1126
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
0.0
0.2
0.4
0.6
0.8
1.0
1.2
25
50
75
100
Accelerometer output(Vrms)
Frequency (Hz)
Input-signal amplitude(s): 0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 Volts
(a)
Back-bonecurve
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
25
50
75
100
Shearstrain (%)
Frequency (Hz)
3 TEST SOIL AND PERFORMANCE VERIFICATION
The soil material used in this work classifies as silty sand (SM)
according to the USCS: 70% sand and 30% silt. The coarse
fraction has particle sizes between 0.5-1.2 mm. The passing No.
40 sieve fraction has liquid limit, LL = 26.4%, and plastic limit,
PL = 22.2%. Samples were statically compacted into a 70-mm
diameter, 130-mm height, compaction split mold via a triaxial
loading frame. Each sample was prepared in three lifts, at a
constant displacement rate of 1.0 mm/min, to a target void ratio,
e = 1.0, and dry unit weight,
d
= 13.13 kN/m
3
. The initial water
content of 26% corresponds to an average degree of saturation
of 72% and initial matric suction of 20 kPa, according to the
soil-water retention curve (Hoyos et al. 2011).
Calibration of the proximitor-based RC device was first
accomplished by conducting resonant column tests on a 9.5 mm
(0.375 in) diameter, stainless aluminum rod, which also yields
the polar moment of inertia of the entire drive system. The test
yielded expected values for torsional stiffness of the aluminum
rod, k = 26.4 GPa, and polar moment of inertia of the drive
system, I
o
= 737.8 kg-mm
2
. Performance verification testing
was then carried out through a comparative analysis of results
from proximitor-based RC tests and accelerometer-based RC
tests (ASTM 1993) on identically prepared samples of SM soil.
Figure 2(a) shows a full set of frequency response curves
obtained from compacted SM soil in the accelerometer-based
RC device. The specimen was subject to different input-voltage
amplitudes ranging from 0.25 to 5 Volts, thus generating a
family of curves with different resonant frequencies and peak
accelerometer outputs, from which shear modulus G and shear
strain amplitude
can be calculated. All tests were performed
under constant 40 psi confinement. Soil softening (degradation)
is manifested by the so-called backbone curve. Likewise, Figure
2(b) shows a full set of frequency response curves obtained
from an identically prepared sample of SM soil tested in the
proximitor-based device. In this case, however, the specimen
was subject to different input-torque magnitudes ranging from 1
pfs (0.1 kN-m) to 10 pfs (1 kN-m). Peak shear strain fractions
(cm/cm) can be readily assessed from each test. All tests were
also performed under a constant 40 psi confinement.
Results show that a 1-pfs input torque in the proximitor-
based apparatus induces a similar response as a 0.25-Volt input
signal in the accelerometer-based apparatus, which is typically
used to ensure shear strain levels below a threshold limit
th
. It
can also be observed that a 10-pfs input torque induces a higher
degree of soil softening than the maximum 5-Volt input signal
in the accelerometer-based device. The scope of the present
work, however, is limited to linear (low-amplitude or small-
strain) stiffness response of unsaturated soils; therefore, a 1-pfs
input torque (0.1 kN-m) was adopted for all subsequent suction-
controlled tests performed in the proximitor-based RC device,
as described in the following section.
Input-torque magnitude(s): 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 pfs
(b)
4 RC/BE TEST PROCEDURES AND SOIL RESPONSE
A series of RC and BE tests were simultaneously conducted on
identically prepared samples of SM soil. Each sample was
tested under constant matric suction, s = 50, 100, 200, or 400
kPa, induced via axis-translation technique; and four different
net confining pressures, (p – u
a
) = 50, 100, 200, and 400 kPa.
The soil was first isotropically compressed to a target confining
pressure, p = 50 kPa. Pore-air pressure u
a
was then gradually
increased (soil drying) to the pre-established value of suction,
while the net confining pressure was kept constant at 50 kPa by
simultaneous and equal increases of the external confinement.
Pore-air pressure u
a
was maintained constant until no further
change in water volume from within the soil (less than 0.035
ml/day) was observed, at which point pore-fluids equalization
was considered complete. A 36-hr equalization time (1.5 days)
was found suitable for all suction states. Equalization stage was
finally followed by a constant-suction ramped consolidation to
the target values of net confining pressure. All RC tests were
conducted by sweeping the entire input-torque frequency scale
until obtaining a thorough frequency response curve, typically
between 50 and 250 Hz. The peak torsional vibration was then
completely cut off to record the free-vibration decay curve.
Figure 3(a) shows a family of typical frequency response
curves obtained from suction-controlled RC tests on SM soil
under constant matric suction, s = 50 kPa, and net confining
pressures, (p – u
a
) = 50, 100, 200, and 400 kPa. Likewise,
Figure 3(b) shows typical curves under constant matric suction,
s = 200 kPa. It can be readily observed the critical influence that
suction has on soil response under resonance, with a significant
rightward shift of all curves for higher suction state, s = 200
kPa. This can be directly attributed to the expected increase in
effective stress and, hence, rigidity (stiffness) of soil skeleton at
higher suctions. The level of net confinement, however, has a
more pronounced effect than matric suction. It can also be
observed that the half-power points, that is, frequencies on each
side of the frequency response curves corresponding to a shear
strain of 0.707(
max
), become less apparent as suction increases,
i.e., the frequency response is less symmetric about the resonant
frequency. Hence, the assessment of material damping using the
half-power bandwidth method becomes less reliable at higher
suction states.
Figure 2. Stiffness degradation of SM soil under 40 psi confinement:
(a) accelerometer RC device; and (b) proximitor RC device.
