Normalized Water Content Research Articles

Predicting the permeability function for unsaturated soils using the soil-water characteristic curve

The coefficient of permeability for an unsaturated soil is primarily determined by the pore-size distribution of the soil and can be predicted from the soil-water characteristic curve. A general equation, which describes the soil-water characteristic curve over the entire suction range (i.e., from 0 to 106 kPa), was proposed by the first two authors in another paper. This equation is used to predict the coefficient of permeability for unsaturated soils. By using this equation, an evaluation of the residual water content is no longer required in the prediction of the coefficient of permeability. The proposed permeability function is an integration form of the suction versus water content relationship. The proposed equation has been best fit with example data from the literature where both the soil-water characteristic curve and the coefficient of permeability were measured. The fit between the data and the theory was excellent. It was found that the integration can be done from zero water content to the saturated water content. Therefore, it is possible to use the normalized water content (volumetric or gravimetric) or the degree of saturation data versus suction in the prediction of the permeability function. Key words : coefficient of permeability, soil-water characteristic curve, unsaturated soil, water content, soil suction.

Simultaneous scaling of soil water retention and hydraulic conductivity curves

Previously, soil water retention and hydraulic conductivity curves have been scaled independently with separate scale factors calculated for each curve. Here we provide a method to scale both hydraulic functions simultaneously to yield a single set of scaling factors. An algorithm was developed to scale the hydraulic data, either as a function of degree of saturation S, or normalized water content Θ. Optimization using Powell's method in combination with a Newton‐Raphson procedure resulted in one set of parameters representing the scaled mean hydraulic functions and one set of scale factors describing the variability of both the retention and conductivity relationships. We present and compare results obtained from (1) scaling water retention data only; (2) scaling hydraulic conductivity data only; (3) simultaneous scaling of soil water pressure head h and the natural logarithm of hydraulic conductivity K; and (4) simultaneous scaling of the logarithms of both h and K. Sets of scale factors for two data sets were analyzed for distribution type and autocorrelation.

Analytical results for prediction of variable rainfall infiltration

The basic equations that govern water movement in unsaturated soils are presented for a boundary condition of variable rainfall rate at the soil surface. In particular, a differential equation for the water content at the soil surface is derived. Solutions are then obtained for the time evolution of water content at the soil surface assuming a power law form for the relative permeability to water as a function of normalized water content. Ponding time formulae are obtained and compared with other previously published relations. Water content profiles are also obtained and their shapes are displayed graphically for the case of an exponent of 2 in the power law form of the relative permeability to water for a constant rainfall rate. Formulae are also derived for the situation of a variable rainfall pattern. A methodology for the coupling of the analytical procedures with an implicit numerical solution of the water content at the soil surface is suggested as a cost-effective alternative to the strict numerical solution of the partial differential equation that governs the water content profile evolution. Postponding infiltration formulae and water content profile equations are also provided.

An initial value problem for the horizontal infiltration of water

An initial value problem for the horizontal infiltration of water is solved by means of a perturbation technique. The diffusivity is assumed to vary as a positive power of the normalized water content. Evolution of the profile is supposed to be taking place in two stages. In the first stage, moisture content at the origin increases steadily as some arbitrary power of dimensionless time until the maximum normalized value of unity is attained; thereafter, in the second stage, moisture content at the origin remains at the constant value of unity. The moisture distribution at the end of the first stage defines the initial values of moisture for the problem in the second stage. This paper derives the flow details for the second stage, and constructs moisture profiles as they evolve for times greater than unity.

The Adaptability of an Exact Solution to Horizontal Infiltration

An exact solution of the concentration‐dependent diffusion equation, which was obtained by J. R. Philip, is shown to be adaptable to the problem of horizontal infiltration into partly saturated porous materials by a suitable approximation of algebraic functions describing the moisture content‐capillary suction and the moisture content‐capillary conductivity relationships. One of the theoretical results that compares favorably with published experimental data gives the cumulative infiltration simply asF = [2k0A(θ0 ‐ θi)/n]1/2t1/2where k0 is the hydraulic conductivity at saturation, θ0 is the porosity or the volumetric water content at saturation, θi is the initial water content, n is the exponent in the power function of the normalized water content describing the relative permeability, and A is a characteristic length parameter depending on the fineness of the pores.