增大而减小。对比土层界面参数对土体固结的影响与非线性参数Nσ对土体固结的影响可知,土层界面参数对土体固结的影响更大。     

结构面力学参数空间变异性表征及边坡可靠性分析

复杂的岩体结构使得岩体参数空间变异性表征与土体参数具有显著的差别。目前针对高度碎裂化/强风化和单结构面占优岩体的参数空间变异性表征及边坡可靠性研究较多,然而关于楔形体和反倾岩体的参数空间变异性表征及边坡可靠性研究非常有限。提出针对楔形体和反倾岩体的边坡结构面力学参数空间变异性表征及可靠性分析方法,并系统统计不同类型岩体力学参数的相关距离和波动范围的取值范围,编写参数空间变异性表征及边坡概率稳定性分析与FLAC3D软件的接口程序,基于反向传播(BP)神经网络构建边坡安全系数与结构面参数随机场向量之间的映射函数关系式,进而采用非侵入式随机有限差分法调查结构面力学参数空间变异性对边坡失效概率的影响规律。结果表明：不同岩体力学参数的相关距离和波动范围的取值范围存在一定的差别,指数型自相关函数是应用最为广泛的理论自相关函数。通过方向模拟和直接蒙特卡洛模拟方法验证提出方法的有效性,表明提出方法具有较高的计算精度和效率,可为楔形体或反倾岩体结构面力学参数空间变异性表征及边坡可靠性分析提供一种有效的途径。此外,忽略结构面参数的空间变异性会高估边坡失效概率,进而导致保守的边坡加固设计方案。     

长江口软土的次固结特性试验研究及应用

对长江口淤泥质软土进行一系列固结实验,研究了荷载、超固结比、土性指标等对软土次固结系数的影响,得出了该区域软土的次固结特性及不同土层的次固结系数。试验结果表明:次固结系数与荷载有关,且随着荷载的增大先增大后减小,最后趋于平稳;次固结系数与最大固结压力有关,且随着超固结比的增大而减小;次固结系数与压缩指数的比值近似为常数0.031;次固结系数与初始孔隙比及初始含水率呈线性关系。提出了一种考虑主次固结同时发生的沉降计算方法,并通过所得次固结系数对横沙围堤进行了沉降预测,与现场监测吻合较好。所提出的计算方法更符合工程实际需要,具有很好的实用价值。试验所得的相关参数及结论对研究长江口软土特性及后期工程的沉降预测具有一定参考意义。     

On the stochastic nature of compact debris flight

The stochastic nature of debris flight is investigated through a series of Monte Carlo simulations based on the debris flight equations for compact debris presented by Holmes (2004). Any given debris flight situation presents a number of uncertainties such as the size of the piece of debris and the time-varying turbulent wind flow. Current debris flight models are largely deterministic and do not account for such uncertainty in input parameters. The simulations presented model the flight of a single spherical particle whose diameter is given by a probability distribution function, driven by a turbulent wind with velocity fluctuations appropriate to the atmospheric boundary layer. The model predicts the mean and standard deviation of the particle flight distance and impact kinetic energy. Results show that introducing uncertainty in particle diameter, horizontal turbulence intensity, or vertical turbulence intensity leads to larger mean values for flight distance and impact kinetic energy, compared to the condition where there is no variability in input parameters. Introducing input parameter variability also leads to variability in flight distance and impact kinetic energy that is quantified in this study. While the simulations presented do not realistically characterize the complex flow within an urban canopy, the results provide significant physical insight into the influence of particle size variability and turbulence on the mean and standard deviation of the flight distance and impact kinetic energy.     

Probabilistic analysis of consolidation that considers spatial variability using the stochastic response surface method

To obtain more accurate and reasonable results in the analyses of soil consolidation, the spatial variability of the soil properties should be considered. In this study, we analyzed the consolidation by vertical drains for soil improvement considering the spatial variability of the coefficients of consolidation. The coefficients for the variation in the vertical and horizontal coefficients of consolidation in Yeonjongdo, South Korea were evaluated, and the probability density function (PDF) was assumed by the Anderson–Darling goodness-of-fit test. Standard Gaussian random fields were generated based on a Karhunen–Loeve expansion, and then transformed using Hermite polynomials in the random field with the log-Gaussian PDF of the coefficient of consolidation. The average degree of consolidation was subsequently calculated using the finite difference method coupled with log-Gaussian random fields. In addition, the stochastic response surface method (SRSM) was applied for the efficient probabilistic uncertainty propagation. A sensitivity analysis was performed for the input parameters of the random field, and the spatial variability was considered using random variables from the Karhunen–Loeve expansion as the input data for the SRSM. The results indicated that when considering the spatial variability of soil properties, the probability of failure for the target degree of consolidation was smaller when the correlation distance was taken into account than when it was not. Additionally, the probability of failure decreased when the correlation distance decreased. Compared with the Monte Carlo simulation (MCS) results, the SRSM analysis can achieve results of similar accuracy to those obtained using the MCS analysis with a sample size of 100,000 (numerical runs), and a third-order SRSM expansion with only 333 numerical runs is sufficient for obtaining the probability with errors less than 0.01.     

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.     

Consolidation Inverse Analysis Considering Spatial Variability and Non-Linearity of Soil Parameters

One-dimensional consolidation inverse analysis based on the stochastic nonlinear consolidation model (SNCM) is discussed in this study. The model is determined from the standard consolidation test results, and represents the nonlinearity and spatial variability of the coefficient of volume compressibility and the coefficient of permeability simultaneously. Furthermore, the inverse analysis method is proposed on the basis of the SNCM and the finite element method mixed with the Monte Carlo simulation. Measured settlement and pore water pressure are used as observation data in the inverse analysis. The method is applied to the consolidation test results of kaolin clay, and its applicability is confirmed firstly. Then the inverse analysis of an actual soft ground is performed. Future consolidation behavior of the ground is predicted, and the spatial variability and the non-linearity of the consolidation parameters are identified. It is clarified in this study that complicated spatial variability and non-linearity of the consolidation parameters could be considered appropriately in the proposed inverse analysis method, and the method gives accurate prediction of consolidation behavior.     

土体固结与溶质运移三维耦合模型

考虑堆场上覆堆积体自重引起的土体固结与溶质运移的耦合效应已成为环境土工领域中的热点问题。在 Biot 固结理论和溶质运移理论相结合的基础上,以孔隙率作为耦合参量,将固结方程与运移方程相联系,考虑土体固结对溶质运移模型参数的影响,建立了溶质在固结变形土体中运移的三维耦合模型。采用多场耦合有限元软件 COMSOL Multiphysics 对模型进行了数值求解。数值模拟结果表明,土体固结变形对溶质运移过程具有较强和持久的阻滞作用,导致溶质运移深度以及污染羽范围的减小,在模拟运移20 a 时,运移距离减小率已高达27．75％,且随着时间的增加而逐渐增大;溶质在水平方向的迁移距离不可忽略,随着横向水力梯度的增大而增大。     

基于改进萤火虫优化算法和考虑空间变异特性的边坡最小安全系数确定研究

在基本萤火虫算法中引入“短视”策略,结合一典型不排水边坡短期稳定问题,考虑土体材料的空间变异特性,构建相应参数的随机场,探讨了萤火虫个体数目N、移动步长β对萤火虫算法搜索效率的影响。结果表明:在其他条件相同的前提下,引入“短视”策略的萤火虫算法较未采取“短视”策略的萤火虫算法结果标准差要小,说明“短视”策略可以提高萤火虫算法的寻优能力;萤火虫个体数目N的增加也会提高算法的寻优能力,但是算法的计算时间T与N^2.1成正比;从安全系数平均值角度来看,移动步长β的合理取值建议介于0~2之间;相同参数设置下萤火虫算法在波动范围较大时搜索到的安全系数标准差较之波动范围较小时的标准差要小,证明了波动范围增大后,边坡稳定最小化安全系数这一优化问题的复杂程度减弱;在考虑土体材料空间变异特性时,要变换算法的参数或者尝试不同的优化算法,以确保找到最小的安全系数及失稳模式。     

软土地基固结与沉降概率分析

本文应用可靠性理论,通过对软土地基土性指标的概率统计处理,对深圳机场场道软基加固试验段的地基沉降量、固结度及差异沉降进行了一次比较完整的概率分析;推导了用砂井排水和超载预压方案加固软基时的沉降量和团结度的概率计算模式;最后得出了固结度、沉降量和差异沉降的概率分析结果。     

Reliable Land Subsidence Mapping Using A Spatial Interpolation Procedure Based on Geostatistics

This paper describes a spatial interpolation procedure for settlements to increase the reliability of subsidence mapping. For this study, a spatial interpolation method based on the ordinary Kriging method was investigated for applicability to a land subsidence area in the northern Kanto plain. First, the spatial variability of settlements using a semivariogram was investigated in detail. For a short distance, the semivariogram of settlements increases. However, after the maximum value at about 35 km, the semivariogram decreases because settlement observation locations are typically arranged around an area in the center of a severe land subsidence zone. Therefore, the semivariogram is only useful up to that maximum value for investigating spatial variability of settlements in a land subsidence area. A spatial interpolation procedure based on Kriging method is proposed. Applicability of that procedure is investigated through comparison of estimations with observations. Drawing both estimations and standard deviations of those estimations represents a reliable land subsidence map. Moreover, to improve the map's accuracy, new allocation for monitoring settlements is undertaken by installation in areas where the estimation standard deviation is greatest. The effect can be investigated using simulated results in the distribution change of the estimated standard deviation.