Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation     

Ruoyi Li  Xu-Sheng Wang 《水文研究》2021,35(2):e14036

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.  相似文献   

Rainfall intensity affects runoff responses in a semi-arid catchment     

Ze Tao  Min Li  Bingcheng Si  Dyan Pratt 《水文研究》2021,35(4):e14100

The source and hydrochemical makeup of a stream reflects the connectivity between rainfall, groundwater, the stream, and is reflected to water quantity and quality of the catchment. However, in a semi-arid, thick, loess covered catchment, temporal variation of stream source and event associated behaviours are lesser known. Thus, the isotopic and chemical hydrographs in a widely distributed, deep loess, semi-arid catchment of the northern Chinese Loess Plateau were characterized to determine the source and hydrochemical behaviours of the stream during intra-rainfall events. Rainfall and streamflow were sampled during six hydrologic events coupled with measurements of stream baseflow and groundwater. The deuterium isotope (²H), major ions (Cl⁻, SO₄²⁻, NO₃⁻, Ca²⁺, K⁺, Mg²⁺, and Na⁺) were evaluated in water samples obtained during rainfall events. Temporal variation of ²H and Cl⁻ measured in the groundwater and stream baseflow prior to rainfall was similar; however, the isotope compositions of the streamflow fluctuated significantly and responded quickly to rainfall events, likely due to an infiltration excess, overland dominated surface runoff during torrential rainfall events. Time source separation using ²H demonstrated greater than 72% on average, the stream composition was event water during torrential rainfall events, with the proportion increasing with rainfall intensity. Solutes concentrations in the stream had loglinear relationships with stream discharge, with an outling anomaly with an example of an intra-rainfall event on Oct. 24, 2015. Stream Cl⁻ behaved nonconservative during rainfall events, temporal variation of Cl⁻ indicated a flush and washout at the onset of small rainfall events, a dilution but still high concentration pattern in high discharge and old water dominated in regression flow period. This study indicates rainfall intensity affects runoff responses in a semi-arid catchment, and the stored water in the thick, loess covered areas was less connected with stream runoff. Solute transport may threaten water quality in the area, requiring further analysis of the performance of the eco-restoration project.  相似文献   

Seasonal connections between meteoric water and streamflow generation along a mountain headwater stream     

Sam J. Leuthold  Stephanie A. Ewing  Robert A. Payn  Florence R. Miller  Stephan G. Custer 《水文研究》2021,35(2):e14029

In snowmelt-driven mountain watersheds, the hydrologic connectivity between meteoric waters and stream flow generation varies strongly with the season, reflecting variable connection to soil and groundwater storage within the watershed. This variable connectivity regulates how streamflow generation mechanisms transform the seasonal and elevational variation in oxygen and hydrogen isotopic composition (δ¹⁸O and δD) of meteoric precipitation. Thus, water isotopes in stream flow can signal immediate connectivity or more prolonged mixing, especially in high-relief mountainous catchments. We characterized δ¹⁸O and δD values in stream water along an elevational gradient in a mountain headwater catchment in southwestern Montana. Stream water isotopic compositions related most strongly to elevation between February and March, exhibiting higher δ¹⁸O and δD values with decreasing elevation. These elevational isotopic lapse rates likely reflect increased connection between stream flow and proximal snow-derived water sources heavily subject to elevational isotopic effects. These patterns disappeared during summer sampling, when consistently lower δ¹⁸O and δD values of stream water reflected contributions from snowmelt or colder rainfall, despite much higher δ¹⁸O and δD values expected in warmer seasonal rainfall. The consistently low isotopic values and absence of a trend with elevation during summer suggest lower connectivity between summer precipitation and stream flow generation as a consequence of drier soils and greater transpiration. As further evidence of intermittent seasonal connectivity between the stream and adjacent groundwaters, we observed a late-winter flush of nitrate into the stream at higher elevations, consistent with increased connection to accumulating mineralized nitrogen in riparian wetlands. This pattern was distinct from mid-summer patterns of nitrate loading at lower elevations that suggested heightened human recreational activity along the stream corridor. These observations provide insights linking stream flow generation and seasonal water storage in high elevation mountainous watersheds. Greater understanding of the connections between surface water, soil water and groundwater in these environments will help predict how the quality and quantity of mountain runoff will respond to changing climate and allow better informed water management decisions.  相似文献   

Subsurface flow measurements using passive flux meters in variably-saturated cold-regions landscapes     

Élise G. Devoie  Ryan F. Connon  James R. Craig  William L. Quinton 《水文研究》2020,34(23):4541-4546

To date, passive flux meters have predominantly been applied in temperate environments for tracking the movement of contaminants in groundwater. This study applies these instruments to reduce uncertainty in (typically instantaneous) flux measurements made in a low-gradient, wetland dominated, discontinuous permafrost environment. This method supports improved estimation of unsaturated and over-winter subsurface flows which are very difficult to quantify using hydraulic gradient-based approaches. Improved subsurface flow estimates can play a key role in understanding the water budget of this landscape.  相似文献   

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis     

Ramin Pakzad  Shanyong Wang  Scott W. Sloan 《国际地质力学数值与分析法杂志》2020,44(10):1472-1494

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.  相似文献   

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law          下载免费PDF全文

Ahmad Hajjar  Luc Scholtès  Constantin Oltéan  Michel Antoine Buès 《水文研究》2018,32(16):2510-2525

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.  相似文献   

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation          下载免费PDF全文

Tongbi Tu  Ali Ercan  M. Levent Kavvas 《水文研究》2018,32(10):1406-1419

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.  相似文献   

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock          下载免费PDF全文

N. Zolfaghari  E. Dontsov  A. P. Bunger 《国际地质力学数值与分析法杂志》2018,42(4):587-617

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.  相似文献   

A modified numerical model for moisture-salt transport in unsaturated sandy soil under evaporation     

Wei Wen  YuanMing Lai  ZheMin You 《寒旱区科学》2020,12(3):125-133

Soil salinization, caused by salt migration and accumulation underneath the soil surface, will corrode structures. To analyze the moisture-salt migration and salt precipitation in soil under evaporation conditions, a mathematical model consisting of a series of theoretical equations is briefly presented. The filling effect of precipitated salts on tortuosity factor and evaporation rate are taken into account in relevant equations. Besides, a transition equation to link the solute transport equation before and after salt precipitation is proposed. Meanwhile, a new relative humidity equation deduced from Pitzer ions model is used to modify the vapor transport flux equation. The results show that the calculated values are in good agreement with the published experimental data, especially for the simulation of volume water content and evaporation rate of Toyoura sand, which confirm the reliability and applicability of the proposed model.  相似文献   

Warm gas kinematics in shell galaxies     

R. Rampazzo  H. Plana  M. Longhetti  P. Amram  J. Boulesteix  J.-L. Gach  O. Hernandez 《Monthly notices of the Royal Astronomical Society》2003,343(3):819-830

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