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 non-
Inputs to and outputs from the TRANSFORM pro-
linear elastic layer analysis for pavements, 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 Mr 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, Mr 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.
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