**Table 2.. Generall fform oof rreslileent mooduuus(***M*r)r )eqqatitins susesd dinin

**2 Genera orm f esi i i nt m dul l s (***M * euua o on u e

**TRANSFORM.**

*Condition*

*Equation*

*Mr *(lb/in.2 ) = *FC*1 *f *(*w*u-g )FC2

Frozen

*Mr *(lb/in.2 ) = *TC*1(100)TC3 f (γ )TC4 f (σ)m*C*2

*T*

Partially thawed

*Mr *(lb/in.2 ) = *TC*1 *f *(*S*)TC3 f (γ )TC4 f (σ)m*C*2

*T*

Thawed, negative pore pressure

*Mr *(lb/in.2 ) = *TC*1(100)TC3 f (γ )TC4 f (σ)m*C*2

*T*

Thawed, positive pore pressure

Notes:

FC1, FC2 =

regression coefficients for the frozen condition

*f *(*w*ug) =

*w*ug/*w*o

β

α

*T*

*w*ug =

grav. unfrozen water content (decimal) = 100 *T*

0

*w*o =

unit water content (1.0)

α, β =

unfrozen water content constants

temperature, C

*T*=

1.0C

*T*0 =

TC1 TC4 =

regression coefficients for the thawed condition

*f *(*S*) =

*S/S*o

*S*=

degree of saturation (%)

*S*o =

1.0 %

*f *(γ) =

γd/ γo

γd =

dry density (Mg/m3)

γo =

1.0 Mg/m3

σ=

stress (lb/in.2)

*f *(σ)m =

a mean value of either *f*1(σ) = *J*1/σo

or *f*2 (σ) =

(*J*2 /τoct)/σo

or *f*3 (σ) =

τoct/σo

σo =

1.0 lb/in.2

bulk stress (lb/in.2) = 3σ3 + σd

*J*1 =

2nd stress invariant (lb/in.2) = 3σ3 + 2 σ3σd

2

*J*2 =

τoct =

octahedral shear stress (lb/in.2) ( 2 / 3) σd

is completely thawed. After complete thawing,

thawed predicted moduli, algorithms were added

the soil undergoes a 120-day "recovery period."

to TRANSFORM for providing a smoother tran-

During this time, the modulus value increases ac-

sition in calculated moduli between the frozen

cording to a power relationship with about one-

and thawed condition. When the soil goes from an

half of the recovery taking place in the first 25

unfrozen to a frozen state, the modulus is held

days about 75% recovery in 75 days and 100%

constant at its unfrozen value until either of two

recovery in 120 days.

changes occur: 1) the soil becomes cold enough

After calculating the predicted modulus of an

that the modulus as calculated by the frozen equa-

element, TRANSFORM also assigns it a Poisson's

tion exceeds the pre-frozen modulus, or 2) the soil

ratio using the criteria shown in Table 3.

warms. When the soil warms, the modulus is set

After a modulus value has been assigned to all

at the value calculated by the frozen equation and

elements from a particular time step, adjacent ele-

continues to follow the frozen curve until the soil

8