Steady infiltration from buried point source into heterogeneous cross‐anisotropic unsaturated soil

The paper presents the analytical solution for the steady‐state infiltration from a buried point source into two types of heterogeneous cross‐anisotropic unsaturated half‐spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half‐space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross‐anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd.     

半无限含水层中带衬砌隧洞渗流解析研究

现有关于半无限含水层中隧洞渗流的解析解不能考虑衬砌部分排水的特性。假定土体和衬砌均为饱和均匀连续介质,采用土体与衬砌分算;利用复变函数解决孔口问题基本方法,对土体采用共形映射坐标变换,将土体中的渗流方程转换为与衬砌部分类似的二维Laplace方程圆环域的Dirichlet问题;通过Fourier解法,根据边界条件并利用流量连续条件,求得半无限空间中带衬砌隧洞渗流量和衬砌周边水头解析解答。分析了径深比、土体与衬砌渗透系数相对值、内壁水压力等因素对渗流量和衬砌周边水头的影响,并与数值算例进行了比较。结果表明,对浅埋隧洞该解析解仍具有较好的精度,是简便、实用的计算方法。     

Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media

Numerical models of groundwater flow require the assignment of hydraulic conductivities to large grid blocks discretizing the flow domain; however, conductivity data is usually available only at the much smaller scale of core samples. This paper describes a geostatistical model for hydraulic conductivity at both the core or point scale and that of grid blocks. Conductivity at the block scale is obtained empirically as a spatial power-average of point scale values. Assuming a multivariate Gaussian model for point log-conductivity, expressions are derived for the ensemble mean and variance of block conductivity. The expression for the ensemble mean of block scale conductivity is found to be similar to an expression for the ensemble effective conductivity of an infinite field derived analytically by earlier authors. Here, block conductivities obtained by power averaging are compared with effective conductivities obtained from a numerical flow model and are found to be in excellent agreement for a suitably chosen averaging exponent. This agreement deteriorates gradually as the log variance of conductivity increases beyond 2. For arbitrary flow field geometry and anisotropic conductivity covariances, the averaging exponent can be calibrated by recourse to numerical flow experiments. For cubic fields and an isotropic spatial covariance, the averaging exponent is found to be 1/3. In this particular case, it was found that flow field discretization at the block scale through local averaging of point conductivities gave similar results to those obtained directly using a point scale discretization of the flow field.     

Analytical solution for transient groundwater flow during slug test in vertical cutoff walls

An analysis method for transient groundwater flow during slug tests performed in vertical cutoff walls is presented. The analytical solution for evaluating hydraulic conductivity of vertical cutoff walls is derived by applying the method of images to the previously developed analytical solution that is exclusively applicable to an infinite aquifer. Two distinct boundary conditions are considered to account for the configuration of the vertical cutoff wall: the wall‐soil formation interfaces with or without the existence of filter cakes, that is, constant‐head boundary and no‐flux boundary conditions. A series of type curves is constructed from the analytical solution and compared with those of a partially penetrated well within an aquifer. The constant‐head boundary condition provides faster hydraulic head recovery than the aquifer case. On the other hand, the no‐flux boundary condition leads to a delayed hydraulic head recovery. The greater the shape factor and well offset from the center of the cutoff wall, and the smaller the width of the cutoff wall, the greater the effect of the boundary condition observed in the type curves. This result shows the significance of considering proper boundary conditions at the vertical cutoff wall in analyzing slug tests. Copyright © 2014 John Wiley & Sons, Ltd.     

均质非饱和土一维稳态流水头垂直分布的解析解

渗流场水头分布计算是进行渗流量和渗流水力坡降计算的基础,准确、有效地求取渗流场水头分布是渗流计算的关键环节。对均质非饱和土体一维稳态流的流动方程进行分析,考虑到渗透系数是与基质吸力相关的函数,通过数学变换,给出了稳定渗流场的解析通式,并基于渗透性函数中的Gardner模型,给出了非饱和土一维稳态流水头垂直分布的解析解。该解析通式表明,均质非饱和土一维稳态流水头垂直分布主要受地表水头、深度和流动率3个因素控制。分别计算了一维稳态蒸发条件下粉土和黏土两种典型土类水头沿垂直方向的分布。计算结果表明：稳态蒸发条件下粉土层和黏土层内的水头分布表现出相似的变化规律,即自地表至地下水位处随着土层深度的增加,水头分布呈现出加速递减的趋势;在相同的蒸发条件下,对于相同深度处的黏土和粉土而言,黏土层内水头更高些;对同一种土类而言,在较大的蒸发状态下同一深度处土层内水头更高。反之,则较低。     

Analysis of soil consolidation by vertical drains with double porosity model

The soil around a drain well is traditionally divided into smeared zone and undisturbed zone with constant hydraulic conductivity. In reality, hydraulic conductivity of the soil changes continuously and it may not be always appropriate to approximate its distribution with two zones. In this study, the horizontal hydraulic conductivity of the soil is described by an arbitrary function of radial distance. The horizontal flow under equal strain condition is analysed for a soil–drain system with a circular or regular polygonal boundary. It is found that the horizontal flow can be generally characterized with a linear equation in which the flow rate of water through soil–drain interface is proportional to the difference between the average excess pore pressure in the soil and the excess pore pressure in the drain well. The water exchange between the drain and the soil is analogous to that between fractures and matrix in a double porosity system, a popular conceptual model of fracture rocks. On the basis of this characterization, a simplified approach to analyse soil–drain systems is developed with one‐dimensional double porosity model (DPM). Analytical solutions for both fully and partially penetrating drains are derived. The solution for partially penetrating drains is compared with both numerical and approximate analytical results in literature. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

快速测量非饱和土渗透系数的湿润锋前进法适用性研究

非饱和土渗透系数函数是非饱和土体渗流分析中必不可少的参数。然而非饱和土渗透系数函数测量非常困难,其中稳态法测量范围过于狭小,而瞬时截面法耗时动辄数月,难以应用。为此,提出了湿润锋前进法,有望在一周内测得渗透系数函数。采用数值模拟手段检验湿润锋前进法的测量精度和适用范围。数值模拟结果显示：对于砂土、粉土、黏土,湿润锋前进法得到的渗透系数函数均与输入的理论渗透曲线一致,但测量范围限于高吸力范围（大于进气值）。此外,还采用瞬时截面法计算了渗透系数函数,结果表明：瞬时截面法计算的渗透系数在理论渗透曲线附近波动,其精度取决于监测截面的间距,间距越大,精度越低。在给出的20、60、100 mm这3种间距中,20 mm间距时计算得到的渗透系数精度最高,但与湿润锋前进法的精度仍有一定差距。因此,湿润锋前进法是一种可靠的能够快速得到渗透系数函数的测量手段。     

Performance of reinforced,DMM column-supported embankment considering reinforcement viscosity and subsoil’s decreasing hydraulic conductivity

It has been widely accepted that reinforcement made of polyethylene and polypropylene is susceptible to creep and soil’s hydraulic conductivity varies with its void ratio. However, unfortunately there is no available sensitivity analysis on time-dependent embankment behaviour taking either reinforcement viscosity or time varying hydraulic conductivity of subsoil into consideration. The influence of geosynthetic reinforcement viscosity and decreasing hydraulic conductivity with consolidation on the time-dependent performance of embankments with floating columns is investigated using a fully 3D coupled model. For an embankment at the working height corresponding to a post-consolidation polypropylene geotextile strain of about 5%, it is shown that the assumption of constant hydraulic conductivity and the failure to consider the viscous behaviour of geosynthetic reinforcement can underestimate time-dependent embankment deformations (including differential crest settlement and horizontal toe movement). The effects of factors including the foundation soil, reinforcement stiffness, column stiffness, column spacing, column type (floating and fully penetrating), and construction rate, on the time-dependent behaviour of column supported embankments are explored.     

Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于现场双管试验确定弱透水层水力参数的方法

弱透水层水力参数对基础工程设计、建设和地下水资源评价、地下水污染预测具有重要意义。现提出一种现场确定含水层系统中弱透水层水力参数的钻孔双管试验方法。利用麻花钻钻孔,到达地下水位线以下揭露到目的层位后布设外管,以起到护壁防止土层塌孔的作用。在外管内通过锤击的方式将内管嵌入到目的层中,使其下部管中有一定厚度的土样作为现场固定试验土柱。待内外管中地下水位稳定后迅速加高内管水头,并通过马里奥特瓶装置保持定水头。建立钻孔双管试验土柱的数学模型,推导了土柱顶底面单位面积流量随时间变化的解析解,将其无量纲化后作出标准曲线。作为该方法应用的实例,在长江下游三角洲苏锡常冲积平原的常州天宁区德安医院附近的空旷场地进行了专门的钻孔试验。确定了该地区的细砂质粉土和粉质黏土的渗透系数和贮水率分别为：K=1.66×10?6 m/s,?s =8.21×10?3 m?1;K=6.06×10?7 m/s,?s =2.26×10?3 m?1。结果表明,该方法对于现场确定弱透水层的水力参数有较好的适用性。     

A coupled analysis of cavity and pore volume changes for pulse tests conducted in soft clay deposits

This paper presents a new interpretation method for pulse tests, a field permeability test that allows for rapid measurements of hydraulic conductivity k in aquitards. This new method applies to soft clay deposits. To initiate a pulse test, a known volume of water is injected into the sand filter of a monitoring well isolated by a packer. The resulting pressure increase yields an outward movement of the sand filter cavity wall. After presenting the usual interpretation methods and their limits, this paper proposes a new interpretation method based on a coupled analysis of the pressure and displacement fields in the soil using the Biot–Darcy formulation. A series of analytical and numerical non‐dimensional velocity graphs, normalized plots of the mean hydraulic head difference versus its rate of change, are given. For a linear elastic material, these type curves show relatively small variations with the sand filter aspect ratio and the Poisson ratio of the tested clay. The type curves are also found to be independent of the clay compressibility (m_v) and k, an important result. A series of pulse tests conducted in a soft marine clay deposit near Montreal, Canada, are interpreted with the proposed method. The hydraulic conductivity values calculated from these tests are closely correlated with independent estimates obtained using long‐duration variable‐head tests. Compared with previous interpretation methods, the proposed method allows soil volume changes to be reconciled with cavity expansion phenomena and the range of type curves available for the interpretation of test data to be constrained. Copyright © 2013 John Wiley & Sons, Ltd.     

Groundwater contaminant source identification based on QS-ILUES

When groundwater pollution occurs,to come up with an efficient remediation plan,it is particularly important to collect information of contaminant source(location and source strength)and hydraulic conductivity field of the site accurately and quickly.However,the information can not be obtained by direct observation,and can only be derived from limited measurement data.Data assimilation of observations such as head and concentration is often used to estimate parameters of contaminant source.As for hydraulic conductivity field,especially for complex non-Gaussian field,it can be directly estimated by geostatistics method based on limited hard data,while the accuracy is often not high.Better estimation of hydraulic conductivity can be achieved by solving inverse groundwater problem.Therefore,in this study,the multi-point geostatistics method Quick Sampling(QS)is proposed and introduced for the first time and combined with the iterative local updating ensemble smoother(ILUES)to develop a new data assimilation framework QS-ILUES.It helps to solve the contaminant source parameters and non-Gaussian hydraulic conductivity field simultaneously by assimilating hydraulic head and pollutant concentration data.While the pilot points are utilized to reduce the dimension of hydraulic conductivity field,the influence of pilot points’layout and the ensemble size of ILUES algorithm on the inverse simulation results are further explored.     

A boundary integral method for steady flow in unsaturated porous media

The governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary-pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well-suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non-linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel.     

Empirical Orthogonal Functions Analysis Applied to the Inverse Problem in Hydrogeology: Evaluation of Uncertainty and Simulation of New Solutions

To fulfil the need to generate more realistic solutions, stochastic inverse simulations in hydrogeology are now constrained on both piezometric head and hydraulic conductivity data. These inverse techniques, often based on geostatistics, allow modifications of an initial solution conditioned only on hydraulic conductivity data to arrive at a final solution that also matches observed heads. By repeating the process as many times as necessary with different initial solutions, one generates an ensemble of final solutions thereby addressing the uncertainty of the inverse problem. This requires a method able to handle the whole ensemble and to work on its relevant characteristics. From this standpoint, the analysis by Empirical Orthogonal Functions (EOF) appears promising. The method builds an orthogonal decomposition of the covariance matrix, calculated over the whole set of solutions, and the areas in space where the first functions have a greater influence corresponding to locations of maximum uncertainty in the solutions. These locations depend both on the hydraulic characteristics of the flow problem and on the spatial distribution of available data. The EOF analysis is used on a synthetic problem that mimics a possible behavior of the Culebra aquifer of the Waste Isolation Pilot Plant (WIPP, New Mexico). The method also allows new solutions to be generated at lower computational cost by a random composition of the functions obtained by the EOF analysis. These new solutions keep the main characteristics of the initial ensemble and because they can be conditioned, they return very good results when they are used to solve the direct problem.     

全吸力范围内渗透系数快速测定方法研究

非饱和土渗透系数函数跨越多个数量级,传统的测量方法动辄耗时数月,且难以实现全吸力范围内渗透系数的测量。为了实现全吸力范围内渗透系数的快速测量,将湿润锋前进法与瞬时剖面法相结合（简称联合测定方法）,利用自行研制的土柱入渗装置,开展了不同干密度条件下青海粉质黏土全吸力范围内渗透系数测量试验。试验结果表明：在联合测定方法中,湿润锋前进法适用于高吸力段（基质吸力ψ > 25 kPa）渗透系数的测量,瞬时剖面法则适用于低吸力段（基质吸力ψ ≤25 kPa）渗透系数的测量,且两种方法在吸力重叠范围内渗透系数测量结果基本一致。联合测定方法可将全吸力范围内渗透系数的测量时长压缩至一周左右,且精度良好。此外,还对两种试验方法的误差来源进行了分析与讨论。研究结果表明：联合测定方法能够实现全吸力范围内渗透系数的快速测量,有望使得非饱和土渗透系数的测量成为土力学的常规试验。     

Hydraulic Conductivity Tests for Evaluating Compatibility of Lateritic Soil—Fly Ash Mixtures with Municipal Waste Leachate

Long term competent performance of liner systems is a critical issue in the design and construction of waste repositories due to adverse interactions associated with leachate generated by wastes. This study was conducted to verify the efficacy of fly ash stabilization in enhancing compatibility between lateritic soil and municipal waste leachate. Applications investigated include soil mixtures containing 0, 5, 10, 15, and 20% fly ash compacted at approximately 2% wet of optimum moisture content with modified proctor energy. Baseline hydraulic conductivity was first established at every level of fly ash content by permeating soil mixtures with tap water before permeation with leachate in a compaction mould permeameter using the falling head test method. Results show that the trend in hydraulic conductivity of specimen containing 0% fly ash was characterized by a gradual but erratic decrease which may suggests partial entry of the leachate cations into the double layer. Conversely, specimens containing fly ash showed a general trend consisting of an initial drop in k (up to an order of magnitude) that was followed by slight decrease sustained until k stabilized and later terminated. Above 10% fly ash content, the relatively high values of k observed was not connected with the reactivity of the soil mixtures with leachate, rather it may be attributed to excessive fly ash content that altered their textural and hydraulic properties. The result of this study is potentially significant in the assessment of fly ash as a compatibility enhancing agent which can be admixed in barrier materials that are susceptible to adverse reactions with the liquid to be contained.     

The 2D Steady Hydraulic Head Field Surrounding a Pumping Well in a Finite Heterogeneous Confined Aquifer

We present a second-order analytic solution [in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions.     

Integration of Tracer Test Data to Refine Geostatistical Hydraulic Conductivity Fields Using Sequential Self-Calibration Method

On the basis of local measurements of hydraulic conductivity,geostatistical methods have been found to be useful in heterogeneity characterization of a hydraulic conductivity field on a regional scale. However,the methods are not suited to directly integrate dynamic production data,such as,hydraulic head and solute concentration,into the study of conductivity distribution. These data,which record the flow and transport processes in the medium,are closely related to the spatial distribution of hydraulic conductivity. In this study,a three-dimensional gradient-based inverse method-the sequential self-calibration (SSC) method-is developed to calibrate a hydraulic conductivity field,initially generated by a geostatistical simulation method,conditioned on tracer test results. The SSC method can honor both local hydraulic conductivity measurements and tracer test data. The mismatch between the simulated hydraulic conductivity field and the reference true one,measured by its mean square error (MSE),is reduced through the SSC conditional study. In comparison with the unconditional results,the SSC conditional study creates the mean breakthrough curve much closer to the reference true curve,and significantly reduces the prediction uncertainty of the solute transport in the observed locations. Further,the reduction of uncertainty is spatially dependent,which indicates that good locations,geological structure,and boundary conditions will affect the efficiency of the SSC study results.