Thermal Model For Roads, Airstrips And Building Foundations In Permafrost Regions
Authors: Meyer G.H. , Keller H.H. , Couch E.J. 
Published: March 2010

Abstract
A thermal model describing the one-dimensional heat conduction in a layered system is developed. Up to ten homogeneous layers, each having different thermal properties porosity, water content and thickness, can be accommodated. A periodic temperature is input for the surface condition. The computed results consist of the depth of the thawed region as a function of time.
The layered model is applied to the design of foundations for roads and airstrips in permafrost regions. A sensitivity study was made to find the effect on thaw depth of varying physical properties of the materials used, the geometry of the construction and the surface temperature. The means for extension of the model to building foundation design by modification of the surface boundary condition is presented.

Introduction
THE DISCOVERY OF OIL in the Prudhoe Bay region of Alaska has focused considerable attention on the engineering problems of developing petroleum production facilities in remote arctic areas. The main source of difficulty is the undesirable thawing of permafrost under such structures as roads) airstrips, buildings and drilling equipment. Subsidence, differential settlement and frost heaving may be expected if the permafrost formation under the structure is allowed to thaw seasonally or permanently(1).
In order to guard against such destruction, building sites may be placed on gravel embankments which; in turn, may rest on a thermal insulator as is common in road construction on the arctic tundra(2). In order to insure adequate and economical protection of the underlying permafrost, accurate predictions of the temperature distribution and the depth of thaw under engineering structures become important. It is the purpose of this paper to present a thermal model for calculating the seasonal depth of thaw in a layered medium; it is applicable to general structures where the heat flow is essentially one-dimensional. In this model heat transfer is assumed to be due exclusively to conduction. For pure ice-water mixtures (such as ice on lakes) this assumption is inadequate because of convective effects(3). It is recognized that on a microscopic scale the exact mode of heat transfer in permafrost is likely to be a combination of conductive, convective and radiative processes(4); however, on the basis of soil temperature measurements, Pearce and Gold(5) were able to conclude that "the annual temperature variation in the soil ... is remarkably consistent with the theory of (conductive) heat flow in a one-dimensional semiinfinite medium." Thus, a conduction model may be used with confidence for temperature studies in permafrost.
This problem has been investigated by Lachenbruch(6) for a system limited to three layers. Our model and discussion to some extent are parallel to that of Kazemi and Perkins(7). The basic difference, apart from the structures studied, is in the solution algorithm used for solving the heat flow equations. The method proposed here is mathematically sound(8), easy to apply, allows a fine spatial resolution and is quite fast. In fact, the discussion of construction methods for roads and airstrips is based on a parameter study conducted via interactive computer graphics.