1057
Technical Committee 105 /
Comité technique 105
only the first and last 10 cycles are shown in the figure. It
should be noted that the variations of pore water pressures
during the remaining 80 cycles are similar with those in these
20 cycles. It can be seen that pore water pressures measured at
the base and mid-height vary with applied deviator stress in
similar manner. The magnitude of variation of measured pore
water pressure is about 10 kPa at the base and 5 kPa at the mid-
height. Previous researchers found that pore water pressure
measurement at the mid-height is more representative, since it is
not affected by end restraint (Hight, 1982).
Figure 3. Applied deviator stress and measured pore water pressure
during a cyclic triaxial test (modified from Ng et al., 2012).
5 INTERPRETATIONS OF EXPERIMENTAL RESULTS
5.1 Effects of number of load applications (N) on resilient modulus
To investigate the influence of number of load applications on
resilient modulus, resilient modulus from the
Nth
cycle (M
N
r
) is
normalised by resilient modulus from the first cycle (M
1
r
).
Figure 4 shows the relationship between M
N
r
/M
1
r
and N at cyclic
stress of 70 kPa, obtained from tests at six different suction (0,
30, 60, 100, 150 and 250 kPa) and two different temperatures
(20 and 40
℃
) (see Figure 2 and Table 1). This figure clearly
reveals two types of soil response at 20
℃
. At zero matric
suction, M
N
r
/M
1
r
increases continuously with increasing N
(obtained from W0T20). The total increase during the 100
cycles of loading-unloading is up to 20%. This is a consequence
of progressive densification resulting from that the application
of repeated cyclic stress (Dehlen, 1969; Ng et al., 2012). In this
study, contractive volumetric strain of specimen W0T20
measured using Hall-effect transducers is 0.25% at the end of
100 cycles of loading-unloading. The decreasing volume and
hence increasing dry density under cyclic loads results in an
increase in M
N
r
/M
1
r
with increasing N. On the other hand, when
matric suction is equal to or larger than 30 kPa (s = 30, 60, 100,
150 and 250 kPa), M
N
r
/M
1
r
varies only slightly with N. One
reason is that volumetric strain under cyclic loads is much
smaller when matric suction is equal to or larger than 30 kPa.
For example, measured contractive volumetric strain at suction
of 30 kPa is only 0.03%, much smaller than 0.25%. Given such
a small volumetric strain as 0.03%, the variation of M
N
r
/M
1
r
with
N becomes insignificant.
By studying the relationship between normalised M
N
r
/M
1
r
and the number of load applications (N), it is evident that
measured
M
R
is sensitive to N values at zero suction but it is
almost independent of N values at different suctions.
Considering temperature effects on M
N
r
/M
1
r
ratios, it is also
revealed in Figure 4 that there is about 5% increase in M
N
r
/M
1
r
ratio when temperature increases from 20
℃ to
40
℃.
This
observation may be explained by thermal effects on the size of
yield surface. Romero et al. (2003) reported that the yielding
stress of unsaturated soil specimen at elevated temperature is
lower than that observed at room temperature, with the same
initial void ratio and suction. Given a smaller yielding stress at a
higher temperature, it may be expected that the contractive
volumetric strain and hence the influence of N on M
N
r
/M
1
r
is
more significant at a higher temperature.
As also revealed in the figure, the variation of M
N
r
/M
1
r
is
negligible when N except for the specimen tested at zero
suction. A steady resilient modulus was generally achieved
within 100 loading-unloading cycles at suctions larger than
zero.
5.2
Effects of suction and temperature on resilient modulus
Figure 5 shows the influence of
q
cyc
on measured
M
R
at different
suctions (0, 30, 60, 150 and 250 kPa) and temperature (20 and
40 °C). Reported
M
R
in the figure is the average resilient
modulus of the last five cycles (i.e. N = 96-100). It can bes een
from this figure that
M
R
decrease with an increase in
q
cyc
at all
suctions except s = 0. For instance,
M
R
decrease by about 40%
when
q
cyc
increase from 30 kPa to 70 kPa at a suction of 30 kPa
and teperature of 20 °C (obtained from W30T20). The observed
decrease of
M
R
with an increase in
q
cyc
is due to the non-
linearity of soil stress-strain relationship. Previous studies have
demonstrated that soil stiffness is high at small strain but it
decays with an increase in strain level (Atkinson, 2000). In the
resilient modulus tests, strain level increases with an increase in
q
cyc
, hence measured
M
R
decreases with an increase in
q
cyc
.
Figure 4. Relationship between normalized resilient modulus and
number of load applications at a cyclic stress of 70 kPa (modified from
Ng et al., 2012).
Figure 5. The influence of cyclic stress on resilient modulus at different
suction and temperature conditions (modified from Ng et al., 2012).
This figure also reveals that
M
R
increases with increasing s
significantly, irrespective of whether it is along a drying or a
wetting path. At cyclic stress of 30 kPa and temperature of 20
℃
,
M
R
increases by up to one order of magnitude when s
increases from 0 to 250 kPa. The beneficial effects of s on
M
R
arise due to at least two possible reasons. Firstly, when a soil
specimen becomes unsaturated, voids are partly filled with
water and partly occupied by air, resulting in an air-water
interface in each void. When there is an increase in matric
suction, the radius of an air-water interface decreases and hence
induces a larger normal inter-particle contact force (Mancuso et
al., 2002; Wheeler et al., 2003; Ng and Yung, 2008). This