Table 2.. Generall fform oof rreslileent mooduuus(Mr)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 ) = FC1 f (wu-g )FC2
Frozen
Mr (lb/in.2 ) = TC1(100)TC3 f (γ )TC4 f (σ)mC2
T
Partially thawed
Mr (lb/in.2 ) = TC1 f (S)TC3 f (γ )TC4 f (σ)mC2
T
Thawed, negative pore pressure
Mr (lb/in.2 ) = TC1(100)TC3 f (γ )TC4 f (σ)mC2
T
Thawed, positive pore pressure
Notes:
FC1, FC2 =
regression coefficients for the frozen condition
f (wug) =
wug/wo
β
α
T
wug =
grav. unfrozen water content (decimal) = 100 T
0
wo =
unit water content (1.0)
α, β =
unfrozen water content constants
temperature, C
T=
1.0C
T0 =
TC1 TC4 =
regression coefficients for the thawed condition
f (S) =
S/So
S=
degree of saturation (%)
So =
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 f1(σ) = J1/σo
or f2 (σ) =
(J2 /τoct)/σo
or f3 (σ) =
τoct/σo
σo =
1.0 lb/in.2
bulk stress (lb/in.2) = 3σ3 + σd
J1 =
2nd stress invariant (lb/in.2) = 3σ3 + 2 σ3σd
2
J2 =
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
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