Constant Head Boundary Conditions Research Articles

RichardsFoam3: A new version of RichardsFoam for continental surfaces hydrogeology modelling

RichardsFoam3 is an updated version of the OpenFOAM® solver RichardsFoam, previously presented in “An open source massively parallel solver for Richards equation: Mechanistic modelling of water fluxes at the watershed scale” by L. Orgogozo, N. Renon, C. Soulaine, F. Hénon, S.K. Tomer, D. Labat, O.S. Pokrovsky, M. Sekhar, R. Ababou, M. Quintard (Comput. Phys. Commun. 185 (2014) 3358-3371, https://doi.org/10.1016/j.cpc.2014.08.004), and in the new version announcement “RichardsFOAM2: a new version of RichardsFOAM devoted to the modelling of the vadose zone” by L. Orgogozo (Comput. Phys. Commun. 196 (2015) 619-620, https://doi.org/10.1016/j.cpc.2015.07.009).This new version includes improvements of memory handling and of on-the-fly control of computations, a better integration in the OpenFOAM® framework, simplifications of the coding of some expressions, as well as new advanced boundary conditions. All together these developments allow to enhance the ease of application of the code to continental surfaces hydrogeology modelling, its computational performances and its readability.The description of the elements contained in this release may be found in the readMe file.Please note that you may also find RichardsFoam3 on the hydrology page of the develop.openfoam.com interface:https://develop.openfoam.com/Community/hydrology/ New version program summaryProgram title: RichardsFoam3CPC Library link to program files:https://doi.org/10.17632/vkr7sd6fhb.1Developer's repository link:https://develop.openfoam.com/Community/hydrology/Licensing provisions: GPLv3Programming language: C++Supplementary material: The full system of equations solved by RichardsFoam3 is presented in the documentation directory of the RichardsFoam3 package, with a numbering that is used in the comments of the main source file RichardsFoam3.C of the solver RichardsFoam3, in order to identify which lines of code are related to which equation.Journal reference of previous version: Comput. Phys. Commun. 196 (2015) 619-620Does the new version supersede the previous version?: YesReasons for the new version: Introducing new functionalities and implementing improvements for ergonomy, computational performances and readabilitySummary of revisions: The new features compared to RichardsFOAM [1] and RichardsFoam2 [2] are the following:(i) better handling of memory use during computation;(ii) possibility of on-the-fly modification of the control parameters of the linearisation procedure;(iii) new boundary conditions to be compiled along with the solver itself, and dedicated to the simulation of rain infiltration (rainFallFlux) or no infiltration (noFlux) conditions while allowing exfiltration with OpenFOAM® stand-alone (i.e. without mandatory use of swak4foam as it was the case in RichardsFoam2 [2]);(iv) Computation of the field of piezometric head along computation. NB: in the demonstration cases, a way to implement a constant piezometric head boundary conditions with OpenFOAM is proposed.(v) new functions that allow to build seasonally variable boundary conditions easily;(vi) use of postprocessing procedures with OpenFOAM® stand-alone (i.e. without mandatory use of swak4foam as it was the case in RichardsFoam2 [2]);(vii) several other minor rewritings/cleanings of the code.Nature of problem: This software solves the non-linear three-dimensional transient Richards equation, which is a very popular model for water transfer in variably saturated porous media (e.g.: soils). It is designed to take advantage of the massively parallel computing performance of OpenFOAM®. The goal is to be able to model natural hydrosystems on large temporal and spatial scales.Solution method: A mixed implicit (FVM in the object oriented OpenFOAM framework) and explicit (FVC in the object oriented OpenFOAM® framework) discretization of the equation with a backward time scheme is coupled with a linearization method (Picard algorithm). Due to the linearization loop the final solution of each time step tends towards a fully implicit solution. The implementation has been carried out with a concern for robustness and parallel efficiency.

On Inflow to a Tunnel in a Fractured Double-Porosity Aquifer.

Inflow to a tunnel is a great public concern and is closely related to groundwater hydrology, geotechnical engineering, and mining engineering, among other disciplines. Rapid computation of inflow to a tunnel provides a timely means for quickly assessing the inflow discharge, thus is critical for safe operation of tunnels. Dewatering of tunnels is another engineering practice that should be planned. In this study, an analytical solution of the inflow to a tunnel in a fractured unconfined aquifer is obtained. The solution takes into account either the spherical or slab-shaped matrix block and the unsteady state interporosity flow. The instantaneous drainage water table and anisotropic hydraulic conductivities of the fractures network are also considered. Both uniform flux and uniform head boundary condition are considered to simulate the constant head boundary condition in the tunnel. The effects of the hydraulic parameters of the fractured aquifer on the inflow variation of the tunnel are explored. The application of the presented solution to obtain the optimum location and discharge of the well to minimize the inflow to a tunnel is illustrated.

Groundwater Circulation Well for Controlling Saltwater Intrusion in Coastal aquifers: Numerical study with Experimental Validation

Saltwater intrusion into coastal aquifers has become a prominent environmental concern worldwide. As such, there is a need to prepare and implement proper remediation techniques with careful planning of freshwater withdrawal systems for controlling saltwater intrusion in coastal marine and estuarine environments. This paper investigates the performance of groundwater circulation well (GCW) in controlling saltwater intrusion problems in unconfined coastal aquifers. The GCWs have been established as a promising in-situ remedial technique of contaminated groundwater. The GCW system creates vertical circulation flow by extracting groundwater from an aquifer through a screen in a single well and injecting back into the aquifer through another screen. The circulation flow induced by GCW force water in a circular pattern between abstraction and recharge screens and can be as a hydraulic barrier for controlling saltwater intrusion problem in coastal aquifers. In this study, an effort has been made to investigate the behavior of saltwater intrusion dynamics under a GCW. An experiment has been conducted in a laboratory-scale flow tank model under constant water head boundary conditions, and the variable-density flow and transport model FEMWATER is used to simulate the flow and transport processes for the experimental setup. The evaluation of the results indicates that there is no further movement of saltwater intrusion wedge towards the inland side upon implementation of GCW, and the GCW acts as a hydraulic barrier in controlling saltwater intrusion in coastal aquifers. The present study reveals the GCWs system can effectively mitigate the saltwater intrusion problem in coastal regions and could be considered as one of the most efficient management strategies for controlling the problem.

Semi-analytical solutions of discharge variation of a qanat in an unconfined aquifer subjected to general areal recharge and nearby pumping well discharge

Qanat is a type of drain that extract water from aquifers by gravity. Significant amount of fresh water used in Middle East and other parts of the world are supplied by qanats. Despite their importance, discharge variation of these type of wells received almost no attention. The aim of this research is to obtain a Laplace domain solution of discharge variation of a qanat installed in an anisotropic unconfined aquifer subjected to arbitrary areal recharge and nearby pumping well(s) discharge. A new semi-analytical solution of drawdown is obtained first to implement the effects of arbitrary areal recharge and nearby pumping well(s) using the principle of superposition. Then, the discharge variation solution of the qanat is obtained from the drawdown solution. To establish a constant-head boundary condition at the qanat periphery, the qanat is discretized into several segments. The results of this study are presented in dimensionless discharge-dimensionless time curves. The effects of hydraulic as well as geometric parameters on the discharge variation of the qanat due to arbitrary areal recharge, falling of water table from its initial position and discharge of nearby wells are explored. We also investigate the influences of distance and screen depth and location of the nearby well on the discharge variation of the qanat. The results of this study can be utilized for multiple purposes: 1) to predict discharge of qanat in response to rainfall and nearby pumping well(s); 2) to estimate the aquifer parameters using hydrograph of the qanat; 3) to determine optimal location and pumping pattern of the nearby wells to minimize their influences on the discharge of the qanat; 4) to calculate water budget of aquifers drained by a qanat. The equation presented in this work can also be used to estimate discharge of a horizontal drain installed in cropland subjected to arbitrary irrigation pattern.

Internal fluctuations in green roof substrate moisture content during storm events: Monitored data and model simulations

Understanding how the moisture content in a green roof substrate varies during a storm event is essential for accurately modelling runoff detention. In this paper, a green roof test bed installed with moisture probes at three depths was used to understand how moisture content varies during storms. Detailed studies were conducted on five selected storm events. Physical characterisation tests and field-data based calibrations were performed to acquire the model parameters. Two alternative detention models, based on Reservoir Routing and Richard’s Equation, were validated against the measured green roof runoff and temporary moisture storage data. Once the moisture content exceeds local field capacity, its response at different depths occurs simultaneously during storms, although the recorded data indicate a vertical gradient in the absolute values of local field capacity. Both Reservoir Routing and Richard’s Equation can provide reasonable estimations of the runoff and the vertical moisture content profiles, although Richard’s Equation exhibited stronger vertical water content gradients than were observed in practise. The vertical water content profile is not sensitive to the soil water release curve, although the hydraulic conductivity function influences both the vertical water content profile and runoff rate. The modelled results are highly sensitive to the bottom boundary condition, with a constant suction head boundary condition providing a more suitable option than a free drainage boundary condition or a seepage boundary condition.

In-situ Observation and Nitrate-N Load Assessment in Madhubani District, Bihar, India

Fertilizers may leach through the vadose zone and eventually reach groundwater in agriculturally intensive areas. Thus, the main focus of this study was to investigate Nitrate-N load and vulnerability of groundwater resources using in-situ observed hydrogeological data. Soil water flow and contaminant transport equation was numerically simulated using HYDRUS 1D for constant head and atmospheric top boundary conditions. Subsurface materials were distributed based on the lithologs of the target area. Observed water table locations were considered as bottom boundary condition to respective numerical domain. The time taken by Nitrate-N to reach groundwater table was considered to estimate vulnerability index. The results show that Nitrate-N load is higher in constant head boundary conditions than atmospheric boundary conditions. The eastern part of the study area shows high vulnerability than northern part followed by western part. In-situ observed nitrate concentrations were well matched with simulated results. The high vulnerability in eastern and northern part is due to alluvial sandy lithologs and very shallow groundwater table. These findings are in line with the observed low water table depths, less runoff, and higher hydraulic conductivity of the vadose zone material in these area. In western part, forest cover dominated land use causes low pollution vulnerabilities to groundwater resources. This study may help to frame agricultural and soil-water conservation practices with more sustainable remedial techniques.

Meshfree Multiquadric Solution for Real Field Large Heterogeneous Aquifer System

Meshfree methods are often tested in literature for the rectangular domain with uniform aquifer properties (e.g. transmissivity or hydraulic conductivity) and constant groundwater head boundary conditions. In this paper, a multiquadric meshfree (Mfree) groundwater model is developed for a real field irregular domain aquifer system which is capable of incorporating variability like heterogeneity, temporally and spatially varied groundwater head and flow boundary conditions. The developed model is free from the inadequacy of meshing which eventually saves the time on computing resources by calculating the groundwater head-derivatives at different nodes sprinkled over the entire flow domain. Initially, two synthetic problems with pre- existing analytical and grid based results are tested against the presented model. Sensitivity analysis of different parameters like time step size, nodal density and support size of basis function are also investigated. Subsequently Mfree solutions are obtained for a large Mahi Right Bank Canal (MRBC) unconfined aquifer located in Gujarat India. The Mfree solution performance on two synthetic and one real field large aquifer problem revealed that the projected method is advantageous over other grid based simulator in terms of computational time consideration. Such a simulation is preferable in groundwater management models where flow models are coupled with the optimization problem.

Performance assessment of an underground gas storage cavern using water-shed scale groundwater flow modeling with large grid spacing

In this study, we simulated the water-shed scale groundwater flow near an underground LPG storage cavern system to assess its performance. To consider the effects of the storage cavern system on groundwater flow with large grid spacing, we proposed a mathematical model of a head-dependent flux boundary condition for a storage cavern system. Then, we examined its applicability by comparing the simulation results from assigning head-dependent flux boundary conditions, to those from assigning constant head boundary conditions for a hypothetical storage cavern system. Then, we applied this new simulation to the performance assessment of a real underground LPG storage cavern system. The results show that the influence of a storage cavern system on groundwater flow can be modeled in a 3-D water-shed scale with large cells by applying the proposed head-dependent flux boundary condition. The proposed model for a head-dependent flux boundary condition was used for performance assessment of the storage cavern systems and discussion of future works for their performance.

Estimate of river seepage by conditioning downward groundwater flow in the Toyohira River alluvial fan, Japan

ABSTRACTRiver seepage serves as the main source of groundwater in alluvial fans. However, reasonable estimates are rarely obtainable due to inaccuracy of vertical flows around the losing river. In the alluvial fan of the Toyohira River, Japan, to provide a straightforward description of vertical hydraulic gradient (VHG), this study demonstrates assignment of constant head boundary conditions on the shallowest aquitard instead of no-flow conditions on the basement. Initial constant heads and layer-scale anisotropy are calibrated in terms of hydraulic heads. As a result, the simulated river seepage is in reasonable agreement with previous discharge measurements, with net water loss determined to be approximately 1 m3/s. Although the simulation fails for water gain in the lower section, due to a lack of sporadic intercalations of fine deposits, the conditioned VHG modelling approach is found to be effective on a regional scale, especially when losing/gaining sections have not been identified in advance.EDITOR D. Koutsoyiannis ASSOCIATE EDITOR J. Ward

Slope stabilisation using EPS block geofoam with internal drainage system

Lightweight expanded polystyrene (EPS) geofoam (geofoam block) is used in slope remediation works as a soil substitute fill to reduce driving forces that can lead to global instability. On the other hand, the presence of seepage flow requires special attention because geofoam block slope systems are vulnerable to seepage-induced lateral forces. In this study, the effect of an internal drainage system on the alleviation of piezometric pressures within the back-slope of a geofoam block slope system was investigated. For this purpose, laboratory experiments were conducted using a small-scale lysimeter with dimensions of 60 cm height, 20 cm width, and 200 cm length. The slope was compacted with sand to obtain an overall dry unit weight of 14 kN/m3. The constant piezometric head boundary conditions of 25, 38 and 50 cm generated the necessary hydraulic energy gradient for the seepage flow directed from the water reservoir of the lysimeter to the 45° angle slope face. The slopes were remediated by using geofoam blocks assembled in an embankment-type configuration at the toe of the slope. The internal drainage system consisted of grooved geofoam blocks that formed the 10, 15 and 22.5 cm high embankments. Deep-seated failures of the non-remediated slope were prevented except for the experiments with 10 and 15 cm high embankments under 50 cm pressure head boundary conditions. In general, the internal drainage system alleviated the piezometric pressure conditions within the back-slope by lowering the phreatic surface using the active drainage channels observed during laboratory experiments. These drainage channels provided a convenient passageway for seepage flow. The coupled numerical variably saturated flow modelling and slope stability modelling predicted the factor of safety for global stability which confirmed the observed physical conditions in the laboratory. The use of the internal drainage system increased the factor of safety of the geofoam block slope system under seepage conditions.

Determination of the location of the groundwater divide and nature of groundwater flow paths within a region of active stream capture; the New River watershed, Virginia, USA

The relatively rapid stream capture of the New River basin by the Roanoke River basin provides a unique example of topographic change within a tectonically inactive environment. A previous investigation of abandoned river deposits has shown the capture of ~225 km2 of New River basin area, which has caused approximately 250 m of incision by the Roanoke River. Difference in base level elevations between the lower Roanoke to the higher New River could be the source of potential energy driving rapid incision. Significant incongruities in base level elevations at the boundaries of an aquifer can steepen the gradient and shift the groundwater divide further toward the higher elevation. If a steep groundwater gradient and expanded groundwater basin exists beneath the Roanoke River tributaries, this would suggest a groundwater control on incision and capture. This investigation incorporates average total head, measured from 18 domestic wells, and constant-head river boundary conditions into numerical models to calculate water levels and gradients between the rivers. Thermal patterns and particle tracking of spring locations were utilized to better understand flow paths in the region. Our results show the groundwater divide is shifted toward the higher elevation boundary, indicating that the groundwater basin is captured prior to surface capture. Flow pathways utilized by groundwater capture can be either diffuse or conduits; however, further work should be done to better understand travel times and flow depths.

Analytical solution for transient groundwater flow during slug test in vertical cutoff walls

SUMMARY 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.

Multi-scale Experimentation and Numerical Modeling for Process Understanding of CO2 Attenuation in the shallow subsurface

Abstract The goal of this study is to quantify the effects of geologic heterogeneity on the dynamic process of CO 2 attenuation in shallow aquifers through the use of multi-scale laboratory experimentation and numerical modelling. First, an experiment was conducted in an intermediate scale two-dimensional cell that was packed with water-saturated porous media in a simple heterogeneous configuration. Constant-head boundary conditions were applied to the system, and then CO 2 -saturated water was injected through it. As the CO 2 -saturated water migrated through the system, gas phase CO 2 evolved within the porous media, as observed by dielectric saturation sensors. The outflow of CO 2 gas from the top of the system was monitored by a gas flow meter, and the outflow of water from the side of the tank was monitored via collection into a container that was placed on a computer-interfaced scale. After the multiphase CO 2 evolution appeared to have reached steady state, clean water was injected through the cell until all of the CO 2 was expelled from the system. In addition to the experiments, numerical models were performed using the Finite Element Heat and Mass transfer (FEHM) code as a first step toward planning larger scale experiments. Results indicate that the presence of geologic heterogeneity, which is ubiquitous in natural environments, can significantly hinder the migration of CO 2 in the shallow subsurface.

Steady-state freshwater–seawater mixing zone in stratified coastal aquifers

Summary The mixing zone between freshwater and intruding seawater, which controls regional groundwater flow dynamics and reactive transport processes, is the most important component in coastal aquifers. Laboratory experiments and numerical simulations were conducted to investigate the effects of aquifer stratification on the thickness of a steady-state freshwater–seawater mixing zone. A series of experiments were implemented in a laboratory tank packed with three layers of coastal sands and manipulated by two flow cells for maintaining constant-head boundary conditions. Packed aquifers included a homogenous aquifer, a high hydraulic conductivity (K)–low K–high K stratified aquifer, and a low K–high K–low K stratified aquifer. Both tank-scale and field-scale density-dependent models were developed to simulate the laboratory experiments and to systematically investigate aquifer stratification effects on the thickness of a steady mixing zone with varying layer configurations. Results showed that when an aquifer layer with a low K overlies a layer with a relatively high K, slanting upward flow of diluted saltwater and re-circulated seawater flow are refracted at the interface between the two layers, resulting in streamline separation and a broad mixing zone in the low-K layer. By contrast, the mixing zone in a high-K layer is slightly narrowed when it overlies a layer with a relatively low K because flow refraction squeezes the streamlines within the mixing zone. The mixing-zone profile in head-controlled systems is a function of K contrast, but independent of the magnitude of K. Our results demonstrated the significant impact of aquifer stratification on controlling groundwater flow and solute transport in coastal subsurface environments and would have significant implications for studying physical, chemical and biological processes in coastal subsurface environments, as aquifer stratification is naturally prevalent.

Theoretical and Experimental Research of Cumulative Infiltration

The main object of this study is the comparative evaluation of Green & Ampt’s (G & A) and Parlange’s (P’s) models and their ability to describe cumulative infiltration of water through various soil types. Three soil samples of different hydraulic properties were packed separately into a transparent vertical column. A constant head boundary condition was applied at the surface of the soil and the incoming amount of water was measured volumetrically. Soil moisture was measured using TDR waveguides at certain locations of the column. At the early times of cumulative infiltration, sorptivity of each soil sample was estimated. Theoretical research showed that both models converge to the same equation at the early times of infiltration and that the slopes of the two models are the same for large times of infiltration, but the curves of the two models are parallel shifted. P’s and G & A’s models approximate well the experimental points of cumulative infiltration of the three soil samples at small times of infiltration, but P’s model approximates better the experimental points at large times of infiltration.

Analytical Interpretation of Slug Test in a Vertical Cutoff Wall

An analysis method for slug tests performed in a partially penetrating well within a vertical cutoff wall is presented. A steady-state shape factor for evaluating hydraulic conductivity of the material within the wall was derived by applying the method of images to the previously developed analytical solution of Zlotnik et al. (2010) for an infinite aquifer. Two distinct boundary conditions were considered: constant-head boundary for the case of direct contact between the wall and the aquifer, and no-flux boundary representing an impermeable filter cake on the sides of the wall. The constant-head and no-flux boundary conditions yield significantly higher and lower shape factors, respectively, than those for the infinite aquifer. Consequently the conventional line-fitting method for slug test analysis would yield an inaccurate estimate of the hydraulic conductivity of a vertical cutoff wall.

Exploring the parameter space of the Green–Ampt model

This study systematically investigates the entire parameter space of the Green–Ampt model for water infiltration and allows for arbitrary constant hydraulic head boundary conditions, any column inclination, hydrophilic and hydrophobic porous media, and a nonzero initial cumulative infiltration. There are five infiltration and five liquid-withdrawal scenarios which differ with respect to the direction of flow and the sign of the acceleration of the liquid. We present analytical solutions for these flow scenarios and 2D phase diagrams that show which flow scenario is predicted depending on the model parameters. All liquid infiltration scenarios, except accelerating downward infiltration (ADI), have already been reported by Green and Ampt. For liquid withdrawal, however, only decelerating downward flow has previously been reported, which is representative of drainage to the water table. We present experimental evidence that ADI may occur in hydrophobic media.

연직차수벽의 비정상 지하수 흐름에 대한 이론해 : 순간변위시험(slug test) 적용과 투수계수 산정

순간변위시험(slug test) 결과를 이용하여 비정상 흐름을 고려한 연직차수벽의 투수계수를 평가할 수 있는 이론해는 지금까지 제시된 바가 없다. 무한 대수층에 부분 관입된 우물(well)형상에 적용 가능하도록 기존 문헌에서 제시한 이론해는 좁은 지중연속벽체 형상의 연직차수벽의 경계조건을 고려할 수 없다. 이러한 연직차수벽 경계조건을 고려하기 위해, 본 연구에서는 가상 우물이론(imaginary well theory)을 도입하여 두 가지 경계조건(즉, 일정 수두 조건과 불투수 조건)을 만족하도록 새로운 이론해를 유도하였다. 제안된 이론해를 이용하여 구한 연직차수벽에서 시간에 따른 수위 회복 곡선(Type Curve)을 무한 대수층의 경우와 비교한 결과, 일정 수두 경계조건을 적용할 경우, 우물의 수위 회복이 무한 대수층의 결과보다 빠르게 진행되고 반면에 불투수 경계조건을 적용할 경우는 더 느리게 진행되었다. 또한, 우물의 형상비가 클수록, 연직차수벽의 폭이 좁을수록, 우물의 편심 정도가 클수록, 연직차수벽과 주변 지반 사이의 경계조건의 영향이 커진다. 본 논문에서 제시한 이론해를 통해 산정된 Type Curve는 기존 문헌에서 수치해석을 통해 산정된 Type Curve와 유사한 경향을 보였다. No analytical solution exists for evaluating in-situ hydraulic conductivity of vertical cutoff walls by analyzing slug test results with consideration of transient flow. There is an analytical solution proposed to interpret a slug test performed in a partially penetrated well within an aquifer. However, this analytical solution cannot be directly applied to the cutoff wall because the solution has been developed exclusively for an infinite aquifer instead of a narrow cutoff wall. To consider the cutoff wall boundary conditions (i.e, constant head boundary and no flux boundary condition), the analytical solution has been modified in this study to take into account the narrow boundaries by introducing the imaginary well theory. Type curves are constructed from the currently derived analytical solution and compared with those of a partially penetrated well within an aquifer. The constant head boundary condition provides faster hydraulic head recovery curve than the aquifer case. On the other hand, no flux boundary condition leads to slower hydraulic head recovery. The bigger the shape factor and deviation of the well and the smaller the width of the vertical cutoff wall are, the more effect of boundary condition was observed. The type curves obtained from the analytical solution for a cutoff wall are similar to those made by the numerical method in the literature.

Influence of heterogeneity on unsaturated hydraulic properties: (1) local heterogeneity and scale effect

Spatial heterogeneity is ubiquitous in nature, which may significantly affect the soil hydraulic property curves. The models of a closed-form functional relationship of soil hydraulic property curves (e.g. VG model or exponential model) are valid at point or local scale based on a point-scale hydrological process, but how do scale effects of heterogeneity have an influence on the parameters of these models when the models are used in a larger scale process? This paper uses a two-dimensional variably saturated flow and solute transport finite element model (VSAFT2) to simulate variations of pressure and moisture content in the soil flume under a constant head boundary condition. By changing different numerical simulation block sizes, a quantitative evaluation of parameter variations in the VG model, resulting from the scale effects, is presented. Results show that the parameters of soil hydraulic properties are independent of scale in homogeneous media. Parameters of α and n in homogeneous media, which are estimated by using the unsaturated hydraulic conductivity curve (UHC) or the soil water retention curve (WRC), are identical. Variations of local heterogeneities strongly affect the soil hydraulic properties, and the scale affects the results of the parameter estimations when numerical experiments are conducted. Furthermore, the discrepancy of each curve becomes considerable when moisture content becomes closer to a dry situation. Parameters estimated by UHC are totally different from the ones estimated by WRC. Copyright © 2012 John Wiley & Sons, Ltd.

Influence of heterogeneity on unsaturated hydraulic properties (2) - percentage and shape of heterogeneity

In subsurface porous media, the soil water retention curve (WRC) and unsaturated hydraulic conductivity curve (UHC) are two important soil hydraulic property curves. Spatial heterogeneity is ubiquitous in nature, which may significantly affect soil hydraulic property curves. The main theme of this paper is to investigate how spatial heterogeneities, including their arrangements and amounts in soil flumes, affect soil hydraulic property curves. This paper uses a two-dimensional variably saturated flow and solute transport finite element model to simulate variations of pressure and moisture content in soil flumes under a constant head boundary condition. To investigate the behavior of soil hydraulic property curves owing to variations of heterogeneities and their arrangements as well, cases with different proportions of heterogeneities are carried out. A quantitative evaluation of parameter variations in the van Genuchten model (VG model) resulting from heterogeneity is presented. Results show that the soil hydraulic properties are strongly affected by variations of heterogeneities and their arrangements. If the pressure head remains at a specific value, the soil moisture increases when heterogeneities increase in the soil flumes. On the other hand, the unsaturated hydraulic conductivity decreases when heterogeneities increase in the soil flumes under a constant pressure head. Moreover, results reveal that parameters estimated from both WRC and UHC also are affected by shapes of heterogeneity; this indicates that the parameters obtained from the WRC are not suitable for predicting the UHC of different shapes in heterogeneous media. Copyright © 2011 John Wiley & Sons, Ltd.