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.

*w*u- g = α / 100 (-*T */ *T*o )β ; *T *< 0C

(3)

The resilient modulus is defined as the applied

deviator stress divided by the strain recovered upon

where *w*ug = 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

*T*o = 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-

strain.

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-

*w*ug, 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, *w*t, 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-

*M*r = *K*1(*w*u-g / *w*t )K2 .

viously tested materials are given in Appendix B.

(4)

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 *w*ug/*w*t is a small number (<< 1). When the

The nonlinear form of the equation used to model

material is just below the freezing point, *w*ug/*w*t

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-

*K*2

*M*r = *K*1P

(1)

,

sign procedure (Bigl and Berg 1996b), the calcu-

lated amount of total water was often very high,

where *K*1 and *K*2 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

were considered.

equation of the form

ln *M*r = *A*0 + *A*1 ln *P *,

(2)

**Table 5. Constants for unfrozen**

**moisture content equations**.

where *A*0 and *A*1 are constants. To conduct the

α

β

*Soil*

regression, the natural log of the modulus was set

as the dependent variable and the natural log of

**Subgrade**

the governing parameter was set as the indepen-

1206

11.085

0.274

dent variable. In this general case,

1232

8.121

0.303

**Class 3**

*K*2 = *A*1 and *K*1 = *e *A0 .

Stockpile

1.497

0.709

**Frozen**

**Class 4**

In attempting to represent the frozen data with

Taxiway A

3.0

0.25*

the general form eq 1, we tried three different gov-

**Class 5**

erning parameters, all related to the unfrozen wa-

Dense stone

2.0

0.40*

ter content of the material, *w*u. The unfrozen water

**Class 6**

content present in the materials at various tem-

Stockpile

0.567

1.115

peratures, expressed in gravimetric form, *w*ug,

had been determined in earlier characterization

* Values for these materials are esti-

tests on the Mn/ROAD materials (Bigl and Berg

mated

8