• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.197-215
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• 2015

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

• Geomechanics and Engineering
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• v.20 no.3
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• pp.175-189
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• 2020

A set of relatively simple five local shear and tension failure variables is presented and then implemented into a generalized poroelastic hydromechanical numerical model to analyze failure potential and stability of variably saturated geologic media. These five local shear and tension failure variables are formulated from geometrical relationships between the Mohr circle and the Mohr-Coulomb failure criterion superimposed with the tension cutoff, which approximate together the Mohr effective stress failure envelope. Finally, fully coupled groundwater flow and land deformation in two variably saturated geologic media, which are associated with a slope (Case 1) and a tunnel (Case 2), respectively, and their failure potential and stability are simulated using the resultant hydromechanical numerical model. The numerical simulation results of both cases show that shear and tension failure potential and stability of variably saturated geologic media can be analyzed numerically simply and efficiently and even better by using the five local shear and tension failure variables as a set than by using the conventional factors of safety against shear and tension failures only.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Economic and Environmental Geology
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• v.42 no.6
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• pp.561-574
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• 2009

Unsaturated/saturated groundwater flow and solute transport model, VSFRT2D(Variable Saturated Flow and Reactive Transport model) was developed considering effects of pumping, irrigation, and denitrification. VSFRT2D employed Richards equation as governing equation for groundwater flow and previously existing unsaturated models modified by including computational procedure of evapotranspiration at surface using Thornthwaite method when precipitation doesn't occur. Bioremediation processes based on monod kinetics are described using four nonlinear contaminant transport equations and three nonlinear microbes transport equations. The developed model was applied to field data in Hongsung area contaminated with nitrate. In order to identify the effect of precipitation, pumping, evapotranspiration, irrigation, fertilizer application, and various bioremediations on groundwater flow and contaminant transport, individual processes were separated and simulated. Then all results obtained from the individual processes are compared with each other. The simulation results show that bioremediation had a negligible effect on nitrate concentration change. However, pumping for irrigation, precipitation, and nitrogen fertilizer application showed profound influences on nitrate concentration change.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.107-107
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• 2012

우리나라의 시설재배는 연중 고품질의 농산물을 요구하는 소비자의 기대와 생산자의 경제적 목적이 부합되어 재배면적이 증가하고 있으며 전체 시설재배면적의 31.3%는 수리시설이 완비된 관개논에 위치한다. 시설재배지에서의 수분관리는 작물의 안정적인 생산과 수자원의 효율적인 사용을 위하여 토양 특성을 고려하여 운영되어야 한다. 따라서 시설재배지 토양 특성을 반영한 작물근군역에서의 물수지와 수분거동 특성에 관한 연구가 선행되어야한다. 불포화토양에서의 수분이동은 토양-작물-대기의 연속계에서 수분의 공급과 증발산, 배수 및 유거에 의한 토양수분 장력의 변화로 이루어지며 토양수분과 토양수분 장력, 수리전도도와의 관계는 토양의 수리적 특성에 따라 상이하다. 실험을 통한 토양수분 거동 분석은 시간적, 비용적 측면에서 비효율적이므로 모형에 의한 분석이 요구된다. 본 연구에서는 불포화토양에서의 수분이동을 모의하기 위하여 Richards 공식을 유한차분법으로 해석하였으며 국내 논 시설재배지 이(異)층토양에 대하여 다양한 관개조건을 적용하여 토양수분 거동 특성을 분석하였다. 관개와 작물의 수분흡수가 지속됨에 따라 근군역을 이탈한 토양수분이 유하되어 밭 토양과 논 토양의 경계에 축적됨을 확인 하였으며 과다관개가 이루어질수록 이러한 현상이 심화되는 것으로 나타났다. 본 연구의 결과는 관개시스템의 설계와 운영에 기초자료로 활용될 수 있다.

• Journal of the Korean Geotechnical Society
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• v.18 no.6
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• pp.5-16
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• 2002

A hydrogeomechanical numerical model is presented to evaluate rainfall impacts on groundwater flow in slopes and slope stability. This numerical model is developed based on the fully coupled poroelastic governing equations for groundwater flow in deforming variably saturated geologic media and the Galerkin finite element method. A series of numerical experiments using the model developed are then applied to an unsaturated slope under various rainfall rates. The numerical simulation results show that the overall hydromechanical slope stability deteriorates, and the potential failure nay initiate from the slope toe and propagate toward the slope crest as the rainfall rate increases. From the viewpoint of hydrogeology, the pressure head and hence the total hydraulic head increase as the rainfall rate increases. As a result, the groundwater table rises, the unsaturated zone reduces, the seepage face expands from the slope toe toward the slope crest, and the groundwater flow velocity increases along the seepage face. From the viewpoint of geomechanics, the horizontal displacement increases, and the vertical displacement decreases toward the slope toe as the rainfall rate increases. This may result from the buoyancy effect associated with the groundwater table rise as the rainfall rate increases. As a result, the overall deformation intensifies toward the slope toe, and the unstable zone, in which the factor of safety against shear failure is less than 1, becomes thicker near the slope toe and propagates from the slope toe toward the slope crest. The numerical simulation results also suggest that the potential tension failure is likely to occur within the slope between the potential shear failure surface and the ground surface.

• Journal of Korea Water Resources Association
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• v.45 no.1
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• pp.39-52
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• 2012

Surface-subsurface interactions are an intrinsic component of the hydrologic response within a watershed. In general, these interactions are considered to be one of the most difficult areas of the discipline, particularly for the modeler who intends simulate the dynamic relations between these two major domains of the hydrological cycle. In essence, one major complexity is the spatial and temporal variations in the dynamically interacting system behavior. The proper simulation of these variations requires the need for providing an appropriate coupling mechanism between the surface and subsurface components of the system. In this study, an approach for modelling surface-subsurface flow and transport in a fully intergrated way is presented. The model uses the 2-dimensional diffusion wave equation for sheet surface water flow, and the Boussinesq equation with the Darcy's law and Dupuit-Forchheimer's assumption for variably saturated subsurface water flow. The coupled system of equations governing surface and subsurface flows is discretized using the finite volume method with central differencing in space and the Crank-Nicolson method in time. The interactions between surface and subsurface flows are considered mass balance based on the continuity conditions of pressure head and exchange flux. The major module consists of four sub-module (SUBFA, SFA, IA and NS module) is developed.