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.     

岩溶区地下水数值模拟研究进展

岩溶含水介质的不均一性导致岩溶地下水流动、溶质运移和热量迁移的数学模拟研究成为地下水模拟的难点。本文综述了岩溶区地下水流模拟的几种方法,重点阐述了等效多孔介质法、双重连续介质法和三重介质法的定义、发展过程和适用范围,并回顾了这几种方法的研究成果。从等效多孔介质法到三重介质法,模拟精度不断提高,适用范围也逐渐由大区域实际问题向小区域理论研究过渡。介绍了溶质运移模拟和热迁移模拟的研究方法及实例。溶质运移模拟以对流弥散方程为基础,其中尺度效应是溶质运移模拟的重点研究问题;热量迁移模拟应考虑地下热水密度变化对地下热水运动的影响。溶质运移模拟和热量迁移模拟往往是将迁移模型和已经调试成功的地下水流动模型相耦合,从而达到模拟溶质及热量迁移的目的。由于溶质运移和热量迁移的复杂性,现阶段水流模型多数处于等效多孔介质模型阶段。综合理论及实际应用,指出精确刻画裂隙及管道和注重基础数学算法是岩溶水数值模拟进步的关键。      

大变形黏土防渗层中的污染物迁移和转化规律研究

国内湖泊疏浚污染底泥堆场一般以较厚的黏土层作为主要防渗层,由于在上覆底泥作用下黏土层会发生较大的固结变形,因此,在研究黏土防渗层中的污染物运移和转化规律时,应该考虑土体变形的影响。基于Gibson一维大变形固结理论和饱和多孔介质中的污染物对流扩散方程,建立了二者耦合的可变形多孔介质中污染物的运移和转化模型,其中首次考虑了土体自重和生物降解作用的影响。利用所建立模型的数值解,研究了在可变形黏土防渗层中的污染物运移和转化规律,同时分析了模型中不同项和主要参数的作用和影响。研究结果表明,土体大变形对黏土防渗层中污染物的运移有着较复杂的影响,一方面土体变形会加速污染物的运移;另一方面土体固结带来的渗透性减小会增加污染物的穿透时间,二者的不同作用取决于众多的影响因素,如土层厚度和吸附作用等。研究结果对于评估天然黏土防渗层对污染物的阻隔作用有重要的指导意义。     

Simulation of long‐term consolidation behavior of soft sensitive clay using an elasto‐viscoplastic constitutive model

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto‐viscoplastic constitutive model considers soil‐structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil‐structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so‐called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long‐term performance of earth structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of gas generation in electro‐osmosis consolidation

This paper presents a numerical model for the elasto‐plastic electro‐osmosis consolidation of unsaturated clays experiencing large strains, by considering electro‐osmosis and hydro‐mechanical flows in a deformable multiphase porous medium. The coupled governing equations involving the pore water flow, pore gas flow, electric flow and mechanical deformation in unsaturated clays are derived within the framework of averaging theory and solved numerically using finite elements. The displacements of the solid phase, the pressure of the water phase, the pressure of the gas phase and the electric potential are taken as the primary unknowns in the proposed model. The nonlinear variation of transport parameters during electro‐osmosis consolidation are incorporated into the model using empirical expressions that strongly depend on the degree of water saturation, whereas the Barcelona Basic Model is employed to simulate the elasto‐plastic mechanical behaviour of unsaturated clays. The accuracy of the proposed model is evaluated by validating it against two well‐known numerical examples, involving electro‐osmosis and unsaturated soil behaviour respectively. Two further examples are then investigated to study the capability of the computational algorithm in modelling multiphase flow in electro‐osmosis consolidation. Finally, the effects of gas generation at the anode, the deformation characteristics, the degree of saturation and the time dependent evolution of the excess pore pressure are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

A three‐phase thermo‐hydro‐mechanical finite element model for freezing soils

Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo‐hydro‐mechanical behavior of freezing soils. With the theory of poromechanics, a three‐phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro‐cryo‐suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. Copyright © 2013 John Wiley & Sons, Ltd.     

A dynamic two‐phase flow model for air sparging

Air sparging (AS) is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air/oxygen through an air sparging well below the zone of contamination. Characterizing the mechanisms governing movement of air through saturated porous media is critical for the design of an effective cleanup treatment system. In this research, micromechanical investigation was performed to understand the physics of air migration and subsequent spatial distribution of air at pore scale during air sparging. The void space in the porous medium was first characterized by pore network consisting of connected pore bodies and bonds. The biconical abscissa asymmetric concentric bond was used to describe the connection between two adjacent pore bodies. Then a rule‐based dynamic two‐phase flow model was developed and applied to the pore network model. A forward integration of time was performed using the Euler scheme. For each time step, the effective viscosity of the fluid was calculated based on fractions of two phases in each bond, and capillary pressures across the menisci was considered to compute the pressure field. The developed dynamic model was used to study the rate‐dependent drainage during air sparging. The effect of the capillary number and geometrical properties of the network on the dynamic flow properties of two‐phase flow including residual saturation, spatial distribution of air and water, dynamic phase transitions, and relative permeability‐capillary pressure curves were systematically investigated. Results showed that all the above information for describing the air water two‐phase flow are not intrinsic properties of the porous medium but are affected by the two‐phase flow dynamics and spatial distribution of each phase, providing new insight to air sparging. Copyright © 2012 John Wiley & Sons, Ltd.     

基于溶质运移模拟的某化工场地污染物对拟建水库污染风险预测

溶质运移模拟是污染风险预测的一种有效手段。本研究为查明研究区内某有机污染场地作为污染源对拟建水库的影响,基于对区内流场的精确测量,建立了准确的地下水流模型和化工厂泄露有机污染物的溶质运移模型,预测分析了研究区拟建水库修建前、后地下水流场及污染物迁移情形的变化。模拟结果表明：水库和周边两种设计水头的截渗沟建成后,改变了自然条件下的流场,形成水库向截渗沟排泄、截渗沟向周边排泄以及水库和周边区域均向截渗沟排泄两种地下水流场。某些污染羽扩散范围虽比自然条件下有所增大,但向水库方向的扩散均未超出300 m,不会对水库水质构成污染风险。     

波浪作用下考虑海床变形影响的溶质运移数值模拟

波浪会促进海水中溶质向海底沉积物运移,但已有研究大多未考虑海床（海底沉积物）变形效应的影响。为揭示波浪作用下海床土变形对溶质运移过程的影响机制,构建了考虑海床土变形影响的溶质运移计算模型,对波浪作用下溶质向砂质海底沉积物中的运移过程进行模拟。结果表明:海床土变形会增大孔隙水流速,进而增大溶质纵向水动力弥散系数,增强溶质运移的机械弥散作用,促进溶质向沉积物中运移;考虑海床变形时的溶质最大纵向水动力弥散系数可达不考虑海床变形时的8.5倍,约为分子扩散系数的545倍;海床土剪切模量越小,土体变形效应越明显,对溶质运移过程的影响越大;海床土饱和度的降低,会进一步加速波浪作用下溶质向海底沉积物的运移过程。     

Recharging of contaminated aquifer with reclaimed sewage water

About 40% of the water supply of Cairo, Egypt, is drawn from a groundwater reservoir located southeast of the Nile Delta. Several thousand shallow wells supply drinking water to the farmers from the same groundwater reservoir, which is recharged by seepage from Ismailia canal, the irrigation canal network, and other wastewater lagoons in the same areas. Sewage water lagoons were located at the high ground of the area, recharging contaminated water into the aquifer. Since the groundwater in this area is used for drinking purposes, it was decided to treat the sewage water recharging the aquifer for health reasons. In this paper a solution to the problem is presented using an injection well recharging good quality water into the aquifer. A pumping well located at a distance downstream is used to pump the contaminated water out of the aquifer. A three-dimensional solute transport model was developed to study the concentration distribution with remediation time in the contaminated zone.     

An operator‐split ALE model for large deformation analysis of geomaterials

Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.     

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

A two‐scale modeling of solute transport in double‐porosity (DP) media under unsaturated water flow conditions is presented. The macroscopic model was developed by applying the asymptotic homogenization method. It is based on theoretical and empirical considerations dealing with the orders of magnitude of characteristic quantities involved in the process. For this purpose a physical model that mimics the behavior of DP medium was built. The resulting two‐equation model relies on a coupling exchange term between micro‐ and macro‐porosity subdomains associated with local non‐equilibrium solute concentrations. The model was numerically implemented (Comsol Multiphysics^®) to simulate the macroscopic one‐dimensional physical process taking place into the porous medium of 3D periodic microstructure. A series of dispersion experiments of NaCl solution under unsaturated steady‐state flow conditions were performed. The experimental results were used first to calibrate the dispersion coefficient of the model, and second to validate it through two other independent experiments. The excellent agreement between the numerical simulations and the measurements of the time evolution of the non‐symmetrical breakthrough curves provides a proof of predictive capacity of the developed model. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Numerical analysis of the transport and restoration schemes of aqueous oil in soils

 On the basis of field investigations and tests, the authors developed a coupling model of water and solute movement to quantitatively analyse the effects of climate condition, irrigation mode, chemical reactions and restoration schemes on aqueous oil (effective oil) distribution using the finite difference method. It is concluded from this study that the effect of strong adsorptive forces between aqueous oil and the soil matrix is the distribution of aqueous oil in the plough layer rather than its migration to groundwater. In addition, restoration schemes involving clean-wastewater mixing irrigation and crop-type adjustment may greatly reduce the aqueous oil concentrations, but clean surface water or groundwater irrigation must be used for complete restoration of the contaminated soils. Received: 26 April 2000 · Accepted: 21 August 2000     

考虑溶质浓度影响的热-水-应力-迁移耦合模型及数值模拟

高放射性核废料地质处置库围岩中地下水的密度因溶质浓度不同而发生变化,这将影响到饱和-非饱和孔隙介质中近场和远场的热-水-应力耦合过程, 同时温度场、应力场也要对地下水中的核素及矿物质迁移产生作用。考虑这两个因素,建立和引入了相关的应力平衡方程、水连续性方程、能量守恒方程和渗透迁移方程,并研制出了对应分析孔隙介质中热-水-应力-迁移耦合问题的二维有限元程序。通过对一个假定的核废料地下处置库在核素泄漏后多场耦合过程的数值计算,考察了近场围岩中的温度、应力、孔隙水压力、核素浓度的分布及随时间的变化。结果初步显示了所建模型及程序可模拟热-水-应力-迁移耦合现象,因而具有一定的实用性。     

砂箱模型模拟休耕田区以砂桩补注地下水对溶质传输影响

水田在休耕期间蓄水,除了可维持水田原有之生态机能外,亦可增加土壤水分涵养与补注地下水.利用砂箱来模拟休耕田区中打入砂桩以补注地下水时,砂桩存在对灌溉水中之溶质在土壤中传输之影响.由试验结果得知当砂桩贯穿牛踏层时可增加水分入渗速率约40倍,相对的,砂桩亦加速溶质在不同土壤层间之传输速率,尤其在牛踏层下方之土壤为砂层时,其影响更为显著.因此,蓄水过程中需注意水源之品质,以避免土壤与地下水受污染.     

地下水开采—地面沉降模型研究

本文建立三维流支－－一维非线性固结地面沉降模型,在混合井流,降雨滞后补给,初始水头形成,人为边界刻画,水流－固结耦合及软土层固结滞后于地下水开采层水头变化等方面有所改进,所建模型用于苏州市,模拟出若干地面沉降重要特征,地面沉降中心偏离地下水漏斗中心,地面沉降动态滞后于地下水的水头动态,软土层渗透系数随固结过程的变化及头在软土层中的传递特征。     

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory,implementation, and application

Although numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F²Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.