As before, K1 was considered to be a function of
the frozen state. Also shown are the data for the
the degree of saturation and the dry density (eq 8).
thawed, undrained condition, which are assumed
In this case, the stress parameter, f(σ), was the
to be valid at a temperature of 0C and were in-
normalized bulk stress, J1. This form of the equa-
cluded as the warmest data point of the regression
tion was able to accommodate negative stress val-
analyses. Superimposed on the data are lines show-
ues that were generated in the layered elastic analy-
ing the moduli predicted by the three types of
sis portion of the predictive model.
regression equations. Where the predictive equa-
tion requires normalization to the total water con-
tent, that parameter was set to be the average value
RESULTS
for all the specimens tested. For the predictive
equation with volumetric unfrozen water, the dry
General
density was also set to be the average value for all
Appendices A and B give a tabulation of all the
the specimens tested.
laboratory test results of the frozen, thawed, and
Figure 4 shows that the frozen modulus does
never-frozen soil specimens. Appendix A contains
vary primarily as a function of the unfrozen water
the data from the current study, which includes
content. A minor amount of variation results from
the two Mn/ROAD subgrade samples 1206 and
the various stress combinations acting on the speci-
1232, the class 6 special base, and the class 3
mens, as shown from the vertical spread in the
special subbase. Appendix B contains the data
data at any particular temperature. To illustrate
determined previously from dense graded stone,
this, Figure 5 shows the data from a few individ-
the substitute for Mn/DOT's class 5 special sub-
ual deviator stress levels plotted separately for the
base, and from Albany, New York, taxiway A sub-
subgrade samples.
base, the substitute for class 4 special subbase.
All three types of predictive equations appear
Data for the never-frozen 1206 subgrade speci-
to represent the data fairly well. The moduli re-
mens were acquired on a different testing ma-
sulting from the governing parameter, normalized
chine than all the other data. After testing of all
to the total water content, increases less rapidly
specimens was completed, we discovered that this
with decreasing temperature at temperatures just
second machine was out of calibration, such that
below freezing than do moduli from the other two
the moduli reported here are much higher than
equations. Unfortunately, the temperature varia-
they should be. However, data from the low density
tion of the environmental chamber of the testing
(CE 5) samples are close to moduli back-calcu-
machine was too great to allow acquisition of data
lated from falling weight deflectometer (FWD)
at temperatures close to the freezing point for the
tests on subgrade at the site during fall of 1991.*
Mn/ROAD materials. When the two substitute ma-
Table 6 summarizes the equations that resulted
terials were tested, a different chamber tempera-
from the regression analysis performed on the data,
ture controlling system was used, and it was pos-
with the frozen and unfrozen equations given in
sible to obtain data nearer to the freezing point. In
separate sections. The number "n" in Table 6 re-
these cases, shown in Figures 4d and 4e, the pre-
fers to the number of points evaluated in the analy-
dictive equations without normalization to total
sis. Each stress combination at a given moisture
water appear to pass nearer to the center of the
level or temperature results in one data point; thus,
range of data collected at temperatures warmer
the test of a single specimen results in many data
than 2.0C.
points. The table also lists the coefficients of de-
Figure 4 also shows that the predictions from
termination (r2) for these analyses.
the equations whose governing parameters are the
gravimetric and volumetric unfrozen water nor-
Frozen
malized to a unit unfrozen water are not very dif-
Figures 4a through 4f illustrate the resilient
ferent. Predictions from the volumetric form rise
modulus data vs. temperature for each material in
less rapidly at temperatures just below freezing,
while at the colder temperatures, they are slightly
larger than the gravimetric form.
*D. Van Deusen, Mn/ROAD, pers. comm. 1992 .
10
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