density and thickness. First, a modulus is calcu-

modulus to degree of saturation, stress condition,

lated for each element; then, elements with moduli

and (when available) to density (Table 1).

not differing by more than 20% are combined in a

single layer. Output files from TRANSFORM are

**NELAPAV**

in the format to be used as input files to NELAPAV.

The program NELAPAV, an acronym for **n**on-

Inputs to and outputs from the TRANSFORM pro-

linear **e**lastic **l**ayer **a**nalysis for **pav**ements, com-

gram are discussed in more detail in Bigl and

putes stresses, strains, and displacements at any

Berg (1996b). The basic equations used to calcu-

point in an n-layered pavement system. The main-

late resilient moduli are given here (Table 1).

frame computer version of the program was de-

Moduli of surface paving materials were calcu-

veloped for CRREL by Lynne Irwin of Cornell

lated as follows. PCC (portland cement concrete)

University and Gregor Fellers of CRREL in 1980.

had the *M*r set at a constant value of 3.4 107 kPa

Further refinements such as a microcomputer ver-

(5,000,000 lb/in.2). In the initial two simulation

sion were developed by Lynne Irwin and Daniel

series, the resilient modulus, *M*r of asphalt con-

Speck at Cornell University in 1984 and 1985

crete layers were calculated by the Schmidt (1975)

(Irwin and Speck 1986). The program uses the

equation, which predicted very low summer val-

Chevron La yered Elastic Systems pr ogram

ues. In a third series of simulations, a second model

(CHEVLAY) to calculate the elastic stresses and

was used for predicting asphalt moduli when the

strains in a multiple layer system.

temperature was above 1C (Ullidtz 1987), and

The primary reason NELAPAV was chosen is

the Schmidt relationship was used when tempera-

because it allows the use of nonlinear (i.e., stress-

tures were below 1C. Modulus values obtained

dependent) modulus values in the analysis. Modu-

from the two models are compared in Figure 7.

lus values for thawing and unfrozen fine-grained

In layers that represent an unstabilized base

soils are highly nonlinear as illustrated in Figure 8.

course, subbase or subgrade material, TRANS-

Table 2, from Yang (1988), illustrates the various

FORM calculates the modulus using regression

types of linear and nonlinear models currently

equations developed from results of laboratory re-

available for use in NELAPAV; however, models

silient modulus testing conducted on frozen and

2 and 7 are not currently incorporated in the rest

thawed soil samples. The equations relate the fro-

of the design procedure.

zen resilient modulus to temperature (through un-

Daily output from NELAPAV includes 1) a re-

frozen water content), and the unfrozen resilient

peat of the input information, 2) moduli of the

(lb/in.2)

(kPa)

7 107

107

7 106

106

7 105

105

Schmidt

Ullidtz

7 104

104

20

10

0

10

20

30

40

50

Temperature (C)

*Figure 7. Comparison of asphalt moduli computed with Schmidt and Ullidtz*

*models.*

5