共查询到20条相似文献，搜索用时 31 毫秒
1.
Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values. 相似文献
2.
Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head–constant head wedge, constant head–barrier wedge and barrier–barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans. 相似文献
3.
The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
《Advances in water resources》2005,28(10):1102-1111
We present a range of analytical solutions to the combined transient water and solute transport for horizontal flow. We adopt the concept of a scale and time dependent dispersivity used for contaminant transport in aquifers and apply it to transient, unsaturated horizontal flow to develop similarity solutions for both constant solute concentration and solute flux boundary conditions. Through the use of a specific form of the water profile as used by Brutsaert [Water Resour Res 1968:4;785], the solute profiles can be reduced to a simple quadrature. We also derive a solution for the instantaneous injection of water and solute into a horizontal media for an arbitrary dispersivity. It is found that the solute concentration remains constant in both space and time as the water redistributes, suggesting that the solute does not disperse relative to the water. 相似文献
5.
Robert G. THOMAS 《水文科学杂志》2013,58(4):50-69
Abstract Graphical solutions to linear and radial ground water flow problems are described. These methods are based on finite difference approximations which have been widely used in heat flow problems. The case of the leaky aquiclude and vertical recharge to unconfined aquifers is discussed as well as constant head at a control and constant discharge or recharge. These solutions are useful only when the physical factors are known and an estimate of water level changes under certain conditions is desired. The methods are not intended to replace more rigorous mathematical solutions. 相似文献
6.
J. X. ZHAO 《地震工程与结构动力学》1997,26(1):93-113
For the one-dimensional analysis of soft-soil layers on an elastic half-space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half-space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd. 相似文献
7.
Similarity solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating non-ideal gas in presence of an azimuthal magnetic field. The density of the medium ahead of the shock is assumed to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be obeying a power law and to be decreasing as the distance from the axis increases. It is found that the similarity solutions exist, in both the cases, when the initial magnetic field is constant or obeying a power law. The effects of an increase in the value of the index for variation of angular velocity of the ambient medium, in the value of the parameter of the non-idealness of the gas and in the strength of the initial magnetic field are obtained. 相似文献
8.
G. Badin 《地球物理与天体物理流体动力学》2013,107(5):526-540
The surface quasi-geostrophic approximation is re-written in an oceanic context using the two-dimensional semi-geostrophic approximation. The new formulation allows to take into account the presence of out-of-balance flow features at scales comparable to or smaller than the Rossby radius of deformation and for small bulk Richardson numbers. Analytical solutions show that, while the surface quasi-geostrophic approximation tends to underestimate the buoyancy anomaly, the inclusion of finite Rossby number allows for larger values of the buoyancy anomaly at depth. The projection of the surface semi-geostrophic solution on the first baroclinic modes is calculated. The result of the projection is a functional form that decreases with the values of the Rossby number and toward smaller scales. Solutions for constant and exponential profile for the background potential vorticity are compared. Results of the comparison show that, in agreement with the results found for balanced flows, even for large Rossby number the exponential profile for the background potential vorticity retains smaller values for the buoyancy anomaly at depth than the solution found using a constant potential vorticity profile. 相似文献
9.
Kinematic equations have been utilized in the past for modeling erosion from a sloping plane subject to rainfall. This paper, part I in a series of two, presents analytical solutions of these equations under the assumption of constant effective rainfall of indefinite duration. These solutions contain a function which is related to a generalization of Dawson's integral. Some pertinent properties of this function are briefly discussed. The solutions obtained by previous investigators constitute a part of the solutions developed here. In part II the solutions are derived for the case when the duration of the effective rainfall is finite. 相似文献
10.
Summary Dispersion curves are described which hold for KCl solutions and for rocks saturated with KCl solutions. These curves are used to determine rock fabric parameters such as formation factors, tortuosities, and cementation factors. The fabric parameters measured by the usual methods were found to be a function of frequency. Therefore, a new method was developed that leads to constant rock fabric parameters. Seven examples are given. 相似文献
11.
Collection efficiency η of rectangular settling basins is studied in this note for two cases: (i) with no mixing and (ii) with perfect vertical mixing. At first, well known reference solutions corresponding to suspended solids with constant settling velocity are presented. The effects on deposition of suspended solids with varying settling velocities are then studied. Finally, original exact solutions for η are obtained for gamma distributed settling velocities. The reference solutions are perfectly compatible with these more general solutions. 相似文献
12.
Vertical movement of snowmelt water through snowpacks is modelled by applying the kinematic wave theory. Analytical solutions are obtained for moisture flux, particle velocity, time history and velocity of meltwater front and total moisture content for a single melt event assuming that the melt rate is constant. These solutions are extended to the case involving more than one event. © 1997 by John Wiley & Sons Ltd. 相似文献
13.
With the increasing emphasis of performance‐based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance‐based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed‐form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed‐form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed‐form solution are fit. This study presents a critical review of the closed‐form solution for the annual rate of structural collapse. The closed‐form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed‐form solution. Via a parametric study, the key variables contributing to the error between the closed‐form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed‐form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
J. H. Daluz Vieira 《Journal of Hydrology》1983,60(1-4):43-58
The solutions of the Saint-Vénant equations are compared with those of the kinematic, diffusion and gravity wave approximations, for a range of constant Froudé and kinematic wave numbers, with two different lower boundary conditions: (1) critical flow; and (2) zero depth gradient. For each lower boundary condition, zones are defined in the F0,k-field in which either kinematic, diffusion or gravity wave solutions may be used to approximate the full Saint-Vénant solutions. 相似文献
15.
Simple closed‐form approximations are presented for calculating the steady‐state groundwater age distribution in two‐dimensional vertical cross sections of idealized fresh water lenses overlying salt water, for aquifers that are vertically semi‐infinite and of finite thickness. The approximations are developed on the basis of existing one‐dimensional analytical solutions for travel‐time calculation in fresh water lenses and approximate streamline formulations. The two‐dimensional age distributions based on the closed‐form solutions match convincingly with numerical simulations. As expected, notable deviations from the numerical solution are encountered at the groundwater flow divide and when submarine groundwater discharge occurs. Ratios of recharge over hydraulic conductivities are varied to explore how the magnitude of the deviations changes, and it is found that the approximate closed‐form solutions perform well over a range of conditions found in natural systems. 相似文献
16.
Analytical solutions for constant‐rate pumping tests are widely used to infer aquifer properties. In this note, we implement a methodology that approximates the time‐varying pumping record as a series of segments with linearly varying pumping rates. We validate our approach using an analytical solution for a sinusoidally varying pumping test. We also apply our methodology to analyze synthetic test data and compare the results with those from a commonly used method where rate variations are represented by a series of constant‐rate steps. 相似文献
17.
《Advances in water resources》2007,30(4):927-936
A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data. 相似文献
18.
Analytic solutions play an important role in the testing of models evaluated by numerical methods. This paper presents a straight forward method for determining analytic solutions to multiple species contaminant transport problems in porous media. The method uses Fourier sine transforms (as opposed to Laplace transforms) to obtain the solution of Cho (1970, Can. J. Soil. Sci., 51: 339–350) in a simpler way. It provides a flexible approach to the introduction of new boundary and initial conditions within the model. New solutions are presented for constant and exponential initial contaminant profiles. 相似文献
19.
Zhixue Zhao Xiaoguang Wang Yonghong Hao Tongke Wang Abderrahim Jardani Herve Jourde Tian‐Chyi Jim Yeh Ming Zhang 《水文研究》2019,33(19):2551-2560
The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified. 相似文献
