EXPLICIT SOLUTIONS FOR SEEPAGE INFILTRATING INTO A POROUS EARTH DAM DUE TO PRECIPITATION

Steady two-dimensional gravity-driven seepage in homogeneous porous lumps is studied with the help of conformal mappings and boundary value problem technique. The Terzaghi flow pattern for a trapezoidal dam exposed to a heavy rainstorm is analysed. For a semi-circular massif, the influence of impervious bed inclination is studied. Recharge–discharge distributions, hinge points, gradients along the lump contour as well as the total flow rate exhibiting water–bearing capacity of the unit are found in explicit form. Generalizations for non-isobaric boundary conditions are discussed.     

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.     

Karstification below dam sites: a model of increasing leakage from reservoirs

Unnaturally steep hydraulic gradients below foundations or across abutments of dams may cause solutional widening of fractures in karstifiable rocks of carbonates or gypsum. This could cause increasing leakage which may endanger the performance of the construction. To investigate this problem recent models on natural karstification have been applied. We have performed numerical simulations of leakage below a model dam with a grouting curtain reaching down to 100 m below its impermeable foundation of 100 m width. Water is impounded to a depth of 100 m. The dam is located on a terrane of fractured rock dissected by two perpendicular sets of fractures with spacing of 5 m, and with a log-normal distribution of their initial aperture widths of about 0.02 cm. In the first state of karstification these fractures widen slowly, until a pathway of widened fractures below the grouting has reached the downstream side with exit widths of about 1 mm. This causes a dramatic increase of leakage, and turbulent flow sets in. After this breakthrough at time T, in the second state of karstification, dissolution rates become even along these fractures and cause widening of about 0.1 cm year^-1 for limestone, and at least of 1 cm year^-1 for gypsum. This leads to an increase in leakage to excessive rates within 25 years for limestone, but only 5 years for gypsum. We have performed a sensitivity analysis of breakthrough time T for the various parameters which determine the problem. The result shows breakthrough times in the order of several tens of years for both limestone and gypsum. We have also modelled leakage to caves or karst channels 200 m below the bottom of the reservoir, which could induce the formation of sinkholes. The model can be extended to more realistic settings. In conclusion, our results support the prediction that increasing leakage at dam sites can be caused by recent karstification which is activated after filling the reservoir, possibly leading to serious problems within its lifetime.     

Approximate analytical and numerical solutions for radial non‐Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect

This study investigated non‐Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite‐thickness skin. The non‐Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non‐Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller B_D results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where B_D is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady‐state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite‐difference solution for such a non‐Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non‐Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.     

西安市黑河水库左坝肩渗漏三维数值模拟及坝肩坡体稳定性分析

直接针对西安市黑河水库左坝肩渗漏这一重大工程实际问题展开研究与计算。应用三维有限差分方法对左坝肩单薄山梁的初始渗流场、蓄水后的渗流场进行了数值模拟 ,分析渗漏方式、计算相应的渗漏量 ,并通过计算说明了断层是集中渗漏通道。而后利用三维数值计算提供的水位值 ,应用极限平衡分析法 ,对左坝肩岩质斜坡稳定性进行计算与分析 ,计算结果对实际工程的决策与治理提供重要的依据。     

坝基两道防渗墙水头分担情况有限元分析

深覆盖层坝址上的高心墙堆石坝,在河床覆盖层中常设置两道混凝土防渗墙防渗。采用开发的有限元软件,参照砂卵石覆盖层深度近50 m的某心墙堆石坝工程的情况,分析了主、副防渗墙6种设置方案中坝基的稳定渗流场,得到了主墙、副墙和覆盖层的水头分担比例。所有方案中河床覆盖层上的水头都小于3 %。当主、副两道墙下部灌浆情况相同、端部之间设置灌浆帷幕封堵绕渗时,副墙承担的水头接近主墙;如果取消封堵绕渗的帷幕,副墙承担的水头下降到总水头的20 %～30 %;而副墙底部和主、副墙两端均不设帷幕的情况,副墙上承担的水头比例下降到总水头的8 %～11 %。副墙位于主墙的下游侧时,其上承担的水头比例比副墙位于主墙上游侧的情况略高。防渗墙承担的水头比例取决于墙整体的防渗能力,而对防渗墙本身的厚度变化不敏感。     

某水库坝基渗透稳定性研究

某拟建高为22 m的混凝土重力坝坐落于第四系冰水堆积层之上。在大坝上下游水头差的作用下,产生库水渗漏。库水的大量漏失,不但可能使大坝蓄水达不到设计高程而影响工程效益,而且,水流的渗透作用还会导致地基岩（土）体的恶化,产生渗透破坏,影响大坝本身的安全。在现场调查基础上,用数值模拟方法评价了该水库在库内设置175 m长铺盖条件下的渗漏问题,计算了水库的渗流量、大坝基底的水力坡度。因其量值较大,必须在渗流出口处采取反滤层等工程措施,给相关部门提供设计依据和决策参考。     

3D numerical modelling of fluid flow in the Val-d’Or orogenic gold district: major crustal shear zones drain fluids from overpressured vein fields

Fluid flow patterns have been determined using oxygen isotope isopleths in the Val-d’Or orogenic gold district. 3D numerical modelling of fluid flow and oxygen isotope exchange in the vein field shows that the fluid flow patterns can be reproduced if the lower boundary of the model is permeable, which represents middle or lower crustal rocks that are infiltrated by a metamorphic fluid generated at deeper levels. This boundary condition implies that the major crustal faults so conspicuous in vein fields do not act as the only major channel for upward fluid flow. The upper model boundary is impermeable except along the trace of major crustal faults where fluids are allowed to drain out of the vein field. This upper impermeable boundary condition represents a low-permeability layer in the crust that separates the overpressured fluid from the overlying hydrostatic fluid pressure regime. We propose that the role of major crustal faults in overpressured vein fields, independent of tectonic setting, is to drain hydrothermal fluids out of the vein field along a breach across an impermeable layer higher in the crust and above the vein field. This breach is crucial to allow flow out of the vein field and accumulation of metals in the fractures, and this breach has major implications for exploration for mineral resources. We propose that tectonic events that cause episodic metamorphic dehydration create a short-lived pulse of metamorphic fluid to rise along zones of transient permeability. This results in a fluid wave that propagates upward carrying metals to the mineralized area. Earthquakes along crustal shear zones cause dilation near jogs that draw fluids and deposit metals in an interconnected network of subsidiary shear zones. Fluid flow is arrested by an impermeable barrier separating the hydrostatic and lithostatic fluid pressure regimes. Fluids flow through the evolving and interconnected network of shear zones and by advection through the rock matrix. Episodic breaches in the impermeable barrier along the crustal shear zones allow fluid flow out of the vein field.     

An artificial boundary approach for unbounded transient seepage problems

A new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd.     

燕山水库坝基防渗墙优化设计

因现场资料不足或分析手段落后等原因,当前进行水库坝基防渗墙设计,往往存在过于保守的倾向。以河南省燕山水库为例,基于优化设计的思路,采用目前较为成熟的二维有限单元法,对不同防渗条件下的坝基渗流场分别进行了模拟,并将计算所得比降、流量与允许比降、允许流量做了对比,从定量的角度提出了既安全、又经济的防渗方案:防渗墙厚度取0.8m,深度取打入破碎带5m。     

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。     

Using zero-thickness elements to simulate suspended cut-off walls in a regional seepage field

A regional seepage field is usually simulated by 2D horizontal seepage finite element method (FEM). However, the Dupuit assumption means that it does not take into account hydraulic head loss caused by vertical flow. In order to simulate a regional seepage field containing suspended cut-off walls by 2D horizontal FEM without any loss of accuracy and efficiency, a zero-thickness element is introduced. The zero-thickness element is used to model suspended cut-off walls and take into account the hydraulic head loss caused by vertical flow near the walls. The matrix equation is deduced. The deduction is based on the resistance coefficient method and the analytical solution of flow near suspended cut-off walls under plane condition. The accuracy of the method is assessed by comparing with 3D FEM results. These coincide with each other both in discharge and hydraulic head. The method is an effective way to simulate a suspended cut-off wall in a regional seepage field with 2D horizontal FEM.     

A new parabolic variational inequality formulation of Signorini's condition for non‐steady seepage problems with complex seepage control systems

By extending Darcy's law to the dry domain above the free surface and specifying the boundary condition on the potential seepage surfaces as Signorini's type, a partial differential equation (PDE) defined in the entire domain of interest is formulated for non‐steady seepage flow problems with free surfaces. A new parabolic variational inequality (PVI) formulation equivalent to the PDE formulation is then proposed, in which the flux part of the complementary condition of Signorini's type in the PDE formulation is transformed into natural boundary condition. Consequently, the singularity at the seepage points is eliminated and the difficulty in selecting the trial functions is significantly reduced. By introducing an adaptive penalized Heaviside function in the finite element analysis, the numerical stability of the discrete PVI formulation is well guaranteed. The proposed approach is validated by the existing laboratory tests with sudden rise and dropdown of water heads, and then applied to capture the non‐steady seepage flow behaviors in a homogeneous rectangular dam with five drainage tunnels during a linear dropdown of upstream water head. The non‐steady seepage flow in the surrounding rocks of the underground powerhouse in the Shuibuya Hydropower Project is further modeled, in which a complex seepage control system is involved. Comparisons with the in situ monitoring data show that the calculation results well illustrate the non‐steady seepage flow process during impounding and the operation of the reservoir as well as the seepage control effects of the drainage hole arrays and drainage tunnels. Copyright © 2010 John Wiley & Sons, Ltd.     

不透水地基上均质土坝渗流自由面的有限元计算

为了保证土坝安全,水利工程中需要对土坝进行渗流计算,首先需要确定自由面。根据达西定律和渗流连续方程,以及水头和流量边界条件,建立了不透水地基上的均质土坝渗流的计算模型。利用Geoslope软件,采用有限元离散的方法计算了土坝的渗流自由面,并分析了土坝在不同的渗透系数情况下的自由面位置的差异。最后,解析解计算的自由面结果验证了有限元计算自由面方法是正确的。     

坝基集中渗漏通道的温度场反分析与试验研究

渗漏是严重影响堤坝安全的主要形式,确定渗漏通道的位置是进行堤坝渗漏整治的前提和基础。温度场探测堤坝渗漏的研究是其中一种较便捷的方法,但是在理论上还需要进一步完善。在库水和地下水存在着温度差异的基础上,考虑堤坝发生集中渗漏后,渗漏通道中的地下水与周围土体进行热量交换,造成渗流通道附近地层温度发生改变,建立起温度场对渗漏通道的反演模型。在前人研究的基础上,考虑地温梯度的影响,可以建立有集中渗漏通道影响下的二维热传导方程,进而以现场测井的温度数据作为边界条件,对泛定方程进行求解,最终得到渗漏通道的位置。计算结果和实测结果的对比表明,通过温度场反推渗漏通道参数的方法是可行的。     

某水利枢纽厂房基坑开挖渗透变形评估

在对渗流评估方法进行一定探讨的基础上,对某水利枢纽工程坝址区厂房基坑开挖进行了渗透变形评估。结果表明,在坝轴线方向上,无防渗墙时坡面土体在渗透力的作用下是不稳定的,有防渗墙时坡面水力坡降降到0.05以下。在砂卵砾石层与基岩的交界处仍存在略大的水力坡降（值为0.56）,如有水在细砂层、砾质中粗砂层渗出,则有可能出现渗流失稳,但总的说来由于防渗墙使水力坡降已降到很小,出现流土和管涌失稳的可能性不大。     

A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers

The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation.     

Investigation of water pressure transients beneath temperate glaciers using numerical groundwater flow experiments

Recent work has identified groundwater flow through basal till aquifers as a key control on melt‐season pressure transients beneath alpine glaciers, with potential implications for climate change studies, glacial geomorphology, tracer test interpretation, and the sediment load and chemistry of glacially derived waters. In this study, we investigate heuristically such subglacial Darcian flow processes using standard groundwater modelling techniques. Our primary result is that a one‐dimensional, transient, confined flow model with recharge, implemented numerically using time‐varying specified‐head and no‐flow boundaries, reproduces overall observed subglacial hydraulic behaviour very well and permits effective visualisation of aquifer responses under different conditions. Spatial variability in hydrogeological parameters is shown to have significant effects, but may be difficult to incorporate reliably into site‐specific models and to identify unambiguously in borehole pressure data. Time‐variance in areal recharge, if present, is apparently not observably expressed in the system, but time‐variance in transmissivity may be significant for some glaciers. Copyright © 2000 John Wiley & Sons, Ltd.     

含节理黄土渗流数值模型研究

本文建立了在考虑黄土中有节理存在时,水分场数值计算的有限元方法。采用质量守恒的观点推导了质点元中饱和度的变化与流速的关系。进而利用达西定律得到以水头为变量的渗流基本方程。针对黄土垂直节理的渗流特点,确定了节理渗流基本方程中的参数。采用四边形等参元,利用Galerkin加权余量法建立考虑节理影响的黄土非饱和渗流的有限元形式。对局部水头边界条件下的黄土节理二维水分入渗问题进行了数值分析。结果表明,节理对黄土场地湿润峰的迁移有很大影响。     

岩溶水库坝基防渗帷幕灌浆幕深与幕长的结构形式及处理

防渗帷幕灌浆是处理岩溶地区水库坝基坝肩渗漏的主要方法之一，它可以杜绝深、浅层的复杂的岩溶漏水问题，帷幕设计的合理性及其效果取决于水文地质、地下水的补排条件，水工建筑物结构之间的帷幕体的搭接形式，布置格局和边界范围。本文根据34处渗漏水库的灌浆实践，提出确定帷幕的深度和长度的原则，并得出了相关曲线和经验公式，对岩溶地区水库的渗漏处理进行探讨。