scholarly journals Analysis of three-dimensional unsaturated-saturated flow induced by localized recharge in unconfined aquifers

2017 ◽  
Author(s):  
Chia-Hao Chang ◽  
Ching-Sheng Huang ◽  
Hund-Der Yeh
Keyword(s):  
Soil Properties ◽  
Unsaturated Soil ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Hydraulic Head ◽  
Richards Equation ◽  
Coupled Flow ◽  
Saturated Flow ◽  
Flow Equations ◽  
Present Solution

Abstract. In the process of groundwater recharge, surface water usually enters an aquifer by passing an overlying unsaturated zone. Up to now, little attention has been given to the effect of unsaturated flow on the hydraulic head within the aquifer due to recharge. This paper develops a mathematical model to depict three-dimensional transient unsaturated-saturated flow in an unconfined aquifer with localized recharge on the ground surface. The model contains Richards’ equation for unsaturated flow, a flow equation for saturated formation, and the Gardner constitutive model describing the behavior of unsaturated soil properties. Both flow equations are coupled through the continuity conditions of the head and flux at the water table. The semi-analytical solution to the coupled flow model is derived by the methods of Laplace transform and Fourier cosine transform. A sensitivity analysis is performed to explore the head response to the change in each of the aquifer parameters. A quantitative tool is presented to assess the recharge efficiency signifying the percentage of the water from the recharge to the aquifer. We found that the effect of unsaturated flow on the saturated hydraulic head is negligible if two criteria associated with the unsaturated soil properties and initial aquifer thickness are satisfied. The head distributions predicted from the present solution match well with those from finite element simulations. The predictions of the present solution also agree well with the observed data from a field experiment at an artificial recharge pond in Fresno County, California.

scholarly journals Analysis of three-dimensional unsaturated–saturated flow induced by localized recharge in unconfined aquifers

2018 ◽  
Vol 22 (7) ◽  
pp. 3951-3963 ◽  
Author(s):  
Chia-Hao Chang ◽  
Ching-Sheng Huang ◽  
Hund-Der Yeh
Keyword(s):  
Soil Properties ◽  
Unsaturated Soil ◽  
Flow Model ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Richards Equation ◽  
Coupled Flow ◽  
Saturated Flow ◽  
Flow Equations ◽  
Present Solution

Abstract. In the process of groundwater recharge, surface water usually enters an aquifer by passing an overlying unsaturated zone. Little attention has been given to the development of analytical solutions to a coupled unsaturated–saturated flow model due to localized recharge up to now. This paper develops a mathematical model to depict three-dimensional transient unsaturated–saturated flow in an unconfined aquifer with localized recharge on the ground surface. The model contains Richards' equation for unsaturated flow, a flow equation for saturated formation, and the Gardner constitutive model describing the behavior of unsaturated soil properties. Both flow equations are coupled through the continuity conditions of the head and flux at the water table. The semi-analytical solution to the coupled flow model is derived by the methods of Laplace transform and Fourier cosine transform. A sensitivity analysis is performed to explore the head response to the change in each of the aquifer parameters. A quantitative tool is presented to assess the recharge efficiency signifying the percentage of the water from the recharge to the aquifer. We found that the effect of unsaturated flow on the saturated hydraulic head is negligible if two criteria associated with the unsaturated soil properties and initial aquifer thickness are satisfied. The head distributions predicted from the present solution match well with those from finite-difference simulations. The predictions of the present solution also agree well with the observed data from a field experiment at an artificial recharge pond in Fresno County, California.

scholarly journals A quasi-three-dimensional model for predicting rainfall-runoff processes in a forested catchment in Southern Finland

2000 ◽  
Vol 4 (1) ◽  
pp. 65-78 ◽  
Author(s):  
H. Koivusalo ◽  
T. Karvonen ◽  
A. Lepistö
Keyword(s):  
Soil Moisture ◽  
Water Table ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Three Dimensional ◽  
Moisture Distribution ◽  
Richards Equation ◽  
Rainfall Runoff ◽  
Forested Catchment ◽  
Soil Moisture Distribution

Abstract. Runoff generation in a forested catchment (0.18 km2) was simulated using a quasi-three-dimensional rainfall-runoff model. The model was formulated over a finite grid where water movement was assumed to be dominantly vertical in the unsaturated soil zone and horizontal in the saturated soil. The vertical soil moisture distribution at each grid cell was calculated using a conceptual approximation to the one-dimensional Richards equation. The approximation allowed the use of a simple soil surface boundary condition and an efficient solution to the water table elevation over the finite grid. The approximation was coupled with a two-dimensional ground water model to calculate lateral soil water movement between the grid cells and exfiltration over saturated areas, where runoff was produced by the saturation-excess mechanism. Runoff was an input to a channel network, which was modelled as a nonlinear reservoir. The proposed approximation for the vertical soil moisture distribution in unsaturated soil compared well to a numerical solution of the Richards equation during shallow water table conditions, but was less satisfactory during prolonged dry periods. The simulation of daily catchment outflow was successful with the exception of underprediction of extremely high peak flows. The calculated water table depth compared satisfactorily with the measurements. An overall comparison with the earlier results of tracer studies indicated that the modelled contribution of direct rainfall/snowmelt in streamflow was higher than the isotopically traced fraction of event-water in runoff. The seasonal variation in the modelled runoff-contributing areas was similar to that in the event-water-contributing areas from the tracer analysis.

OpenCAL system extension and application to the three-dimensional Richards equation for unsaturated flow

2021 ◽  
Vol 81 ◽  
pp. 133-158 ◽  
Author(s):  
Alessio De Rango ◽  
Luca Furnari ◽  
Andrea Giordano ◽  
Alfonso Senatore ◽  
Donato D’Ambrosio ◽  
...  
Keyword(s):  
Unsaturated Flow ◽  
Three Dimensional ◽  
Richards Equation ◽  
System Extension

scholarly journals On the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells in unconfined aquifers

2017 ◽  
Vol 21 (2) ◽  
pp. 1251-1262 ◽  
Author(s):  
Xiuyu Liang ◽  
Hongbin Zhan ◽  
You-Kuan Zhang ◽  
Jin Liu
Keyword(s):  
Unsaturated Zone ◽  
Horizontal Well ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Water Volume ◽  
Saturated Flow ◽  
Flow Process ◽  
Pumping Tests ◽  
Screen Length ◽  
Unconfined Aquifers

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated–saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace–finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

scholarly journals On Coupled Unsaturated-Saturated Flow Process Induced by Vertical, Horizontal and Slant Wells in Unconfined Aquifers

2016 ◽  
Author(s):  
Xiuyu Liang ◽  
Hongbin Zhan ◽  
You-Kuan Zhang ◽  
Jin Liu
Keyword(s):  
Unsaturated Zone ◽  
Horizontal Well ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Early Time ◽  
Saturated Flow ◽  
Flow Process ◽  
Pumping Tests ◽  
Screen Length ◽  
Unconfined Aquifers

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns coupled unsaturated-saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated-saturated flow process and well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation, and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in Laplace domain is derived by the Laplace-finite Fourier transform and the method of separation of variables. It is found that the unsaturated zone has significant effects on the drawdown of pumping test with any angle of inclination of the pumping well, and this impact is more significant for the case of a horizontal well. The effects of unsaturated zone on the drawdown are independent of the length of the horizontal well screen. For the early time of pumping, the water volume drained from the unsaturated zone (W) increases with time, and gradually approaches an asymptotic value with time progress. The vertical well leads to the largest W value during the early time, and the effects of the well orientation become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

Soil Water Flow

2003 ◽  
Author(s):  
Arthur W. Warrick
Keyword(s):  
Soil Water ◽  
Water Flow ◽  
Darcy’S Law ◽  
Soil Water Potential ◽  
Hydraulic Head ◽  
Flow Equation ◽  
Darcy's Law ◽  
Richards Equation ◽  
Flow Equations ◽  
Soil Water Flow

The definitions of hydraulic head and soil water potential in chapter 1 assumed equilibrium. However, the primary motivation was to develop a background useful to describe dynamic systems. If a system is in equilibrium, no flow will occur; otherwise, flow will occur from regions of high to low hydraulic head. The primary flow equation will be Darcy’s law. When Darcy’s law is combined with conservation of mass, the result is a continuity equation that can have several different forms. We will refer to all of those forms generically as soil water flow equations. Generally, for unsaturated conditions, the soil water flow equation is called the Richards equation. A starting point is to examine two classical relationships from fluid dynamics, the Bernoulli and the Poiseuille laws. Bernoulli’s law relates the total potential for ideal fluids and is commonly derived in introductory physics and fluid mechanics texts (see Serway, 1990). Assumptions include an ideal fluid (non-viscous), which is one that is incompressible and which exhibits steady and irrotational flow. For these conditions, the sum of gravitational, pressure, and inertial energy at positions S1and S2 are the same along any streamline For a real fluid, viscosity causes a loss of energy as friction that must be overcome. Additionally, for most problems of interest in soils, the velocity head will be negligible compared with the pressure and gravitational terms.

Protocol for the assessment of unsaturated soil properties in geotechnical engineering practice

2009 ◽  
Vol 46 (6) ◽  
pp. 694-707 ◽  
Author(s):  
Delwyn G. Fredlund ◽  
Sandra L. Houston
Keyword(s):  
Soil Properties ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Soil Property ◽  
Unsaturated Flow ◽  
Soil Mechanics ◽  
Geotechnical Engineering ◽  
Engineering Practice ◽  
Engineering Project ◽  
Estimation Procedures

The implementation of unsaturated soil mechanics into routine geotechnical engineering practice requires an evaluation of methodologies that may be used for the assessment of “unsaturated soil property functions.” Guidelines and recommendations need to be provided to practicing engineers. The guidelines need to take the form of “engineering protocols” that define acceptable standards for engineering practice. “Engineering protocols” for unsaturated soils engineering practice can be divided into “preliminary design” protocols and “final design” protocols. Both design levels involve the use of a variety of estimation procedures that have been proposed for various classes of geotechnical problems (e.g., unsaturated flow, shear strength, volume change, and distortion). The hierarchy in methodologies is based mainly on the costs and risks associated with a particular engineering project. In this paper, “hierarchical levels” are suggested that take into consideration the cost of various direct and indirect methodologies for the determination of unsaturated soil properties. Recommendations and suggestions are provided for methods for the determination and use of the soil-water characteristic curves (SWCC) and consequently, for the computation of unsaturated soil property functions (USPFs). Primary attention is given to estimation procedures best known to the authors and most appropriate for geotechnical engineering practice.

Capillary effect on flow in the drainage layer of highway pavement

2012 ◽  
Vol 39 (6) ◽  
pp. 654-666 ◽  
Author(s):  
Han-Cheng Dan ◽  
Pei Xin ◽  
Ling Li ◽  
Liang Li ◽  
David Lockington
Keyword(s):  
Unsaturated Flow ◽  
Groundwater Table ◽  
Richards Equation ◽  
Capillary Effect ◽  
Saturated Flow ◽  
Drainage Layer ◽  
Flow Models ◽  
Model Based ◽  
D Model ◽  
Highway Pavement

This paper aims to examine capillarity effect on flows in the drainage layer of highway pavement. A two-dimensional (2-D) model based on the Richards equation was used to simulate saturated and unsaturated flows in the drainage layer. For comparison, flows were also simulated using a 1-D Boussinesq equation based model and a 2-D model based on the Laplace equation, both assuming saturated flow only. The drainage layer was modeled with sand and gravel, which possess similar hydraulic properties to those of commonly used filling materials in practice. The results showed that the two saturated flow models agreed well with each other, indicating the dominance of horizontal flow in the drainage layer. However, their predictions differed significantly from those of the variably saturated flow models. The latter model predicted significant flow activities in a relatively large unsaturated zone, especially for a sandy drainage layer. Such unsaturated flow contributes to and enhances the capacity of the drainage layer. With the unsaturated flow neglected, the saturated flow models over-predicted the extent of the saturated zone and hence the groundwater table elevation. As the current engineering design of the drainage layer is typically based on the groundwater table elevation predicted by the saturated flow models, the finding of this study suggests that the design criterion is likely to lead to over-design of the drainage system. Further work is also required to prove the practical significance of the capillary effect and account for other factors.

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