Proof of multiplicity of solutions for groundwater seepage in recharged heterogeneous unconfined aquifers

A new analytical proof is presented for steady‐state seepage in recharged heterogeneous unconfined aquifers. The paper also presents a detailed procedure and important rules for performing correctly numerical studies of unsaturated seepage. Once a numerical solution is calibrated with field data, using a set of spatially distributed values for hydraulic conductivity K and effective infiltration EI, any new numerical analysis with a set of αK and αEI values, where α is a constant, yields an equally good calibration. However, if the effective porosities of each layer are unchanged, the groundwater velocities are multiplied by α, whereas the travel times are divided by α, which may help to select α in order to match known travel time data. This is a clear example of multiple solutions to an inverse problem. The paper underlines the role and the need to finely mesh unsaturated zones and also contacts between layers to reach the asymptotic convergence range, as it was carried out to verify the proof and as it should be completed to study any seepage problem. A few consequences of the new analytical proof and the rigorous procedure are shown with examples. Copyright © 2016 John Wiley & Sons, Ltd.     

BP神经网络在BOULTON法确定潜水含水层参数中的应用

本文在分析具有迟后排水的N.S.Boulton第二潜水井流模型解析解的基础上,利用复合高斯求积法和学习速率、动量因子自适应的BP神经网络相结合对该模型数值求解,提出了确定潜水含水层系统参数的Boulton-BP法.实例计算结果表明,用Boulton-BP法求得参数正演出的降深-时间过程与抽水试验所得降深-时间过程拟合很好.该方法简单,快速,不需要将抽水试验所得降深-时间过程分为前、后两段分别求参,不仅简化潜水含水层的求参过程,而且有良好的求参效果.     

确定含水层渗透系数的冲击试验方法

运用Hvorslevr冲击试验方法测定CIRP试验场地下研究设施(URF)试验含水层的渗透系数。由于含水层厚度小、富水性差,正在进行核素迁移试验,以及操作空间有限,因此不能进行抽水或注水试验,同时考虑到试验范围较小,故采取冲击试验求含水层的渗透系数。含水层介质为亚粘土,隔水底板距URF底板面约6m。试验的冲击量小,可以忽略URF内南部含水层对试验结果的影响。试验钻孔的孔径和井管内径相近,减小了钻孔结构对试验结果的影响。试验结果(472×10-4、658×10-4cm/s)与采用自URF内试验含水层的未扰动土柱所作的室内渗透试验结果(41×10-4～82×10-4cm/s)在同一数量级。     

The hydraulic conductivity field and groundwater flow in the unconfined aquifer system of the Keta Strip,Ghana

This study investigates the hydraulic conductivity field and the groundwater flow pattern as predicted by a calibrated steady state groundwater flow model for the Keta Strip, southeastern Ghana. The hydraulic conductivity field is an important parameter in evaluating aquifer properties in space, and in general basin-wide groundwater resources evaluation and management. This study finds that the general hydraulic conductivity of the unconsolidated unconfined aquifer system of the Keta Strip ranges between 2 m/d and 20 m/d, with an average of 15 m/d. The spatial variation in horizontal hydraulic conductivity appears to take the trend in the variations in the nature of the material in space. Calibrated groundwater recharge suggests that 6.9–34% of annual precipitation recharges the shallow aquifer system. This amount of recharge is significant and suggests high fortunes in terms of groundwater resources development for agriculture and industrial activities in the area. A spatial distribution of groundwater recharge from precipitation is presented in this study. The spatial pattern appears to take the form of the distribution in horizontal hydraulic conductivity, and suggests that the vertical hydraulic conductivity takes the same pattern of spatial variation as the horizontal hydraulic conductivity. This is consistent with observations in other areas. The resulting groundwater flow is dominated by local flow systems as the unconfined system is quite shallow. A general northeast – southwest flow pattern has been observed in the study area.     

Determination of the parameter pattern and values for a one-dimensional multi-zone unconfined aquifer

In an aquifer, heterogeneity plays an important role in governing groundwater flow. Hence, aquifer characterization should involve both the pattern and values of the hydrogeological parameters. A new analytical solution describing the one-dimensional groundwater flow in a multi-zone unconfined aquifer is presented, and a methodology developed from the analytical solution and a heuristic approach for determining the pattern and values of the aquifer parameters are proposed. The analytical solution demonstrates that the hydraulic head varies spatially and is influenced by aquifer heterogeneity. Simulated annealing, a heuristic approach, is incorporated with the solution to simultaneously identify the pattern and values of the hydraulic conductivity for a horizontal multi-zone unconfined aquifer. This approach may be used to give an approximate result for a two-dimensional problem by dividing the model area into a number of transects along the transverse direction, identifying the parameter values along the longitudinal direction for each transect, and then smoothing the identified results.     

Electrical-hydraulic conductivity model for a weatheredfractured aquifer system of Olbanita,Lower Baringo Basin,Kenya Rift

Groundwater yield in the Kenya Rift is highly unsustainable owing to geological variability.In this study,field hydraulic characterization was performed by using geoelectric approaches.The relations between electrical-hydraulic(eh)conductivities were modeled hypothetically and calibrated empirically.Correlations were based on the stochastic models and field-scale hydraulic parameters were contingent on pore-level parameters.By considering variation in pore-size distributions over eh conduction interval,the relations were scaled-up for use at aquifer-level.Material-level electrical conductivities were determined by using Vertical Electrical Survey and hydraulic conductivities by analyzing aquifer tests of eight boreholes in the Olbanita aquifer located in Kenya rift.VES datasets were inverted by using the computer code IP2Win.The main result is that ln T=0.537(ln Fa)+3.695;the positive gradient indicating eh conduction through pore-surface networks and a proxy of weathered and clayey materials.An inverse(1/F-K)correlation is observed.Hydraulic parameters determined using such approaches may possibly contribute significantly towards sustainable yield management and planning of groundwater resources.     

Electrical-hydraulic conductivity model for a weathered-fractured aquifer system of Olbanita,Lower Baringo Basin,Kenya Rift

Groundwater yield in the Kenya Rift is highly unsustainable owing to geological variability. In this study, field hydraulic characterization was performed by using geo-electric approaches. The relations between electrical-hydraulic (eh) conductivities were modeled hypothetically and calibrated empirically. Correlations were based on the stoch-astic models and field-scale hydraulic parameters were contingent on pore-level parameters. By considering variation in pore-size distributions over eh conduction interval, the relations were scaled-up for use at aquifer-level. Material-level electrical conductivities were determined by using Vertical Electrical Survey and hydraulic conductivities by analyzing aquifer tests of eight boreholes in the Olbanita aquifer located in Kenya rift. VES datasets were inverted by using the computer code IP2Win. The main result is that ln T=0.537 (ln Fa)+3.695; the positive gradient indicating eh conduction through poresurface networks and a proxy of weathered and clayey materials. An inverse (1/F-K) correlation is observed. Hydraulic parameters determined using such approaches may possibly contri-bute significantly towards sustainable yield management and planning of groundwater resources.     

含水层渗透系数空间变异性对地下水数值模拟的影响

地下水数值模拟是目前定量研究地下水水量和水质的重要手段。使用基于随机理论的MonteCarlo方法来进行地下水数值模拟。这种方法能较好地考虑水文地质参数的空间变异性。主要将MonteCarlo方法和确定性模型模拟方法的模拟结果在渗透系数场、水头场、速度场和浓度场等方面进行了比较。结果表明:在模拟三维非均质含水层中的溶质运移问题时,充分考虑了含水层渗透系数空间变异性的MonteCarlo法比确定性方法更为有效,模拟精度提高了很多,且对模拟误差及误差来源有合理的数学解释。     

含水层层状非均质对地下水流系统的影响

区域尺度上含水层非均质具有复杂的结构性和随机性,难以准确刻画,造成非均质对区域地下水流系统的影响机制研究不够深入。本文以鄂尔多斯盆地白垩系地下水流系统为研究实例,选择典型剖面,采用剖面二维随机数值模拟方法,通过对比不同非均质刻画方法下地下水流场的变化,探讨含水层层状非均质对地下水流系统的影响机制。结果显示,均质条件下模型各向异性（含水层水平和垂向渗透系数比值Kh/Kv）取值为1000时,地下水流场与实际条件较为接近;非均质条件下,渗透系数方差取值0.91,水平相关长度取值5000 m,Kh/Kv取值150时,接近实际条件。研究表明,在大尺度地下水流模拟研究中,采用水平相关长度、渗透系数方差和各向异性值三个变量生成的随机场能很好地刻画含水层的层状非均质特征及其对水流系统的影响控制作用。由于含水层不同尺度层状非均质的叠加效应,采用均质各向异性介质等效概化含水层层状非均质性会造成等效各向异性值偏大失真的效应。     

An accelerated algorithm for parameter identification in a hierarchical plasticity model accounting for material constraints

The parameter identification procedure proposed in this paper is based on the solution of an inverse problem, which relies on the minimization of an error function of least‐squares type. The solution of the ensuing optimization problem, which is a constrained one owing to the presence of physical links between the optimization parameters, is performed by means of a particular technique of the feasible direction type, which is modified and improved when the problem turns to an unconstrained one. The algorithm is particularly efficient in the presence of hierarchical material models. The numerical properties of the proposed procedure are discussed and its behaviour is compared with usual optimization methods when applied to constrained and unconstrained problems. Copyright © 2001 John Wiley & Sons, Ltd.     

稳定井流直线图解法确定含水层参数

对于潜水井流,利用Dupuit公式计算的参数往往相差很大,难以直接选用。对Dupuit公式进行线性化,建立降深(s)与距离(r)的s-lnr直线关系,利用直线斜率、直线在x轴上的截距,可以直接求得唯一的渗透系数K和影响半径R。利用松花江河谷的承压水井抽水试验资料和洮儿河扇形地27个潜水抽水井及其观测孔的抽水试验资料,应用直线图解法分析计算,得到唯一的含水层参数T、K和R。将计算结果与直接利用Dupuit公式所计算的结果相比较,前者的求参效果较好。     

裂隙岩溶含水系统溢流泉演化过程的数值模拟

本文利用非连续裂隙网络介质模型,耦合水动力条件和碳酸盐溶蚀动力条件,建立岩溶含水系统演化的数学模型,并用数值法进行模拟分析。在已建数值模型基础上,构造了两组实例模型(降水入渗补给的裂隙岩溶含水系统和河流补给的裂隙岩溶含水系统)来研究裂隙岩溶系统中溢流泉早期演化过程。模拟发现,裂隙岩溶含水系统演化过程中,裂隙不断被溶蚀拓宽,致使系统中潜水位不断下降,许多小泉被疏干;同时不同裂隙之间存在溶蚀差异,在潜水位及优势通道附近的裂隙溶蚀速度快,而其它位置则相对慢得多,差异溶蚀促使系统形成优势溶管,优势溶管逐渐袭夺水流,形成大泉。另外对比两模型发现,降水入渗为主要补给源的裂隙岩溶含水系统,泉管道从汇向源发育;而河流入渗为主要补给源的裂隙岩溶含水系统,泉管道则由源向汇发育。      

A novel analytical solution for constant‐head test in a patchy aquifer

A mathematical model describing the hydraulic head distribution for a constant‐head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer‐region transmissivity to patch‐region transmissivity as α. The dimensionless hydraulic head for α=0.1 case is about 2.72 times to that for α=10 case at dimensionless large time (e.g. τ?10⁶) when the dimensionless distance (ρ) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two‐zone formations. Copyright © 2006 John Wiley & Sons, Ltd.     

A local identification technique for geotechnical and geophysical systems

Geotechnical structures and natural soil deposits are massive multi‐phase particulate systems characterized by the development of localized response mechanisms under extreme loading conditions. Identification and analysis of such systems based on inverse boundary value problem formulations and sparse measurements are generally indeterminate. This paper presents an alternative local inverse problem technique. Point‐wise identification analyses of the constitutive behaviour of water‐saturated geotechnical and geophysical systems are performed using acceleration and pore pressure records provided by a cluster of closely spaced sensors. The developed novel technique does not require the availability of boundary condition measurements, or solution of an associated boundary value problem. The constitutive behaviour at a specific location of a soil‐system is analysed independently of adjacent response mechanisms or material properties. Numerical simulations and centrifuge tests of a soil‐retaining wall system are used to demonstrate the capabilities of the developed technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Inverse analysis for geomaterial parameter identification using Pareto multiobjective optimization

An inverse analysis method that combines the back propagation neural network (BPNN) and vector evaluated genetic algorithm (VEGA) was proposed to identify mechanical geomaterial parameters for a more accurate prediction of deformation. The BPNN is used to replace the time‐consuming numerical calculations, thus enhancing the efficiency of the inverse analysis. The VEGA is used to find the Pareto‐optimal solutions to multiobjective functions. Unlike traditional back‐analysis methods which are based on only 1 type of field measurement and a single objective function, this proposed method can consider multiple field observations simultaneously. The proposed method was applied to the Shapingba foundation pit excavation located in Chongqing city, China. Two types of measurements are considered in the method simultaneously: the displacements in the x‐direction (north orientation) and those in the y‐direction (east orientation). Five deformation modulus parameters for artificial backfill soil, silty clay, siltstone, sandstone, and mudstone were selected as the inversion parameters. Compared with the weighted sum approach, the proposed method was demonstrated as an efficient multi‐objective optimization tool for back calculating undetermined parameters. After performing a forward‐calculation using the optimized parameters obtained by the inverse analysis, the predicted results were well consistent with the practical deformation in magnitude and trend.     

Sensitivity analysis for parameter identification in quasi‐static poroelasticity

This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.     

潜水回水初始阶段的定性半定量分析及对水跃成因的解释

文章提出并采用水力坡度分析方法,对潜水回水初始阶段进行了定性-半定量分析,为了解潜水回水过程提供了新的视角。通过分析潜水回水初始时刻的水力坡度,河渠侧的界面被分为2段:河间潜水位之上的铅直段和之下的水平段。水平段上点的水力坡度最大且相等,方向为水平向右;铅直段上点的水力坡度方向趋于铅直向下,越向上水力坡度越小。经过微小时间段Δt后,水力坡度均相应变小,铅直段相邻点间地下水运动发生冲突,水力坡度方向由趋于铅直向下向右偏转。将水力坡度分析方法用于分析潜水井流的过程和特征,水跃的成因可解释为:在相同水力坡度和过水断面面积下,井内大空间水流速度远大于孔隙中的潜水流速度,井内水位急速下降,从而形成水跃;水跃越大,进入井内的流量就越大。     

A transversely isotropic thermo-poroelastic model for claystone: parameter identification and application to a 3D underground structure

A transversely isotropic thermo-poroelastic constitutive law is developed and implemented in the finite element code Code_Aster (EDF, France). It is then validated using an analytic solution for an inclined borehole in a transversely isotropic medium. A strategy for identifying the parameters of the transversely isotropic thermo-poroelastic model based on an inverse method is proposed on the basis of different laboratory tests. To demonstrate the efficiency and applicability of the model, it is then applied in a three-dimensional numerical model of an underground structure in a parameter sensitivity study. The results of the modelling highlight the importance of accounting for anisotropic phenomena when determining the dimensions of underground facilities. The whole approach is presented in the paper, from model development to application to 3D numerical modelling to an engineering case study.     

Numerical modelling of surfacewater/groundwater flows for freshwater/saltwater hydrology: the case of the alluvial coastal aquifer of the Low Guadalhorce River, Malaga, Spain

This applied research deals with the numerical modelling and transient simulation of the joint surfacewater/groundwater flows that characterize the freshwater/saltwater hydrology of the coastal alluvial valley of the Low Guadalhorce River, Malaga, Spain. The MELEF model used was mainly adapted and calibrated for a simulation period of two hydrological years 1989/1990–1990/1991, before the current channelling of the river, where floods and low precipitations have been recorded. The model calibration process was performed with the aid of phreatic levels measured in numerous wells and piezometers, as well as recharges from precipitation and irrigation on the alluvial surface, which was also assessed by the hydrologic model SSMA-2. The present numerical approach can predict the forthcoming hydrology of the coastal alluvial of the Guadalhorce River after its final channelling.