Observations made at Goat Meadows - a small sub-alpine basin located near Pemberton, British Columbia -demonstrated that a layer which is either water repellent or has only a limited affinity for water is present at most vegetated sites. The layer is typically a few centimetres in thickness, and is usually located at or near the top of the profile: it was present only in the zone of accumulation of organic matter. The spatial distribution of the layer did not appear to be related to the distribution of any particular species of plant. Sampling of sub-alpine sites in the Cascade, Selkirk, and Purcell Mountains indicated that such layers are common in the alpine - sub-alpine ecotone of southern British Columbia. The relationship between ponding depth and infiltration rate was explored through experiments conducted on samples collected near Ash Lake, in Goat Meadows. These samples were chosen for analysis because the repellent layer was in excess of thirty centimetres thick at this site. Infiltration rates remained below 2x10⁻⁹ m/s for all samples, even given ponding depths of up to forty centimetres. Breakthrough of liquid water was not observed, even after one month, which implies that most of the infiltration occurred as vapour transfer. In order to observe the movement of liquid water through water repellent media, a plexiglas cell was constructed. A synthetic water repellent sand with uniform surface properties was used as the medium. It was found that up to some critical depth, there was no entry of water into the medium. As the ponding depth was increased in steps, the front would advance in steps: it remained stationary between these step-increases in ponding depth. As the front advanced, protuberances or "fingers" began to develop. At some critical ponding depth, a finger would grow without bound. These observations pose a challenge to existing models of infiltration, since it appears that heterogeneity at the scale of individual pores must be invoked to explain them, but it is usually assumed that the properties of a porous medium are continuous at this scale. The thermodynamics of filling and emptying of pores is considered with emphasis on the effects of pore shape and of variations in the physicochemical properties at the scale of the pore. This thermodynamic analysis provides the conceptual basis for development of a model of infiltration in which pore-scale heterogeneity is preserved. Although it was not developed as such, the model follows the approach of cellular automata, in which local relations between pores or "cells" govern the behaviour of the system. The model replicated the observations of infiltration into synthetic water repellent porous media well: both the halting advance of the front as the ponding depth was increased and the development of fingers were simulated. The fact that such complex behaviour was predicted using only a simple set of physically based rules confirms the power of the approach. / Arts, Faculty of / Geography, Department of / Graduate

No description available.

The purpose of this study is to present the development and application of residual flow procedure for analysis of three-dimensional (3-D) steady-state and transient seepage. The finite element equations are derived using a pseudo-variational principle which leads to a transient residual flow (load) vector that, in turn, is used to correct the position of the free surface iteratively. The procedure involves a fixed mesh which requires no mesh regeneration during transient analysis and during iterations. The procedure is also capable of handling material nonhomogeneities and anisotropy with relative ease. Several applications are made including verification with respect to closed-form solutions, and with results from a laboratory glass bead model simulating three-dimensional situations. For these glass beads, the coefficients of permeability and specific storage are also evaluated experimentally.

A three-dimensional finite element model for the analysis of steady state seepage has been presented in this study. The theory of unsaturated flow has been used in the analysis of steady state seepage. The model applies the invariant mesh procedure in the finite element analysis. Galerkin's method is used in the formulation of the finite element equations. The pre and the post processor developed in the generation and viewing of the finite element mesh and the free surface has also been discussed in this study. The study presents the comparison of results obtained from the three-dimensional model with a previously validated two-dimensional model. / Master of Science

Many environmental studies of water transport through the vadose zone require a field determination of saturated hydraulic conductivity. The purpose of this dissertation is to analyze the reliability of existing methods to determine saturated hydraulic conductivity, K(s), in the vadose zone from constant head borehole infiltration test data. In methods developed by the U. S. Bureau of Reclamation [USBRI, and in lesser known ones, K(s) is computed knowing the height of water in the borehole, length open to the formation, borehole radius, distance above the water table, and steady flow rate. The mathematical formulas on which these methods rest are derived on the basis of numerous simplifying assumptions. The free surface approach is used as the conceptual model of flow from a borehole. Results of numerical simulations are used to compare with the analytical solutions. Simulations with a steady-state finite element computer program, FREESURF, show that the Nasberg-Terletskata solution most closely approximates flow from a borehole with the free surface approach. The influence of capillarity is simulated for saturated-unsaturated porous media in four soils using a finite element computer program, FLUMP, and an integrated finite difference program, TRUST. Contrary to what one finds with the free surface approach, only a small portion of the flow field near the borehole is saturated at steady-state and the cross sectional area normal to the flow path increases with depth below the borehole. For deep water table conditions in fine textured soils, values of K(s) computed using the USBR open-hole equations may be more than 160% greater than the true values; and in coarse sands the USBR solutions may under-estimate the actual value by more than 35%. Mostly because of the influence of unsaturated soil properties there is no unique relationship between K(s), borehole conditions, and steady flow rate, as implied in the analytical solutions. Steady-state simulations demonstrate that existing solutions for borehole infiltration tests in anisotropic or nonuniform soils may also lead to significant errors. Time dependent simulations show that the time to reach a steady flow rate may be more than several days in very dry, low-permeable soils. The time to reach a steady flow rate can be significantly reduced by decreasing the open area between the borehole and formation while increasing the height of water in the borehole. Two methods are proposed to minimize the time, water volume requirements, and cost of conducting constant head borehole infiltration tests. Simulations show that a plot of the inverse of flow rate versus logarithm of time departs from a straight line after about 80% of the steady rate is achieved for various soil and borehole conditions; the steady rate is approximately 0.8 times the rate at the break in slope. In the second method flow rate is plotted versus the inverse of the square root of time and the steady rate is estimated within about 10% by linear extrapolation of early time measurements. USBR field data generally support this linear relationship. Two empirical equations are proposed to compute K(s). The first is applicable for a range of borehole conditions and approximately accounts for capillary effects with a single parameter. The second applies if the height of water in the borehole is I meter, and is based on the time to reach 80% of the steady rate and saturation deficit of the field soil.