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International Conferences on Recent Advances 2010 - Fifth International Conference on Recent
in Geotechnical Earthquake Engineering and
Advances in Geotechnical Earthquake
Soil Dynamics
Engineering and Soil Dynamics
26 May 2010, 4:45 pm - 6:45 pm
Dynamic Properties of Sand in Constant-Volume and ConstantLoad Tests
F. Jafarzadeh
Sharif University of Technology, Iran
H. Sadeghi
Sharif University of Technology, Iran
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Jafarzadeh, F. and Sadeghi, H., "Dynamic Properties of Sand in Constant-Volume and Constant-Load
Tests" (2010). International Conferences on Recent Advances in Geotechnical Earthquake Engineering
and Soil Dynamics. 11.
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DYNAMIC PROPERTIES OF SAND IN CONSTANT-VOLUME
AND CONSTANT-LOAD TESTS
Jafarzadeh, F.
Sharif University of Technology
Tehran, Iran 11365-9313
Sadeghi, H.
Sharif University of Technology
Tehran, Iran 11365-9313
ABSTRACT
Constant-volume and constant-load tests were performed on Babolsar and Toyoura sands by using a modified SGI cyclic simple shear
device which provides the capability of back pressure saturation. All tests were shear strain controlled and conducted under different
values of relative density, vertical effective stress and shear strain amplitude. Results revealed that Dr, σ′v and γ affect shear modulus
and damping ratio under both constant-volume and constant-load conditions in similar ways except the shear strain amplitude which
has no important influence on damping of constant-volume tests. The effects of Dr, σ′v, γ and the number of cycles on variations of
shear modulus and damping ratio of sand were found to be more pronounced under constant-load condition. It seems that the
differences between the results may be due to the different fabric produced in two kinds of test samples rather than to the test method.
However, further study is needed to clarify this issue.
INTRODUCTION
Wide application of dynamic properties of soil in geotechnical
earthquake engineering problems (such as the analysis of soilstructure interactions, dynamic bearing capacity of machines
foundations, soil structures subjected to cyclic loadings) has
made researchers to investigate a variety of factors which
affect shear modulus and damping ratio of soil (e.g. Hardin
and Drnevich 1972a) and to develop various field and
laboratory tests methods so far (Kramer 1996). A cyclic
simple shear test is a convenient laboratory test method in
evaluating G and D of soil, especially at large shear strains.
LABORATORY PROCEDURE
Results of truly undrained and conventional constant-volume
tests by using a developed NGI direct simple shear device
were compared by Dyvik et al. 1987. On the basis of static
tests on clay, they concluded that the results obtained by two
methods are equivalent for saturated soils. Theoretically, since
there is no real pore pressure generation in the specimen under
constant-volume condition, it is not necessary to saturate the
specimen. However, poor saturation can modify soil resistance
(Vanden Berghe et al. 2001).
Silt
The main objective of the present study is to investigate shear
modulus and damping ratio of cyclically loaded sand under
constant-volume and constant-load conditions. Additionally,
the effects of some parameters on dynamic properties of sand
under mentioned conditions will be presented and discussed.
Paper No. 1.11a
Test Materials
Two poorly graded sands, Babolsar and the Japanese standard
Toyoura sand were selected as test materials. The former is
natural sand obtained from the South coast of Caspian Sea.
Particle size distribution curves of sands are shown in Fig. 1.
100
90
80
70
60
50
40
30
20
10
0
Sand
Fine
Medium
Coarse
Gravel
Finer by weight (%)
Babolsar sand
Toyoura sand
ASTM Babolsar Toyoura
D422-63
0.01
D 10
0.14
0.14
D 30
D 50
0.22
0.25
0.16
0.19
Uc
1.79
1.56
Cc
1.32
0.95
0.1
1
Particle size (mm)
10
Fig. 1. Gradation curves of test materials.
1
Principal index tests were performed following the procedure
of the ASTM standards. The physical properties of soils
utilized in the all conducted tests are summarized in Table 1.
Table 1. Physical properties of test materials
Soil type
Babolsar sand
Toyoura sand
Standard
designation
Specific gravity
2.753
2.645
ASTM D854–02
emax
emin
0.777
0.549
0.973
0.609
ASTM
ASTM
D4254–00 D4253–00
Apparatus
A servo-controlled pneumatic SGI cyclic simple shear, CSS;
apparatus manufactured by Wykeham Farrance Co. was used
in order to perform the cyclic loading of soil samples. This
apparatus is capable of conducting stress and strain controlled
tests in the both horizontal and vertical directions. Loading
forces are applied through the pneumatic actuators mounted
horizontally and vertically. A circular specimen is mounted
between the base pedestal and piston top cap and surrounded
by a number of circular rings to prevent lateral displacement
during consolidation or shearing stages. Indeed, the specimen
can be laterally restrained by rigid boundary plates
(Cambridge-type device), a wire-reinforced membrane (NGItype device), or a series of stacked rings (SGI-type device)
according to the description of Kramer 1996.
The apparatus was equipped with a pressure test device made
by ELE. The pressure test device which can introduce water
pressure into the specimen was utilized in order to improve the
apparatus so that it can be used in conducting undrained tests
on fully saturated samples. On the other hand, the capability of
saturating the specimen with back pressure has been possible
using this ancillary device. A schematic illustration of the
modified CSS apparatus is given in Fig. 2.
Sample Preparation
Constant-Volume Tests. Solid cylindrical samples with the
nominal diameter of 70 mm and height of 22 mm were used in
cyclic simple shear tests. Samples were prepared by using the
moist placement method suggested by Ishihara 1996. The
mixture of soil with 5% water content was poured in the mold
with a spoon and the specimen was compacted until
approaching the desired density. The relative density of the
specimen was controlled by adjusting its height using a 0.01
mm digital caliper. This method of sample preparation was
utilized in constant-volume and constant-load tests.
Estimation of Pore Pressure Parameter. Use of Skempton’s
pore pressure parameter, B value; in triaxial loading condition
as a guide to achieve full saturation is conventional but, for the
stress conditions other than triaxial condition e.g. where the
specimen is consolidated under K0 condition (Fig. 3a), there is
no criteria for assuring full saturation of the sample. It seems
that a proper evaluation of pore pressure parameter under this
special loading condition is inevitable. Figure 3a shows a
saturated soil element subjected to an increase of total stress in
which the intermediate and minor principal stresses are equal.
The pore water pressure will grow by ∆u if drainage is not
allowed from the soil. The change in the volume of pore water
due to the increase of pore pressure by an amount of ∆u can be
expressed as (Das 1983):
∆V
nV C ∆u
(1)
where n is porosity, V0 is the original volume of soil element
and Cp is the compressibility of pore water.
On the other hand, the change in volume of the soil skeleton
due to the effective stress increment indicated in Fig. 3b will
be:
∆V
C V ∆σ
∆σ
∆V
C V ∆σ
2K ∆σ
∆σ
C V ∆σ
2∆σ
(2a)
where ∆σ′1, ∆σ′2 and ∆σ′3 are principal effective stresses as
shown in Fig. 3b corresponding to the total stresses in Fig. 3a
and Cc is the compressibility of the soil skeleton. Figure 3c
shows the determination of Cc from laboratory compression
test results under uniaxial stress application with zero excess
pore water pressure. By simplifying Equation 2a, we obtain:
Fig. 2. Schematic view of cyclic simple shear (SGI type)
apparatus and pressure test device.
Paper No. 1.11a
C V ∆σ 1
2K
(2b)
2
If the soil element is fully saturated with water, the change in
the volume of both pore water and soil skeleton under the
application of three principal total stresses plotted in Fig. 3a
must be equal. So, a comparison of Equations 1 and 2c gives:
Δσ 1
(a)
Δσ 3 = Δσ 2
Δσ 2
Δσ 3 = Δσ 2
(b)
1
2K
(4a)
Δσ 1′
Δσ 3′ = K 0 Δσ 1′
Δσ 1′
V
V0
Cc =
ΔV V0
Δσ ′
ΔV
V0
Δσ ′
σ′
Fig. 3. (a) Total stresses and (b) Effective stresses imposed on
a saturated soil element consolidated under K0 condition and
(c) Definition of compressibility of soil skeleton (Das 1983).
where K0 is the coefficient of at‒rest earth pressure. After
substitute of ∆σ1‒ ∆u for ∆σ′1 in Equation 2b we have:
2K
1⁄ 1
nC ⁄ C 1
2K
(4b)
Since the compressibility of water is much smaller than
compressibility of soil skeleton, the value of Cp/Cc converges
to zero. So it would appear that, the value of ∆u/∆σ1 mainly
depends on Cp/Cc than n/(1+2K0). Hence, the effect of K0
value on the estimation of pore pressure parameter can be
neglected. However, the value of n/(1+2K0) is less than unity
and makes the term, nCp/[Cc(1+2K0)] to decrease more.
Subsequently, it can be inferred from the above expressions
that, the upper limit of pore pressure parameter where the
specimen is consolidated under the application of K0
condition, is equal to one.
Traditionally, the value of pore pressure parameter under
triaxial stress conditions, B value, equals to 0.95 is accepted as
representing virtually full saturation in laboratory reports. As
an alternative, if several successive equal increments of
confining pressure give identical values of B, full saturation of
the specimen could be assured (Head 1998).
(c)
Paper No. 1.11a
2K ⁄ nC ⁄C
(3)
∆u⁄∆σ
Δσ 2′ = K 0 Δσ 1′
∆u 1
1
2K
Δσ 1
Δσ 2′ = K 0 Δσ 1′
C V ∆σ
∆u⁄∆σ
∆u 1
Finally, by more simplification of Equation 4a, the pore
pressure parameter can be estimated based on Equation 4b:
Δσ 3′ = K 0 Δσ 1′
∆V
C V ∆σ
The pore pressure parameter, ∆u/∆σ1, is extracted from
Equation 3 as:
Δσ 2
Δu
nV C ∆u
(2c)
Constant-Load Tests. After preparation of samples on the
basis of wet tamping method, CO2 was percolated through the
specimens and de-aired water was then introduced into the soil
sample, while the vertical stress was kept at 15 kPa to prevent
the sample disturbance. After one stage of saturation using 25
kPa of vertical stress and 15 kPa of back pressure was taken,
back pressure was raised following the vertical stress increase
to the next step by 10 kPa and the procedure of raising the
vertical stress and back pressure was then repeated.
Considering the mentioned criteria for assuring full saturation,
the saturation of the specimens by the application of back
pressure was continued until two or three equal increments of
vertical stress give identical values of pore pressure parameter,
∆u/∆σ1. The samples were then consolidated to a given
vertical consolidation stress. The values of total vertical stress,
effective consolidation stress and back pressure as well as the
corresponding ratio of pore water pressure parameter, ∆u/∆σ1,
at the last step of saturation for 16 undrained tests are
summarized in Table 2.
3
Table 2. Measured ∆u/∆σ1 in constant-load tests at the end of
saturation stage
σv
Back pressure
Dr
(%) (kPa)
(kPa)
9 (B*)
31
175
125
10 (B) 35
175
125
11 (B) 71
205
155
12 (B) 67
205
155
13 (B) 32
275
125
14 (B) 30
275
125
15 (B) 74
305
155
16 (B) 71
305
155
25 (T**) 32
175
125
26 (T) 33
175
125
27 (T) 71
205
155
28 (T) 70
205
155
29 (T) 28
275
125
30 (T) 39
275
125
31 (T) 68
305
155
32 (T) 70
305
155
B*: Babolsar sand, T**: Toyoura sand
Test no.
σ′v
∆u/∆σ1
(kPa)
50
0.90
50
0.88
50
0.88
50
0.88
150
0.89
150
0.87
150
0.90
150
0.89
50
0.91
50
0.90
50
0.88
50
0.85
150
0.86
150
0.91
150
0.82
150
0.83
Test Program
Whereas the after consolidation relative density should be
taken into account, a series of calibration consolidation tests
were conducted to specify the initial relative density of the
partially and fully saturated specimens. The values of initial Dr
for different vertical σ′v and post consolidation relative
densities as results of preliminary tests are reported in Table 3.
The main experimental program included tests with different
Table 3. Preliminary tests results
Post
σ′v Initial Dr
consolidation
(kPa)
(%)
Dr (%)
P1–B* Constant-volume
30
50
23.2
P2–B Constant-volume
70
50
64.9
P3–B Constant-volume
30
150
16.6
P4–B Constant-volume
70
150
59.5
P5–B
Constant-load
30
50
3.5
P6–B
Constant-load
70
50
57.9
P7–B
Constant-load
30
150
– 3.7
P8–B
Constant-load
70
150
52.0
P9– T** Constant-volume
30
50
25.0
P10–T Constant-volume
70
50
65.7
P11–T Constant-volume
30
150
20.5
P12–T Constant-volume
70
150
62.1
P13–T
Constant-load
30
50
4.5
P14–T
Constant-load
70
50
62.7
P15–T
Constant-load
30
150
– 1.7
P16–T
Constant-load
70
150
58.3
B*: Babolsar sand, T**: Toyoura sand
Test no.
values of σ′v, Dr and γ which were performed under constantvolume and constant-load conditions. Unsaturated samples
were sheared under equivalently undrained or constantvolume condition. On the other hand, truly undrained tests
were carried out on fully saturated specimens under constantload condition. Half of the specimens were consolidated to 50
kPa and the others to 150 kPa. Test samples had two different
post-consolidation relative densities 30, 70% representing
loose and medium dense conditions; respectively. All tests
were shear strain-controlled with an approximately sinusoidal
shape of cyclic straining at large shear strain amplitudes of 1.0
and 1.5%. The frequency of cyclic loading was 0.5 Hz and the
number of loading cycles varied from 1 to 200 or to the cycle
of initial liquefaction, which ever occurred first. General
testing conditions at the beginning of cyclic shear stage are
listed in Table 4 for 32 cyclic simple shear tests.
Table 4. Tests conditions at the beginning of cyclic stage
Sand
Vertical load
type
condition
1, 2
B*
Constant-volume
3, 4
B
Constant-volume
5, 6
B
Constant-volume
7, 8
B
Constant-volume
9, 10
B
Constant-load
11, 12
B
Constant-load
13, 14
B
Constant-load
15, 16
B
Constant-load
17, 18 T** Constant-volume
19, 20
T
Constant-volume
21, 22
T
Constant-volume
23, 24
T
Constant-volume
25, 26
T
Constant-load
27, 28
T
Constant-load
29, 30
T
Constant-load
31, 32
T
Constant-load
B*: Babolsar sand, T**: Toyoura sand
Test no.
γ
(%)
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
1.0, 1.5
Dr
(%)
32, 29
69, 69
29, 30
70, 69
31, 35
71, 67
32, 30
74, 71
31, 29
70, 69
29, 30
69, 69
32, 33
71, 70
28, 39
68, 70
σ′v
(kPa)
50
50
150
150
50
50
150
150
50
50
150
150
50
50
150
150
Test condition
Paper No. 1.11a
Calculation of G and D
Dynamic stiffness and damping ratio of each cycle can be
determined from a graph of stress against strain, knowing as
hysteresis loop. Figure 4 illustrates a schematic hysteresis loop
and how secant modulus and damping can be determined
based on data achieved from stress-strain curve. By using 50
data point per cycle which transferred through CDAS to PC,
the area of hysteresis loop can be estimated precisely
according to Equation 5.
A
0.5
γ
τ
γ
τ
γ
τ
γ
τ
γ
τ
γ
τ
(5)
in which Aloop is the area of hysteresis loop with vertices of
(γ1, τ1), (γ2, τ2)…(γ50, τ50) and γi, τi are shear strain and shear
stress at ith point; respectively. Jafarzadeh and Sadeghi 2009
4
-10
-2
-1
0
1
2
-20
γ min
(
Shear Strain (%)
γ max
Fig. 4. Estimation of G and D fro
om data of a hyysteresis loop.
indicaated that the algorithm
a
can also
a be used inn estimation off
dampping ratio underr drained cond
dition.
Shear Stress,
τ (kPa)
Aloop
ΔW
=
2πW 2πGsec[(γ max − γ min ) 2]2
10
0
-10
-20
0
10
20
30
Number of Cyycles
2000
40
50
40
Sheaar Modulus
1500
30
Dam
mping Ratio
1000
20
500
10
0
Typiccal Test Resultts
Shear Stress (kPa)
RESU
ULTS AND DIISCUSSION
Shear Stress,
τ (kPa)
20
30
40
50
Number of Cycles
30
First Cycle
10
-10 -2
-1
0
1
2
-30
(
Shear Strain (%)
30
20
10
0
-10
-20
-30
0
10
20
30
40
50
Number of Cyycles
Shear Modulus,
G (kPa)
Figurres 6 and 7 shoow the variation
ns of shear moodulus with thee
numbber of cycles foor two tested materials.
m
Resuults of the testss
performed under 500 kPa vertical effective
e
consoolidation stresss
repressented in Fig. 6 while Fig. 7 includes thee data obtainedd
from the other tests with 150 kPa
k vertical efffective stress.
Sampple specificatioon and testing
g conditions arre also plottedd
abovee each chart. These
T
figures compare
c
dynam
mic stiffness off
soil specimens unnder constant--volume and constant-loadd
condiitions. Accordiing to the resu
ults, shear moddulus decreasess
with the number of cycles un
nder all testiing conditionss
ntrolling modee. In the otherr
indeppendent of verrtical load con
wordss, the excess pore water pressure deveeloped due too
increaase in the num
mber of cycles under
u
constant--load conditionn
as well
w
as consttant-volume condition,
c
caauses stiffnesss
degraadation.
10
(a)
Typiccal results of constant-load
c
and
a constant-voolume tests aree
illustrrated in Fig. 5.. Figure 5a sho
ows the resultss of a constant-load test
t (Test #11)) conducted on
n a sample withh 70% relativee
density and 50 kPaa vertical effecctive stress. Thhe shear strainn
ampliitude was 1.0%
%. Typical resu
ults of Test #244 on a medium
m
densee sample withh 150 kPa con
nsolidation strress and 1.5%
%
shearr strain amplittude under con
nstant-volume condition aree
also presented
p
in diagrams
d
of Fig. 5b. Figure 5 contains thee
variattions of shear stress, shear modulus and damping ratioo
with the number of cycles along
g with the shear stress-strainn
curvees.
Effecct of Number of Cycles
0
0
Test # 24, Toyoura sand, σ'v =150 kPa, γ=1.5 %,
Dr=70 %, Uunder Constant-Volume condition
τ γ min
D=
20
Shear Modulus,
G (kPa)
τ c τ γ max − τ γ min
Gsec
=
s =
γ c γ max − γ min
Paperr No. 1.11a
Test # 11, Babolsar sand, σ'v =50 kPa, γ=1.0 %,
Dr=70 %, Uunder Constant-Load condition
0
Damping Ratio,
D (%)
1
W
First Cycle
10
1500
1000
20
500
15
0
10
0
(b)
25
Sheaar Modulus
Dam
mping Ratio
10
20
30
40
Damping Ratio,
D (%)
ΔW
Shear Stress (kPa)
20
Gsec
τ γ max
50
Number off Cycles
Fig. 5. Typical resuults of a (a) connstant-load tesst, (b) constanttvolume test.
5
3500
σ′v=50 kPa, γ=11.0 %, Dr=30 %
B-C-V
B-C-L
B: Bab
bolsar
T: Toy
youra
C-V: Constant-volume
C
e
C-L: Constant-load
C
1
1200
800
Shear Modulus, G (kPa)
Shear Modulus, G (kPa)
1
1600
T-C-V
T-C-L
400
0
σ′v=150 kPa, γ=
=1.0 %, Dr=30 %
B-C-V
B: Baabolsar
T: Toyoura
C-V: Constant-volum
me
C
C-L: Constant-load
B-C-L
2
2800
2
2100
700
3
6
9
12
15
0
5
10
Numberr of Cycles
15
20
25
30
Number of Cycles
2
2500
σ′v=50 kPa, γ=1
1.5 %, Dr=30 %
B-C-V
Shear Modulus, G (kPa)
Shear Modulus, G (kPa)
1
1200
B-C-L
900
T-C-V
600
T-C-L
300
0
σ′v=150 kPa, γ=
=1.5 %, Dr=30 %
B-C-V
2
2000
B-C-L
1500
T-C-V
T-C-L
1000
500
0
0
2
4
6
8
10
0
3
Numbeer of Cycles
6
9
12
15
Number of Cycles
4
4000
σ′v=50 kPa, γ=1
1.0 %, Dr=70 %
B-C-V
Shear Modulus, G (kPa)
2
2000
Shear Modulus, G (kPa)
T-C-L
1400
0
0
B-C-L
1
1500
T-C-V
1
1000
T-C-L
500
0
σ′v=150 kPa, γ=
=1.0 %, Dr=70 %
B-C-V
3
3200
B-C-L
2
2400
T-C-V
T-C-L
1
1600
800
0
0
10
20
30
40
50
0
30
Numbeer of Cycles
3500
σ′v=50 kPa, γ=1
1.5 %, Dr=70 %
1
1500
60
90
120
150
Number of Cycles
B-C-V
Shear Modulus, G (kPa)
1
1800
Shear Modulus, G (kPa)
T-C-V
B-C-L
1
1200
T-C-V
900
T-C-L
600
300
0
σ′v=150 kPa, γ=
=1.5 %, Dr=70 %
3000
B-C-V
B-C-L
2
2500
T-C-V
2
2000
T-C-L
1500
1000
500
0
0
7
14
21
28
35
Numbeer of Cycles
Fig. 6. Variations of
o shear modullus with the num
mber of cycles
for sppecimens conssolidated to 50 kPa vertical efffective stress.
Paperr No. 1.11a
0
10
20
30
40
50
Number of Cycles
Fig. 7. Variations of shear modulus with the nuumber of cycless
for sppecimens consolidated to 1500 kPa vertical effective stresss.
6
Althoough both speccimens for con
nstant-volume and constant-load tests
t
were preppared by wet taamping and hadd same relativee
densities at the beeginning of cyclic
c
stage, the
t
specimenss
shearred under connstant-load co
ondition seem
m to be moree
homoogenous because of the wateer flushed into the specimenss
during saturation stage.
s
The watter lubricates the surface off
grainss and makes the
t movementt of grains on each other inn
desiraable directionss easier. So it would
w
appear that,
t
the higherr
valuee of shear modulus
m
at cy
ycle 1 under constant-loadd
condiition comparedd to the constan
nt-volume tests is because off
the more
m
homogennous fabric produced for fully
f
saturatedd
samples than unsaaturated samp
ples prepared for constant-volum
me tests.
As shhown previously in Figs. 6 and
a 7, the valuues of dynamicc
stiffness obtained through the constant-load tests are lesss
comppared to the results
r
of constant-volume tests after thee
specim
mens reach to the initial liquefactionn. A possiblee
explaanation for thee higher values of shear modulus
m
underr
consttant-volume condition may
y be the resiidual strengthh
remaiined in the speecimens after liquefaction
l
duue to the inter-granuular suction forrces. Indeed th
he water contennt of about 5%
%
whichh is mixed withh dried sand makes
m
the placeement of moistt
sand in a very loosse structure po
ossible, becausse of capillaryy
effectts between paarticles (Ishihaara 1996). Thhis amount off
waterr remains in thhe sample as well as the capillary forcess
betweeen grains evven after thee occurrence of imaginaryy
liqueffaction. Thereffore, constant--volume tests represent
r
moree
valuees of shear modulus in contrast to the consstant-load testss
run on
o the fully saaturated specim
mens which coompletely losee
their shear strength..
The dependence
d
off damping ratiio on the num
mber of cycless
underr constant-loadd condition is shown in Fig. 8.
8 Based on thee
diagraams of Fig. 8 the
t variations of damping with the numberr
of cyycles can be neeglected up to 10th cycle before the initiall
liqueffaction. Afterw
ward, damping
g increases subbstantially withh
the nuumber of cycles. It means th
hat for the sam
mples liquefiedd
beforre 10th cycle, damping valuess are in ascendding order from
m
cycle 1. On the otther hand, forr samples liquuefied after 100
cycles, the numbeer of cycles has a negligiible effect onn
dampping variationss until 10 cyccles to Nl andd a significantt
growtth in dampingg ratio takes place in the last 10 cycless
Paperr No. 1.11a
Damping Ratio, D (%)
45
40
35
30
25
20
15
10
5
0
Test No.
9
10
11
12
13
14
15
16
Babolssar
1
10
100
Numbeer of Cycles
(a)
1000
40
Damping Ratio, D (%)
The trends
t
of sheaar modulus variations with the
t number off
cycles are similar under the both
b
truly andd equivalentlyy
undraained conditionns but, the valu
ues differ from
m each other too
some extent. The values
v
of shearr modulus at cycle
c
1 for alll
samples sheared unnder constant-load condition are more thann
v
of constaant-volume tessts. In addition,
the coorresponding values
in conntrast to a specific constant-volume test, loower values off
dynam
mic stiffness are obtained for the corressponding fullyy
saturaated sample unnder constant-lo
oad condition after it reachess
to thhe cycle of initial
i
liquefaction and losses its laterall
resisttance to shear stresses. It means that the range
r
of shearr
moduulus variationss with the num
mber of cyclees under trulyy
undraained conditioons is higher compared to the constant-volum
me tests while the number off cycles varies between 1 andd
N l.
Test No.
25
26
27
28
29
30
31
32
35
30
25
20
15
10
5
Toyourra
0
1
(b)
10
Numberr of Cycles
100
Fig. 8. Variations of damping ratio with the nuumber of cycless
for the tessts under consttant-load conddition.
beforre Nl. Results indicated thaat, the developped pore wateer
presssure has an impportant influence on dampingg variations.
In thhis study dampping values aree represented from
f
cycle 1 too
Nl. By
B getting closse to the cyclee of initial liquuefaction, sheaar
strenngth of a speccific sample decreases
d
signiificantly whichh
resullts in a signifiicant decrease in shear moddulus. Dampingg
increeases with a decrease in shear moduulus until the
occurrrence of initiial liquefactionn, according too Fig. 4. Afteer
liqueefaction, the hoorizontal load cell
c which direectly connectedd
to thhe pneumatic actuator cannnot sense the lateral forcees
preciisely. Therefoore, the shaape of hysteresis loop iis
miscalculated alongg with the loopp area and sheaar modulus thaat
subseequently makees damping raatio unreliable. So, it is jusst
assum
med that dampping values aft
fter a sample is liquefied, are
the saame as dampinng at Nl.
Figurre 9 indicates the variations of damping ratio with the
numbber of cycles for
f all constannt-volume testss. As shown inn
the diagrams
d
of Fig.
F
9, dampinng ratio decreeases with the
numbber of cycles. By
B comparing the results of Figs.
F
8 and 9, iit
is innferred that thhe trends of damping
d
variaations with the
numbber of cycles under constannt-volume conndition are noot
compparable with thhose of constannt-load tests. Inn contrast to the
consttant-load tests,, damping willl not increase by
b approachingg
to thhe cycle of initial liquefacction under coonstant-volume
conddition. It seem
ms that, the tessts performed in the presennt
studyy under constaant-load condiition representt more reliable
7
Damping Ratio, D (%)
25
Babbolsar
Tesst No.
22
1
5
2
6
3
7
4
8
19
16
13
10
0
20
(a)
40
60
Number of Cycles
80
100
Damping Ratio, D (%)
26
Toyooura
23
Test No.
17
21
18
22
19
23
20
24
20
17
14
0
20
(b)
40
60
Number of Cycles
80
100
Fig. 9. Variations of
o damping rattio with the num
mber of cycles
for the testss under constan
nt-volume conddition.
trendss for damping variations witth the number of cycles thann
consttant-volume tessts.
The main
m
reason foor rapid growtth in damping ratio with thee
numbber of cycles by getting clo
ose to the liquuefaction statee
underr truly undraained conditio
on was the low shearingg
resisttance of specim
mens to lateral forces which was correlatedd
with the shear modulus. Subseq
quently, the loower values off
shearr modulus resuult in the high
her values of damping ratioo
(Fig. 4). But, undeer constant-volume conditionn the trends off
dampping variationss with the num
mber of cycless are different.
Sincee the specimens were no
ot fully saturrated and thee
develloped pore watter pressure is imaginary
i
evenn after the totall
verticcal load was omitted
o
from the specimen, there was ann
amouunt of shear modulus
m
which was more in contrast to thee
truly undrained testts. It means th
hat the specim
mens had shearr
strenggth to the latteral load eveen after the occurrence off
liqueffaction due to the capillary effects.
e
This residual value off
shearr modulus prevvents damping from increase as in constant-load tests and keepps it nearly co
onstant with a few scatteringg
until cycle 100.
Effeccts of Dr, σ′v annd γ
The tests
t
were condducted under tw
wo different leevels of Dr, σ′v
and γ,
γ while the othher testing con
nditions were kept
k
the same..
Paperr No. 1.11a
t effects of relative
r
densityy, vertical effecctive stress andd
So, the
shearr strain amplittude on shear modulus and damping ratioo
can be
b investigatedd under constaant-volume andd constant-loadd
condditions. Compaarisons will be
b presented and discussedd
basedd on the valuees of shear modulus and daamping ratio aat
cyclee 5.
Effecct of Relative Density. Figuure 10 indicatees the effect oof
relatiive density on shear moduluus and dampingg ratio of sandd.
The increase in sheear modulus as
a a result of 40%
4
increase inn
Dr caan be seen in Fig.
F 10a for coonstant-volumee and constanttload tests. Legendss shown at thee right side off each diagram
m
contaain the numbbers of indivvidual tests. Complete tesst
condditions were sum
mmarized in Table
T
5. Conveersely, dampingg
ratio descends withh an increase in relative denssity under trulyy
and equivalently
e
u
undrained
condditions as show
wn in Fig. 10bb.
The rate of increase in shear modulus due to the growth oof
relatiive density froom 30 to 70%
% is more signnificant for the
tests conducted on
o saturated samples
s
underr constant-loadd
conddition as well as the rate off reduction in damping ratioo.
This is because off the effect off excess pore water pressure
developed during cyclic sheariing and resullts in stiffnesss
degraadation especiaally for samplees with 30% relative
r
densityy.
In the other words, high amount of
o excess pore water pressure
is geenerated when a specimen iss cyclically shheared with the
appliication of largee shear strain. This mechanissm makes loose
sampples to lose moost of their strrength to the laateral forces inn
the first
fi few cycles, which subseqquently results in a substantiaal
decreease in shear modulus
m
along with an increaase in dampingg
valuee. But, as desscribed previouusly, the valuues of moduluus
undeer constant-voolume conditioon don’t redduce with the
numbber of cycles as much as those of consstant-load testts
becauuse of the capillary effect.
Effecct of Vertical Effective Stress. The variaations of sheaar
moduulus and dampping ratio with σ′v are illustraated in Fig. 111.
Withh an increase inn vertical effecttive stress from
m 50 to 150 kPa
the values
v
of dynaamic stiffness significantly
s
inncrease in bothh
consttant-load andd constant-vollume tests for
fo all testingg
condditions, based on
o the results of Fig. 11a. As depicted inn
Fig. 11b, damping ratio decreasess with the incrrease in verticaal
effecctive consolidaation stress in all the tests peerformed undeer
consttant-load conddition except one, and mosst of constanttvolum
me tests. Trennd of dampingg variation wiith σ′v for twoo
consttant-load tests (i.e. 26 and 30) is different from the otheer
tests.. These tests had
h a nominal relative densiity of 30% andd
weree sheared with 1.5% shear strrain amplitudee. Both samplees
liqueefied until cycle 5 that meanss, the values off damping at Nl
are not
n so reliablee. However, baased on the daata depicted inn
Fig. 8b, the valuess of damping for
f the test coonsolidated to a
higheer vertical effeective stress (ttest # 30) are less comparedd
with the test # 26 up
u to third cyclle, which is equual to the cycle
of innitial liquefaction for the teest # 26. Withh regard to the
resullts of constannt-volume tessts illustrated in Fig. 11bb,
dampping ratio att cycle 5 inncreases slighhtly with thhe
increease in σ′v in two cases off constant-voluume tests. The
menttioned trend is not expected and
a also differss from the trendd
of othher cases.
8
3
3000
2
2500
2
2000
1
1500
1
1000
500
0
1
1200
1&3
2&4
5&7
6&8
17 & 19
18 & 20
21 & 23
22 & 24
1
1000
800
600
400
200
0
10
3
30
50
70
Reelative Density, Dr (%)
(a)
Damping Ratio, D5 (%)
2
2000
1500
1000
500
50
75 100 125
1
150 175
5
Verticcal Effective Streess, σ′v (kPa)
1400
Constant-volume
1200
800
600
400
200
0
25
(a)
50
75 100 125
1
150 175
5
Verticcal Effective Streess, σ′v (kPa)
40
Test No.
35
9 & 11
10 & 12
13 & 15
14 & 16
25 & 27
26 & 28
29 & 31
30 & 32
30
25
20
15
10
5
Consstant-load
0
3
30
50
70
Reelative Density, Dr (%)
10
Test No.
35
30
25
20
15
10
5
Consstant-load
0
25
90
Test No.
Test No.
22
1&3
2&4
5&7
6&8
17 & 19
18 & 20
21 & 23
22 & 24
20
18
16
14
Constaant-volume
12
10
(b)
330
50
70
Reelative Density, Dr (%)
Figg. 10. Effect of relative densityy on (a) shear modulus, (b)
dam
mping ratio of constant-load
c
and
a constant-vvolume tests .
Paperr No. 1.11a
22
20
18
16
14
Constaant-volume
12
25
90
(b)
9 & 13
10 & 14
11 & 15
12 & 16
25 & 29
26 & 30
27 & 31
28 & 32
75 100 125
1
150 175
5
50
Vertical Effective Streess, σ′v (kPa)
24
24
Test No.
1&5
2&6
3&7
4&8
17 & 21
18 & 22
19 & 23
20 & 24
1000
90
40
Damping Ratio, D5 (%)
2
2500
25
Test No.
Constaant-volume
Test No.
9 & 13
10 & 14
11 & 15
12 & 16
25 & 29
26 & 30
27 & 31
28 & 32
3000
0
Damping Ratio, D5 (%)
Shear Modulus, G5 (kPa)
1
1400
Constant-load
3500
90
Shear Modulus, G5 (kPa)
330
50
70
Reelative Density, Dr (%)
Shear Modulus, G5 (kPa)
9 & 11
10 & 12
13 & 15
14 & 16
25 & 27
26 & 28
29 & 31
30 & 32
10
4
4000
Test No.
Constant-load
3
3500
Damping Ratio, D5 (%)
Shear Modulus, G5 (kPa)
4
4000
1&5
2&6
3&7
4&8
17 & 21
18 & 22
19 & 23
20 & 24
75 100 125
1
150 175
5
50
Verticcal Effective Streess, σ′v (kPa)
Fig. 11. Effect of veertical effectivee stress on (a) shear moduluss,
(b) damping
d
ratio of
o constant-loaad and constant-volume tests .
9
Basedd on the resultss of Fig. 13a, for
f example, a decrease in σ′v
from 150 to 50 kPa causes 55% and 60% deccrease in G2 off
consttant-volume annd constant-loaad tests; respecctively. G5 alsoo
decreeases by 45% and 65% on average
a
under the mentionedd
condiitions. Accordding to the results of Fiig. 13b, 40%
%
reducction in Dr (i.ee. 70 to 30%),, decreases dam
mping ratio off
consttant-volume annd constant-load
d tests at cyclee 2 by 11% andd
29% on average; reespectively. Also,
A
the averagge decrease inn
dampping ratio at cyycle 5 due to the
t reduction in
i Dr grows too
13% and 42%; respectively, for co
onstant-volumee and constant-n charts indicaated in Fig. 133
load tests. Thereforre, the column
b used to moderately
m
specify how much
m
a certainn
can be
param
meter affects shhear modulus and damping ratio
r
of similarr
materrials under diffferent loading conditions.
c
Of particular intereest was a com
mparison betw
ween constant-volum
me and constaant-load condiitions on test results. If thee
influeences of Dr, σ′v and γ on sheaar modulus andd damping ratioo
of teested sands under
u
constantt-volume and constant-loadd
condiitions were coompletely the same, the horiizontal axis inn
the coolumn charts of
o Fig. 13 woulld act like a miirror. Actually,
Dr, σ′v and γ have similar effectss on trends of shear moduluss
variattions under both
b
constant-volume and constant-loadd
condiitions, but the quantities are somewhat diffferent. Dr andd
σ′v allso affect dam
mping ratio in similar way with differentt
magnnitudes under both
b
conditions but, it seemss that dampingg
ratio is not affectedd by shear straiin amplitude under
u
constant-volum
me compared with
w constant-lo
oad condition.
Shear Modulus, G5 (kPa)
Test No.
Con
nstant-load
3500
9 & 10
11 & 12
13 & 14
15 & 16
25 & 26
27 & 28
29 & 30
31 & 32
3000
2
2500
2
2000
1500
1000
500
0
0.75
1.00
1.25
1.50
1.75
5
Shear Strain Amplittude, γ (%)
Shear Modulus, G5 (kPa)
1400
Constant-volume
1200
Test No.
1&2
3&4
5&6
7&8
17 & 18
19 & 20
21 & 22
23 & 24
1000
800
600
400
200
0
0.75
(a)
1.00
1.25
1.50
1.75
5
Sheear Strain Amplittude, γ (%)
40
Damping Ratio, D5 (%)
A staatistical study has
h done in ord
der to comparee the effects off
Dr, σ′
σ v and γ on shhear modulus and damping ratio of sandss
testedd in the currrent study under
u
constannt-volume andd
consttant-load condditions. Resultss are shown in
i the columnn
diagraams in Fig. 13. The average decrease in sheear modulus off
2nd, 5th and 10th cyccles due to thee decrease in Dr and σ′v andd
increaase in γ is show
wn in Fig. 13a. Results of connstant-load andd
consttant-volume tessts are pasted in
n the upper and lower half off
diagraam of Fig. 133a; respectivelly. The averagge decrease inn
dampping ratio becauuse of the incrrease in Dr andd σ′v as well ass
the deecrease in γ foor truly and eq
quivalently unddrained tests iss
also shown
s
in uppeer and lower half of Fig. 13bb; respectively,
for cyycles 2, 5 and 10.
1
4
4000
Test No.
35
9 & 10
11 & 12
13 & 14
15 & 16
25 & 26
27 & 28
29 & 30
31 & 32
30
25
20
15
10
5
Connstant-load
0
0.75
1.00
1.25
1.50
1.75
5
Sheear Strain Ampliitude, γ (%)
24
Damping Ratio, D5 (%)
Effecct of Shear Straain Amplitude.. The influencee of γ on shearr
moduulus and dampiing ratio of Bab
bolsar and Toyyoura sands aree
demoonstrated in Figg. 12. The varriations of sheaar modulus aree
in descending ordder with thee increase in shear strainn
olume and constant-loadd
ampliitude, under constant-vo
condiitions. With 0.5% increase in shear strainn amplitude, a
signifficant increase in damping raatio of saturateed samples cann
be seeen from the reesults of truly undrained tests in Fig. 12b.
Dampping doesn’t follow
f
a speciffic trend in coonstant-volumee
tests. In the other words,
w
damping
g ratio increasees slightly withh
the shhear strain ampplitude in som
me cases and thhe trend is vicee
versaa in the other cases.
c
It seemss that, shear sttrain amplitudee
has no
n important efffect on dampiing variation under
u
constant-volum
me condition.
Test No.
22
20
18
16
14
Constant-volume
12
0.75
(b)
1.00
1.25
1.50
1&2
3&4
5&6
7&8
17 & 18
19 & 20
21 & 22
23 & 24
1.75
5
Sheear Strain Amplittude, γ (%)
Fig. 12. Effect of shhear strain ampplitude on (a) shear
s
moduluss,
(b) damping
d
ratio of
o constant-loaad and constant-volume tests .
Paperr No. 1.11a
100
6
60
3
30
0
Decrease in Dr
Decreease in σ′v
Increase in γ
(70 to 30 %)
(150 to 50 kPa)
( to 1.5 %)
(1.0
3
30
6
60
(a) 90
9
Cycle 2
Cycle 5
Cycle 10
Connstant-volume
tests
Average Decrease in D by Percent
5
50
Coonstant-load
tests
4
40
3
30
2
20
1
10
0
Increase in Dr
0 %)
(70 to 30
Norm. Shear Modulus, G/Gmax
Coonstant-load
tests
Increease in σ′v
(150 to 50 kPa)
Decrease in γ
D
( to 1.5 %)
(1.0
1
10
4
40
(b) 50
5
Cycle 2
Cycle 5
Cycle 10
Data of shear moddulus and dam
mping ratio of Babolsar sandd
were compared wiith the corresp
ponding values for Toyouraa
dulus as well as
a lower valuess
sand. Higher valuess of shear mod
for damping
d
were observed for Babolsar sandd compared too
Toyoura sand durinng cyclic simplee shear tests peerformed in thee
currennt study. Acccording to thee results, sheaar modulus off
Toyoura sand is appproximately 30% less than Babolsar
B
sand.
Dampping ratio of Toyoura
T
sand iss also more thhan damping off
Babolsar sand by neearly 20% on average.
a
Figurre 14 compares the measured
d normalized shear moduluss
and damping
d
ratio in
i this study with
w the previoously publishedd
curvees of other invvestigators. Vaalues of Gmax were
w
estimatedd
on thee basis of Equaation 6 suggestted by Kokushoo 1980.
Paperr No. 1.11a
0.1
Constaant-Volume tests
Constaant-Load tests
1
10
0
Cyclic Sh
hear strain, γ (%)
σ m (kPa)
σ'
33.3
3
Hardin & Drnevicch (1972)
1
100
- -Seed
et al. (1986) - Range
- -3
33.3
g (1993)
Ishibashi & Zhang
1
100
2
24.5
Tatsuoka
et
al.
(19
978)
9
98.1
3
33.3
Constant-volume tests
t
1
100
3
33.3
Constant-load
test
ts
1
100
40
30
20
10
0
0.0001
0
0.001
0.01
0.1
1
Cyclic Sheear strain, γ (%)
(b)
Fig. 13. Effects off Dr, σ′v and γ on
n (a) shear moodulus and (b)
dam
mping ratio in constant-load and constant-vvolume tests.
s
Shearr modulus and damping ratio of two tested sands
33.3
100
33.3
100
50
Connstant-volume
tests
Basedd on the resultts of Fig. 13, it is revealed thhat, the effectss
of Dr, σ′v and γ on variations of shear moduluss and dampingg
ratio are more proonounced und
der constant-looad condition.
Somee of possible exxplanations for differences observed
o
underr
both conditions aree the differen
nt fabric of unnsaturated andd
saturaated testing samples, the capillary
c
effeccts in sampless
prepaared for constaant-volume tests and the reeal pore waterr
pressuure developed under con
nstant-load coondition. Thee
mentiioned reasons were
w discussed
d previously in detail.
σ'm (kPa)
33.3
Hardin
n & Drnevich (1972)
100
--Seed et
e al. (1986) - Range
--33.3
Ishiba shi & Zhang (1993)
100
0.01
2
20
3
30
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
(a)
Damping Ratio, D (%)
Average Decrease in G by Percent
9
90
Figg. 14. Compariison of measurred (a) G/Gmax-γ
- and (b) D-γ
witth the previoussly published cuurves of other investigators.
i
G
8400 2.17
7
e
σ
.
⁄ 1
e
kPa
(66)
wherre σ′m and e arre mean princiipal effective stress and voidd
ratio;; respectively. As shown in Fig. 14a, data obtainedd
throuugh cyclic simp
mple shear testss follow the cuurves of Hardinn
and Drnevich
D
19722b as well as thhe lower boundd of Seed et all.
19866 for sands. Comparison
C
off damping ratiio measured inn
consttant-volume and
a
constant-looad tests withh the proposedd
curvees by other ressearchers in Fiig. 14b revealss that, althoughh
theree is not a goodd agreement between
b
data obtained
o
in thiis
studyy, but the diffferences betweeen reported cuurves of otherrs
for damping
d
ratio of sand at largge shear strainn amplitude are
also tremendous.
t
H
However,
somee of damping values measuredd
in thee current studyy fall between the
t lower bounnd of Seed et all.
19866 and curve off Tatsuoka et al.
a 1978 for a mean principaal
effecctive stress equuals to 24.5 kPaa.
NCLUSIONS
CON
GI cyclic simple shear apparatus was instruumented with a
A SG
presssure test deviice in order to
t modify thee conventionaal
devicce, so it can bee used in conduucting tests onn fully saturatedd
speciimens. This meethod of saturaation yields relliable results byy
perfoorming real unndrained tests. Testing prograam included 322
consttant-volume annd constant-loaad tests on parrtially and fullyy
saturrated specimenns; respectivelyy, under differrent conditionss.
11
The following can be drawn on the basis of the current
experimental study.
Ishihara K. [1996]. “Soil Behavior in Earthquake
Geotechnics”. Oxford University Press, Great Britain.
An increase in Dr and σ′v as well as a decrease in γ, result in a
growth in shear modulus along with a reduction in damping
ratio under constant-load condition. These parameters have
similar effects on shear modulus and damping ratio under
constant-volume condition except the shear strain amplitude
which has no significant effect on damping ratio. Trends of
shear modulus variations with the number of cycles are in
descending order under both conditions. Damping didn’t
widely vary with the number of cycles until 10 cycles to Nl
under constant-load condition and afterward a significant
growth in damping values were observed. Conversely,
damping ratio of constant-volume tests decreases with the
number of cycles and the trend is complicated to be judged.
Jafarzadeh, F., and H. Sadeghi [2009], “Effect of Water
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Comparisons between the results of constant-volume and
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under constant-load condition. It is found that some
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Second, capillary forces affect the response of constantvolume test samples during the whole cyclic stage whereas
such effects do not exist in saturated specimens. So, it would
appear that observed differences between the results of
constant-volume and constant-load tests may be because of the
different fabric produced in saturated and unsaturated samples
rather than of the vertical load controlling mode. However,
further work is needed to compare the results of constantvolume tests on completely dry and saturated sand with
constant-load test results on saturated sand.
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Paper No. 1.11a
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