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.     

Influence of rock mass properties on tunnel inflow using hydromechanical numerical study

One of the primary geotechnical problems encountered during tunnel construction involves the inflow of groundwater into the tunnel. Heavy inflows make tunnel construction difficult and result in higher costs and delays in construction period. Therefore, it is essential to estimate the volume and rate of water inflow that is likely to appear in the tunnel. In this research, water inflow to the tunnel was calculated using numerical hydromechanical analysis. Effect of rock mass properties including fracture characteristics (normal and shear stiffness, hydraulic aperture, dilation angle, and fracture nonlinear behavior) on inflow was studied using a two-dimensional distinct element method. Results show that fracture properties play important role in inflow to the tunnel and must be considered in prediction of inflow to the tunnel. Based on numerical analysis results, inflow of groundwater into the tunnel increases with the increasing of normal and shear stiffness, dilation angle, and hydraulic aperture of rock mass fractures. The measured inflow with considering nonlinear fracture behavior was more than the calculated inflow with linear constitutive behavior.     

Constraining the uncertainty in fracture geometry using tracer tests

In fractured-rock aquifers, the geometric and hydraulic properties of the fractures commonly have a dominant influence on transport. Tracer tests are often used to estimate directly the gross transport properties of a fractured rock mass. The prospects for understanding characteristics of the heterogeneities in a fractured porous medium were explored from evidence provided by tracer experiments. The approach was to simulate flow and transport on a large set of prescribed fracture networks in a two-dimensional homogeneous permeable medium, thus generating synthetic tracer test data. The fracture orientation, aperture, spacing and network geometry were systematically altered from one case to the next. A classification scheme was devised for the tracer breakthrough curves using principal component analysis and this classification was linked to the fracture pattern properties. Even under highly simplified and controlled conditions, quite different fracture patterns can produce very similar breakthrough curves. The classification scheme thus demonstrates that a single breakthrough curve cannot reveal the fracture geometry with any precision. However, the scheme provided a methodology for rejecting geometric properties that do not belong to the fracture pattern under investigation, thus reducing the uncertainty in fracture geometry.     

Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas

The fluid flow in rock fractures during shear processes has been an important issue in rock mechanics and is investigated in this paper using finite element method (FEM), considering evolutions of aperture and transmissivity with shear displacement histories under different normal stress and normal stiffness conditions as measured during laboratory coupled shear-flow tests. The distributions of fracture aperture and its evolution during shearing were calculated from the initial aperture, based on the laser-scanned sample surface roughness results, and shear dilations measured in the laboratory tests. Three normal loading conditions were adopted in the tests: simple normal stress and mixed normal stress and normal stiffness to reflect more realistic in situ conditions. A special algorithm for treatment of the contact areas as zero-aperture elements was used to produce more accurate flow field simulations, which is important for continued simulations of particle transport but often not properly treated in literature. The simulation results agree well with the measured hydraulic apertures and flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow fields with changing normal loading conditions and increasing shear displacements. With the new algorithm for contact areas, the tortuous flow fields and channeling effects under normal stress/stiffness conditions during shearing were more realistically captured, which is not possible if traditional techniques by assuming very small aperture values for the contact areas were used. These findings have an important impact on the interpretation of the results of coupled hydro-mechanical experiments of rock fractures, and on more realistic simulations of particle transport processes in fractured rocks.     

Estimating regional-scale permeability–depth relations in a fractured-rock terrain using groundwater-flow model calibration

The trend of decreasing permeability with depth was estimated in the fractured-rock terrain of the upper Potomac River basin in the eastern USA using model calibration on 200 water-level observations in wells and 12 base-flow observations in subwatersheds. Results indicate that permeability at the 1–10 km scale (for groundwater flowpaths) decreases by several orders of magnitude within the top 100 m of land surface. This depth range represents the transition from the weathered, fractured regolith into unweathered bedrock. This rate of decline is substantially greater than has been observed by previous investigators that have plotted in situ wellbore measurements versus depth. The difference is that regional water levels give information on kilometer-scale connectivity of the regolith and adjacent fracture networks, whereas in situ measurements give information on near-hole fractures and fracture networks. The approach taken was to calibrate model layer-to-layer ratios of hydraulic conductivity (LLKs) for each major rock type. Most rock types gave optimal LLK values of 40–60, where each layer was twice a thick as the one overlying it. Previous estimates of permeability with depth from deeper data showed less of a decline at <300 m than the regional modeling results. There was less certainty in the modeling results deeper than 200 m and for certain rock types where fewer water-level observations were available. The results have implications for improved understanding of watershed-scale groundwater flow and transport, such as for the timing of the migration of pollutants from the water table to streams.     

Assessing flow paths in a karst aquifer based on multiple dye tracing tests using stochastic simulation and the MODFLOW-CFP code

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.     

Semi-empirical equations for the systematic decrease in permeability with depth in porous and fractured media

Permeability loss with depth is a general trend in geological media and plays an essential role in subsurface fluid flow and solute transport. In the near surface zone where groundwater movement is active, the decrease in permeability with depth is dominated by the mechanical compaction of deformable media caused by the increase in lithostatic stress with depth. Instead of using empirical equations from statistical analysis, by considering the well-defined relationships among permeability, porosity, fracture aperture and effective stress under lithostatic conditions, new semi-empirical equations for the systematic depth-dependent permeability are derived, as well as the equations for the depth-dependent porosity in a porous medium and the depth-dependent fracture aperture in a fractured medium. The existing empirical equations can be included in the new equations as special cases under some simplification. These new semi-empirical equations perform better than previous equations to interpret the depth-dependent permeability of the Pierre Shale (with a maximum depth of approximately 4,500 m) and the granite at Stripa, Sweden (with a maximum depth of about 2,500 m).     

Numerical analysis of the hydrogeologic controls in a layered coastal aquifer system, Oahu, Hawaii, USA

 The coastal aquifer system of southern Oahu, Hawaii, USA, consists of highly permeable volcanic aquifers overlain by weathered volcanic rocks and interbedded marine and terrestrial sediments of both high and low permeability. The weathered volcanic rocks and sediments are collectively known as caprock, because they impede the free discharge of groundwater from the underlying volcanic aquifers. A cross-sectional groundwater flow and transport model was used to evaluate the hydrogeologic controls on the regional flow system in southwestern Oahu. Controls considered were: (a) overall caprock hydraulic conductivity; and (b) stratigraphic variations of hydraulic conductivity in the caprock. Within the caprock, variations in hydraulic conductivity, caused by stratigraphy or discontinuities of the stratigraphic units, are a major control on the direction of groundwater flow and the distribution of water levels and salinity. Results of cross-sectional modeling confirm the general groundwater flow pattern that would be expected in a layered coastal system. Groundwater flow is: (a) predominantly upward in the low-permeability sedimentary units; and (b) predominantly horizontal in the high-permeability sedimentary units. Received, October 1996 Revised, August 1997 Accepted, September 1997     

Permeability and stress in crystalline rocks

Groundwater from crystalline rocks is a significant resource in many areas of the world. It is also an important medium for contaminant transport from, for example, deep nuclear waste repositories. Stress distributions in fractured rocks are important in controlling groundwater flow in several ways: (i) palaeostress fields are responsible for the evolution of fracture systems which transmit groundwater; (ii) current in situ stress fields will influence the shape and aperture of fractures; (iii) humans can influence the natural stress field in a rock mass to enhance fracture flows. The significance of stresses for groundwater flow can be investigated by field techniques (hydraulic fracturing), laboratory techniques (stress cells) or by numerical modelling.     

裂隙剪胀效应对双重孔隙介质热-水-应力耦合现象影响的有限元分析

为了探讨在法向应力和剪应力的共同作用下裂隙开度的变化对于耦合的温度场、渗流场和应力场的作用,引入裂隙的渗透系数与开度关系的“立方定律”,建立了裂隙渗透系数演化式。应用开发的遍有节理岩体双重孔隙-裂隙介质热-水-应力耦合二维有限元程序,以一个假定的位于非饱和地层中的高放废物地质处置库为算例,分别在2组裂隙斜交和正交的条件下,针对与裂隙开度3种计算方式对应的6种工况进行了数值分析,考察了围岩中的温度、孔隙和裂隙水压力、裂隙开度、裂隙的渗透系数、地下水流速、应力的变化、分布状态。结果显示,当裂隙开度仅取决于法向应力时,裂隙开度受压应力作用产生的闭合量最大,从而裂隙水压力最高;而当裂隙开度是法向应力和剪切位移的函数时,由于“剪胀”效应,裂隙开度闭合量较前述情况为小,裂隙水压力居中;而当裂隙开度是常数时,裂隙水压力最低     

Interpretation of single-well tracer tests using fractional-flow dimensions. Part 1: Theory and mathematical models

Generalized equations using fractional-flow dimensions were derived to estimate the Darcy and seepage velocities obtained from the point-dilution and the single-well injection-withdrawal field tests conducted in fractured-rock aquifers. Seepage velocities can only be estimated from single-well tests if the hydraulic conductivity and the hydraulic gradient are known a priori. However, if a radial-convergent test is also performed between two boreholes, the kinematic porosity can be estimated and be used to estimate the seepage velocity from the single-well test results. To apply the generalized equations, the flow dimension and the extent of the flow region must be known. Therefore, the generalized radial flow (GRF) model of Barker (1988; a generalized radial flow model for hydraulic tests in fractured rock. Water Resour Res 24(10):1796–1804) is used to estimate the flow dimension because of its wide range of applications. A pumping test performed on the boreholes will yield an estimate of the fractional-flow dimension by applying the GRF model. Electronic Publication     

The role of in situ stress in determining hydraulic connectivity in a fractured rock aquifer (Australia)

Fracture network connectivity is a spatially variable property that is difficult to quantify from standard hydrogeological datasets. This critical property is related to the distributions of fracture density, orientation, dimensions, intersections, apertures and roughness. These features that determine the inherent connectivity of a fracture network can be modified by secondary processes including weathering, uplift and unloading and other mechanisms that lead to fracture deformation in response to in situ stress. This study focussed on a fractured rock aquifer in the Clare Valley, South Australia, and found that fracture network connectivity could be discriminated from several geological, geophysical and hydrogeological field datasets at various scales including single well and local- to regional-scale data. Representative hydromechanical models of the field site were not only consistent with field observations but also highlighted the strong influence of in situ stress in determining the distribution of fracture hydraulic apertures and the formation of hydraulic chokes that impede fluid flow. The results of this multi-disciplinary investigation support the notion that the hydraulic conductivity of a fracture network is limited to the least hydraulically conductive interconnected fractures, which imposes a physical limit on the bulk hydraulic conductivity of a fractured rock aquifer.     

Assessment of groundwater residence times in the pore aquifers of the River Elbe Basin

An area covering assessment of the groundwater residence times for the upper pore aquifers in the River Elbe Basin was performed. Residence times were determined by combining groundwater velocities and flow distances along each flow-path to the surface waters using a two-dimensional model approach. Groundwater velocity was calculated as a function of hydraulic conductivity, hydraulic gradient and effective yield of pore space. Flow paths were obtained by an analysis of the morphology of the groundwater table. The mean groundwater residence time in the pore aquifers of the River Elbe Basin was quantified to about 25 years. A strong temporal blurring in the different regions between less than one year and more than 250 years was obtained. For the regional groundwater management in the Elbe Basin the groundwater residence times are an important parameter, which helps to take into account the temporal dimension in the assessment of the impact of political measures aiming at the improvement of groundwater quality with regard to diffuse pollutants (e.g. nitrate).     

裂隙刚度随应力变化对双重孔隙介质热-水-应力耦合影响的有限元分析

引入并修正了变刚度的连续屈服节理模型,同时考虑应力拉压和压力（化学）溶解对裂隙开度的综合影响,对所建立的双重孔隙-裂隙介质热-水-应力耦合有限元计算程序作了改进。通过一个假定的高放废物地质处置库的数值模拟,就岩体裂隙刚度变化的2种工况,分析了岩体中的温度、裂隙刚度、正应力、孔（裂）隙水压力和地下水流速的变化、分布情况。结果显示：与裂隙刚度是常数时相比,裂隙刚度是法向应力的函数时计算域中温度较低;岩体应力的大小也有一定不同,其分布与裂隙刚度“场”有明显的相似性;并且负孔（裂）隙水压力的绝对值要略小一点,约是常数时的98%。     

Review: Regional land subsidence accompanying groundwater extraction

The extraction of groundwater can generate land subsidence by causing the compaction of susceptible aquifer systems, typically unconsolidated alluvial or basin-fill aquifer systems comprising aquifers and aquitards. Various ground-based and remotely sensed methods are used to measure and map subsidence. Many areas of subsidence caused by groundwater pumping have been identified and monitored, and corrective measures to slow or halt subsidence have been devised. Two principal means are used to mitigate subsidence caused by groundwater withdrawal??reduction of groundwater withdrawal, and artificial recharge. Analysis and simulation of aquifer-system compaction follow from the basic relations between head, stress, compressibility, and groundwater flow and are addressed primarily using two approaches??one based on conventional groundwater flow theory and one based on linear poroelasticity theory. Research and development to improve the assessment and analysis of aquifer-system compaction, the accompanying subsidence and potential ground ruptures are needed in the topic areas of the hydromechanical behavior of aquitards, the role of horizontal deformation, the application of differential synthetic aperture radar interferometry, and the regional-scale simulation of coupled groundwater flow and aquifer-system deformation to support resource management and hazard mitigation measures.     

应力腐蚀和压力溶解引起的裂隙开度-刚度变化对THMM耦合过程影响的数值模拟

在使用Yasuhara等建立的裂隙开度的应力腐蚀和压力溶解模型的基础上,考虑裂隙闭合量对裂隙刚度的影响,针对一个假设的位于非饱和双重孔隙-裂隙岩体中且有核素泄漏的高放废物地质处置模型,拟定两种计算工况：（1）裂隙的刚度系数是裂隙闭合量的线性函数;（2）裂隙刚度为常数,进行热-水-应力-迁移耦合的二维有限元数值模拟,考察了岩体中的温度、裂隙开度的闭合速率、闭合量、孔（裂）隙水压力、地下水流速、核素浓度、裂隙刚度和正应力的变化、分布等情况。结果表明,两种工况岩体中的温度场、孔（裂）隙水压力、地下水流速、核素浓度无明显差别;裂隙闭合基本由应力腐蚀产生;在相同计算时间内两种工况的裂隙闭合量较为接近,工况1略大;工况1中离玻璃固化体越近,裂隙刚度值越高,并且在玻璃固化体附近的应力值较大,且集中程度较高。     

等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响

等效水力隙宽和水力梯度是影响岩体裂隙网络渗流特性的重要因素。制作裂隙网络试验模型,建立高精度渗流试验系统;求解纳维-斯托克斯方程,模拟流体在裂隙网络内的流动状态,研究等效水力隙宽和水力梯度对非线性渗流特性的影响。结果表明,当水力梯度较小时,等效渗透系数保持恒定的常数,流体流动属于达西流动区域,流量与压力具有线性关系,可采用立方定律计算流体流动;当水力梯度较大时,等效渗透系数随着水力梯度的增加而急剧减少,流体流动进入强惯性效应流动区域,流量与压力具有强烈的非线性关系,可采用Forchheimer方程计算流体流动。随着等效水力隙宽的增加,区别线性和非线性流动区域的临界水力梯度呈幂函数关系递减。当水力梯度小于临界水力梯度时,控制方程可选立方定律;当水力梯度大于临界水力梯度时,控制方程可选Forchheimer方程,其参数A和B可根据经验公式计算得到。其研究结果可为临界水力梯度的确定及流体流动控制方程的选取提供借鉴意义。     

Gas flow in anisotropic claystone: modelling triaxial experiments

Selected gas pulse tests on initially saturated claystone samples under isotropic confinement pressure are simulated using a 3D thermo‐hydro‐mechanical code. The constitutive model considers the hydro‐mechanical anisotropy of argillaceous rocks. A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is considered to enhance the initiation of flow through preferential paths, following the direction of the bedding planes. The numerical simulations were performed considering two different bedding orientations, parallel and normal to the imposed flow in the test. Simulations are in agreement with recorded upstream and downstream pressures in the tests. The evolution of fluid pressures, degree of saturation, element permeability and stress paths are presented for each case analysed. This information provides a good insight into the mechanisms of gas transport. Different flow patterns are obtained depending on bedding orientation, and the results provide an explanation for the results obtained in the tests. Copyright © 2012 John Wiley & Sons, Ltd.     

渗透水压对节理应力-渗流耦合特性的影响试验研究

为研究渗透水压对节理应力-渗流耦合特性的影响,通过对6组人造节理试件恒定法向载荷和恒定法向刚度的压剪渗流试验,分析了应力和位移、节理水力开度以及透过率随剪切位移的变化趋势,获得了渗透水压对节理岩石应力-渗流耦合特性的影响规律。结果表明：节理试件的剪切应力和位移、水力开度以及透过率都与渗透水压密切相关。剪切应力随渗透水压的增大而减小,法向变形、水力开度和透过率却随渗透水压的增大而增大。在压剪渗流试验过程中,不同渗透压力的节理试件都发生了剪胀效应。研究可为深部岩体工程围岩遇水作用稳定性及渗流灾害控制技术提供科学的理论依据。     

A modeling study of seawater intrusion in Alabama Gulf Coast,USA

A numerical model of variable-density groundwater flow and miscible salt transport is developed to investigate the extent of seawater intrusion in the Gulf coast aquifers of Alabama, USA. The SEAWAT code is used to solve the density-dependent groundwater flow and solute transport governing equations. The numerical model is calibrated against the observed hydraulic heads measured in 1996 by adjusting the zonation and values of hydraulic conductivity and recharge rate. Using the calibrated model and assuming all the hydrogeologic conditions remain the same as those in 1996, a predictive 40-year simulation run indicates that further seawater intrusion into the coastal aquifers can occur in the study area. Moreover, the predicted intrusion may be more significant in the deeper aquifer than the shallower ones. As the population continues to grow and the demand for groundwater pumping intensifies beyond the 1996 level, it can be expected that the actual extent of seawater intrusion in the future would be more severe than the model prediction. Better strategies for groundwater development and management will be necessary to protect the freshwater aquifers from contamination by seawater intrusion.