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

Duan

et al. 2019

Water

The double-ring infiltrometer is widely used to measure soil unsaturated hydraulic conductivity in the field. The scale effect of the inner and outer ring size (especially the inner one) affects the measurement results. In the semi-arid steppe, where water is scarce and transportation is inadequate, studying the scale effect caused by the inner-ring diameter of the infiltrometer can reduce the test consumption on the premise of ensuring the test accuracy. In this paper, a total of 190 double-ring infiltration tests with different inner-ring diameters (15,20,25,30, and 40 cm) and 0.33 times outer buffer index were carried out at 38 sites with five soil types in the Xilin river basin, China. Results showed that: (1) When comparing the simulated parameters of six infiltration models, parameters increased with the increase of the infiltrometer inner diameter, but the trend gradually slowed down, indicating that the increase of the infiltrometer inner diameter would weaken the influence of the infiltrometer scale effect. However, the infiltrometer with an inner diameter of 40 cm is not enough to completely overcome the scale effect. (2) Through principal component analysis, the infiltration process is mainly affected by the particle size and the initial moisture content. (3) The soil infiltration map based on infiltration tests was more practical than the soil type map, which can provide a theoretical basis for ecological and soil restoration in the future. species diversity does not reduce, but rather improves, the soil erosion resistance [13,14], and finally allows the whole ecosystem to achieve a positive cycle [15].To achieve the goal of obtaining the soil water retention characteristics of the study area, it is necessary to accurately evaluate this capacity, which can be estimated by the final infiltration rate (FIR) and infiltration time when the infiltration rate first reaches the final infiltration time (FIT). A slower infiltration rate indicates that the soil has better water retention [10]. The process of soil infiltration can be simulated in the laboratory using the ring-knife or a soil column [16,17]. However, such studies are influenced by disturbances of the original soil bulk density, porosity, and other soil physical properties. Instead, an infiltration test based on in situ undisturbed soil is capable of reflecting the original state of soil more effectively.Compared with a single-ring infiltrometer, a double-ring infiltrometer can be used to construct an infiltration buffer, which reduces the main external interference factors on the infiltration process of the inner ring [18]. Previous studies have shown that the average infiltration rate increases with the infiltrometer diameter [19,20]. Lai et al. [21] found through a large number of simulations that, compared with the outer buffering index (bi), the inner-ring diameter (di) plays a more important role in obtaining a relatively stable and representative measurement result. When the bi is equal or larger than 0.33, the buffer may meet the measureme...

Section: Infiltration Modelsmentioning

confidence: 99%

“…Green-Ampt (1911) [28] I(t) = K Ha+sm+z z K is the saturated hydraulic conductivity of the transmission zone (cm/min), H a is the thickness of surface water (cm), s m is the average potential suction of the wetting front (cm), and z is forward distance of the wetting front (cm). Philip (1954) [29]…”

Section: Model Type Model Name Equation Parametersmentioning

confidence: 99%

The Scale Effect of Double-Ring Infiltration and Soil Infiltration Zoning in a Semi-Arid Steppe

Duan

et al. 2019

Water

“…The Richards equation, as shown in Equation (1), is highly nonlinear because K x (h), K y (h), K z (h) and C(h) are functions of h. To solve the Richards equation, three characteristic functions are required and they are the unsaturated hydraulic conductivity function, the soil-water characteristic curve, and the specific moisture capacity function [19]. Assuming that the unsaturated soils are homogeneous and isotropic, the Richards equation governing two-dimensional flow in unsaturated soils can be obtained as…”

Section: The Linearized Richards Equationmentioning

confidence: 99%

“…Numerical approaches to the simulation of the Richards equation using the mesh-based methods, such as the finite difference method [16][17][18][19] or the finite element method [20][21][22][23], are well documented in the past. Despite the great success of the mesh-based methods as effective numerical tools for the solution of problems on complex domains, there is still growing interest in the development of new advanced computational methods [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Transient Modeling of Flow in Unsaturated Soils Using a Novel Collocation Meshless Method

Xiao

et al. 2017

Water

Self Cite

Abstract:In this paper, a novel meshless method for the transient modeling of subsurface flow in unsaturated soils was developed. A linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in the unsaturated zone was adopted. For the transient modeling, we proposed a pioneering work using the collocation Trefftz method and utilized the coordinate system in Minkowski spacetime instead of that in the original Euclidean space. The initial value problem for transient modeling of subsurface flow in unsaturated soils can then be transformed into the inverse boundary value problem. A numerical solution obtained in the spacetime coordinate system was approximated by superpositioning Trefftz basis functions satisfying the governing equation for boundary collocation points on partial problem domain boundary in the spacetime coordinate system. As a result, the transient problems can be solved without using the traditional time-marching scheme. The validity of the proposed method is established for several test problems. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for the transient modeling of subsurface flow in unsaturated soils.

“…where * h is the pressure head of the linearized Richards equation and χ is a constant which is a key transformation allowing the solution of the linearized Richards equation using the transform methods (Duffy 1994;Tracy 2006Tracy , 2011Liu et al 2015). The parameter χ has no physical meaning and can be expressed as…”

Section: Formulation Of the Variably Saturated Flow Equationmentioning

confidence: 99%

Numerical Modeling of Unsaturated Layered Soil for Rainfall-Induced Shallow Landslides

Journal of Environmental Engineering and Landscape Management

Xiao

et al. 2017

Self Cite

In this paper, a pioneer study on numerical modeling of rainfall-induced shallow landslides in unsaturated layered soil using the variably saturated flow equation is presented. To model the shallow landslides, the infinite slope stability analysis coupled with the hydrological model with the consideration of the fluctuation of time-dependent pore water pressure and Gardner equation for soil water characteristic curve was developed. A linearization process for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived using the Gardner model. 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 discretization of the finite difference method. The validity of the proposed model is established in three numerical problems by comparing the results with the analytical and other numerical solutions. Application examples have also been conducted. Obtained results demonstrate that the fluctuation of pore water pressure in unsaturated layered soil dominates slope stability of landslides and the lowest factor of safety may occur at the interface between two consecutive layers. The findings observed in this study are a fundamental contribution to environmental protection engineering for landslides in areas with higher occurrence and vulnerability to extreme precipitation.