(lb/in.2)
(kPa)
7 107
107
7 106
106
7 105
105
Schmidt
Ullidtz
7 104
104
20
10
0
10
20
30
40
50
Temperature (C)
Figure 4. Comparison of predicted values from the Schmidt and Ullidtz
asphalt modulus equations.
Table 1. Classification of soil for corresponding modulus equation.
Classification
Definition
Frozen: the ice content is greater than or equal to 0.005, the temperature not equal to 0C, and the
1
pore pressure less than 0.
2
Partially thawed: the ice content is greater than or equal to 0.005 and the pore pressure is greater
than or equal to 0.
3
Thawed, with negative pore pressure: the ice content is less than 0.005 and the pore pressure is
less than 0.
4
Thawed, with positive pore pressure: the ice content is less than 0.005 and the pore pressure is
greater than 0.
Recently frozen layer: the temperature is less than 0C and was recently thawed. This layer
5
retains its modulus prior to freezing until the frozen equation predicts a higher modulus or until
the temperature rises.
6
Recovering thawed layer: for 120 days subsequent to having been frozen, a thawed layer has its
modulus reduced according to a ratio that diminishes over time.
sion coefficients for the resilient modulus in the
series. It is calculated by multiplying the gravi-
thawed condition, 3) f(σ)m, an approximation of
metric unfrozen water content by the dry density
the mean stress condition, and 4) α and β, unfro-
in Mg/m3.
zen water content constants.
TRANSFORM uses an approximation of the
f(σ) stress term in its equations to predict moduli
Several forms of the unfrozen water content
function were investigated for predicting the fro-
of unfrozen soils. Since this term is constant for
zen moduli of the Mn/ROAD materials, as re-
each soil, the unfrozen moduli calculated by
ported in Berg et al. (1996). The form used for the
TRANSFORM are not dependent on stress. The
Phase 1 simulation series of this study is the nor-
approximation used was the mean stress condi-
malized gravimetric unfrozen water content, cal-
tion applied during the laboratory resilient modu-
culated as shown in Table 2. A second, normal-
lus testing.
ized volumetric form of the unfrozen water content
Because some materials have a significant dis-
function was used in Phases 2 and 3 simulation
continuity between the minimum frozen and
7
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