Undrained Shear Strength of Granular Soils with Different
Particle Gradations
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Takeji Kokusho, M.ASCE1; Tadashi Hara2; and Ryousuke Hiraoka3
Abstract: A series of undrained tests were performed on granular soils consisting of sand and gravel with different particle gradations
and different relative densities reconstituted in laboratory. Despite large differences in grading, only a small difference was observed in
undrained cyclic shear strength or liquefaction strength defined as the cyclic stress causing 5% double amplitude axial strain for specimens
having the same relative density. In a good contrast, undrained monotonic shear strength defined at larger strains after undrained cyclic
loading was at least eight times larger for well-graded soils than poorly graded sand despite the same relative density. This indicates that
devastating failures with large postliquefaction soil strain are less likely to develop in well-graded granular soils compared to poorly
graded sands with the same relative density, although they are almost equally liquefiable. However, if gravelly particles of well-graded
materials are crushable such as decomposed granite soils, undrained monotonic strengths are considerably small and almost identical to
or lower than that of poorly graded sands.
DOI: 10.1061/共ASCE兲1090-0241共2004兲130:6共621兲
CE Database subject headings: Liquefaction; Gravel; Sand; Particle size distribution; Relative density; Triaxial tests; Dilatancy;
Crushing; Shear strength.
Introduction
Liquefaction of gravelly soils, though less frequent in past records
than that of sands, has increasingly been witnessed during recent
earthquakes. During the 1995 Hyogoken Nambu earthquake in
Japan, reclaimed ground in Kobe filled with decomposed granite
soil called Masado containing a large quantity of gravel and fines
fraction liquefied extensively despite a widely accepted perception that gravelly soil was harder to liquefy than sand because of
larger uniformity coefficient and larger dry density. The standard
penetration test 共SPT兲 N-value of the gravelly soil unadjusted by
overburden stress was as low as 5 to 15. During the 1993 Hokkaido Nansei-Oki earthquake, rock debris avalanche soil containing large size rocks as well as sands and silts liquefied in Mori
town in Hokkaido causing differential settlements of wooden
houses. Its SPT N-value was 8 –16 and the S-wave velocity was
as low as 60–90 m/s 共Kokusho et al. 1995兲. During the 1983
Borah Peak earthquake in Idaho, fluvial sandy gravel liquefied
extensively triggering lateral spread in gently sloping ground. The
N-value of the loosely deposited gravel layers was 5–9 and the
1
Professor, Civil Engineering Dept., Science and Engineering Faculty,
Chuo Univ., 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.
E-mail: kokusho@civil.chuo-u.ac.jp
2
Associate Researcher, Civil Engineering Dept., Science and
Engineering Faculty, Chuo Univ., 1-13-27, Kasuga, Bunkyo-ku, Tokyo
112-8551, Japan.
3
Ex-Graduate Student, Civil Engineering Dept., Science and
Engineering Faculty, Chuo Univ., 1-13-27, Kasuga, Bunkyo-ku, Tokyo
112-8551, Japan.
Note. Discussion open until November 1, 2004. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and possible publication on December 27, 2002; approved on September 17,
2003. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 130, No. 6, June 1, 2004. ©ASCE, ISSN
1090-0241/2004/6-621– 629/$18.00.
S-wave velocity 90–160 m/s 共Andrus 1994兲. Besides these cases,
liquefaction of gravelly soils was also reported during several
earthquakes, such as the 1948 Fukui earthquake in Japan, the
1964 Alaskan earthquake, Chinese earthquakes, etc.
Fig. 1 indicates a relationship between the mean grain size
(D 50) and the uniformity coefficient (Cu) for recently liquefied
gravelly soils for which soil data are available. So far, the upper
limits for D 50 and Cu are about 20 and 300 mm, respectively, but
no limit may reasonably be justified, indicating that gravelly soils
can liquefy if they are loose enough no matter how coarse they
may be. Dry densities of these gravelly soils are relatively high
(1.7– 2.0 t/m3 for reclaimed soil in Kobe and 2.0– 2.1 t/m3 for
debris avalanche soil in Hokkaido兲 due to large uniformity coefficients, actually much higher than typically liquefiable loose
sands. However, those liquefied gravelly soils exhibit quite low
N-values and Vs as mentioned above.
Gravelly soils in natural deposits are normally well-graded
compared to poorly graded sands as indicated in Fig. 2 where
typical grain size curves of gravelly soils liquefied recently are
shown. In other words, they are in most cases actually the mixture
of gravels, sands, and sometimes even finer soils. Therefore,
gravel soils can be densely packed and are normally believed to
be stiffer and seismically more stable than sand layers. However,
well-graded gravelly soils as previously mentioned can sometimes have unexpectedly low N-value and S-wave velocity.
Kokusho and Yoshida 共1997兲 demonstrated by large scale soil
container tests for sands and gravels with varying particle gradations that such well-graded soils can exhibit N-values and S-wave
velocities as low as loose sands if their relative densities are low
enough. The same writers developed empirical formula to correlate N-value and S-wave velocity with fundamental soil parameters, such as the relative density, the uniformity coefficient, the
confining stress, etc.
Undrained cyclic strength of gravelly soils has not been investigated as much as sands with regard to their density, particle
gradations, etc., though they have significance in liquefaction po-
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Fig. 1. Mean grain size versus uniformity coefficient relationship for
recently liquefied gravelly soils
tential evaluation for seismic design. In an earlier study, Wong
et al. 共1975兲 conducted large scale undrained cyclic triaxial tests
of poorly graded gravelly soils of the same uniformity coefficient
(Cu⫽1.3) and found that the cyclic stress ratio to cause initial
liquefaction in gravelly soils was somewhat larger than sand possibly due in part to the artificial effect of membrane compliance in
the test specimens. Tanaka et al. 共1987兲 performed undrained cyclic triaxial tests for granular soils with different Cu and found
that the stress ratio of gravelly soils corresponding to 5% double
amplitude 共DA兲 axial strain, which was not corrected by the
membrane compliance effect, was larger than sand. More recently, Evans and Zhou 共1995兲 carried out undrained cyclic triaxial tests to quantify the effect of gravel content on the liquefaction resistance of sandy gravel composites. They prepared soil
specimens by mixing poorly graded sand and poorly graded
gravel with different ratios to make gap-graded specimens with
different gravel contents. In order to reduce the membrane compliance effect in the triaxial tests, test specimens were sluiced
with sand. They found that gravelly soils showed evidently larger
liquefaction resistance than sand with the same relative density.
Though some experimental studies were already carried out on
the undrained cyclic shear behavior of gravelly soils as mentioned
above, they are too small in number to draw general conclusions
with respect to particle gradations, relative densities, etc. Furthermore, little is known for gravelly soils on the relationship between cyclic loading behavior and monotonic loading behavior in
the undrained condition, which is important in considering postliquefaction large ground deformations.
Fig. 3. Three kinds of particle gradation for river soils or
decomposed granite soils
As demonstrated in Fig. 2 and by other data 共Kokusho and
Tanaka 1994兲, gravelly soils in nature are mostly well-graded
with smooth grain size curves. In this experimental research,
granular river soils consisting of hard particles were reconstituted
to have smooth grain size curves analogous to natural sandy or
gravelly soil with uniformity coefficient Cu, varying from 1.44 to
13.1. Systematic undrained triaxial tests were performed by loading either cyclically or monotonically on the granular specimens
with different relative densities Dr and different Cu. In addition,
the effect of particle crushability on the undrained strength was
also investigated by comparing test results on decomposed granite
soils of weathered soil particles possessing the same grain size
with those on the river soils of hard particles.
Soil Materials and Maximum and Minimum
Density Test
Soil materials tested are two types; river soils and decomposed
granite soils, abbreviated as RS and DGS, respectively, hereafter.
The former is reconstituted from river sands or gravels originated
from a river. The particles consisting of andesite 共30%兲, chert
共30%兲, rhyolite 共21%兲, slate 共13%兲, sandstone, etc., are subrounded and hard to crush. The latter is reconstituted from decomposed weathered granite originated from reclaimed ground in
Higashinada in Kobe City, where extensive liquefaction took
place during the 1995 Hyogoken Nambu earthquake. The particles are angular and weathered with brownish color. Three kinds
of particle gradation; RS1, RS2, and RS3 for the river soils and
DGS1, DGS2, and DGS3 for the decomposed granite soils are
prepared as in Fig. 3. The physical properties of these soils are
listed in Table 1. Although the tested soils are not so well-graded
as natural gravelly deposits often encountered in situ due to limitations of the testing apparatus mentioned later, the uniformity
coefficient changes from Cu⫽1.44 to Cu⫽13.1 to investigate the
effect of particle gradations.
As will be discussed later, relative density Dr is a pertinent
parameter to evaluate undrained cyclic strength of granular soils
of different particle gradations and defined by the maximum and
minimum dry density ␳ max and ␳ min , respectively, as
Dr⫽
Fig. 2. Typical grain size curves of gravelly soils recently liquefied
1/␳ min⫺1/␳
⫻100%
1/␳ min⫺1/␳ max
(1)
Here, ␳ max and ␳ min were determined by a test method utilizing a
soil mold 共195 mm inner diameter and 200 mm depth兲. For the
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Table 1. Physical Properties of River Soils and Decomposed Granite
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Soils
Soil
name
Mean
grain size
D 50 共mm兲
Uniformity
coefficient
Cu
Soil particle
density
Min.
density
Max.
density
RS1
RS2
RS3
DGS1
DGS2
DGS3
0.14
0.40
1.15
0.14
0.40
1.15
1.44
3.79
13.1
1.44
3.79
13.1
2.696
2.697
2.655
2.649
2.645
2.602
1.198
1.421
1.675
1.146
1.328
1.515
1.502
1.839
2.038
1.514
1.737
1.979
␳ s (g/cm3 )
␳ d min
␳ d max
maximum density ␳ max , soil was compacted in the mold by a
vibrating disc in five layers. For the minimum density ␳ min , soil
was fed into the mold through a metal funnel elevated slowly with
zero drop height. The number of repetition in the density tests was
9 and 18 for the maximum and minimum density for RS and 5
and 10 for DGS, respectively. Details of the test method are described in Hara 共1999兲 and Hiraoka 共2000兲. As indicated in Fig. 4,
the average maximum and minimum densities obviously increase
with an increasing uniformity coefficient. Their coefficients of
variances 共the standard deviation divided by the average兲 also
tend to increase with the uniformity coefficient although the value
are lower than 0.5%.
Test Method
In a triaxial apparatus used in this research, the specimen size is
100 mm diameter and 200 mm height. The diameter of 100 mm is
about five times the maximum particle size of RS3. It is slightly
smaller than six times recommended in previous research 共e.g.,
Wong et al. 1975兲 but the effect may not be so significant because
the soil is not poorly graded. The soil specimen can be loaded
cyclically by a pneumatic actuator from above as a stress-control
test and also monotonically loaded from below as a strain-control
test as indicated in Fig. 5. The upper loading piston is locked by
a screw-up system and the bottom deck is raised by a prescribed
strain-rate when the monotonic loading test is conducted. The cell
pressure and the pore-water pressure are measured with electric
piezometers with the maximum capacity of 490 kPa and the axial
Fig. 4. Averages and variation coefficients of maximum and
minimum densities with increasing uniformity coefficient
Fig. 5. Triaxial apparatus used in this research
deformation is measured with LVDT of 50 mm maximum capacity outside the pressure chamber.
The soil specimens were prepared by wet tamping because
other preparation methods such as air-pluviation or waterpluviation tend to intensify soil particle segregation for wellgraded granular soils. The relative density of the specimen was
adjusted by tamping to approximate six target values, Dr⫽20,
35, 50, 60, 70, and 90%. The specimen was fully saturated by
using CO2 -gas and deaired water and isotropically consolidated
by the effective stress of 98 kPa with the back-pressure of 294
kPa. The Skempton’s B-value larger than 0.90 was measured in
all tests. It indicates that almost perfect saturation was attained
considering that well-graded soils with smaller void ratios have
theoretically smaller maximum B-values even if they are fully
saturated 共Kokusho 2000兲.
In the undrained cyclic loading tests, the axial stress was cyclically controlled by sinusoidal waves with the frequency of 0.1
Hz based on the fact that undrained strength of noncohesive soils
is almost independent of the loading frequency. The cyclic loading was continued until the double amplitude axial strain attained
about 10%. In the undrained monotonic loading tests, the axial
strain was increased with the strain rate of 0.09% per minute.
Rubber membranes used in the tests were made of latex with a
thickness 0.2 mm for RS1 and 0.3 mm for RS2 or RS3. The effect
of membrane penetration during cyclic loading was taken into
consideration by employing a modification method proposed
originally by Tokimatsu and Nakamura 共1987兲 and modified by
Tanaka et al. 共1991兲, in which pore pressure response to a small
axial stress amplitude in an elastic range is utilized. The difference in undrained cyclic strength due to this effect was found
generally small, less than 10% 共Hara 1999兲 even for the coarsest
RS3 material, because the specimen surface was actually smooth
because of the rich content of the sand. Hence, the membrane
penetration effect does not seem to have significant influence on
the test results in general, although the modification was not
implemented in the monotonic loading tests.
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Fig. 6. Typical relationships between cyclic stress ratio for attaining
5% DA strain and number of loading cycles for river soils of relative
density Dr⬇50%
Fig. 8. Relationship between stress ratio R L20 and uniformity
coefficient Cu for different relative densities
Undrained Cyclic Shear Behavior of River Soils
Open symbols in Fig. 6 exemplifies typical relationships between
the cyclic stress ratio, R L (␴ d /2␴ ⬘c ; ␴ d ⫽single axial stress amplitude and ␴ ⬘c ⫽effective confining stress兲, for attaining 5%
double amplitude and the number of loading cycles N L for the
three river soils for relative density Dr⬇50%. This stress ratio
defined by 5% DA strain is almost identical with that defined by
nearly 100% pore pressure buildup at least for Dr⬇60% or
smaller 共Hara 1999; Hara and Kokusho 2000兲. The stress ratios
for 5% DA strain corresponding to N L ⫽20, R L20(DA⫽5%),
which are often used as liquefaction strength in a normal engineering practice in Japan, are plotted versus relative density Dr in
Fig. 7, although the trend is almost identical except for Dr
⫽70% or larger if N L ⫽10 is chosen as shown in the same figure.
The data points for soils RS1, RS2, and RS3 seem to be almost
coinciding with each other although some differences are visible
at around Dr⫽50 and 90%. The three curves in the charts are the
regressions of the plots for the three types of soils by polynomials.
In order to clearly see the effect of grain size distributions on
the strength, Fig. 8 indicates the relationship between R L20 and
Cu for different Dr. Small differences in Dr for individual plots
in Fig. 7 are adjusted based on the slopes of the regression curves
to evaluate R L20 at the target relative densities Dr⫽20– 90%.
The stress ratio R L increases with increasing Cu for Dr⫽50 and
Fig. 7. Stress ratios R L20 or R L10 corresponding to N L ⫽20 or 10
plotted versus relative densities
90% while it decreases a little or stays almost constant for other
Dr. Hence, it may be said that the undrained cyclic strength is not
so much dependent on Cu or soil particle gradation in contrast to
its large dependency on Dr. Data points by Tanaka et al. 共1987兲
in Fig. 8 indicate that the trend is essentially the same although
there exists one distinct separation. In other words, the undrained
cyclic strength defined by the stress ratio for attaining DA⫽5%
may be considered largely dependent on the relative density despite large difference in absolute density due to the difference in
particle gradation.
Undrained Monotonic Shear Behavior of River Soils
Fig. 9 indicates undrained monotonic shear behavior for the three
soils with the relative density of about 50% in terms of the deviatoric stress q (⫽␴ 1 ⫺␴ 3 , where ␴ 1 and ␴ 3 are the axial and
lateral stresses兲 versus the axial strain ␧ and pore pressure change
⌬u versus axial strain ␧ relationships. Although the soils have
almost the same relative density, their behavior during undrained
shearing is surprisingly different. The maximum stress is much
higher for RS3 or RS2 than RS1 and the differences are too large
to be comparable with those of the undrained cyclic strength of
the same soils already discussed. The pore pressure change mea-
Fig. 9. Deviatoric stress or pore pressure change versus axial strain
relationships in undrained monotonic loading tests for Dr⬇50%
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Fig. 10. Effective stress path on p ⬘ versus q plane 共a兲 and its
enlargement near the origin 共b兲
sured as a difference from the initial value tends to decrease considerably into a negative value for the well-graded soils with
higher Cu because of considerable positive dilatancy compared to
the poorly graded sand, RS1.
An effective stress path drawn on the mean effective stress
关 p ⬘ ⫽(␴ ⬘1 ⫹2␴ ⬘3 )/3兴 versus deviatoric stress (q) plane is shown in
Fig. 10共a兲. The first part of p ⬘ ⫺q stress path is enlarged in Fig.
10共b兲. The dashed straight line in the two charts are the total
stress path in the triaxial compression test with the slope
⌬q/⌬p⫽3 where ⌬p and ⌬q are increments of the mean stress
and the deviatoric stress. The horizontal distance between the
effective stress path and the total stress path indicates the excess
pore pressure. All effective stress paths eventually go up along
straight failure lines to the right end marked with open circles.
For RS1, the pore pressure increases at the initial stage of the
loading and then starts to decrease until it converges to a final
value at q⫽0.19 kPa.
For RS3, in a good contrast, the pore pressure increases at first
only slightly and decreases later until the deviatoric stress attains
an immensely high value of q⫽1.64 Mpa. At this point, the pore
pressure becomes negative, much lower than the initial confining
stress of 0.098 MPa as indicated by an arrow in the figure. If this
negative value exceeds some threshold, then cavitation is expected to occur due to the appearance of gas, which has been
solved in pore water. This suddenly violates the undrained condition, relaxing the negative pore pressure or decreasing the effective stress, leading to abrupt failure at Point A in Fig. 10共a兲. The
potential of cavitation depends on the absolute value of the initial
pore pressure, namely, the backpressure. In this test, the back
pressure is set as 0.294 MPa. Considering that the excess pore
Fig. 11. Deviatoric stress or pore pressure versus axial strain relationships in undrained postcyclic monotonic loading tests for Dr
⬇50% 共a兲 and enlarged deviatoric stress versus axial strain relationships near the origin 共b兲
pressure read off from Fig. 10共a兲 is ⫺0.350 Mpa and the atmospheric pressure of about 0.098 Mpa is also effective, the absolute
pore pressure at A is evaluated as 0.042 Mpa, about 40% of the
atmospheric pressure. This low value of the absolute pore pressure appears to be a threshold for the abrupt failure due to cavitation. The soil RS2 is not so dilative as RS3, but the pore pressure still tends to decrease into negative at q⫽1.20 MPa. It would
still decrease further if the axial deformation were not limited due
to the mechanical capacity in the triaxial test device.
The effective stress paths during the dilation for the three soils
may be approximated by straight lines starting from the origin as
shown in Fig. 10共a兲. Near the right ends, the paths tend to come
slightly lower presumably due to soil particle breakage or some
other reasons. From the slopes of the straight lines, the internal
friction angles for effective stress ␾ ⬘ can be calculated as 36.9°
for RS1, 40.1° for RS2, and 41.5° for RS3, respectively, and
clearly increases with increasing Cu. This implies that the fundamental strength parameter ␾ ⬘ is also different due to different
grain size distributions despite the same relative density.
Postliquefaction Undrained Monotonic Shear
Behavior of River Soils
Fig. 11共a兲 exemplifies deviatoric stress versus axial strain and
pore pressure versus axial strain relationships obtained in undrained monotonic loading tests carried out just after the cyclic
loading tests without any drainage of water for the river soils with
the relative density of about 50%. In the cyclic loading tests, all
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Fig. 12. Effective stress path on p ⬘ versus q plane after cyclic
loading
specimens attained almost 100% pore pressure buildup and about
10% DA axial strain and hence can be defined as being already
liquefied in a normal engineering practice. The initial response to
monotonically increasing strain in Fig. 11共a兲, in which deviatoric
stress and pore pressure change vary gradually below some
threshold strain, is quite different from that of specimens without
cyclic loading history in Fig. 9.
The initial part of the stress-strain curve in Fig. 11共a兲 is enlarged in Fig. 11共b兲. Thin straight lines Fig. 11共b兲 are the initial
tangents of the stress-strain curves. The solid dots represent the
points where the initial tangents deviate from the straight lines,
and may be interpreted as thresholds where liquefied soils are
solidified again due to the soil dilatancy effect by undrained
shearing and start to recover effective stress or shearing strength.
The slopes of the straight lines, therefore, should exclusively reflect the stiffness of the liquefied soil specimens. Postliquefaction
shear moduli G 0L can be calculated from the slopes by assuming
the Poisson’s ratio equal to 0.5. They are evaluated as about 0.4 –
0.04 MPa which corresponds to 0.3–0.04% of the initial shear
moduli of the same gravelly soils under the isotropic confining
stress of 0.098 Mpa evaluated by an empirical equation for
S-wave velocity proposed by Kokusho and Yoshida 共1997兲 based
on Cu and Dr. The cause of this wide variation in the postliquefaction modulus is not clear. The postliquefaction moduli
seem to be influenced by various testing techniques such as the
thickness of rubber membrane covering the specimen 共thicker
membranes were used for coarser soils兲 or other details.
In Fig. 12, typical effective stress paths are shown on the mean
effective stress ( p ⬘ ) versus deviatoric stress (q) plane for the
three types of soils. All paths start near the origin after the full
pore pressure buildup and go up along straight failure lines to the
right end marked with open circles, although in the soil RS2 the
path is a little curved near the right end. From the slopes of the
straight sections, internal friction angles for effective stress ␾ ⬘ are
evaluated as 36.1° for RS1, 38.4° for RS2, and 39.0° for RS3,
indicating that the postliquefaction tan ␾ ⬘ , compared to that before liquefaction, is decreased by 3, 6, and 8%, respectively. The
decrease though small in magnitude may be attributable to the
soil particle rearrangement during liquefaction.
In Fig. 11共b兲, the solidified strain ␧ 1sol can be clearly read off
at the separation points. The relationship between ␧ 1sol and Cu
obtained by all postliquefaction monotonic loading tests carried
out for the river soils of Dr⬇50% is shown in Fig. 13. Despite
large data scatters, ␧ 1sol of well-graded soils is evidently smaller
Fig. 13. Relationship between ␧ 1sol and Cu obtained by postcyclic
loading tests for Dr⬇50%
than that of poorly graded soil as approximated by the solid
curve. This indicates that postliquefaction dilatancy is more pronounced in well-graded soils despite the same relative density. In
Fig. 14, deviatoric stresses q at large strain of about 25% evaluated by all postliquefaction tests are plotted versus Cu with open
circles. The data points for the tests without cyclic loading defined at 15% strain are also plotted on the same chart with open
triangles. Drastic increase in shear resistance for large strain with
increasing Cu is evidently seen whether or not the soil is subjected to cyclic loading. However, the increase seems to occur
mostly in the interval of Cu between 1.4 and 4. The rate of
increase in large-strain strength by monotonic loading is about
eight times between poorly graded sand of Cu⫽1.4 and wellgraded soil of Cu⫽13. This is a good contrast to the moderate
increase of at most 50% in the undrained cyclic strength shown in
Fig. 8.
Based on the above findings, it may be said in general that
well-graded gravelly soils are prone to liquefaction corresponding
to almost full pore pressure buildup and 5% DA axial strain in
nearly the same degree as poorly graded sands so long as their
relative density is the same. However, if the strength at larger
strain is concerned, the relative density is no more a pertinent
Fig. 14. Deviatoric stress at large strain of about 25% versus Cu by
postcyclic loading tests
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parameter. Instead, the particle gradation represented here by the
uniformity coefficient Cu makes a big difference even for soils of
the same relative densities. This implies that well-graded gravelly
soils are less prone to postliquefaction failure accompanying large
deformation. Considering that the uniformity coefficients of natural gravelly soils are normally larger than several tens as indicated
in Fig. 1, their postliquefaction undrained strength corresponding
to 15 to 25% axial strain may be judged at least eight times larger
than poorly graded sands.
Undrained Strength of Crushable Decomposed
Granite Soils
All the test results mentioned so far were obtained for river soils
consisting of roundish soil particles hard to crush. In some engineering problems, e.g., stability of slopes or landfill composed of
residual soils, highly weathered and crushable soils are sometimes
involved. In order to explore the effect of the crushability of soil
particles on the undrained shear behavior, decomposed granite
soil 共DGS兲, named locally as Masado and sampled in the Higashinada Power Station of Kansai Electric Power Company in Kobe
City, Japan, was tested 共Hara et al. 2002兲. This soil was originated
from the Rokko granite mountains at the back of Kobe City and
had been used for filling reclaimed land in the coastal areas. The
degree of weathering may be somehow related with the water
absorption rate Q of the soil material. The value of Q for the
grain size of 4.75–9.5 mm and that of 9.5–19 mm were 1.1 and
1.0% for the river soils, respectively, while those corresponding
values of the decomposed granite soils were 2.8 and 2.4%. This
indicates the influence of weathering on larger particles of the DG
soils, which together with angular particle shapes may result in
higher crushability than the river soils. The DG soil was reconstituted to have exactly the same grain size distributions as RS1,
RS2, and RS3 of the river soils and used in the test. They are
named here as DGS1, DGS2, and DGS3, correspondingly, whose
physical properties are listed also in Table 1. The relative density
of the specimens was adjusted to be about 50% by the wet tamping method.
The undrained cyclic strength of the DG soils is shown in Fig.
6 in terms of the stress ratio R L (DA⫽5%) versus the number of
loading cycles N L with solid symbols. Obviously, the strength of
DGS is smaller than RS particularly for coarser soils with larger
Cu, while that of DGS1 is almost equivalent to RS1. The same
trend can be confirmed in Fig. 8 where R L (DA⫽5%, N L ⫽20) is
plotted versus Cu and compared with the result of Dr⬇50% for
the river soils although the strength reduction with Cu is not so
drastic.
Fig. 15 shows volumetric strain (␧ v ) versus isotropic effective
stress (p ⬘ ) relationships obtained by consolidation tests carried
out before and after undrained cyclic loading tests for the DG
soils and the river soils. Before cyclic loading, p ⬘ is increased
from 29.4 to 98.0 kPa while in the postcyclic loading stage, p ⬘ is
changed from zero 共complete liquefaction兲 to 98 kPa. The volumetric strain of the DG soils is larger both before and after the
cyclic loading than the river soils presumably because of higher
particle crushability. The difference is particularly large in the
initial part of consolidation after the cyclic loading. For river
soils, postcyclic loading volumetric strain is larger for soils with
smaller Cu, because, quite reasonably, sands with smaller Cu
have larger void ratios than coarser soils with higher Cu for the
same relative density. DGS1 shows almost identical consolidation
strain to the river sand RS1. However for soils with higher Cu,
the volumetric strain is evidently larger for the DG soils than for
Fig. 15. Volumetric strain versus isotropic effective stress relationships by consolidation tests carried out before and after cyclic loading
for DG soils and river soils
the river soils. Furthermore, the strain in DGS2 exceeds that of
DGS1. The majority of the postliquefaction settlement occurs at
the initial stage of consolidation; p ⬘ ⫽0 to 0.02 Mpa, and its
magnitude is evidently larger than the river soils with the same
grain size distribution for coarser soils of DGS2 and DGS3. The
subsequent portion of the consolidation curve is almost in parallel
with that before liquefaction. These observations strongly evidence that the volume change characteristics have changed during
cyclic loading presumably due to particle crush of coarse grains
in the DG soils. For DGS1, the curve is almost coincidental with
RS1 even after the cyclic loading, indicating little effect of the
particle crush presumably due to freshness of the smaller particles.
Fig. 16 exemplifies relationships between the deviatoric stress
versus the axial strain and the pore-water pressure versus the axial
strain obtained in the undrained monotonic loading tests carried
out for the DG soils with Dr⬇50%. If this result is compared
with the similar relationships of the river soils of Dr⬇50%
shown in Fig. 9, considerable difference in undrained strength can
be recognized between the two. The obvious difference in the
strength between soils of different grain size distributions in the
river soils is hardly recognizable in the DG soils. Even the soils
with higher Cu, DGS2 and DGS3, show almost identical strength
Fig. 16. Deviatoric stress or pore-water pressure versus axial strain
relationships obtained by monotonic loading tests for DG soils with
Dr⬇50%
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Fig. 17. Effective stress paths drawn on mean effective stress versus
deviatoric stress plane for DG soils with Dr⬇50%
with DGS1, resulting in considerably lower strength than the river
soils. The pore pressure curves indicate that the DG soil is much
less dilative than the river soils. This considerable difference in
shear behavior may be mainly attributable to the difference in
crushability of soil particles of the DG soil. Fig. 17 indicates the
corresponding effective stress paths drawn on the mean effective
stress ( p ⬘ ) versus deviatoric stress (q) plane. A comparison with
the stress paths of the river soils in Fig. 10共b兲 reveals that in the
soils of higher Cu, DGS2, or DGS3, the pore pressure cannot
develop negative values as the river soils, RS2 or RS3, and suddenly turns to the reverse direction resulting in smaller undrained
shear strength. This probably reflects the crushability of the DG
soils in which the contacts between coarser grains are too weak to
bear strong contact pressure exerted in the dilative environment.
Fig. 18 shows relationships between the deviatoric stress versus the axial strain and the pore-water pressure versus the axial
strain obtained in undrained monotonic loading tests carried out
just after the cyclic loading tests for the DG soils with the relative
density of about 50%. In the cyclic loading tests, all specimens
attained almost 100% pore pressure buildup and about 10% DA
axial strain. Comparing this with similar stress-strain curves of
river soils in Fig. 11共a兲, considerable decrease in postliquefaction
undrained strength can be noticed for coarser soils, DGS2 and
DGS3 in particular. In Fig. 14, the strengths of Masado which are
read off either at the peak or at ␧ a ⫽20% of the stress-strain
Fig. 19. Normalized strength versus absolute dry density relationship by monotonic undrained tests for all tested granular materials
curves are plotted versus the uniformity coefficient Cu. In good
contrast with the river soils, the strength of the DG soils stays
almost constant with increasing Cu both before and after liquefaction, again mostly due to the soil particle crushability. This test
result may be able to explain at least a part of the reason why
such large flow deformation could occur in coastal areas in Kobe
reclaimed by the decomposed granite soils during the 1995
Hyogoken Nambu earthquake as reported for example by Ishihara
et al. 共1996兲.
In summary, a diagram correlating the undrained shear
strength versus the absolute dry density for the granular soils is
prepared in Fig. 19 to show a total picture of the principal findings in this research. The strengths shown in Figs. 8 and 14 are
averaged if necessary and normalized by those of the poorly
graded soil of Cu⫽1.44. This figure clearly indicates that natural
well-graded granular soils consisting of sound particles are at
least eights times more resistant to large strain failures compared
to poorly graded sands even after the onset of liquefaction simply
because they exhibit higher dilatancy due to higher absolute density or lower void ratio. Liquefaction strength normally defined
by 5% double amplitude strain or nearly 100% pore pressure
buildup, on the other hand, is not so much sensitive to the absolute density but more dependent on the relative density because
the strain level is not large enough for the strength to be controlled by the absolute density. On the contrary, if coarser particles are weak and crushable, not only liquefaction strength but
also undrained shear strength for large strain tend to be smaller
for soils of larger Cu as indicated in Fig. 19. Though quantitative
conclusions applicable in general are difficult to draw with the
limited test cases in this research, it may be recommended for
design purposes that the strength of sand of the same Dr should
be reduced by 50% for the cyclic or monotonic undrained shear
strength for soils containing weak and crushable coarse soils.
Conclusions
Fig. 18. Deviatoric stress or pore-water pressure versus axial strain
relationships after cyclic loading for DG soils with Dr⬇50%
Undrained cyclic and monotonic loading triaxial tests on granular
soils have been systematically carried out. River soils consisting
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of relatively hard grains have been reconstituted to have three
grain size curves and tested to investigate the effect of the particle
gradation on the undrained shear characteristics. These experimental studies have yielded the following major findings:
1. Liquefaction strength of granular soils 共undrained cyclic
strength defined by 5% double amplitude axial strain兲 may
be roughly evaluated by the index of relative density Dr,
despite large difference in particle gradations;
2. Undrained monotonic loading strength corresponding to
larger axial strain of 15–20% shows a drastic increase with
increasing uniformity coefficient Cu for the same relative
density and may be evaluated by the index of absolute density; and
3. Postliquefaction undrained strength for larger strain of 20–
25% is not uniquely determined by relative density but
largely dependent on particle gradations. Namely, soils with
larger Cu and larger absolute density tend to show considerably larger undrained strength.
Then, decomposed granite soils, which possess identical particle
gradations as the river soils, have also been tested to examine the
effect of soil particle crushability, revealing the followings:
1. If the quality of soil particles are weak and crushable, the
undrained cyclic strength 共5% double amplitude兲 tends to
decrease with increasing Cu, because larger size particles
are more prone to crush and, hence, less dilative during cyclic shearing; and
2. Strengths of crushable soils corresponding to large axial
strain of 20% by undrained monotonic loading do not increase with increasing Cu unlike soils consisting of noncrushable particles. This may be attributable to soil crushability which impedes development of soil dilatancy and
negative pore pressure because crushable larger size particles
cannot bear high contact pressure.
It may be inferred based on the series of element tests of
granular soils, therefore, that although well-graded granular soils
tend to liquefy almost as readily as poorly-graded sands of
smaller Cu with identical relative densities, significant failures
caused by larger soil strains are less likely to occur as long as
coarser particles are good in quality and hard to crush such as
fluvial gravels. This finding cannot be applicable to granular soils
containing weak and crushable coarser particles.
Acknowledgments
Kansai Electric Power Company who donated the Masado decomposed granite soils of the Higashinada Power Station, Kobe,
to be used in this research, is gratefully acknowledged.
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