Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

Water flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

One‐dimensional contaminant transport through a deforming porous medium: theory and a solution for a quasi‐steady‐state problem

Contaminant migration through soil is usually modelled mathematically using the dispersion–advection equation. This type of model finds application when planning the remediation of contaminated land, predicting the movement of polluted groundwater and designing engineered landfills. Usually the analysis assumes that the porous media through which the contaminant migrates is stationary. However, the construction of landfills on clay soils means that the soil beneath the landfill will undergo time‐dependent deformation as the soil consolidates. To date, there are no published data on the effect a deforming porous media may have on contaminant transport beneath a landfill; indeed, there appears to be no theory of contaminant migration through a deforming soil. In this paper, a one‐dimensional theory of contaminant migration through a saturated deforming porous media is developed based on a small and large strain analysis of a consolidating soil and conservation of contaminant mass. By selection of suitable parameters, the new transport equation reduces to the familiar one‐dimensional dispersion–advection equation for a saturated soil with linear, reversible, equilibrium controlled sorption of the contaminant onto the soil skeleton. Analytic solutions to a quasi‐steady‐state contaminant transport problem for a deforming media are presented, and a preliminary assessment made of the potential importance of soil deformation on the results of a contaminant migration analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

The effects of aquifer heterogeneity on the 3D numerical simulation of soil and groundwater contamination at a chlor-alkali site in China

The simulation of groundwater flow and solute transport at contaminated sites often neglects the important influence that aquifer heterogeneity can have on the sub-surface distribution of contaminants. In this paper, the method of transition probability for geological statistics (T-PROGS) included in the Groundwater Model System (GMS) was applied to a chlor-alkali-contaminated site that was sampled with 68 soil borings and 15 groundwater monitoring wells. A 3-D groundwater numerical model and solute transport model was developed that was constrained by soil and groundwater data from the site. The spatial distribution of chloroethylene concentrations was simulated for a number of times using the levels measured in the field as a baseline. The results of these simulations showed that shapes and distribution of contaminant plumes are irregular both vertically and horizontally. The solute-transport simulations indicated that much of the contamination will preferentially move in groundwater through silt and fine-sands whereas flow is largely blocked in clays. Consequently, fine sand and silts become the most seriously polluted zones at the site, whereas, areas underlain by clays are largely uncontaminated. Heterogeneous lithologies beneath a site increase the complexity of coupling simulations of soil and groundwater.     

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

Simulation of polychlorinated biphenyls transport in the vadose zone

Polychlorinated biphenyls (PCBs) are the main constituents of clophen (the liquid of the electric transformers and capacitors) and have been characterized as potential human carcinogens. PCBs can be a hazardous contaminant of soil and groundwater. We used the mathematical model variably saturated 2D flow and transport (VS2DT model) to simulate the transport of PCBs from the soil surface to groundwater for a time period of 30 years. We also used a mathematical model to simulate the colloid-facilitated PCB transport, under saturated flow conditions. The results showed that PCBs dissolved in water cannot be transported to large depths in unsaturated soils, because of their strong sorption onto soil and low solubility in water. For soils with very low or no organic matter content, PCB transport is much faster and the probability of groundwater contamination is much higher. PCBs can partition to colloids originating from dissolved organic matter in groundwater. Colloid-facilitated PCB transport is faster compared to PCB transport in aqueous solution with no colloids present.     

Theoretical investigation of the effects of consolidation on contaminant transport through clay barriers

Consolidation of clayey contaminant barriers such as landfill liners has been postulated as a cause of early breakthrough of contaminants. In this paper we theoretically investigate this proposition. For this purpose a sophisticated one‐dimensional, large‐deformation model of coupled mechanical consolidation and solute transport is employed. This new model is a generalization of existing coupled consolidation and solute transport models described in the literature. It takes into account both non‐linearities in geometry as well as constitutive relations. The latter relate the compressibility, hydraulic conductivity and coefficient of effective diffusivity to the deformation of the soil. The model is applied to a case study of a clay liner and geomembrane system. Results obtained from numerical solution of the model equations are compared with those from various simplified models, including a ‘diffusion only’ (i.e. a rigid soil) model traditionally used in contaminant barrier design. For barriers incorporating low compressibility soils (as for many well compacted clays), there is little difference between contaminant transit (i.e. breakthrough) times predicted by the two models. However, for contaminant barriers incorporating more compressible soils, consolidation is shown to significantly accelerate transport. These results indicate the potential importance of accounting for the effects of soil consolidation and highlight the limitations of existing models when modelling solute transport through composite barriers utilizing soft soils. Based on these limited results, we suggest a possible way of taking into account soil consolidation using simplified models. Copyright © 2008 John Wiley & Sons, Ltd.     

土壤水分运动空间变异性尺度效应的染色示踪入渗试验研究

探讨了土壤水非均匀流动特性和描述方法,通过染色示踪剂调查了三种试验尺度条件下非均匀流动模式,并采用随机层叠模型对不同实验尺度条件下非均匀流动模式进行了模拟。随机层叠模型中具有对数正态分布性质的随机层叠发生器被用来描述水流入渗过程,不同的方法被用于模型参数求解。试验观测和模拟计算结果均表明,尺度特性是非均匀流动的重要影响因素之一,准确的描述不同研究尺度下的非均匀流动特征,须同时考虑流动在水平和垂直方向的变异性。随着研究尺度的增加,流动的非均匀性变异程度更加明显。     

Analytic solutions to the advective contaminant transport equation with non-linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright © 1999 John Wiley & Sons Ltd.     

非均质土体中盾构隧道开挖面支护力上限分析

基于对数螺旋破坏模式,考虑黏土的非均质特征,采用极限分析上限法推导了盾构隧道掌子面支护力计算公式,通过优化计算得到了不同条件下的最优上限解。采用该破坏模式与已有的模型试验、工程实例进行对比,验证了在非均质土中采用双对数螺旋极限分析上限法的适用性;同时详细分析了在土体不同参数条件下,隧道掌子面支护力、滑动面范围的变化趋势以及工程影响,结果显示在非均质土中,掌子面支护效率的主导因素是初始黏聚力与掌子面超前核心土,最后通过归一化处理得到了非均质土中极限支护力的设计推荐图,可为工程中初步确定盾构隧道掌子面支护压力提供理论依据。     

Delineation of groundwater protection zones based on tracer tests and transport modeling in alluvial sediments

 Regulations aiming to protect exploitable groundwater resources were edicted in Belgium a few years ago. Therefore, prevention and protection zones are defined by law and must be determined practically around each pumping well or spring, based on local hydrogeological conditions. The determination of hydrodynamic and hydrodispersive parameters, characterizing the local flow and transport properties of the aquifer, requires pumping and tracing tests. The interpretation of these field experiments, considering the heterogeneity of the geological layers, is performed through the use of numerical FEM simulations of the groundwater flow and pollutant transport conditions in a deterministic framework. After calibration of the model on experimental measurements, multiple simulations with contaminant injections at various points of the modeled domain allow the determination of the transfer time of the pollutant in the studied aquifer whilst taking the updated heterogeneity into account. On the basis of the computed transfer times in the saturated zone, the various prevention and protection areas can be assessed based on provisions of the law. Received: 27 June 1997 · Accepted: 29 July 1997     

考虑土体固结变形的污染物运移模型

土体的固结压缩变形对污染物的运移具有重要的影响,而目前国内关于污染物在变形多孔介质中运移规律的研究尚处于空白,在国外也是近几年才有人开始这方面的研究工作。在Biot固结理论和污染物运移理论相结合的基础上,提出了污染物在黏土防渗层中迁移转化的一维数学模型,该模型的最大特点是考虑了土体受力变形对污染物运移的影响,在合理简化的基础上给出了模型的解析解,并将计算结果与太湖疏浚污染底泥堆场的实测结果进行了比较分析,模拟计算的结果在一定程度上能够反映实际土层中污染物的运移情况。     

Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments

Spatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required. Copyright © 2011 John Wiley & Sons, Ltd.     

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。      

Model for analysis of fiber-reinforced clayey soil

Fiber-reinforced soils have many applications in improving the response of clayey soils. In this paper, an analytical model for the analysis of fiber-reinforced soil in the framework of modified cam clay model is presented. The analytical model is verified using experimental results from the standard undrained triaxial tests with pore water pressure measurements. Tests have been conducted on clayey soil specimens reinforced with randomly oriented discrete coir fibers with different percentages of fiber contents. Numerical simulations of triaxial compression tests on fiber-reinforced clay specimens were also performed. Results are presented in the form of stress vs. strain curves for plain soil as well as fiber-reinforced soil for various fiber contents based on the model developed. The results demonstrate the applicability of proposed analytical model in predicting the stress strain response of fiber-reinforced soils.     

粗颗粒土的应力应变特性及其数学描述研究

大型三轴试验研究了粗颗粒土的应力应变特性及邓肯-张模型的适用性。试验结果表明粗颗粒土表现出明显的低围压下体胀高围压下体缩的体变性质,邓肯-张模型在描述粗颗粒土的体变特性方面存在不足。基于试验结果提出了新的体变描述公式,在未增加模型参数的条件下提出了邓肯-张模型的改进模型。采用改进模型对多种粗颗粒土三轴试验结果进行了预测,结果初步表明改进模型能够更好地模拟粗粒土的体变特性。     

基于FEFLOW的三维土壤-地下水耦合铬污染数值模拟研究

`土壤-地下水耦合数值模拟是定量刻画水流和溶质运移的主要手段。现有大范围场地尺度的研究受到数据采集难度及模拟计算量的限制,多是将土壤和地下水分成两个系统,这种方式不利于模型之间的计算反馈,易出现计算误差,因此将土壤和地下水作为整体系统研究具有重要意义。为精确刻画实际场地土壤-地下水系统中污染物迁移规律,揭示变饱和反应溶质迁移模型的参数敏感性,以某铬污染场地为研究对象,基于现场试验及前人研究所获数据,采用Galerkin有限元法建立三维土壤-地下水模型,定量描述六价铬在土壤-地下水中的迁移规律。在此基础上,通过改变补给条件,研究潜水面在土壤-地下水系统中的波动。并讨论阻滞系数和反应常数对溶质运移的影响。结果表明:在土壤中,污染物最大水平迁移距离为场地东南侧300 m;地下水中污染晕最大分布面积约为1.632 km2;垂向上土壤中的六价铬仅需15.6 h即可下渗至潜水面,第6天贯穿含水层。当潜水面随着补给量变化而波动时,地下水中六价铬会随水流进入土壤,影响土壤中污染分布。对溶质运移参数的讨论显示,当反应常数由0增大至10?6 s-1时,迁移出场区边界时地下水中污染物浓度约减少2000 mg/L,较难迁移至涟水河。基于FEFLOW的数值模型,能够解决各系统之间交互性差的问题,提供较为精确的模拟结果。     

Lead contamination of soil along road and its remediation

With a rapid development of road systems and an associated drastic increase in number of automobiles, the traffic has induced more and more obvious environmental pollution such as noise, dust, emission and heavy metal contamination. Lead, as one of the most harmful heavy metal contaminants, can execute a significant impact on soil quality and plant growth, depending on its form, as well as its transport and accumulation in soil. This paper describes the source and characteristics of Pb contaminant in soil along a road, and reviews the results of research on remediation of Pb-contaminated soils, aiming at identifying promising approaches to soil remediation along roads.     

基于太沙基土拱效应考虑基质吸力影响的松动土压力计算模型

传统的土拱效应理论是基于上覆土体为无黏性土或饱和黏性土建立的,但非饱和状态是实际土体的常见情形,其力学特性受自然环境变化的影响。针对这一问题,基于太沙基（Terzaghi）平面土拱效应分析模型和土体单元主应力轴旋转理论,建立了考虑基质吸力的土拱效应松动土压力分析模型。依次给出了基质吸力在上覆土体内呈均匀分布、梯形分布、正三角分布和倒三角分布时的松动土压力和侧压力系数表达式。为验证该分析模型的正确性,采用FLAC建立了Trapdoor数值模型,理论计算与FLAC模拟结果非常吻合。最后,着重分析了上覆土体的饱和度、厚度、Trapdoor宽度、地下水上升和降雨等因素对松动土压力的影响。研究发现,松动土压力随土体饱和度先减小后增大,当达到进气值所对应的饱和度时松动土压力最小。     

Pesticide transport and transformation modeling in soil column and groundwater contamination prediction

Pesticide transport and transformation were modeled in soil column from the soil surface to groundwater zone. A one dimensional dynamic mathematical and computer model is formulated to simulate two types of pesticides namely 2,4-dichlorophenoxy acetic acid and 1,2-dibromo 3-chloro propane in soil column. This model predicts the behavior and persistence of these pesticides in soil column and groundwater. The model is based on mass balance equation, including convective transport, dispersive transport and chemical adsorption in the phases such as solid, liquid and gas. The mathematical solution is obtained by finite difference implicit method. The model was verified with experimental measurements and also with analytical solution. The simulation results are in good agreement with measured values. The major findings of this research are the development of the model which can calculate and predict the concentration of pesticides in soil profiles, as well as groundwater after 4, 12, 31 days of pesticide application under steady state and unsteady water flow condition. With the results of this study, the distribution of various types of pesticides in soil column to groundwater table can be predicted.     

Identifying variably saturated water-flow patterns in a steep hillslope under intermittent heavy rainfall

The objective of this paper is to identify water-flow patterns in part of an active landslide, through the use of numerical simulations and data obtained during a field study. The approaches adopted include measuring rainfall events and pore-pressure responses in both saturated and unsaturated soils at the site. To account for soil variability, the Richards equation is solved within deterministic and stochastic frameworks. The deterministic simulations considered average water-retention data, adjusted retention data to account for stones or cobbles, retention functions for a heterogeneous pore structure, and continuous retention functions for preferential flow. The stochastic simulations applied the Monte Carlo approach which considers statistical distribution and autocorrelation of the saturated conductivity and its cross correlation with the retention function. Although none of the models is capable of accurately predicting field measurements, appreciable improvement in accuracy was attained using stochastic, preferential flow, and heterogeneous pore-structure models. For the current study, continuum-flow models provide reasonable accuracy for practical purposes, although they are expected to be less accurate than multi-domain preferential flow models. Electronic Publication