set at a constant value of 3.4 107 kPa (5,000,000

Standard procedures of FROST calculations

lb/in.2). In the initial two simulation series, the

were selected as follows. The fully implicit method

resilient modulus, *M*r , of asphalt concrete layers

was used for the moisture time domain solution,

were calculated by the equation (Schmidt 1975):

and the Crank-Nicolson method for the heat trans-

fer time domain solution. Simulations were run

-2

*M*r (lb/in.2 ) = 10(6.285-1.93110 * T*

with a time step of 0.2 hours, which is the time at

which boundary conditions are adjusted; updates

*T *-3.28010-4 T 2 -1.88810-5 T 3

of the thermal and hydraulic properties were set to

occur once per hour.

+1.17510 -7 T 4 +1.50210 -8 T 5

FROST produces what can be a very large out-

(8)

-2.02210 -10 T 6 )

put file. The first part of the file is a listing of the

initial profile conditions, including all the input

where *T *is the temperature of the element (C).

material properties. The next section is an incre-

For pavement temperatures greater than 50C, the

mental (usually daily) listing of the conditions

asphalt modulus was set to 1.7 105 kPa (25,000

generated for each node, including temperature,

lb/in.2); for temperatures less than 29C, it was

pore water pressure, water content, ice content,

set to 3.3 107 kPa (4,840,000 lb/in.2). In a third

density, and porosity. The final section of the out-

series of simulations, a second model was used

put file is a summary of the predicted frost heave

for predicting asphalt moduli when the tempera-

and frost/thaw penetration data.

ture was above 1C (Ullidtz 1987):

**TRANSFORM**

*M*r (lb/in.2) = [15,000

TRANSFORM was developed at CRREL by

7900 log (T)] 145.04.

Chamberlain et al. (in prep.) and was modified

(9)

extensively by Wendy Allen and Gregor Fellors,

At below 1C, the Schmidt (1975) relationship

both of CRREL, for this study. The TRANSFORM

was used. Predictions of the two asphalt models

program uses FROST daily output files as input

are compared in Figure 4.

and produces files of layered pavement systems

In the layers that represent an unstabilized base

where each layer is assigned a resilient modulus,

course, subbase or subgrade material, TRANS-

Poisson's ratio, density and thickness. Output files

FORM calculates the modulus using regression

from TRANSFORM are in the format to be used

equations developed from results of laboratory

as input files to NELAPAV, the layered elastic

resilient modulus testing conducted on frozen and

program used to compute stresses and strains in

thawed soil samples (Berg et al. 1996). Each soil

the pavement system. NELAPAV requires a single

element is first classified using the criteria in Table

file containing both load and structural data for

1 to determine which type of modulus equation is

each day of the simulation.

appropriate. The modulus is then calculated using

TRANSFORM first reads from a separate file a

one of the equations shown in general form in

series of material type identifiers and their associ-

Table 2. The equations relate the frozen resilient

ated parameters needed for calculating the moduli

modulus to temperature (through unfrozen water

of the materials in the frozen and thawed condi-

content), and the unfrozen resilient modulus to

tion (see below). Then, TRANSFORM reviews

degree of saturation, stress condition, and to den-

the initial part of the FROST output file to deter-

sity for the class 6 special base course and the

mine the material type identifier for each element.

1206 subgrade. The specific parameters for the

From the incremental (daily) listings of the

Mn/ROAD materials will be discussed in a later

FROST output file, TRANSFORM next reads the

section.

following conditions for each element: tempera-

The following parameters, which are specific

ture, water content, ice content, material density,

to each material, are used in the regression equa-

and porosity. A modulus value is then calculated

tions (Table 2): 1) FC1 and FC2, regression coef-

for each element.

ficients for the resilient modulus in the frozen

Moduli of surface paving materials were calcu-

condition, 2) TC1, TC2, TC3, and TC4, regres-

lated as follows. PCC concrete had the modulus

6