Page 58 - Mechanics of Asphalt Microstructure and Micromechanics

Mechanical Proper ties of Constituents 51

2.4.3 Resilient Modulus (Repeated Load Indirect Tensile) M Test
R
Resilient modulus is the most common parameter of measuring stiffness for AC sam-
ples that are field cored or laboratory prepared. Mr test is a repeated-load indirect ten-
sion test method covered in ASTM D4123. The specimen used for the resilient modulus
test is 62.5 mm by 101.6 mm diameter. The applied stress is calculated the same way as
for tensile strength, but the specimen is not loaded to failure. For this test, the speci-
men is loaded to a stress level between 5 and 20% of indirect tensile strength. The load
is typically applied for 0.1 s along with a rest period of 0.9 s. This loading sequence is
repeated 100 times and the resilient axial strain is measured by linear variable dis-
placement transducers (LVDT). The following equation is used to calculate the resil-
ient modulus:

M = P (μ + .027 ) (2-22)
R
Ht
where P = applied load (lb)
H = horizontal deformation
t = sample thickness (in)
m = Poisson’s ratio

2.4.4 Dynamic Complex Modulus Test
The dynamic (complex) modulus is determined by applying sinusoidal vertical loads to
cylindrical samples while measuring their deformation (Roberts et al., 1996). The test
procedure is provided in ASTM D3497. The height-to-diameter ratio of the samples has
to be at least 2 to 1 to minimize the effect of friction at the top and bottom of the sam-
ples. Also, the diameter of the sample must be at least twice the maximum aggregate
size. The most commonly used sample sizes are 101.6 203.2 mm and 152.4 304.8
mm. The applied load is around 35 psi (241.5 kPa) and is usually defined as a percent-
age of the mixture strength. Specimens are tested at five different temperatures—10, 5,
21, 38, and 55°C and at five loading frequencies—25, 10, 5, 1, 0.5, and 0.1 Hz. The dy-
namic modulus is calculated with the following formula:

(2-23)
|E*| = s 0 /e 0
where s 0 = amplitude of applied sinusoidal loading
e 0 = amplitude of resulting sinusoidal strain

Also, a phase angle, which is a measure of the viscous properties of the material, is
calculated using the following formula:

(2-24)

where T l = time lag (s)
T p = period of sinusoidal loading (s)