Investigating the role of hydromechanical coupling on flow and transport in shallow fractured-rock aquifers

Fractured-rock aquifers display spatially and temporally variable hydraulic conductivity generally attributed to variable fracture intensity and connectivity. Empirical evidence suggests fracture aperture and hydraulic conductivity are sensitive to in situ stress. This study investigates the sensitivity of fractured-rock hydraulic conductivity, groundwater flow paths, and advection-dominated transport to variable shear and normal fracture stiffness magnitudes for a range of deviatoric stress states. Fracture aperture and hydraulic conductivity are solved for analytically using empirical hydromechanical coupling equations; groundwater flow paths and ages are then solved for numerically using groundwater flow and advection-dispersion equations in a traditional Toth basin. Results suggest hydraulic conductivity alteration is dominated by fracture normal closure, resulting in decreasing hydraulic conductivity and increasing groundwater age with depth, and decreased depth of long flow paths with decreasing normal stiffness. Shear dilation has minimal effect on hydraulic conductivity alteration for stress states investigated here. Results are interpreted to suggest that fracture normal stiffness influences hydraulic conductivity of hydraulically active fractures and, thus, affects flow and transport in shallow (<1 km) fractured-rock aquifers. It is suggested that observed depth-dependent hydraulic conductivity trends in fractured-rock aquifers throughout the world may be partly a manifestation of hydromechanical phenomena.     

Phreatic Surface in Island Aquifers with Regular Geometry and Time-Independent Recharge and Pumping

The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater interface below mean sea level follows from the Dupuit–Ghyben–Herzberg relation. The method of solution presented in this work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping.     

1-, 2-, and 3-dimensional effective conductivity of aquifers

Starting with a stochastic differential equation with random coefficients describing steady-state flow, the effective hydraulic conductivity of 1-, 2-, and 3-dimensional aquifers is derived. The natural logarithm of hydraulic conductivity (lnK) is assumed to be heterogeneous, with a spatial trend, and isotropic. The effective conductivity relates the mean specific discharge in an aquifer to the mean hydraulic gradient, thus its importance in predicting Darcian discharge when field data represent mean or average values of conductivity or hydraulic head. Effective conductivity results are presented in exact form in terms of elementary functions after the introduction of special sets of coordinate transformations in two and three dimensions. It was determined that in one, two, and three dimensions, for the type of aquifer heterogeneity considered, the effective hydraulic conductivity depends on: (i) the angle between the gradient of the trend of lnK and the mean hydraulic gradient (which is zero in the one-dimensional situation); (2) (inversely) on the product of the magnitude of the trend gradient of lnK, b, and the correlation scale of lnK, and (3) (proportionally) on the variance of lnK, _f ² . The productb plays a central role in the stability of the results for effective hydraulic conductivity.     

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.     

江汉平原土壤饱和渗透系数变化规律及影响因素

目前对影响土壤饱和渗透系数规律的机理缺乏深刻认识.以不同沉积环境、不同岩性及不同土地利用方式的江汉平原汉江下游浅层土壤为对象,采用改进的TST-55型土壤渗透仪开展室内变水头达西实验.结果表明,研究区内土壤饱和渗透系数平均值为4.94×10-5cm/s,服从对数-正态分布;粉砂壤土冲积物和湖积物的饱和渗透系数平均值为3.53×10-5cm/s和1.98×10-5cm/s,粉砂质粘壤土中,两者分别为8.13×10-7cm/s和5.88×10-7cm/s,同一岩性冲积物的饱和渗透系数较湖积物大;冲积物中,砂壤土、粉砂壤土和粉砂质粘壤土饱和渗透系数平均值为1.98×10-5 cm/s、3.53×10-5 cm/s和8.13×10-7 cm/s,表现为砂壤土>粉砂壤土>粉砂质粘壤土;耕作土壤中,粉砂壤土、粉砂质粘壤土的饱和渗透系数平均值为3.75×10-5 cm/s和8.11×10-7cm/s,非耕作土壤中,两者分别为1.88×10-6cm/s、5.93×10-7cm/s,同一岩性耕作土壤饱和渗透系数较非耕作土壤大.      

岩体裂隙网络渗流变水温影响分析

考虑岩体裂隙渗流变水温影响,推导单裂隙变水温水流近似解析解和有限元解,在此基础上分别建立裂隙二维网络变水温渗流数值求解方程,分别对应裂隙网络变水温渗流分析的近似解析法和子结构法。分析变温水流运动规律发现：（1）单裂隙内水流水头与水力坡降成非线性关系,当水流由高温区向低温区流动时,水头分布曲线为凸曲线,此时按线性渗流简化水头整体偏小;当由低温区向高温区流动时,水头分布曲线为凹曲线,此时按线性渗流简化水头整体偏大。（2）单裂隙内,高水温处水力坡降小,低水温处水力坡降大;裂隙平均水温越高,流速越快;裂隙网络内存在与裂隙宽度相似的温度偏流效应,即交叉节点水流有偏向水流温度高的裂隙流动的趋势。在温度较高和温度梯度较大的区域,应该考虑水流温度变化对渗流场的影响。     

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.     

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。     

基于局域化EnKF同时同化地下水水流和溶质运移数据的渗透系数场识别研究

局域化改进集合卡尔曼滤波（EnKF）可以克服EnKF方法在使用小集合时,对参数识别精度较低的缺陷,其能同化 地下水位观测数据有效识别渗透系数场。实际工作中,溶质运移数据也较容易获得。崔凯鹏（2013）尝试增加溶质运移 数据以改进只同化水流数据对渗透系数的估计结果,但是精度提高有限。本文在其基础上修改模型,进一步增加溶质注 入井,探究同时同化水头和溶质运移数据,对渗透系数场识别效果,之后对比了局域化EnKF与非局域化EnKF参数识别结 果,并分析了溶质影响范围与参数识别的关系。结果表明：同时同化溶质运移和水头资料,比同化单一种类观测数据识别 的渗透系数精度更高;相同实现数目下,局域化EnKF比EnKF对渗透系数场的估计结果与真实场更为接近;仅考虑溶质影 响范围内的渗透系数,同化水头数据在最后时刻参数识别结果好于同化溶质运移数据参数识别结果,但差别不大。     

Calculation of head difference at two sides of a cut-off barrier during excavation dewatering

This paper proposed a series of simple equations to calculate the head difference at the two sides of waterproof curtain. The barrier effect of waterproof curtain is considered from two situations with respect to without barrier case: (i) groundwater head difference below the barrier and (ii) groundwater head difference by convergence into the opening. The solution for the first situation can be derived from hydraulic analyses and the second situation can be obtained using a numerical analysis. The final groundwater head difference is the sum of these two situation according to the superposition principal. In the proposed equations, the head difference is expressed as a function of the inserted depth of the barrier into confined aquifer, the ratio of the hydraulic conductivity of the aquifer, the thickness of the aquifer, and hydraulic gradient under normal conditions. Finally, the proposed equation was applied to a field case to verify the validity of the proposed approach. Compared with the field data, the results show that the proposed method is reasonable.     

高围压下砂土的渗透特性试验研究

利用高压三轴渗透试验系统,对某矿区深部的粗砂和细砂进行了高围压条件下的渗透试验。研究了同一水力梯度下渗透系数与围压的关系;同一围压下渗透系数与渗透水力梯度的关系;同一水力梯度下,围压逐级加载的渗透系数与一次加载的渗透系数之间的差别。结果表明,粗砂和细砂在同一水力梯度下渗透系数均随围压的增大而逐渐减小,在同一围压下,渗透系数会随渗透水力梯度的增大而逐渐增大;同一水力梯度下,围压逐级加载下的渗透系数明显小于一次加载条件下的渗透系数。根据围压与渗透系数的关系拟合出了两种砂样渗透系数与围压关系的数学表达式。为探究高围压下渗透系数变化的原因,研究了砂样试验过程中的体积变化和试验前后的粒度成分变化。结果表明,围压的施加过程伴随着试样的体积减小,相应的孔隙度减小,渗透系数降低;高围压条件下,砂土颗粒被挤碎成细颗粒,使得砂土的细粒含量增多,孔隙度减小,导致了砂土渗透系数的降低。     

Application of statistical approaches to analyze geological,geotechnical and hydrogeological data at a fractured-rock mine site in Northern Canada

Mine site characterization often results in the acquisition of geological, geotechnical and hydrogeological data sets that are used in the mine design process but are rarely co-evaluated. For a study site in northern Canada, bivariate and multivariate (hierarchical) statistical techniques are used to evaluate empirical hydraulic conductivity estimation methods based on traditional rock mass characterisation schemes, as well as to assess the regional hydrogeological conceptual model. Bivariate techniques demonstrate that standard geotechnical measures of fracturing are poor indicators of the hydraulic potential of a rock mass at the study site. Additionally, rock-mass-permeability schemes which rely on these measures are shown to be poor predictors of hydraulic conductivity in untested areas. Multivariate techniques employing hierarchical cluster analysis of both geotechnical and geological data sets are able to identify general trends in the data. Specifically, the geological cluster analysis demonstrated spatial relationship between intrusive contacts and increased hydraulic conductivity. This suggests promise in the use of clustering methods in identifying new trends during the early stages of hydrogeological characterization.     

心墙堆石坝渗透稳定可靠性分析的随机响应面法

将大规模渗流有限元计算与随机响应面法相结合,对双江口心墙堆石坝进行渗透稳定可靠性分析。在基于随机响应面法的可靠度分析框架内,堆石坝稳定渗流有限元计算过程和可靠度分析过程分开独立进行,通过对心墙渗透坡降较大区域的节点建立统一的渗透稳定功能函数,采用渗流有限元分析方法和随机响应面法,计算出该区域每个节点处的渗透破坏失效概率,并将最大失效概率作为心墙的失效概率。最后,分析了心墙渗透系数、覆盖层渗透系数、上游水位与心墙具有最大失效概率节点处渗透坡降的相关关系,以及心墙渗透系数和上游水位的变异性对心墙渗透破坏失效概率的影响。计算结果表明,随机响应面法3阶Hermite展开就能够保证良好的计算精度,且计算耗时较小;双江口堆石坝心墙具有最大失效概率节点处的渗透坡降与上游水位密切相关,而与心墙本身的渗透系数呈弱负相关关系,与覆盖层渗透系数的相关性不显著;随着上游水位变异性的增大,心墙失效概率急剧增大,而这种效应对于心墙渗透系数并不明显。研究成果为随机响应面法在实际工程中的应用奠定了一定的基础。     

美国内布拉斯加州普拉特河河床沉积物渗透系数的现场测定

竖管测定法可现场测定河床的渗透系数.采用人工梯度法和自然梯度法两种方法,对普拉特河位于卡尼市(KearneyCity)东南河段河床的垂直、水平和任意方向的渗透系数进行了野外现场测定.10个测点的垂向渗透系数的平均值为30.51m/d,一个测点的水平方向渗透系数为97.2m/d,其各向异性比率约为3.结果表明:普拉特河床沉积物剖面上具有一定的各向异性,平面上为非均匀介质.     

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.     

A numerical analysis of dimensionality and heterogeneity effects on advective dispersive seawater intrusion processes

Two-dimensional (2D) and 3D numerical simulations of the dispersive Henry problem show that heterogeneity affects seawater intrusion differently in 2D and 3D. When the variance of a multi-Gaussian isotropic hydraulic conductivity field increases, the penetration of the saltwater wedge decreases in 2D while it increases in 3D. This is due to the combined influence of advective and dispersive processes which are affected differently by heterogeneity and problem dimensionality. First, the equivalent hydraulic conductivity controls the mean head gradient and therefore the position of the wedge. For an isotropic medium, increasing the variance increases the equivalent conductivity in 3D but not in 2D. Second, the macrodispersion controls the rotation of the saltwater wedge by affecting the magnitude of the density contrasts along the saltwater wedge. An increased dispersion due to heterogeneity leads to a decreasing density contrast and therefore a smaller penetration of the wedge. The relative magnitude of these two opposite effects depends on the degree of heterogeneity, anisotropy of the medium, and dimension. Investigating these effects in 3D is very heavy numerically; as an alternative, one can simulate 2D heterogeneous media that approximate the behaviour of the 3D ones, provided that their statistical distribution is rescaled.     

Highly parameterized model calibration with cloud computing: an example of regional flow model calibration in northeast Alberta,Canada

Expanding groundwater datasets collected by automated sensors, and improved groundwater databases, have caused a rapid increase in calibration data available for groundwater modeling projects. Improved methods of subsurface characterization have increased the need for model complexity to represent geological and hydrogeological interpretations. The larger calibration datasets and the need for meaningful predictive uncertainty analysis have both increased the degree of parameterization necessary during model calibration. Due to these competing demands, modern groundwater modeling efforts require a massive degree of parallelization in order to remain computationally tractable. A methodology for the calibration of highly parameterized, computationally expensive models using the Amazon EC2 cloud computing service is presented. The calibration of a regional-scale model of groundwater flow in Alberta, Canada, is provided as an example. The model covers a 30,865-km² domain and includes 28 hydrostratigraphic units. Aquifer properties were calibrated to more than 1,500 static hydraulic head measurements and 10 years of measurements during industrial groundwater use. Three regionally extensive aquifers were parameterized (with spatially variable hydraulic conductivity fields), as was the aerial recharge boundary condition, leading to 450 adjustable parameters in total. The PEST-based model calibration was parallelized on up to 250 computing nodes located on Amazon’s EC2 servers.     

A multidimensional fuzzy least-squares regression approach for estimating hydraulic gradients in unconfined aquifer formations and its application to the Gulf Coast aquifer in Goliad County,Texas

Epistemic uncertainties arise during the estimation of hydraulic gradients in unconfined aquifers due to planar approximation of the water table as well as data gaps arising from factors such as instrument failures and site inaccessibility. A multidimensional fuzzy least-squares regression approach is proposed here to estimate hydraulic gradients in situations where epistemic uncertainty is present in the observed water table measurements. The hydraulic head at a well is treated as a normal (Gaussian) fuzzy variable characterized by a most likely value and a spread. This treatment results in hydraulic gradients being characterized as normal fuzzy numbers as well. The multidimensional fuzzy least-squares regression has an exact analytical form and as such can be implemented easily using matrix algebra methods. However, the method was noted to be sensitive to round-off and truncation errors when the epistemic uncertainties are small. A closeness index based on the cardinality of a fuzzy number is used to evaluate how well the regression model fits the fuzzy hydraulic head observations. A fuzzy Euclidian distance measure is used to compare two fuzzy numbers and to evaluate how fuzziness in the observed hydraulic heads affects the fuzziness in the estimated hydraulic gradients. The Euclidian distance measure is also used to ascertain the influence of each well on the fuzzy hydraulic gradient estimation. The fuzzy regression framework is illustrated by applying it to evaluate hydraulic gradients in the unconfined portion of the Gulf Coast aquifer in Goliad County, TX. The results from the case-study indicate that there is greater uncertainty associated with the estimation of the hydraulic gradients in the vertical (Z-axis) direction. The epistemic uncertainties in the hydraulic head data at the wells have a significant impact on the gradient estimates when they are of the same order of magnitude as the most likely values of the observed heads. The influence analysis indicated that 5 of the 13 wells in the network had a critical influence on at least one of the hydraulic gradients. Three wells along the northeastern section of the study area and bordering the Victoria County were noted to have the least influence on the regression estimates. The fuzzy regression framework along with the associated goodness-of-fit and influence measures provides a useful set of tools to characterize the uncertainties in the hydraulic heads and gradients arising from data gaps and planar water table approximation.     

Transient Modeling of Hyperfiltration Effects

Transient models are needed to analyze time-dependent problems like hyperfiltration associated with head differences across clay barriers. Hyperfiltration (solute-sieving) effects create an increased concentration of natural groundwater solutes outside the clay barrier due to the inward head gradient. The purpose of our model is to predict solute buildup and distribution during hyperfiltration providing a basis for time analysis of solute migration. Required input parameters for the model include membrane properties like reflection coefficient, hydraulic conductivity, and solute concentration on the high-pressure side of the membrane before the onset of steady state, solution flux, and the effluent concentration. Model verification is based on published experimental results. The transient hyperfiltration model presented herein may prove useful in elucidating clay membrane (hyperfiltration) effects in the subsurface, however the sole purpose of this paper is to develop a transient model of hyperfiltration effects and test it by using published experimental data.     

Evaluation of hydraulic conductivity of gap-graded granular soils based on equivalent void ratio concept

Gap-graded granular soils are used as construction materials worldwide, and their hydraulic conductivity depends on their relative content of coarse and fine grains, initial conditions, and particle shape. In this study, a series of constant head hydraulic conductivity tests were performed on gap-graded granular soils with different initial relative densities, fine contents, and particle shapes. The test results show that the hydraulic conductivity decreases with an increase in fine fraction and then remains approximately constant beyond the “transitional fine content.” The role of the structural effect on the hydraulic conductivity is different from that on the mechanical properties (such as stiffness and shear strength). This can be attributed to the degree of filling within inter-aggregate voids, disturbance of soil structure, and densified fine bridges between coarse aggregates. The equivalent void ratio concept was introduced into the Kozeny–Carman formula to capture the effect of fines (aggregates) on the “coarse-dominated” (“fine-dominated”) structure, and a simple model is proposed to capture the change of hydraulic conductivity of gap-granular soils. The model incorporates a structural variable to capture the effect of fines on “coarse-dominated” structure and coarse aggregates on “fine-dominated” structure. The performance of the model was verified with experimental data from this study and previously reported data compiled from the literature. The results reveal that the proposed model is simple yet effective at capturing the hydraulic conductivity of gap-graded granular soils with a wide range of fine contents, initial conditions, and particle shapes.