This equation is often called the generalized Clausius-Clapeyron equation that describes the
equality of chemical potentials of ice and water subjected to two different pressures. Radd
and Oertle (1973) empirically validated eq 215.
The soil water is known to be expelled from the frost front under certain conditions
depending upon soil type, stress level, etc., when a frost front advances through a saturated
soil. Such a phenomenon is often called the pore water expulsion, and a concise review of
papers on the subject was written by McRoberts and Morgenstern (1975). We have found
that the unique solution of Problem P exists such that fo < 0 if σ ≥ σc. It is clear that the pore
water expulsion occurs in this solution. We will examine the accuracy of M1 by using exper-
imental data of Kanto loam on water expulsion below.
Takashi et al. (1978) conducted numerous freezing tests similar to the test described
above on overconsolidated samples of silt and clay to determine empirical descriptions for
the heave ratio h and the water intake ratio hw. In their tests, Ta > 0C was kept constant at a
value 0.20.3C higher than the freezing point of the sample, while Tb (t) was decreased with
time from the initial value Tb (0) = Ta in such a manner that Vo was kept nearly constant.
After each test h and hw were determined by measured total amounts of heave and water
intake, respectively, for a given set of σ and Vo. The empirical descriptions obtained are giv-
en as
h = (m1/σ)[1 + (m2/Vo)1/2] + mo
(216)
hw = d2(m1/σ)[1 + (m2/Vo)1/2] s2m3
(217)
where mi (i = 0,1,..., 3) are positive numbers that depend on a given soil. The sets of con-
stants mi for a few kinds of soils have been reported (Ohrai and Yamamoto 1991). Ryokai
(1985) determined the set of constants mi for Kanto loam by a series of freezing tests similar
to those of Takashi et al. (1978). The values of mi are mo = 0.0002, m1 = 0.980 kPa, m2 = 8.07
103 cm/d and m3 = 0.439. In his tests (Ryokai 1985) the height of samples was 2.0 cm and Ta =
0.5C.
In the Takashi's freezing test, σ and Vo are constants but αo and δo vary with time. For
instance, in the test by Ryokai (1985), the value of δo was 2.0 cm at the start and decreased
with time. The value of αo was 0.25C/cm at the start, increased to about 1.0C/cm when a
quarter of a sample remained unfrozen, and increased further with time. It has been recog-
nized (Ohrai and Yamamoto 1991) that the empirical formulas (eq 216 and 217) must be
applied for cases where Vo is greater than about 1.5 cm/d, because the behavior of these
216 and 217 that r and fo vanish as Vo vanishes. But in reality when Vo vanishes, an ice layer
begins growing so that r and fo do not vanish. It is also important to mention that the empir-
ical formulas must be applied for cases where σ is greater than about 50 kPa.
Ideally, the results of Takashi's tests should be compared with the theoretical predictions
based on the solution under the same initial and boundary conditions as those of actual
tests. Since such unsteady solutions are not yet known, we will use eq 160 and 161 based on
the traveling wave solutions studied above. Differentiating eq 98 with respect to σ, we ob-
tain
T1
= -1.
(218)
E1(T1)
σ
Since E1 is positive, T1 and y are decreasing functions of σ. It follows from eq 160 and 216
that h is a positive and decreasing function of σ and Vo. From eq 161 and 217 we find that hw
is also a decreasing function of σ and Vo and that hw becomes negative when σ and Vo be-
come large, namely, water expulsion occurs.
28
to Contents
Previous Page
