Yoshisuke Nakano

MATHEMATICAL MODELING AND VALIDATION OF THE THERMAL REGIMES IN TUNDRA SOILS, BARROW, ALASKA

Efforts were made to develop a mathematical model. Accuracy in simulating the field obsermodel of the thermal regimes in tundra soils. vations by the model is found satisfactory. The results of field investigations during the Effects of important factors affecting the thersummer and fall of 1970 in the vicinity of Bar- mal regime are also discussed. row, Alaska, were used for validation of the

Quasi-steady problems in freezing soils: I. Analysis on the steady growth of an ice layer

Abstract The steady growth of a segregated ice layer in freezing soils is studied mathematically under three distinct and representative hypotheses on the properties of the frozen fringe, chosen among many such hypotheses reported in the literature. It was found that the condition of steady growth is determined by the temperature gradient in the unfrozen part of the soil at the 0 (°C) isotherm and the temperature gradient in the ice layer at the interface between the ice layer and the frozen fringe in all three hypothetical models studied. The transport equation of water in the frozen fringe was found to be the major factor determining the condition of steady growth. This is the first of a two-part presentation on the subject; the experimental aspects of the study will be presented in a second paper.

Transport of water in frozen soil: I: Experimental determination of soil-water diffusivity under isothermal conditions

Abstract A new experimental method for measuring the soil-water diffusivity of frozen soil under isothermal conditions is introduced. The theoretical justification of the method is presented and the feasibility of the method is demonstrated by experiments conducted using marine deposited clay. The measured values of the soil-water diffusivity are found comparable to reported experimental data.

Transport of water in frozen soil II. Effects of ice on the transport of water under isothermal conditions

Abstract Effects of ice on the transport of water in frozen soil were investigated under isothermal conditions. Based on the experimental results obtained using a marine-deposited clay at −1.0°C, the presence of ice is shown to significantly affect the transport of water under certain circumstances. A theoretical analysis of the experimental results and a discussion of a possible mechanism for water transport in frozen soil are presented.

Quasi-steady problems in freezing soils: II. Experiment on the steady growth of an ice layer

A series of freezing tests on three kinds of soil were conducted to find the steady growth condition of a segregated ice layer by using a new steady-state method in which the temperature profiles of soil specimens were controlled. It was found that the steady growth condition is determined by the absolute value of the temperature gradient of the unfrozen part of the soil αu and that of the frozen part of the soil αf under a given hydraulic condition as follows: αu=Sαf, k1k0 > S > S0, αf<A; where k1 and k0 are the thermal conductivity of the frozen and the unfrozen parts, respectively, and S0 a constants that are the properties of a given soil. Comparing these experimental results with the results of the mathematical analysis presented in part I, we have found that the model M1 is consistent with the experimental results while the models M2 and M3 contradict them. This is the second of a three-part presentation on the subject.

Transport of water in frozen soil: III. Experiments on the effects of ice content

Abstract Effects of ice content on the transport of water in frozen soil are studied experimentally and theoretically under isothermal conditions. A physical law, that the flux of water in unsaturated frozen soil is proportional to the gradient of total water content, is proposed. Theoretical justification is made by the use of the two-phase flow theory. The experimental results are shown to support the proposed physical law. The results of this study are presented in two parts. The experimental aspects of the study are presented in this paper and the second paper contains the theoretical aspects of the study.

Transport of water due to a temperature gradient in unsaturated frozen clay

Abstract As reported experimental data indicate, the net flux of water f in a fine-grained soil column was assumed to be given as: f=−D 1 (w,T) αw αx −ρD 2 (w,T) αT αx where ϱ is the dry density, T is the temperature (°C), w is the content of water in all phases, x is the coordinate, and empirical functions D1 and D2 are the properties of a given soil. Under this assumption a new experimental method was introduced to determine D2 of a soil with known D1. The D2 of Morin clay was determined as a function of w at several temperatures ranging between − 1.0 and 1.0°C. A common feature found is that D2 increases with increasing w, attains its maximum near or not far from a point where w is equal to the equilibrium unfrozen water content, and then decrease when T is negative. However, D2 increases with increasing w up to about 14%, and then remains more or less constant as w increases when T is positive. Because of this behavior of D2 a sudden change (or discontinuity) of D2 occurs near a point where T = 0°C when w is greater than 14%. The validity of the assumed functional description of the flux f is discussed based on some recent results of mathematical analysis on degenerate quasi-linear equations of parabolic type.

Transport of water in frozen soil IV. Analysis of experimental results on the effects of ice content

Abstract Effects of ice content on the transport of water in frozen soil are studied experimentally and theoretically under isothermal conditions. A physical law, that the flux of water in unsaturated frozen soil is proportional to the gradient of total water content is proposed. Theoretical justification is made by the use of the two-phase flow theory. The experimental results are shown to support the proposed physical law. The results of this study are presented in two parts and this is the second paper describing the theoretical aspects of the study.

Application of recent results in functional analysis to the problem of water tables

Abstract The traditional viewpoint in hydrology and soil physics purports that water tables appearing in porous media described by Darcys law and the extended Darcys law are not singular surfaces. Several particular solutions in which singularities occur are presented as counter-examples to the traditional viewpoint and as evidence supporting the new theory that water tables are generally singular surfaces.

Particular solutions to the problem of horizontal flow of water and air through porous media near a wetting front.

Abstract Particular solutions to the problem of horizontal flow of water and air through homogeneous porous media are derived and regularity properties of the solutions are presented. It is found that a singularity occurs in the solutions at the wetting fronts. Effects of air flow on water flow are discussed.