Estimating finite difference block equivalent hydraulic conductivity for numerically solving the Richards' equation

2007 ◽  
Vol 21 (26) ◽  
pp. 3587-3600 ◽  
Author(s):  
Chih-Yung Feng ◽  
Tim Hau Lee ◽  
Wen Sen Lee ◽  
Chu-Hui Chen
Keyword(s):  
Hydraulic Conductivity ◽  
Finite Difference ◽  
Richards Equation

scholarly journals Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model

2019 ◽  
Vol 22 (2) ◽  
pp. 423-439
Author(s):  
Mohanasundaram Shanmugam ◽  
G. Suresh Kumar ◽  
Balaji Narasimhan ◽  
Sangam Shrestha
Keyword(s):  
Hydraulic Conductivity ◽  
Finite Difference ◽  
Soil Water ◽  
Unsaturated Zone ◽  
Estimation Methods ◽  
Richards Equation ◽  
Difference Model ◽  
One Dimensional ◽  
Soil Water Flow ◽  
Effective Saturation

Abstract Richards equation is solved for soil water flow modeling in the unsaturated zone continuum. Interblock hydraulic conductivities, while solving for Richards equation, are estimated by some sort of averaging process based on upstream and downstream nodes hydraulic conductivity values. The accuracy of the interblock hydraulic conductivity estimation methods mainly depends on the distance between two adjacent discretized nodes. In general, the accuracy of the numerical solution of the Richards equation decreases as nodal grid discretization increases. Conventional interblock hydraulic conductivity estimation methods are mostly mere approximation approaches while the Darcian-based interblock hydraulic conductivities involve complex calculations and require intensive computation under different flow regimes. Therefore, in this study, we proposed an effective saturation-based weighting approach in the soil hydraulic curve functions for estimating interblock hydraulic conductivity using a one-dimensional vertical finite-difference model which provides a parametric basis for interblock hydraulic conductivity estimation while reducing complexity in the calculation and computational processes. Furthermore, we compared four test case simulation results from different interblock hydraulic conductivity methods with the reference solutions. The comparison results show that the proposed method performance in terms of percentage reduction in root mean square and mean absolute error over other methods compared in this study were 59.5 and 60%, respectively.

scholarly journals Finite-Difference Numerical Simulation of Dewatering System in a Large Deep Foundation Pit at Taunsa Barrage, Pakistan

2019 ◽  
Vol 11 (3) ◽  
pp. 694 ◽  
Author(s):  
Ijaz Ahmad ◽  
Muhammad Tayyab ◽  
Muhammad Zaman ◽  
Muhammad Anjum ◽  
Xiaohua Dong
Keyword(s):  
Hydraulic Conductivity ◽  
Finite Difference ◽  
Three Dimensional ◽  
Rehabilitation Program ◽  
Diaphragm Wall ◽  
Deep Foundation ◽  
Foundation Pit ◽  
Deep Foundation Pit ◽  
Constant Head ◽  
Design Depth

This study investigates a large deep foundation pit of a hydraulic structure rehabilitation program across the Indus river, in the Punjab province of Pakistan. The total area of the construction site was 195,040 m2. Two methods, constant head permeability test and Kozeny–Carman equation, were used to determine the hydraulic conductivity of riverbed strata, and numerical simulations using the three-dimensional finite-difference method were carried out. The simulations first used hydraulic conductivity parameters obtained by laboratory tests, which were revised during model calibration. Subsequently, the calibrated model was simulated by different aquifer hydraulic conductivity values to analyze its impact on the dewatering system. The hydraulic barrier function of an underground diaphragm wall was evaluated at five different depths: 0, 3, 6, 9, and 18 m below the riverbed level. The model results indicated that the aquifer drawdown decreases with the increase in depth of the underground diaphragm wall. An optimal design depth for the design of the dewatering system may be attained when it increases to 9 m below the riverbed level.

scholarly journals A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media

2017 ◽  
Vol 22 (4) ◽  
pp. 935-964 ◽  
Author(s):  
Hong Zhang ◽  
Paul Andries Zegeling
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Moving Mesh ◽  
Richards Equation ◽  
Time Step ◽  
Central Difference ◽  
Monitor Function ◽  
Non Equilibrium

AbstractAn adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure effect in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive monitor function with directional control is applied to redistribute the mesh grid in every time step, then a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the proposed method.

scholarly journals Further tests of the HYPROP evaporation method for estimating the unsaturated soil hydraulic properties

2018 ◽  
Vol 66 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Camila R. Bezerra-Coelho ◽  
Luwen Zhuang ◽  
Maria C. Barbosa ◽  
Miguel Alfaro Soto ◽  
Martinus Th. van Genuchten
Keyword(s):  
Hydraulic Conductivity ◽  
Unsaturated Soil ◽  
Hydraulic Properties ◽  
Water Retention ◽  
Measurement Techniques ◽  
Richards Equation ◽  
Water Retention Curve ◽  
Soil Hydraulic Properties ◽  
Evaporation Method ◽  
Soil Hydraulic

AbstractMany soil, hydrologic and environmental applications require information about the unsaturated soil hydraulic properties. The evaporation method has long been used for estimating the drying branches of the soil hydraulic functions. An increasingly popular version of the evaporation method is the semi-automated HYPROP©measurement system (HMS) commercialized by Decagon Devices (Pullman, WA) and UMS AG (München, Germany). Several studies were previously carried out to test the HMS methodology by using the Richards equation and the van-Genuchten-Mualem (VG) or Kosugi-Mualem soil hydraulic functions to obtain synthetic data for use in the HMS analysis, and then to compare results against the original hydraulic properties. Using HYDRUS-1D, we carried out independent tests of the HYPROP system as applied to the VG functions for a broad range of soil textures. Our results closely agreed with previous findings. Accurate estimates were especially obtained for the soil water retention curve and its parameters, at least over the range of available retention measurements. We also successfully tested a dual-porosity soil, as well as an extremely coarse medium with a very high van Genuchtennvalue. The latter case gave excellent results for water retention, but failed for the hydraulic conductivity. In many cases, especially for soils with intermediate and highnvalues, an independent estimate of the saturated hydraulic conductivity should be obtained. Overall, the HMS methodology performed extremely well and as such constitutes a much-needed addition to current soil hydraulic measurement techniques.

Effect of stones on soil hydraulic properties: measurement and modeling

2020 ◽  
Author(s):  
Mahyar Naseri ◽  
Sascha C. Iden ◽  
Wolfgang Durner
Keyword(s):  
Hydraulic Conductivity ◽  
Soil Temperature ◽  
Hydraulic Properties ◽  
Evaporation Rate ◽  
Sandy Loam ◽  
Stage Ii ◽  
Richards Equation ◽  
Water Retention Curve ◽  
Soil Hydraulic Properties ◽  
Soil Hydraulic

<p>Stony soils are soils that contain a high amount of stones and are widespread all over the world.  The effective soil hydraulic properties (SHP), i.e. the water retention curve (WRC) and the hydraulic conductivity curve (HCC) are influenced by the presence of stones in the soil. This influence is normally neglected in vadose zone modeling due to the considerable measurement challenges in stony soils. The available data on the effect of stones on SHP is scarce and there is not a systematic modeling approach to obtain the effective SHP in stony soils. Most of the past studies are limited to the effect of stones on the WRC and saturated hydraulic conductivity and low and medium stone contents (up to 40 % v/v). We investigated the effect of stone content on the effective SHP of stony soils through a series of evaporation experiments. Two soil materials a) sandy loam and b) silt loam as background soils were packed with different volumetric contents (0, 10, 30 and 60 %) of medium stones were in containers with a volume of 5060 cm<sup>3</sup>. Volumetric stone contents were chosen in a way to present stone-free, moderately stony and highly stony soils. All of the experiments were carried out in two replicate packings with an almost identical bulk density. Packed samples were saturated with water from the bottom and subjected to evaporation in a climate-controlled room. During the evaporation experiments, the pressure head and soil temperature were continuously monitored and the water loss from the soil columns was measured with a balance. The dewpoint method provided additional data on the WRC in the dry soil. The resulting data were evaluated by inverse modeling with the Richards equation to identify effective SHP and to analyze the effect of stone content on the evaporation rate, soil temperature, the effective WRC and the effective HCC. The applied methodology was successful in identifying effective SHP with high precision over the full moisture range. The results reveal a quicker transition from stage I to stage II of evaporation in highly stony soils. Evaporation rate reduces with the increase of the volumetric stone content. The existence of a high amount of stone content shorten stage II of evaporation driven by the vapor diffusion through the restricted soil evaporative surface.</p>

Characterization of Soil Moisture Distribution and Movement Under the Influence of Watering-dewatering Using AHFO and BOTDA Technologies

2019 ◽  
Vol 25 (3) ◽  
pp. 189-202 ◽  
Author(s):  
Ding-Feng Cao ◽  
Bin Shi ◽  
Hong-Hu Zhu ◽  
Chao-Sheng Tang ◽  
Zhan-Pu Song ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Hydraulic Conductivity ◽  
Fine Particles ◽  
Water Movement ◽  
Particle Migration ◽  
Moisture Distribution ◽  
Water Infiltration ◽  
Richards Equation ◽  
Laboratory Model ◽  
Soil Moisture Distribution

ABSTRACT The infiltration and distribution of water through unsaturated soil determine its mechanical and hydrological properties. However, there are few methods that can accurately capture the spatial distribution of moisture inside soil. This study aims to demonstrate the use of actively heated fiber optic (AHFO) and Brillouin optical time domain analysis (BOTDA) technologies for monitoring soil moisture distribution as well as strain distribution. In addition to a laboratory model test, finite element analyses were conducted to interpret the measurements. During the experiment, the fine particle migration was also measured to understand its influence on soil hydraulic conductivity. The results of the experiment indicate that (i) for a soil that has never experienced a watering-dewatering cycle, water infiltration can be accurately calculated using the Richards’ equation; (ii) migration of fine soil particles caused by the watering-dewatering cycle significantly increases the hydraulic conductivity; and (iii) two critical zones (drainage and erosion) play significant roles in determining the overall hydraulic conductivity of the entire soil. This study provides a new method for monitoring the changes in soil moisture, soil strain, and hydraulic conductivity. The observations suggest that the effect of fine particles migration should be considered while evaluating soil moisture distribution and water movement.

Numerical Solutions for Groundwater Flow in Unsaturated Layered Soil with Extreme Physical Property Contrasts

2015 ◽  
Vol 16 (7-8) ◽  
pp. 325-335 ◽  
Author(s):  
Chih-Yu Liu ◽  
Cheng-Yu Ku ◽  
Chi-Chao Huang ◽  
Der-Guey Lin ◽  
Wei-Chung Yeih
Keyword(s):  
Hydraulic Conductivity ◽  
Groundwater Flow ◽  
Numerical Solutions ◽  
Physical Property ◽  
Layered Soil ◽  
Richards Equation ◽  
Test Problems ◽  
Pressure Potential ◽  
Numerous Test ◽  
Novel Method

AbstractIn this paper, the numerical solutions for groundwater flow in unsaturated layered soil using the Richards equation are presented. A linearisation process for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived. To solve one-dimensional flow in the unsaturated zone of layered soil profiles, flux conservation and the continuity of pressure potential at the interface between two consecutive layers are considered in the numerical model. In addition, a novel method, named the dynamical Jacobian-inverse free method, incorporated with a two-side equilibration algorithm for solving ill-conditioned systems with extreme contrasts in hydraulic conductivity is proposed. The validity of the model is established in numerous test problems by comparing the numerical results with the analytical solutions. The results show that the proposed method can improve convergence and numerical stability for solving groundwater flow in unsaturated layered soil with extreme contrasts in hydraulic conductivity.

Estimate of hydrodynamic parameters with a coupled hydrogeophysical inversion using GPR surveys

2021 ◽  
Author(s):  
Rohianuu Moua ◽  
Nolwenn Lesparre ◽  
Jean-François Girard ◽  
Benjamin Belfort ◽  
François Lehmann
Keyword(s):  
Hydraulic Conductivity ◽  
Objective Function ◽  
Arrival Time ◽  
Soil Surface ◽  
Water Infiltration ◽  
Richards Equation ◽  
Velocity Models ◽  
Hydrodynamic Parameters ◽  
Infiltration Front ◽  
Infiltration Experiment

<p>We develop a methodology to estimate soil hydrodynamic parameters from a water infiltration experiment monitored with a GPR (Ground Penetrating Radar). Such an experiment, carried out on both controlled and natural site, consists in applying a water charge in a tank on the soil surface. During the water infiltration, the water layer thickness above the soil surface in the tank and the GPR response on the infiltration water front are monitored. The infiltration experiment is then modelled numerically using hydrogeological parameters which describe the constitutive relationships between water content, pressure and hydraulic conductivity. In that goal, we use the WAMOS-1D code which combines the 1D Richards equation and the Mualem – van Genuchten model. From the hydrogeological models outputs and petrophysical relationships, corresponding GPR velocity models are created to generate the resulting GPR signals. Then, an inversion algorithm couples both the hydrogeological and the geophysical models to seek the optimal hydrodynamic parameters. The inverse problem objective function is calculated from the estimated arrival time of the GPR waves reflected by the water infiltration front and compared to the measured ones. Preliminary inversion tests explore the hydrodynamic parameters space using synthetic data. First results show that the saturated hydraulic conductivity parameter can be estimated. Further tests are performed to improve both our experimental set-up and methodology and allow an estimation of the other hydrodynamic parameters. An emerging idea is to complete the objective function by analyzing the arrival time corresponding to additional reflectors to the water infiltration front.</p>

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