Fremond (1985) published a model of soil frost heav-
cesses, including adiabatic (no heat transfer between
ing and thaw settlement that utilized the continuum
system and surroundings), isothermal, isobaric, or iso-
approach. The constitutive laws used to describe the
choric (constant volume).
soil behavior were elastic for the unfrozen soil and
Equilibrium is defined as a state of rest--i.e., the
viscoplastic when frozen. Michalowski (1992, 1993)
system properties do not change with time. Thermody-
extended that work to account for more factors affect-
namic equilibrium is an equilibrium state where there
ing frost heave (e.g., three-dimensional stress state of
is a balance of thermal, mechanical, and chemical
the soil). He used constitutive relations to describe the
forces. If a system always deviates from equilibrium
rate of deformation of the soil during frost heave, as
only infinitesimally during a process, then the process
well as the constitutive relations of heat conduction
is reversible. Real processes are always irreversible, but
(Fourier's Law), water flow (Darcy's Law), and a con-
reversible processes are studied to determine maximum
stitutive law describing the relation between stress and
or minimum amounts of work that can be produced by
strain in the frozen soil or soil skeleton. Recently, Harti-
them.
kainen and Mikkola (1997) reported progress on using
Heat flows across a system boundary in response to
equilibrium thermodynamics to predict the movement
a temperature gradient. Heat is path-dependent, mean-
and phase change of water in freezing soil along with
ing that the amount of heat flow that occurs depends on
constitutive models to predict the deformation of the
the process itself. Heat appears only at the boundary of
soil due to frost heave.
a system during a change in state. It is manifested by
temperature change in the surroundings.
Work is energy that flows across the boundary of a
THERMODYNAMIC FUNDAMENTALS
system during a change in state that is completely con-
Definitions, first, and second laws
vertible to lifting a weight in its surroundings. Like heat,
A thermodynamic system is a portion of the uni-
work is path-dependent, appearing only at the bound-
verse set aside for study. There are three types: open,
ary of a system during a change in state, and is mani-
closed, and isolated. An open system can exchange
fested by an effect in the surroundings (e.g., the lifting
energy and mass with its surroundings. The open sys-
of a weight). It occurs as a result of a potential gradient
tem is thus specified by space rather than the matter
other than temperature (e.g., a pressure gradient). The
equation for mechanical work is δW = Fdl, where F
contained within the space, and the volume occupied
by an open system is a control volume. In freezing soil,
refers to a "generalized force," and l refers to a "gener-
alized displacement." (The symbol δ indicates path
a volume through which water, heat, and soil flow is an
open system. A closed system can exchange only ener-
dependence and d, path independence.) If the force is
gy with its surroundings and is modeled with a control
independent of direction and the rate of change of the
mass; a mass of soil through which heat but no matter
process (i.e., it is path-independent), then the work mode
flows is a closed system. An isolated system can exchange
is reversible (that is, the amount of energy added in a
neither energy nor mass with its surroundings.
forward process is equal to the amount of energy
A property is a system characteristic that can be
removed in a reverse process).
measured or determined from other measurements. The
All intensive thermodynamic properties are gener-
state of a system is defined when all of its properties
alized forces, and all extensive properties are general-
are specified. Properties are classified as either exten-
ized displacements--including length, volume, area,
sive or intensive. Extensive properties are additive,
mass, and number of moles of a substance. Reversible
meaning that the value of the property is obtained by
work is an idealization of real processes--examples are
summing the values of the property in every part of the
frictionless pulleys or resistanceless wires. Types of
system. These include mass, volume, length, area, and
reversible work are defined in Table 1. For nonrevers-
number of moles of a species in a system. Intensive
ible work, relationships other than those given in Table
properties do not depend on system size. These include
1 must be used to account for the energy that is not
pressure, temperature, specific volume, stress, surface
converted to work.
tension, and force per unit length.
A change in the state of a system results from pro-
ciated with heat energy, and temperature is the inten-
sive property. Heat can be expressed as δQrev = TdS,
cesses such as energy or mass flow across its bound-
where S is the entropy. Entropy is a measure of the
aries or internal processes that cause its properties to
decrease in the system's ability to do work. It can be
change. A process is a series of events causing a change
associated with mass entering or leaving a system, or
of state, and a path is the sequence of states that the
both, and can be exchanged across system boundaries
system assumes between initial and final states. There
because of heat transfer.
are many different types of processes, or stages in pro-
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