基于不同地质统计方法的渗透系数场对污染物运移的影响

渗透系数场的空间变异性是影响污染物运移结果的决定因素,而地质统计方法是解决渗透系数空间变异性的主要技术手段。本文利用野外场地实测数据,采用普通克里格法和指示克里格法、顺序高斯模拟法和顺序指示模拟法四种地质统计方法,插值估测和模拟再现随机渗透系数场,进而对比研究四种渗透系数场对大尺度污染物运移的影响。研究结果表明,污染羽的质心位置（一阶矩）主要由渗透系数的平均值来决定;污染羽在空间上的展布范围（二阶矩）主要受渗透系数空间变异方差的影响;条件模拟克服了估计法的平滑效果,较好地再现真实曲线的波动性,渗透系数（ lnK）估计方差与污染羽空间二阶矩随着条件模拟次数的增加而减小,并且顺序指示模拟程度更加明显。     

渗透系数空间变异性研究

水文地质参数的空间变异性是随机理论研究的基础,而渗透系数是最为重要的水文地质参数。国外有关渗透参数空间变异性的研究工作已开展很多,但渗透系数究竟服从什么分布目前尚无确切答案。利用Borden含水层试验数据,对渗透系数的空间变异性进行探讨,结果表明若处理方法得当,渗透系数应服从对数正态分布。同时,还对今后野外开展含水层渗透系数空间变异性试验研究提出几点建议。     

多个相关随机参数的空间变异性对溶质运移的影响

根据给定渗透系数、孔隙度以及吸附系数的概率分布,采用顺序高斯模拟生成相关的多参数随机场的实现,作为地下水流和溶质运移模型的输入参数,对污染物浓度进行随机分析。研究结果表明,与仅考虑渗透系数空间变异性相比,考虑相关的多参数空间变异性导致污染羽的扩散程度有显著不同。当孔隙度与渗透系数呈正相关关系时,会减少污染羽的扩散程度,反之,当孔隙度与渗透系数为负相关关系时,会加剧污染羽的扩散程度。吸附系数也是如此。在考虑吸附系数的空间变异性之后,污染羽的分布表现出拖尾现象。同时考虑渗透系数、孔隙度以及吸附系数空间变异性时,孔隙度非均质性对溶质运移的影响较吸附系数非均质性的影响更大。     

不同地质统计方法在确定渗透系数场中的对比研究

应用地质统计方法研究渗透系数场的空间变异性。利用MMR含水层场地实测数据,通过去类分析、特异值处理、正态变换,逐步逼近研究区渗透系数的稳健变差函数,得到三维渗透系数场的几何各向异性套合模型。在此基础上,采用普通克里格法和指示克里格法、高斯序列模拟法和指示序列模拟法分别对数据进行插值和条件模拟。最后结合具体的地质条件,对四种方法在渗透系数场生成中的应用进行对比分析和评价。     

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。      

考虑参数空间变异性的非饱和土坡可靠度分析

在考虑多个土体参数空间变异性的基础上,提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系,采用拉丁超立方抽样技术产生输入参数样本点,通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场,并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时,边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时,忽略土体参数空间变异性会明显高估边坡失效概率。     

含水层和土壤的随机特征对水分运动的影响

将土壤或含水层的介质参数视为随机分布,建立了饱和非饱和水流运动的随机微分方程,利用随机数值求解方法,得到各种随机参数对水头分布和含水量空间变异性的影响。分析结果表明,随着渗透系数空间变异性和相关尺度的增大,含水层水头分布的变异性增大;对于区域内有抽水井分布的问题,在井点附近区域,z向水流速度空间变异性大,而在井点处变异性较小。当采用Gardner-Russo模型描述非饱和水分特征时,其非饱和土壤介质参数α的变异性对土壤负压和含水量变异性的影响大于饱和渗透系数,土壤含水量越小,含水量的空间变异性越大。初步讨论了根据随机数值方法研究地下水运动问题的可靠性分析方法。     

石川河富平地下水库渗透系数空间变异性研究

渗透系数的空间变异性研究是进行地下水库人工回灌的基础。为研究石川河富平地下水库渗透系数的空间变化规律，引入Box-Cox变换及Johnson变换对库区65组野外双环渗水试验及勘探孔数据进行预处理，并以变异函数为工具，运用传统统计学和地统计学方法分析渗透系数的空间变异性。结果表明：库区等效渗透系数变化范围为0.02～6.44 m/d，既服从对数正态分布也服从Box-Cox变换的正态分布。渗透系数空间相关程度中等，最优拟合模型为高斯模型。基于最优模型，渗透系数插值结果整体上呈现西北方向较大、东南方向较小的特点，在梅家坪镇及南社乡附近最大，范围为2.84～6.44 m/d，空间变异尺度小；在觅子乡、庄里镇附近变化明显，空间变异尺度大；在东上官乡南部最小，均小于0.2 m/d，变异尺度小。空间变异受地形、地貌、地层岩性、水文气象条件、试验点及勘探点分布、人类活动等因素的综合影响。回灌位置应选择在梅家坪镇等渗透系数大，空间变异尺度小及受人为扰动影响小的地段。研究结果可为地下水库建设提供理论参考。     

渗透系数的空间变异性对污染物运移的影响研究

随机水文地质学方法,较传统的确定性方法而言,是解决非均质含水层中水流和溶质运移问题的一种更为合理的手段。据以往研究,假设渗透系数场遵循对数正态分布,利用直接傅立叶变换方法来生成渗透系数随机场。应用基于随机理论的蒙特卡罗方法,来研究渗透系数的空间变异性对污染物运移结果的影响。实例研究表明,污染物在含水层中运移过程中污染羽的展布范围(二阶矩)随着渗透系数空间变异方差的增大而扩大,而污染羽在空间上的质心位置(一阶矩)基本不受方差的影响,仅取决于渗透系数随机场的均值大小。另外还分析了污染羽在各点的浓度变化方差和变异系数分别随渗透系数变异方差的变化状况。     

横观各向同性饱和地基竖向振动的衰减特性

基于提出的横观各向同性饱和多孔介质Biot波动方程的一般解,研究了饱和半空间地基在竖向点源简谐激振荷载作用下地表振动的衰减特征,分析了激振频率以及横观各向同性饱和土介质的各向异性参数和孔隙渗透系数对地表振动特征的影响。计算结果表明,低频和高频激振时,地表位移衰减特性存在明显差异;在饱和土的各向异性参数中,纵向和水平方向动态渗透系数比值和刚度系数比值对地表位移衰减影响最大,这也说明采用各向同性饱和介质的动力学模型不能准确地描述具有明显各向异性特性的饱和土地基的动力特性。     

水力传导度空间变异性的分形模拟研究进展

水力传导度是描述孔隙介质物理特性的重要参数,水力传导度的空间变异性直接影响到水分与溶质在介质中的运移状况。由于基于随机理论的方法难于描述具有多重变异尺度的水力传导度的空间变异性,使得基于分形理论的方法得到了较快发展和应用。详细介绍并评述了分形理论和方法的基本特征及研究进展,水力传导度的空间变异分形与弥散尺度效应的关系及其对溶质运移的影响。     

库水升降条件下考虑饱和渗透系数空间变异性的白水河滑坡渗流变形分析

堆积层滑坡的岩土体渗透系数具有一定的不确定性,且渗透系数是饱和-非饱和渗流分析的重要参数,开展考虑其空间变异性的库岸堆积层滑坡渗流变形分析具有重要意义。以三峡库区中的白水河滑坡为研究对象,基于地面核磁共振技术获取的岩土体渗透系数,分析滑坡体渗透系数的空间变异特征,采用半变异函数方法求得滑坡体渗透系数的竖直波动范围,在此基础上建立渗透系数的非平稳随机场模型。以非侵入式随机有限元的方式开展库水升降两种工况下不确定模型与确定模型的流固耦合模拟,分析两种模型的渗流场、位移变形特征及其差异。结果表明：相比于确定模型,不确定模型孔压改变的滞后性更为明显,且库水下降工况下整体的变形更大,若忽略滑体渗透系数的非平稳空间变异特征将会低估滑坡的实际变形。     

Stochastic analysis of the effect of heterogeneity and fractures on radionuclide transport in a low-permeability clay layer

Deep low-permeability clay layers are considered as safe environments for disposal of high-level radioactive waste. In Belgium, the Boom Clay is a candidate host rock for deep geological disposal. In this study, we analyze the effects of fractures and spatially variable hydraulic conductivity on radionuclide migration through the clay. Fracture geometry and properties are simulated with Monte Carlo simulation. The heterogeneity of hydraulic conductivity is simulated by direct sequential co-simulation using measurements of hydraulic conductivity and four types of secondary variables. The hydraulic conductivity and fracture simulations are used as input for a transport model. Radionuclide fluxes computed with this heterogeneous model are compared with fluxes obtained with a homogeneous model. The output fluxes of the heterogeneous model differ at most 8% from the homogeneous model. The main safety function of the Boom Clay is thus not affected by the fractures and the spatial variability of hydraulic conductivity.     

Stochastic analysis of the effect of spatial variability of diffusion parameters on radionuclide transport in a low permeability clay layer

Most studies that incorporate subsurface heterogeneity in groundwater flow and transport models only analyze and simulate the spatial variability of hydraulic conductivity. Heterogeneity of the other flow and transport parameters are usually neglected. This approach is often justified, but there are, however, cases in which disregarding the heterogeneity of the other flow and transport parameters can be questionable. In low permeability media, for instance, diffusion is often the dominant transport mechanism. It therefore seems logical to incorporate the spatial variability of the diffusion parameters in the transport model. This study therefore analyses and simulates the spatial variability of the effective diffusion coefficient and the diffusion accessible porosity with geostatistical techniques and incorporates their heterogeneity in the transport model of a low permeability formation. The formation studied was Boom clay (Belgium), a candidate host rock for the deep geological disposal of high-level radioactive waste. The calculated output radionuclide fluxes of this model are compared with the fluxes calculated with a homogeneous model and a model with a heterogeneous hydraulic conductivity distribution. This analysis shows that the heterogeneity of the diffusion parameters has a much larger effect on the calculated output radionuclide fluxes than the heterogeneity of hydraulic conductivity in the low permeability medium under study.     

Stochastic groundwater flow analysis in the presence of trends in heterogeneous hydraulic conductivity fields

Due to changes in lithostatic pressure, differential fracturing across bedding planes and irregularities in depositional environments, hydraulic conductivity exhibits heterogeneities and trends at various spatial scales. Using spectral theory, we have examined the effect of trends in hydraulic conductivity on (1) the solution of the mean equation for hydraulic head, (2) the covariance of hydraulic head, (3) the cross-covariances of hydraulic head and log-hydraulic conductivity perturbations and their gradients, and (4) the effective hydraulic conductivity. It is shown that the field of hydraulic head is sensitive to the presence of trends in ways that cannot be predicted by the classical analysis based on stationary hydraulic conductivity fields. The controlling variables for the second moments of hydraulic head are the mean hydraulic gradient, the correlation scale of log-hydraulic conductivity and its variance, and the slope of the trend in log-hydraulic conductivity. The mean hydraulic gradient introduces complications in the analysis since it is, in general, spatially variable. In this respect, our results are approximate, yet indicative of the true role of spatially variable patterns of log-hydraulic conductivity on groundwater flow systems.     

Probabilistic failure analysis of infinite slopes under random rainfall processes and spatially variable soil

Rainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns.