Karhunen-Loeve展开在土性各向异性随机场模拟中的应用研究

研究了Karhunen-Loeve(简称KL)展开在土性参数随机场模拟中的应用,分析了KL展开的特点,针对不规则区域和任意类型协方差函数提出了积分方程的Galerkin数值解法,模拟了土壤渗透系数各向异性随机场。分析结果表明：较低阶Karhunen-Loeve展开能够较好描述随机场的空间结构,与转动带法相比,KL展开法在模拟随机场的各向异性特性方面更具优势;与谱展开法相比,KL展开法具有更优的收敛性。     

纵向弥散作用与渗透介质非均质性定量关系的模拟研究

在地下水污染模拟预报中,弥散参数是很难确定的一个模型参数。因实验室小尺度弥散规律一般不能用于大尺度弥散过程,而野外示踪试验却耗资大、周期长,限制了其实用性。文中利用随机数值模拟手段、基于随机理论的蒙特卡罗方法及序贯高斯模拟技术来生成渗透系数随机场,并研究渗透系数对数场的方差、相关长度以及变异函数类型在不同尺度上对纵向弥散度的影响,进而建立纵向弥散度与随机分布渗透系数场的方差和相关长度的统计定量关系,并与Gelhar理论计算结果进行比较。数值模拟结果表明,经过一定迁移距离后纵向弥散度与随机分布渗透系数对数场的方差和相关长度具有良好的线性统计关系,与Gelhar理论公式表达的关系类型类似。但对于较大的方差,纵向弥散度模拟结果明显大于Gelhar理论计算值,而对于较大相关长度在迁移距离不很大时,纵向弥散度模拟结果明显小于Gelhar理论计算值。本研究可为野外大尺度地下水污染预报模型中水动力弥散参数的确定提供方法借鉴。     

基于原位双环、试坑浸水试验和数值模拟反演的Q3黄土饱和渗透系数对比研究

为准确获取原状Q3黄土的竖向和水平饱和渗透系数,进行了原位、室内试验测试以及数值模拟反演,并应用大型试坑浸水试验检验了所获饱和渗透系数的可靠性。进行了不同内径尺寸的原位双环入渗试验,获取了竖向饱和渗透系数,并应用室内试验测试了竖向和水平饱和渗透系数以及持水曲线;应用COMSOL软件对双环入渗试验进行数值模拟,检验了所测饱和渗透系数的可靠性,利用正交试验获得了最优的竖向和水平饱和渗透系数取值,并利用反演结果对试坑进行数值模拟,将其水分入渗情况与实测值对比。研究结果表明：在现场进行双环入渗试验时选取较大内径的双环获得的竖向饱和渗透系数更为合理。针对双环入渗试验,数值模拟反演所得最优饱和渗透系数在竖向上接近于原位试验所得竖向饱和渗透系数、水平向上接近室内所测水平向饱和渗透系数,竖向饱和渗透系数比水平向饱和渗透系数更加显著地影响水分入渗过程。通过对大型试坑水分入渗情况的验证,检验了反演所得最优饱和渗透系数的可靠性。     

基于饱和渗透系数空间变异结构的斜坡渗流及失稳特征

以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性,对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架,提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡,对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（K_s）各进行了200次条件随机场模拟,基于条件随机场模拟结果进行了有限元渗流和稳定性计算,对每种空间变异结构多次计算结果进行了统计分析.结果表明:本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性,通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟,同时利用现场观测数据对随机场模拟结果进行条件限制,从而提高了随机场的赋值精度;K_s的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.      

衬垫中污染物运移的一维概率分析

衬垫中污染物的运移分析一般采用确定性方法。为了研究渗透系数变异性对污染物运移的影响,基于土层剖面随机场理论,将渗透系数模拟成服从对数正态分布的空间随机场,利用Monte-Carlo和数值积分两种方法进行分析。两种方法得到的结果有很好的一致性。衬垫渗透系数的空间变异性对污染物运移有重要影响。变异系数较大时,衬垫失效概率在前期较大而后期较小,但衬垫底部出现高浓度(相对浓度0.9～1.0)的几率也较高。衬垫的可靠性要综合考虑渗透系数的变异性和渗透系数数值范围的影响。      

甘肃黑方台黄土固结-渗透特性试验研究

室内渗透试验过程中由于土样经过了卸荷回弹,所测得的渗透系数并不是土体真实应力状态下的渗透系数,为此对传统渗透仪进行改装,并以黑方台黄土为研究对象,对不同深度的黄土试样进行不同压力下土的固结-渗透试验,对比分析了土的变形及渗透特征。结果表明,室内常规变水头渗透试验所得黄土渗透系数较固结-渗透试验所测得数据大25-40倍。将常规渗透试验和固结-渗透试验测得的渗透系数应用于SEEP/W软件进行灌溉入渗模拟,将两种模拟结果与实际调查情况进行对比,得到后者与实际情况较一致,可见进行固结-渗透试验得到的试验数据更具有实际应用价值。     

甘肃黑方台黄土固结-渗透特性试验研究

室内渗透试验过程中由于土样经过了卸荷回弹,所测得的渗透系数并不是土体真实应力状态下的渗透系数,为此对传统渗透仪进行改装,并以黑方台黄土为研究对象,对不同深度的黄土试样进行不同压力下土的固结-渗透试验,对比分析了土的变形及渗透特征。结果表明,室内常规变水头渗透试验所得黄土渗透系数较固结-渗透试验所测得数据大25-40倍。将常规渗透试验和固结-渗透试验测得的渗透系数应用于SEEP/W软件进行灌溉入渗模拟,将两种模拟结果与实际调查情况进行对比,得到后者与实际情况较一致,可见进行固结-渗透试验得到的试验数据更具有实际应用价值。     

五彩湾矿区一号矿井地下水水文地质参数获取的试验研究

水文地质参数是研究地下水运动的重要参数,抽水试验是获取水文地质有关参数的一种重要方法。本文以五彩湾矿区一号矿井地下水为研究对象,在分析区域水文地质条件资料的基础上,进行了7组单孔稳定流抽水试验。研究结果表明:对具有供水意义的第四系松散岩类孔隙含水层渗透系数为0.13~2.85 m/d,新近系碎屑岩类裂隙孔隙含水层渗透系数为0.07~0.316 m/d,白垩系碎屑岩类裂隙孔隙含水层渗透系数为0.02 m/d,侏罗系碎屑岩类裂隙孔隙含水层渗透系数为0.009~0.034 m/d。本次实验结果与对比收集资料结果完全一致。     

基于含水层非均质性随机特征的地下水脆弱性评价

由于地质条件的复杂性,人们所能获取的地质和水文地质资料是有限的,这就导致对水文地质条件的认识具有不确定性,其中以含水层非均质特征最为显著,这对地下水脆弱性评价显然会产生显著的影响。考虑含水层的非均质特性,提出具有非平稳随机场空间相关性的地下水脆弱性评价方法。以南京市江宁区中部地区为例,用改进的连续随机增加方法(Successive Random Additional method,简称SRA)生成了渗透系数对数(lnK),具有分维Levy运动统计特征的随机场,模拟含水层渗透系数可能的非均质空间分布,采用DRASTIC方法进行地下水脆弱性评价。结果表明由此方法生成的渗透系数场变化的程度相对传统的普通克里金方法更加剧烈,更加符合复杂分布的非平稳随机场特征,在此基础上建立的地下水脆弱性评价更加符合客观事实,丰富和发展利用随机理论解决地下水环境问题的理论和方法。     

基于遗传算法-支持向量机的滑坡渗透系数反演

求解库岸边坡岩土体的渗透系数是研究滑坡渗流场及多场演化的基础,一般通过原位试验和室内试验求得,但试验成本较高且试验位置具有一定的随机性。本文以三峡库区马家沟滑坡为例,提出一种利用地下水位动态观测资料反演滑坡岩土层渗透系数的方法。具体步骤为:（1）依据滑坡的勘察资料和水位观测数据,构建滑坡数值模型;（2）利用SPSS生成不同渗透系数正交试验组合,并将渗透系数代入数值模型中计算监测井的水位,得到不同渗透系数及其对应的模拟水位数据;（3）应用遗传算法优化的支持向量机构建坡体模拟水位与渗透系数的非线性映射关系,再通过代入实际动态监测水位值求得滑坡岩土层的渗透系数;（4）将求得的渗透系数代入数值模型,用计算的模拟水位与实际观测水位进行对比验证。研究结果表明:遗传算法优化的支持向量机具有良好的学习预测效果,能准确预测渗透系数与水位的关系。该反演方法具有高效、准确的优点,反演结果的精度满足实际应用需要。     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.     

Three-dimensional finite element analysis of spatially variable PVD improved ground

A stochastic approach that investigates the effects of soil spatial variability on stabilisation of soft clay via prefabricated vertical drains (PVDs) is presented and discussed. The approach integrates the local average subdivision of random field theory with the Monte Carlo finite element (FE) technique. A special feature of the current study is the investigation of impact of spatial variability of soil permeability and volume compressibility in the smear zone as compared to that of the undisturbed zone, in conjunction with uncoupled three-dimensional FE analysis. A sensitivity analysis is also performed to identify the random variable that has the major contribution to the uncertainty of the degree of consolidation achieved via PVDs. The results of this study indicate that the spatial variability of soil properties has a significant impact on soil consolidation by PVDs; however, the spatial variability of soil properties in the smear zone has a dominating impact on soil consolidation by PVDs over that of the undisturbed zone. It is also found that soil volume compressibility has insignificant contribution to the degree of consolidation estimated by uncoupled stochastic analysis.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive–frictional soil slope of 30°, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability values, and taking different values of correlation distance in the range of 0.5–15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect of stochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit′s) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties.     

高有机质软土固结特性与机制分析

有机质中的纤维素和腐殖质会影响软土的力学性质,有机质含量越高,软土的力学特性就会越差。为研究高有机质软土的固结特性,通过对不同深度高有机质软土的渗透性、固结以及微、细观结构特征进行试验,并利用分解程度试验结果,分析高有机质软土的特殊渗透、固结和结构特征的形成机制。研究结果表明,不同埋深的高有机质软土渗透系数差别较大,且渗透固结速度较快,基本处于粉砂到粉质黏土数量级;0.5～1.8 m埋深的土层垂直渗透系数小于水平渗透系数,其余深度垂直渗透系数均大于水平渗透系数;分解程度的研究表明,分解程度直接影响高有机质软土的压缩固结特性,低分解程度的土层更容易发生塑性变形。由埋藏从浅到深,结构由絮凝结构逐渐向叠片结构转化,最后转变为集块结构。结合土体的分解程度分析,得出高有机质软土的分解程度高低直接影响高有机质软土的渗透、固结以及结构特性。     

Reliability of passive earth pressure

Passive earth pressure calculations in geotechnical analysis are usually performed with the aid of the Rankine or Coulomb theories of earth pressure based on uniform soil properties. These traditional earth pressure theories assume that the soil is uniform. The fact that soils are spatially variable leads to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire soil mass and does spatial variability in soil properties lead to passive earth pressures that are significantly different from those predicted using traditional theories? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions. The specific case investigated is a two-dimensional frictionless passive wall with a cohesionless drained soil mass. The wall is designed against sliding using Rankine's earth pressure theory. The unit weight is assumed to be constant throughout the soil mass and the design friction angle is obtained by sampling the simulated random soil field. For a single sample, the friction angle is used as an effective soil property in the Rankine model. For two samples, an average of the sampled friction angles is used. Failure is defined as occurring when the Rankine predicted passive resistance acting on the wall, modified by a factor of safety, is greater than that computed by the random finite element method. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety using and the spatial variability of the soil.     

不排水抗剪强度非平稳随机场模拟及边坡可靠度分析

边坡可靠度分析中通常假定采用平稳或准平稳随机场表征土体参数的空间变异性,然而大量现场试验数据表明,土体参数如不排水抗剪强度沿土体埋深常呈现明显的非平稳分布特征,即其均值和标准差均随埋深发生变化,因此亟需发展土体参数非平稳随机场模型及其模拟方法。针对目前不能有效单独模拟土体参数趋势分量和随机波动分量的不确定性,提出了一种有效的不排水抗剪强度参数非平稳随机场模型,并给出了土体参数二维非平稳随机场模拟方法计算流程,同时将新提出的模型与现有非平稳随机场模型及平稳随机场模型进行了系统比较。最后通过不排水饱和黏土边坡算例验证了提出模型的有效性,并揭示了不排水抗剪强度非平稳分布特征对边坡可靠度的影响规律。结果表明：提出模型能够有效地单独模拟土体参数趋势分量和随机波动分量的不确定性,考虑土体参数均值和标准差随埋深增加而增大的特性,可为表征土体参数非平稳分布特征提供了一条有效的途径。此外,与采用非平稳随机场模拟土体参数空间变异性相比,采用常用的平稳随机场模型会低估边坡失效概率,从而造成偏危险的边坡工程设计方案。     

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。     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体(分辨率3.7μm)为研究对象,在空间节点数多达64 000 000的情况下,基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数,并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现,结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD(即10^-13m^2)量级,远低于规则堆叠的圆球结构(>20 000 mD);土壤的迂曲度为1.40~1.60,明显高于规则堆叠的圆球结构。研究结果表明,渗透率大的样品具有较小的迂曲度,这与结构的空间异质性有较强的关系;土壤的渗透率和迂曲度呈现各向异性;在水力梯度一定的前提下,渗透率较大的样品,纵向弥散系数也较大;同时,结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟,可用于土壤多孔介质在孔隙尺度下的水力学特性研究。