TM 5-822-13/AFJMAN 32-1018
APPENDIX B
PROCEDURE FOR DETERMINING THE MODULUS OF ELASTICITY OF UNBOUND
GRANULAR BASE AND SUBBASE COURSE MATERIALS
B-l. Procedure.
a. The procedure is based on relationships developed for the resilient modulus of unbound granular layers
as a function of the thickness of the layer and type of material. The modulus relationships are shown in figure
B-l. Modulus values for layer n (the upper layer) are indicated on the ordinate, and those for layer n + 1 (the
lower layer) are indicated on the abscissa. Essentially linear relationships are indicated for various thicknesses
of base and subbase course materials. For subbase courses, relationships are shown for thicknesses of 4,5,6,7,
and 8 inches. For subbase courses having a design thickness of 8 inches or less, the applicable curve or appropri-
ate interpolation can be used directly. For a design subbase course thickness in excess of 8 inches, the layer
should be divided into sublayers of approximately equal thickness and the modulus of each sublayer determined
individually. For base courses, relationships are shown for thicknesses of 4, 6, and 10 inches. These relationships
can be used directly or by interpolation for design base course thicknesses up to 10 inches. For design thick-
nesses in excess of 10 inches, the layer should also be divided into sublayers of approximately equal thickness
and the modulus of each sublayer determined individually.
b. To determine modulus values from this procedure, figure B-l is entered along the abscissa using modulus
values of the subgrade or underlying layer (modulus of layer n + 1). At the intersection with the curve applicable
to this value with the appropriate thickness relationship, the value of the modulus of the overlying layer is read
from the ordinate (modulus of layer n). This procedure is repeated using the modulus value just determined as
the modulus of layer n + 1 to determine the modulus value of the next overlying layer.
B-2. Examples.
ct. Assume a pavement having a base course thickness of 4 inches and a subbase course thickness of 8 inches
over a subgrade having a modulus of 10,000 psi. Initially, the subgrade is assumed to be layer n + 1 and the
subbase course to be layer n. Entering figure B-l with a modulus of layer n + 1 of 10,000 psi and using the 8-inch
subbase course curve, the modulus of the subbase (layer n) is found to be 18,500 psi. In order to determine the
modulus value of the base course, the subbase course is now assumed to be layer n + 1 and the base course to be
layer n. Entering figure B-l with a modulus value of layer n + 1 of 18,500 psi and using the 4-inch base course
relationship, the modulus of the base course is found to be 36,000 psi.
b. If, in the first example, the design thickness of the subbase course had been 12 inches, it would have been
necessary to divide this layer into two 6-inch-thick sublayers. Then, using the procedure described above for the
second example, the modulus values determined for the lower and upper sublayers of the subbase course and for
the base course are 17,500, 25,500, and 44,000 psi, respectively.
c. The relationships indicated in figure B-l can be expressed as follows for base course materials:
En = En+1 (1 + 10.52 log t - 2.10 log E n+l log t)
where
n = a layer in the pavement system
En= resilient modulus ( in psi) of layer n
E n+l = the resilient modulus (in psi) of the layer beneath
t = the thickness (in psi) of layer n
The relationship can be expressed as follows for subbase course materials:
En = En+1 (1 + 7.18 log t - 1.56 log E n+1log t)
B-l
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