RIGIDICE Model of Secondary Frost Heave

RIGIDICE Model of Secondary Frost Heave

PATRICK B. BLACK

INTRODUCTION

RIGIDICE

In an earlier paper, Black and Miller (1985) re-

Black and Miller (1985) simplified the solution

ported on progress to numerically solve the dif-

of the differential equations for secondary frost

ferential equations of secondary frost heave (Miller

heave (Miller 1978) by employing two physical

1978) using a simplified approach. They presented

assumptions and one numerical trick. Their model,

a series of scenarios that predicted anticipated re-

as well as this model, is valid for one-dimensional,

sults. The program was experimentally confirmed

incompressible, air-free and solute-free soil. The

by comparing observed behavior of independently

solute-free restriction assumes that no additional

conducted frost heave tests to model predictions

osmotic gradient is imposed over the ever present

using hydraulic and thermal properties for the test

osmotic gradient in the double layer of the unfro-

soil. They found that the model indicated that the

zen water surrounding the grains. The incompress-

experimental data were flawed in their stress mea-

ible restriction excludes the process of consolida-

surements, but agreed within acceptable tolerance

tion at this time. Finally, the air-free condition states

with the thermal measurements. No additional ef-

that the region undergoing heave must be water

fort was made at that time to extend the analysis

saturated. This makes perfect sense, since air does

or increase the utility of the program.

not freeze, which means that the soil must have

This report is an extension of the earlier work.

been saturated, or within 10%, because of the vol-

It presents improvements in two areas. First, a

ume expansion necessary for a lens to appear.

minor mistake in the calculation of the water flux

These restrictions are minor since they result in

is corrected; also, the current formulations for the

the model predicting the behavior of the highly

scaled equations of ground freezing are used

frost-susceptible fine-grain silts.

(Miller 1990). Second, the computer code is pre-

sented in a form readily available for enhance-

First physical approximation

ments. This is accomplished by employing the

(lensing cycle)

concepts of Object Oriented Numerics (OON),

First, the progression of frost heaving through

which allow the code to be easily added to with-

soil is approximated physically by a series of in-

out directly changing the original source code

dependent lensing cycles. A lensing cycle is de-

(Wong et al. 1993).

fined to be the time step that begins with the for-

The concepts and equations of the RIGIDICE

mation of a lens and ceases with the initiation of a

(Black and Miller 1985) model are first reviewed.

new lens. During each individual lensing cycle,

The new C++ formulation of the code is then dis-

the frozen soil above the fringe is composed of a

cussed and presented in its entirety in Appendix

series of identical layers of ice and frozen soil as

A. The code is linked as a Dynamically Linked

depicted in Figure 1. The thickness of these lenses

Library (DLL) that is attached to MathCad 5.0+

and the frozen soil between them is equal to the

(MathSoft 1994). A preliminary sensitivity study

thickness of the mature lens and interspaced fro-

is conducted to examine the influence of uncer-

zen soil at the end of the lensing cycle.

tainty in input parameters on the variability of the

This approximation bounds the fringe between

calculated output parameters.

the lower freezing front and the upper boundary