dial strains were recorded, and thus were used to
1996a). It is related to the temperature in the form
calculate a resilient modulus and Poisson's ratio.
wu- g = α / 100 (-T / To )β ; T < 0C
The resilient modulus is defined as the applied
deviator stress divided by the strain recovered upon
where wug = gravimetric unfrozen moisture con-
unloading for a representative loading cycle, or
tent, in decimal form
resilient axial strain. To calculate the resilient axial
T = temperature, C
strain, the measured resilient axial deformation is
To = 1.0C
divided by the gauge length over which it is deter-
α and β = constants.
mined. Poisson's ratio is defined as the recover-
able radial strain divided by the recoverable axial
Table 5 presents the α and β constants characteris-
tic of each material.
The following data were then tabulated in a
The first governing parameter we tried was
spreadsheet: confining stress, deviator stress, re-
wug, expressed as a decimal, which had been nor-
silient axial strain, resilient radial strain, density,
malized to the total gravimetric water content in
and moisture condition or temperature. The tables
the sample, wt, also expressed as a decimal. The
in Appendix A contain these data along with the
resulting equation was as follows:
calculated results. The equivalent data for the pre-
Mr = K1(wu-g / wt )K2 .
viously tested materials are given in Appendix B.
These tables also show the actual stress combina-
This governing parameter has a good physical ba-
tions applied to each specimen.
sis. When the material is very cold and solidly
The frozen and unfrozen data were analyzed
frozen, there is very little unfrozen water and the
separately using statistical regression techniques.
ratio wug/wt is a small number (<< 1). When the
The nonlinear form of the equation used to model
material is just below the freezing point, wug/wt
the resilient modulus was the same in both cases,
approaches a value of 1. However, when this form
as given by
of the equation was used in the mechanistic de-
Mr = K1P
sign procedure (Bigl and Berg 1996b), the calcu-
lated amount of total water was often very high,
where K1 and K2 are constants and P is a govern-
and the ratio of unfrozen water to total water was
ing parameter. This equation was linearized by
unreasonably small. Therefore, other relationships
taking the natural log of both sides, resulting in an
equation of the form
ln Mr = A0 + A1 ln P ,
Table 5. Constants for unfrozen
moisture content equations.
where A0 and A1 are constants. To conduct the
regression, the natural log of the modulus was set
as the dependent variable and the natural log of
the governing parameter was set as the indepen-
dent variable. In this general case,
K2 = A1 and K1 = e A0 .
In attempting to represent the frozen data with
the general form eq 1, we tried three different gov-
erning parameters, all related to the unfrozen wa-
ter content of the material, wu. The unfrozen water
content present in the materials at various tem-
peratures, expressed in gravimetric form, wug,
had been determined in earlier characterization
* Values for these materials are esti-
tests on the Mn/ROAD materials (Bigl and Berg