Infiltration In Unsaturated Soils Research Articles

Tsallis Entropy Theory for Derivation of Infiltration Equations

An entropy theory is formulated for deriving infiltration equations for the potential rate (or capacity) of infiltration in unsaturated soils. The theory is comprised of five parts: (1) Tsallis entropy, (2) principle of maximum entropy (POME), (3) specification of information on the potential rate of infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, and (5) derivation of the probability distribution of infiltration and its maximum entropy. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two-term, Green-Ampt, Overton, and Holtan, and the determination of the least biased probability distributions underlying these infiltration equations and the entropies thereof. The theory leads to the expression of parameters of the derived infiltration equations in terms of three measurable quantities: initial infiltration capacity (potential rate), steady infiltration rate, and soil moisture retention capacity. In this sense, these derived equations are rendered nonparametric. With parameters thus obtained, infiltration capacity rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the capacity rates computed using parameters of these equations obtained by calibration. It is found that infiltration capacity rates computed using parameter values yielded by the entropy theory are in reasonable agreement with observed as well as calibrated infiltration capacity rates.

Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils

AbstractAn analytical solution to 1D coupled water infiltration and deformation is derived using a Fourier integral transform. Exponential functional forms are used to represent the hydraulic conductivity–pore‐water pressure relationship and the soil‐water characteristic curve. Fredlund's incremental‐linear constitutive model for unsaturated soils is adopted. The analytical solution considers arbitrary initial pore‐water pressure distributions and flux and pressure boundary conditions. The corresponding analytical solutions to coupled steady‐state problems are also obtained. The analytical solutions demonstrate that the coupling of seepage and deformation plays an important role in water infiltration in unsaturated soils. In the early stages of infiltration, the difference between uncoupled and coupled conditions becomes marked over time, and in late stages, the difference caused by the coupling effects diminishes toward the steady state. The difference between the uncoupled and coupled conditions increases with decreasing desaturation coefficient (α). Pore‐water pressure or deformation changes caused by the coupling effects are mainly controlled by the degree of soil volume change due to a change in soil suction (H). The smaller the absolute value of H, the greater the effect of coupling on the infiltration and deformation. The ratio of rainfall intensity to saturated permeability (q/ks) also has a strong influence on the coupled seepage and deformation. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical modeling of rainstorm-induced shallow landslides in saturated and unsaturated soils

For the assessment of shallow landslides triggered by rainfall, the physically based model coupling the infinite slope stability analysis with the hydrological modeling in nearly saturated soil has commonly been used due to its simplicity. However, in that model the rainfall infiltration in unsaturated soil could not be reliably simulated because a linear diffusion-type Richards’ equation rather than the complete Richards’ equation was used. In addition, the effect of matric suction on the shear strength of soil was not actually considered. Therefore, except the shallow landslide in saturated soil due to groundwater table rise, the shallow landslide induced by the loss in unsaturated shear strength due to the dissipation of matric suction could not be reliably assessed. In this study, a physically based model capable of assessing shallow landslides in variably saturated soils is developed by adopting the complete Richards’ equation with the effect of slope angle in the rainfall infiltration modeling and using the extended Mohr–Coulomb failure criterion to describe the unsaturated shear strength in the soil failure modeling. The influence of rainfall intensity and duration on shallow landslide is investigated using the developed model. The result shows that the rainfall intensity and duration seem to have similar influence on shallow landslides respectively triggered by the increase of positive pore water pressure in saturated soil and induced by the dissipation of matric suction in unsaturated soil. The rainfall duration threshold decreases with the increase in rainfall intensity, but remains constant for large rainfall intensity.

Upscaling of soil hydraulic properties for steady state evaporation and infiltration

Estimation of effective/average soil hydraulic properties for large land areas is an outstanding issue in hydrologic modeling. The goal of this study is to provide flow‐specific rules and guidelines for upscaling soil hydraulic properties in an areally heterogeneous field. In this study, we examined the impact of areal heterogeneity of soil hydraulic parameters on soil ensemble behavior for steady state evaporation and infiltration. The specific objectives of this study are (1) to address the impact of averaging methods of shape parameters and parameter correlation on ensemble behavior of steady state flow in an areally heterogeneous field and (2) to investigate the effectiveness of the “average parameters” in terms of the degree of correlation between hydraulic property parameters for the steady state evaporation and infiltration in unsaturated soil. Using an analytical solution of Richards' equation, the ensemble characteristics and flow dynamics based on average hydraulic property parameters are studied for evaporation and infiltration. Using various flow and average scenarios, we illustrated the resulting differences among the various averaging schemes. For vertical evaporation and infiltration the use of a geometric mean value for the shape parameter α of Gardner‐Russo model and Brooks‐Corey model and arithmetic mean value for the saturated hydraulic conductivity Ks simulates the ensemble flow behavior the best. The efficacy of the “average parameters” depends on the flow condition and the degree of correlation between the hydraulic property parameters. With the α and Ks parameters perfectly correlated, the “average parameters” were found to be generally most effective. The correlation between the hydraulic conductivity Ks and the parameter α results in an ensemble soil behavior more like a sand.

Simulating transient infiltration in unsaturated soils

Transient responses to various infiltration events have been examined using an unsaturated flow model. Numerical simulations reveal a range of infiltration patterns which can be related to the ratio of infiltration rate to unsaturated hydraulic conductivity. A high value of this ratio reflects a prevailing hydraulic conductivity which cannot readily redistribute the newly infiltrated moisture. Moisture accumulates in the near-surface region before advancing down through the soil as a distinct wetting front. In contrast, low values of the ratio of rainfall to unsaturated hydraulic conductivity show minimal moisture accumulation, as the relatively small volumes of infiltrating moisture are readily redistributed through the soil profile.Key words: numerical modelling, infiltration, unsaturated soil, soil suction, groundwater.

Simulating transient infiltration in unsaturated soils

Transient responses to various infiltration events have been examined using an unsaturated flow model. Numerical simulations reveal a range of infiltration patterns which can be related to the ratio of infiltration rate to unsaturated hydraulic conductivity. A high value of this ratio reflects a prevailing hydraulic conductivity which cannot readily redistribute the newly infiltrated moisture. Moisture accumulates in the near-surface region before advancing down through the soil as a distinct wetting front. In contrast, low values of the ratio of rainfall to unsaturated hydraulic conductivity show minimal moisture accumulation, as the relatively small volumes of infiltrating moisture are readily redistributed through the soil profile.Key words: numerical modelling, infiltration, unsaturated soil, soil suction, groundwater.

Steady infiltration in unsaturated soil from a buried circular cylinder: The separate contributions from top and bottom halves

Waechter and Philip (1985) obtained the asymptotic expansion of the mean infiltration rate for large s from a buried circular cylinder using a scattering analog. Here s(= αl/2) is defined as the ratio of the characteristic length l of the water supply surface (in fact, its radius) to the sorptive length 2α−1 of the soil and a satisfies the relationship K(ψ) = K(0) eαψ, where K is the hydraulic conductivity, and ψ is the moisture potential. This exact solution cannot be used directly to obtain the separate contributions to the mean infiltration rate from the top and the bottom halves of the cylinder; our analysis is based on a new class of special functions derived from the modified Bessel equation with a forcing term. In this paper, we obtain the separate asymptotics for the two halves for large s to make a comparison with the results of the trench problem (Waechter and Mandal, 1993). The asymptotic expansions for top and bottom halves are (2/π)(0.69553s−2/3) and (2/π)(1+0.30066s−2/3), respectively, whereas for a semicircular trench, the mean infiltration rate is given by (2/π)(1+0.30066s−2/3).

Moving finite element model for one-dimensional infiltration in unsaturated soil : Gottardi, G; Venutelli, M Water Resour ResV28, N12, Dec 1992, P3259–3267

Moving finite element model for one-dimensional infiltration in unsaturated soil : Gottardi, G; Venutelli, M Water Resour ResV28, N12, Dec 1992, P3259–3267

The recharge of a backfilled excavation: an examination of field behaviour

This Technical Note describes a comparison of the field behaviour of infiltration in unsaturated soil of dissimilar types with a numerical simulation. A trench excavated in undisturbed Kimmeridge clay was backfilled with crushed limestone imported fill and capped with a layer of clay. Details of the field experiment and measurement of specific moisture capacity and unsaturated hydraulic conductivity are described and the results are presented. The numerical model used to simulate field behaviour is outlined. Correlation was good and the model is recommended as a predictive tool for flow through dissimilar soil types.

Moving finite element model for one‐dimensional infiltration in unsaturated soil

The numerical integration of Richards' equation for infiltration into homogeneous unsaturated soil is carried out by a moving finite element (MFE) method. Accurate solution of this one‐dimensional nonlinear partial differential equation by standard finite difference (FD) or finite element (FE) methods can be obtained by using a fine discretization on space and time. This can lead to large computer times. With the MFE method, grid points are moved during computation along the wetting front, so that accuracy can be maintained by using a small number of nodes for simulating cases several meters in depth. For these cases the MFE method is faster than FD and FE methods. The numerical MFE model is verified through comparison with the quasi‐analytical solution by Philip (1957). Moreover, we compare, for some other test problems, the computational efficiency of this method with that of two efficient pressure head‐based FD and FE fixed grid formulations.

Numerical Method For Solving the Nonlinear Diffusion Equation: Study of Two-Dimensional Infiltration in Unsaturated Soils

Numerical Method For Solving the Nonlinear Diffusion Equation: Study of Two-Dimensional Infiltration in Unsaturated Soils