unit stress of 6.9 kPa (1.0 lb/in.2); *C*o, *C*1, and *C*2

The two other forms that were used to repre-

sent the unfrozen water content in the governing

are constants; *S *is the degree of saturation, in %;

*S*o is a unit saturation, 1.0%; γd is dry density, in

parameter of eq 1 were directly related to the un-

Mg/m3; and γo is a unit density (1.0 Mg/m3). To

frozen water content, as follows: 1) *w*ug, expressed

as a decimal, normalized to a unit unfrozen water

conduct the regression analysis, we linearized this

content, *w*o, of 1.0; and 2) the volumetric unfro-

equation to form

zen water content, *w*uv, expressed as a decimal,

ln *M*r = *A*0 + *A*1 ln (S / *S*0 )

normalized to a unit unfrozen water content, *w*o,

of 1.0. The volumetric unfrozen water content was

+ *A*2 ln (γ d / γ o ) + *A*3 ln [ f (σ)] .

(9)

determined with

*w*u- v = *w*u-g γ d

(5)

For a particular set of conditions, then

where γd = dry density (Mg/m3). The resulting

*K*1 = *e *A0 (S / *S*0 )

(λ d / γ o ) A2

*A*1

and *K*2 = *A*3 .

equations with these terms substituted as the gov-

erning parameter were:

Three stress parameters were investigated to

help characterize the stress dependence of the ma-

(

)K

*M*r = *K*1 wu-g / *w*o

2

terials tested. These included *J*1, the bulk stress

(or first stress invariant); τoct, the octahedral shear

*M*r = *K*1(wu- v / *w*o )

*K*2

stress; and *J*2/τoct, the ratio of the second stress

.

invariant to the octahedral shear stress. In our re-

peated-load triaxial test, where σ2 = σ3 and σ1 =

In analyzing the frozen resilient modulus data,

the value of the governing parameter wu- g / *w*t ,

σ3 + σd, the functions are given as:

*w*u- g / *w*o , or *w*u- v / *w*o at each test point was de-

*J*1 = 3σ3 + σd

termined from the temperature (and total water

content, if necessary.) Then, regression analysis

2

was conducted to determine the relationship be-

τoct =

σd

tween these values and the measured resilient

3

modulus. Data from the thawed, undrained state

and

(assigned to be at a temperature just barely below

9σ32 + 6σ3σd

freezing) were analyzed along with the frozen data.

*J*2 / τoct =

2σd

**Thawed/never frozen**

where J1 = σ1 + σ2 + σ3

For the never frozen and thawed data, the gov-

erning parameter in the general form equation (eq

*J*2 = σ1σ2 + σ2σ3 + σ1σ3

1) was set to be a stress function. The constant *K*1

was considered to be a function of the moisture

level expressed as the degree of saturation in the

τoct = 12 (σ1 - σ2 )2 + (σ2 - σ3 )2 (σ1 - σ3 )2 .

sample and, when a range of data were available,

the dry density. Thus, the general equation be-

We found that the bulk stress parameter (*J*1) pro-

comes

vided the best fit to the data for the class 6 special

base material. The ratio *J*2/τoct was the stress pa-

*M*r = *K*1[ f (σ)]K2 ,

(6)

rameter that best fit the data of the three subbases

class 3 special, class 4 special, and class 5 special,

which includes the term

and τoct best characterized the clay subgrades.

*K*1 = *C*0 (*S */ *S*0 )C1

(7)

We also analyzed the data from the class 6

special base material in the thawed condition us-

or

*K*1 = *C*0 (*S */ *S*0 )C1 (γ d / γ o )C2

ing an equation of the form

(8)

*M*r = *K*1 e K2 [ *f *(σ)].

where *f*(σ) is a stress parameter normalized to a

(10)

9