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Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
significant effect on the G/G
max
~ log(
curves, which agrees
with Ishihara (1996)’s observation on sandy soils that the
manner of shear modulus decreasing with strain is almost the
same irrespective of the void ratio.
6 CONCLUSIONS
Figure 4(a) shows the average G/G
max
~ log(
curves for the
PA samples and the WA samples at different confining
pressures, along with typical ranges for G/G
max
~ log(
curves
recommended by Seed et al. (1986) and Rollins et al. (1998).
Similar to sandy material, the gravelly materials behave more
linearly with increasing isotropic confining pressure. The
comparison also shows that the curves for the WA samples
generally fall in the ranges suggested by Seed et al. (1986),
while those for the PA samples are more consistent with the
G/G
max
~
range suggested by Rollins et al. (1998).
The RCTS tests were performed on two types of compacted,
crushed gravel produced in a rock quarry, with one of them
being poorly-graded and the other one being relatively well-
graded. The results show that for the same type of material,
neither test frequency nor relative density (or void ratio) affects
the G/G
max
~ log(
curves significantly. The factors that most
affect the G/G
max
~ log(
curves are confining pressure and
grain size distribution (expressed by C
u
). Similar to sandy
material, the compacted gravel behaves more linearly with
increasing confining pressure. Also, under the same confining
pressure, the poorly-graded gravel behaves more linearly than
the well-graded gravel.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0001
0.001
0.01
0.1
1
Cyclic Shear Strain,
(%)
G/G
max
Average (Seed et al., 1986)
Variation Range
(Seed et al., 1986)
Variation Range
(Rollins et al., 1998)
Average (Rollins
et al., 1998)
WA (414 kPa)
PA (52 kPa)
WA (52 kPa)
WA (207 kPa)
WA (827 kPa)
PA (207 kPa)
Comparisons with published curves also show that the
G/G
max
~ log(
curves of the well-graded gravel agree well
with the typical G/G
max
~ log(
curves of gravelly soils
suggested by Seed et al. (1986), while those of the poorly-
graded gravel are within the range recommended by Rollins et
al. (1998). However, the effect of confining pressure is
neglected in each set of the published curves. The equation
based on sub-rounded river gravel suggested by Menq (2003) to
describe the G/G
max
~ log(
relationship correctly indicates the
effect of C
u
on the G/G
max
~ log(
curves, but comparison with
this study shows the effect of C
u
is somewhat different for
crushed gravel.
7 REFERENCES
(a) Compared to Seed et al. (1986) and Rollins et al. (1998)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0001
0.001
0.01
0.1
1
Cyclic Shear Strain,
(%)
G/G
max
52, 207, 414, 827 kPa; C
u
= 150 (Menq, 2003)
WA (414 kPa)
PA (52 kPa)
WA (52 kPa)
WA (207 kPa)
WA (827 kPa)
PA (207 kPa)
52, 207 kPa; C
u
= 2.1
(Menq, 2003)
Darendeli B.M. 2001.
Development of a new family of normalized
modulus reduction and material damping curves
. Ph. D.
Dissertation, Univ. of Texas at Austin., TX, USA, 362.
Goto S., Nishio S. and Yoshimi Y. 1994. Dynamic properties of gravels
sampled by ground freezing.
Ground failures under seismic
conditions
. GSP No. 44, ASCE, 141–157.
Goto S., Suzuki Y., Nishio S. and Oh-oka H. 1992. Mechanical
properties of undisturbed tone-river gravel obtained by in-situ
freezing method.
Soils and Foundations
, 32 (3): 15–25.
Hatanaka M. and Uchida A. 1994. Effects of test methods on the cyclic
deformation characteristics of high quality undisturbed gravel
samples.
Static and dynamic properties of gravel soils
, GSP No. 56,
ASCE, 136–151.
Hwang S.K. 1997.
Investigation of the dynamic properties of natural
soils
, Ph.D. Dissertation, University of Texas at Austin, 394.
Ishihara K. 1996.
Soil behavior in earthquake geotechnics
, Oxford
Science Publications, 350.
Kokusho T. 1980. Cyclic triaxial test of dynamic soil properties for
wide strain range.
Soils and Foundations
, 20: 45-60.
(b) Compared to Menq (2003)
Figure 4. G/G
max
~ log(
curves for compacted gravel in this study
compared with gravel curves in the literature.
Kokusho T. and Tanaka Y. 1994. Dynamic properties of gravel layers
investigated by in-situ freezing sampling.
Ground failures under
seismic conditions
. GSP No. 44, ASCE, 121–140.
As shown in Table 1, the C
u
values for WA-1 and WA-3 are
174.5 and 150.6, respectively, while it is 2.1 for PA. Taking C
u
= 150 and C
u
= 2.1 separately, the relationship between G/G
max
and
under different confining pressures can be predicted using
the hyperbolic model proposed by Menq (2003) (i.e, Eq. (1)).
Menq (2003)’s predictions are compared with the results from
this study in Figure 4(b). The measured G/G
max
~ log(
curves
of the WA material degrade somewhat less than those predicted
using Menq (2003), while the G/G
max
~ log(
curves of the PA
material degrade somewhat more than the predicted curves. The
comparison shows that effect of C
u
determined using sub-
rounded river gravel (Menq, 2003) is less significant for crushed
gravels used in this study. Also, it should be noted that model
recommended by Menq (2003) is based on dry specimens with
few to no fines, maximum particle size of 25 mm, 19.1 mm ≥
D
50
≥ 0.11 mm, 50 ≥ C
u
≥ 1.1, 405 kPa ≥
0
' ≥ 14.2 kPa, and 1.1
≥ e ≥ 0.23, and some of the tested gravel specimens are outside
of this range.
Lin S.Y., Lin P.S., Luo H.S., Juag C.H. 2000. Shear modulus and
damping ratio characteristics of gravely deposits.
Canadian
Geotechnical J.
37:638–651.
Menq F.Y. 2003.
Dynamic properties of sandy and gravelly soils
, Ph.D.
Dissertation, University of Texas at Austin, TX, USA, 364.
Menq F.Y. and Stokoe K.H. 2003. Linear dynamic properties of sandy
and gravelly soils from large-scale resonant tests.
Deformation
Characteristics of Geomaterials
, Swets & Zeitlinger, Lisse, 63-71.
Ni S.H. 1987.
Dynamic Properties of Sand Under True Triaxial Stress
States from Resonant Column/Torsional Shear Tests
. Ph.D.
Dissertation, University of Texas at Austin, TX, USA, 421.
Rollins K.M., Evans M., Diehl N. and Daily W. 1998. Shear modulus
and damping relationships for gravels.
J. of Geotechnical and
Geoevironmental Engrg.
, 124 (5), 396-405.
Seed H.B., Wong R.T., Idriss I.M., and Tokimatsu K. 1986. Moduli and
damping factors for dynamic analyses of cohesionless soils.
J. of
Geotechnical Engineering
, 112 (11), 1016-1032.
Zhang J., Andrus R.D., and Juang C.H. 2005. Normalized Shear
Modulus and Material Damping Relationships.
J. of Geotechnical
and Geoenvironmental Engineering
, 131(4): 453-464.
