where e and a′ are defined in Figure 8 (bottom).
munication) claimed that repeated loading of the
only geotextile that he tested resulted in an effec-
ra′
d) s =
tive modulus that was "many times lower" than
for a > a and
a + a′
that determined from monotonically loaded
uniaxial and biaxial tests. Furthermore, in typical
2ra2
s=
stressstrain relations for tensile loading of needle-
for a > a
(12)
2
2
2a + 3aa′ a′
punched geotextiles, the slope of the stressstrain
curve is initially quite low, resulting in low modu-
lus values at low strains. Therefore, research to
where s and r are defined in Figure 8 (bottom).
determine the effective modulus values when
geotextiles are being repeatedly loaded or traf-
Applicability for use by the Army
ficked in-situ would be useful.
The design curves based on the Giroud and
In addition to including the tensile support pro-
Noiray (1981) method currently published are for
vided by the geotextile, there are two more ways
standard 80-kN (18,000-lb) axle loads for on-high-
in which the Giroud and Noiray theory differs
way trucks with tire inflation pressures of 480 and
from that presented by Barenberg et al. (1977).
620 kPa (70 and 90 psi) (e.g., Fig. 6 and 7). Esti-
Most significant is the shape of the stress distribu-
mated axle loads for U.S. Army vehicles range up
tion through the aggregate layer to the subgrade.
to 324 kN (73,000 lb), and tire pressures can be as
Giroud and Noiray (1981) used a trapezoidal dis-
low as 241 kPa (35 psi) (Table 1). In addition, con-
tribution of the stress beneath a loaded rectangle
sideration should be given to the shape of the
(Fig. 10) as opposed to the Boussinesq distribu-
wheel load applied on the surface. Giroud and
tion beneath a circular plate used by Barenberg et
Noiray (1981) assumed a single-axle dual-wheel
al. (1975). The assumed shape of the load and the
configuration, whereas many Army vehicles have
assumed stress distribution through the aggregate
single tires on tandem axles (e.g., the HEMTT).
layer to the subgrade results in significant differ-
Thus, if this design technique were to be adopted
ences in the estimated stresses at the subgrade for
by the Army, design curves for Army vehicles
certain loading and soil conditions. The difference
should be developed for higher axle/wheel loads
is especially significant for relatively thin aggre-
and for variations in the shape of the applied
loading.
gate layers (less than approximately 0.3 m or 12
The method published by Giroud and Noiray
in.), as will be demonstrated in the next section.
(1981) uses geotextile tensile modulus values rang-
Giroud and Noiray (1981) also assumed a mini-
mum CBR value of 80 for the overlying aggregate,
ing from 10 to 450 kN/m. Geotextile modulus val-
but Barenberg et al. (1975) did not discuss the
ues at 5% strain, provided by the manufacturers
for a variety of geotextiles, are presented in Table
mechanical properties of aggregate, although the
3. Based on limited field experiments, 5% strain
tests they performed utilized crushed-rock aggre-
gate.
appears to be a reasonable estimate for static load-
ing of geotextiles performing reinforcement over
In addition to eq 8, the design equations from
low-bearing-capacity soils (e.g., Fannin and
Giroud and Noiray are
Sigurdsson 1996). Table 3 indicates that the ten-
sile modulus values in the cross-machine direc-
B
a) L =
for off-highway trucks and
tion, the direction that would be transverse to traf-
2
fic, of some products commercially available today
are significantly greater than those for which
B
L=
for on-highway trucks
(9)
Giroud and Noiray (1981) provided design curves.
2
This suggests that the design method should in-
clude higher modulus values. However, recall
where L is the length of the rectangle formed by a
from the above discussion that modulus values
set of dual wheels (Fig. 9).
are higher in biaxial tension, but possibly far lower
for repeated loading than for monotonically
b) 2a = B + 2h tan α
(10)
loaded uniaxial tests. In reinforcing low-bearing-
capacity soil, the geotextile is expected to undergo
where a is defined in Figure 8b.
both biaxial tension and repeated loading. There-
fore, field or other experimental work is needed
c) 2a' = e B 2h tan α
(11)
to help establish the effective modulus values of
12
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