Natural Frequency of a Horizontal Soil Layer
Part II: Saturated Sand Bed
S.P.G. Madabhushi
CUED/IbSOILS/TR273
(1994)
Synopsis
The dynamic response of a saturated, horizontal soil layer is investigated by conducting
two centrifuge tests. The depth of the sand bed in each of these centrifuge tests was
arranged such that the small strain natural frequency of the sand bed was very high
compared to the driving frequency of the earthquake. When the correct natural
frequency of the sand bed was estimated using the shear modulus corrected for shear
strain amplitude induced by the earthquake loading and taking into account the
reduced effective stresses within the sand bed following the generation of excess pore
pressures, the natural frequencies of the sand beds were much lower and close to the
driving frequency of the earthquakes.
In the first centrifuge test a strong earthquake was fired first followed by a smaller
second earthquake. All the subsequent earthquakes had increasing intensity. Smaller
excess pore pressures were generated during the smaller second earthquake and all
other earthquakes resulted in large excess pore pressures. Also during the second
earthquake the attenuation of base shaking was small as it travelled towards the sand
surface. Calculation of the natural frequency of the sand bed during earthquake 2 has
shown that it is indeed close to the driving frequency of the earthquake there by
resulting in the smallest attenuation. In all other earthquakes the driving frequency was
far from the natural frequency causing significant attenuation of base shaking as it
travelled towards the sand surface. Also the data suggested that the rate of excess pore
pressure build up is a function of the strength of the earthquake.
In the second centrifuge test all the earthquakes had increasing intensity. Also all the
earthquakes resulted in more or less the same magnitude of excess pore pressures
within the sand bed. During the second earthquake the attenuation of base shaking was
small as it travelled towards the sand surface. Calculation of the natural frequency of
the sand bed during earthquake 2 has shown that it is indeed close to the driving
frequency of the earthquake there by resulting in the smallest attenuation. In the first
earthquake it was shown that the natural frequency is far above the driving frequency
and in all other earthquakes the driving frequency was far below the natural frequency
causing significant attenuation of base shaking as it travelled towards the sand surface.
As in the previous centrifuge test the data suggested that the rate of excess pore
pressure build up is a function of the strength of the earthquake.
Natural Frequency of a Horizontal Soil Layer
Part II: Saturated Sand Bed
1.0 Introduction
The present series of centrifuge experiments consider the dynamic response of a
horizontal sand bed subjected to earthquake loading. In the first series of experiments
we have considered the dynamic behaviour of a dry sand bed and analysed the data in
terms of amplification of accelerations within the sand bed at different heights and at
different frequencies, Madabhushi (1994).
However some of the major concerns regarding a saturated sand bed during an
earthquake are the phenomena associated with liquefaction. During the recent
Northridge earthquake in the Los Angeles area there were extensive sand boils
observed on the upstream side of the old lower San Fernando dam. This dam is not in
service following the 1971 earthquake which inflicted severe damage to this dam, Seed
et al (1975). Also sand boils were observed following the Northridge earthquake along
the Pacific coast and a severe liquefaction induced failure of quay wall at the Ring
Harbour in the Redando beach area of Los Angeles. In this report the dynamic
response of saturated sand beds in the presence of excess pore pressures induced by
earthquake loading will be studied
The dynamic response of a horizontal sand bed will depend on
i) the stiffness of soil ;
ii) the material damping in the soil.
The stiffness of a soil element depends on the void ratio and confining pressure to
which it is subjected. In the case of a saturated sand bed it also depends on the excess
pore pressure generated during the earthquake. For a given soil layer we can find the
average confining stress at the mid depth of the soil layer and estimate the small strain
shear modulus of soil. Based on this we can calculate the shear wave velocity in the
1
soil and hence the natural frequency of the soil layer. The dynamic response in the case
of saturated sand bed depends strongly on the magnitude of the excess pore pressures
generated during the earthquake. The material damping in the soil will have two
components namely
i) hystertic damping in the soil skeleton ;
ii) viscous damping in the pore fluid.
The effects of material damping on the soil have been discussed elsewhere (Bolton and
Wilson, 1992 and Madabhushi, 1994) and will not be considered in this report. The
main aim of this report will be to compare dynamic response of the saturated sand bed
based on the data from the present series of experiments with the dynamic response of
the dry sand bed presented in the earlier report, Madabhushi (1994).
In the present report the data from the centrifuge tests on horizontal sand bed which is
completely saturated and subjected to model earthquakes will be presented. In the next
two sections the stiffness of the saturated soil bed and the generation of excess pore
pressures during the earthquake loading will be explained. Following this the
centrifuge modelling technique and model preparation methods will be explained.
Finally the data from the centrifuge tests and the analysis of the data will be presented.
Conclusions based on the analyses of the present series of centrifuge test data and
future research planned will be presented in the end.
2.0 Excess Pore Pressures
On shearing a soil element exhibits two distinct types of behaviour depending upon its
initial relative density. A dense soil deposit experiences dilation on shearing while a
loose soil deposit undergoes densifrcation. In Fig.1 these two distinct behaviours are
presented schematically under drained conditions.
During an earthquake loading the soil element is subjected to cyclic shear stresses as
the stress waves propagate from the bed rock towards the surface of the soil layer. In
the case of a loose saturated sand bed these cyclic shear stresses will induce a tendency
2
of ‘densification’ as shown in Fig.1. However unlike the static loading, during a
dynamic loading event like an earthquake there is no time for drainage of the pore fluid
from the soil layer. Hence the tendency for densification is manifested as a rise in the
pore pressure. We term this as an excess pore pressure which is over and above the
0
LOOSE
.
AXIAL STRAIN
AXIAL STRAIN
7
Fig. 1 Loose and dense sand behaviour under drained conditions
normal hydrostatic pore pressure. The effective stress within the soil layer under these
conditions may be expressed as
With the generation of excess pore pressures the effective stress is reduced. This in
turn will cause a degradation in the soil stiffness. The dynamic response of the sand
layer will reflect the degradation in soil stiffness.
3.0 Stiffness of the soil layer
Consider a horizontal saturated sand bed as shown in Fig.2. Let the depth of the soil
layer be ‘z’. The effective vertical stress at any depth of this saturated soil layer may be
obtained as
3
b
4.0 Natural frequency
The natural frequency of the dry soil bed may be obtained in terms of the shear wave
velocity in the soil. If ‘Vs’ is the shear wave velocity in soil then the natural frequency
may be obtained as
(n + $Vs
a, =
. . . . . . . (6)
h
where an is the natural frequency in the n* mode. In the case of a saturated sand bed
the shear wave velocity V, depends on the shear modulus and the saturated density of
soil (7). In general we can write
v, = Y......(7)
$
Using Eqs. 2 to 7 the small strain natural frequency of a soil layer can be estimated.
However this calculation will change when the earthquake loading induces significant
shear strains in the soil.
5.0 Shear strains
The shear strain amplitude may be large in a strong earthquake. The shear modulus in
such a case will be only a fraction of the small strain shear modulus. Hardin and
Drnevich (1972) suggested a hyperbolic variation of shear modulus with shear strain.
Using this variation the tangent modulus (Gt) at any shear strain amplitude (7) is
obtained as
G, = Gmax
where yr is the reference shear strain given by
Zmax
Yr = - . . . . . . . . . . (9)
G max
5
I
The maximum shear stress can be obtained from the Mohr circle of stresses as
where Cp is the angle of internal friction. The shear stress z induced in a soil element at
my depth
‘z’ due to the earthquake loading is calculated as
z = mysz . . . . . . . . . . (11)
where Kh is the horizontal acceleration due to earthquake loading. The shear strain y is
obtained as
y=
Knowing
=
. . . . . . . . . . (12)
GmZt+
r
y and yr and using Eq.8 the tangent modulus of soil is calculated. Using
Eq.6 the natural frequency of the soil is obtained.
6.0 Sand beds in centrifuge tests
As explained in earlier section a centrifuge model with a horizontal sand bed is
constructed to have its natural frequency close to one of the driving frequencies of the
earthquake. Centrifuge tests MG-4 and MG-5 were carried out on two such horizontal
sand beds. In this section the calculation of the sand bed depths which have a resonant
frequency at one of the driving frequencies observed in earlier section will be
explained.
In the first centrifuge test MG-4 the sand bed was to have a depth of 155.0 mm. The
dry density of the sand bed was 1208.21 kg/m3 and the void ratio was 1.19. The
saturated density of the soil layer is calculated to be 1752.31 kg/m3. Using Eqs.l to 6
the small strain natural frequency of this soil layer was estimated as 233.7 HZ.
Assuming a 21 % earthquake and using Eqs. 7 to 11 the natural frequency of the soil
layer during this earthquake is estimated as 105.3 Hz. In this calculation no excess
pore pressures were taken into consideration. As explained earlier the
6
generation
of
excess pore pressures will lead to a degradation in soil stiffness and the natural
frequency calculated above will be even lower in such an event.
In the second centrifuge test MG-5 the sand bed was to have a depth of 100.0 mm.
The dry density of the sand bed was 1315.3 kg/m3 and the void ratio was 1.015. The
saturated density of the soil layer was calculated to be 1818.9 kg/m3. Using Eqs.2 to 7
the small strain natural frequency of this soil layer was estimated as 43 1.5 Hz.
Assuming a 22 % earthquake and using Eqs. 8 to 12 the natural frequency of the soil
layer during this earthquake is estimated as 278.0 Hz. Again in this calculation no
excess pore pressures were taken into consideration. As explained in the previous
sections the generation of excess pore pressure will lead to a degradation in the soil
stiffness and the natural frequency will be even lower in such an event.
7.0 Sand
For the centrifuge tests reported here Leighton Buzzard 100/170 sand was used. This
type of sand has been extensively used in the triaxial and centrifuge tests and is
available commercially. The maximum and minimum void ratio’s of this soil are 1.318
and 0.475 respectively.
8.0 Instrumentation
8.1 Accelerometers
Jn the centrifuge tests reported here miniature piezoelectric accelerometers
manufactured by D.J. Birchall were used to measure acceleration in the soil, on the
model container during earthquakes. The device has a resonant frequency of about 50
kHz and a maximum error of 5%. The weight of the transducer is about 5 grams. Fig.
3. shows the dimensions of the transducer. For tests on saturated soil accelerometers
were sealed with silicone rubber.
7
8.2 Pore Pressure Transducers
Pore pressures in the saturated soil were monitored by Druck PDCR 81 pore pressure
transducers. This type of pore pressure transducers have a linear range up to 300 kPa
and weigh about 10 grams. The corner frequency of the dynamic response of the
transducer is 15 kHz. The maximum error is 0.2 %. In the centrifuge tests reported
here, the active diaphragm of the PPT is covered with a porous brass stone. The
dimensions of the PPT are presented in Fig.4.
All the pore pressure transducers were calibrated by applying standard water
pressures on the active diaphragm. The output generated by the device was measured
using a digital voltmeter and calibration constant was obtained in the units of ‘kPa/mV’.
9.0 Model Preparation
The sand in the model was poured into the package through a hopper system in the
model preparation room at the Cambridge Geotechnical Centrifuge Centre. The void
ratio of the sand in the model was controlled by the height and the flow rate of sand
pouring, of which trial tests were performed in advance. At the appropriate places the
transducers were put into the sand. After the required height of sand layer had been
achieved the surface of sand was levelled by a modified vacuum cleaner. The void ratio
and density of the model were estimated and the natural frequency of the soil layer was
calculated using Eqs.2 to 12.
After the final profile of the horizontal sand bed was achieved the model was vacuum
levelled. The strong box is then covered with a lid and is subjected to a vacuum
pressure of -30 cm of Mercury. After evacuating the model under this pressure for
about 1 hour the blended silicone oil with a viscosity of 50 centistokes is admitted at
the base of the embankment and the saturation is carried out very slowly until the level
of silicone oil coincided with the crest of the embankment. Care was exercised to see
that the silicone oil level on both the slopes of the embankment are the same through
8
.
.
unit: mm
mass: 0.005 kg
Fia 3 Typical dimensions of an accelerometer
0.60
0.25
c
.
.
f-+ 5.8
11.4
.* -
Tulbn tuba
outsiclo
dia 2.3
7
T’ *I
B
/
-‘Filter
krmmic)
, Idl,,r:4l CU~IIW~lIUI~ /
Rod
Supply Poritivr
ho SUP~Y nrwiw
Yolbw Output poiitivr
Green Output rwgatk0
unit: mm
mass: 0.004kg
Fig.4 Typical dimensions of a pore pressure transducer
i” = ylz....(2)
4
b
Bed rock
Base shaking
Fig.2. Saturated sand bed of depth ‘z’
In the centrifuge model of this soil layer the depth of the soil bed is reduced by the
gravity scale factor (n) but the stresses and strains at homologous points will be the
same. Let us assume the height of the soil layer in the centrifuge model be ‘h’ such that
h = Z/n. The effective vertical stress at any depth in the centrifuge model is calculated
as
dv = jhng.....(3)
The confining pressure (O’m) at any depth is obtained as
t
0, =
(l+ 2Ko) ’
(4)
3
cb----
where I& is the coefficient of the earth pressure at rest. Assuming a value for K. we
can calculate the confining pressure in terms of the effective stress. The small strain
shear modulus G,, may be calculated following Hardin and Drnevich (1972) as
Gmax= l~~{&Jo5 . . . . . . . . . . (5)
U+el
where B’m and G,, are in Mpa and ‘e’ is the void ratio of the soil.
4
out the saturation process. The whole process of saturation took about 10 hours for
each model.
10.0 Test Procedure
After the saturation was completed the centrifuge model was transported very carefully
on to the centrifuge arm. Immediately after the loading procedure was complete the
strong box was fixed using wooden wedges to make the centrifuge model level. Pre
flight checks were completed at this stage. Just before starting up the centrifuge motor,
the strong box was released to hang freely at the end of the arm.
The centrifuge acceleration was increased in steps of 2Og, 40g and 5Og. At each
stage the pore pressures within the model were monitored using a DVM. After the
testing acceleration of 5Og was achieved at the centroid of the model the steady
acceleration was maintained for 20 minutes before any earthquake was fired. The pore
pressures were monitored again after the 20 minutes. An earthquake was fired and the
data was plotted. The strength of the subsequent earthquakes was gradually increased.
When the test was finished the centrifuge was showed down and stopped. The model
was recovered from the pit carefully and the post test profile of the horizontal sand bed
was measured.
11.0 Data Acquisition
Data from the instruments in the centrifuge model was acquired using two systems. A
14 Channel Racal tape recorder was used to record data by running the tape recorder
at high speed. Subsequent digitisation was carried out by playing back the tape at a
slower speed. This enables to capture more than 1000 data points per channel during
the 100 ms earthquake event. Also a direct data acquisition system which uses high
speed A/D converter card working under Global Lab data acquisition system was used
to acquire 16 channels of data directly on to the PC in real time. Data are plotted out
0
-.
g
-50
.
.
I
I
-100
0
500
1000
t500
Fig.5 Filter Characteristics
I
2000
2500
channel by channel and also recorded in the accompanying diskettes. Photographs
were taken during the model preparation, before and after each centrifuge test. A
standard low pass Bessel filter was used to smooth the data and reduce the high
frequency electrical noise. The filter characteristics are presented in Fig.5
All the acceleration time histories recorded during the present series of centrifuge tests
are expressed as a percentage of the centrifuge acceleration. For example, the peak
acceleration of 25 % means that the magnitude of the peak acceleration is
25/100x50x9.81 = 122.6 m/s2 in a ‘5Og’ centrifuge test.
12.0 Centrifuge test MG-4
As explained in Sec.6 the depth of the sand bed for this centrifuge test was 155.0 mm.
The construction of the centrifuge model was in three stages and at the end each stage
the void ratio and dry density of sand bed were estimated. The natural frequency of the
soil was computed using Eqs.1 to 12. The final depth of sand bed required so that its
natural frequency is close to the driving frequency of the model earthquake was
determined after each stage. The schematic diagram showing the section of the model
and placement of the instruments during this centrifuge test is presented in Fig.6. In
table 1 the exact location of each transducer during this experiment is presented. A
total of five earthquakes were fired on this centrifuge model at 5Og. The data from
these earthquakes is presented in Figs.7 to 26. The salient features of the data are
presented here while a detailed analysis of the data is presented in next section.
AS explained in Sec. 11 two data acquisition systems were used during this centrifuge
test. Important transducers were logged on both these systems so that reliable
measurements can be made. Earthquake 1 had a strength of about 25 %. In Figs.7 and
8 the data from all the instruments acquired using the Racal tape recorder are
presented, In Figs.9 and 10 the data obtained directly using Global Lab data acquisition
system are presented. Considering the three accelerometers 1926, 3477 and 3441 (see
10
Fig.6) which are placed along the vertical column in the middle of the sand bed we can
see that there is significant attenuation of peak acceleration from 21.8 % at the base of
the sand column to about 9 % at the surface of the sand bed. Note that ACC 1926
was not recorded on the Racal tape recorder due to a fault on this channel but was
recorded by the Global Lab acquisition system (see Figs.6 and 9). Traces recorded by
ACC 3477 and 3441 in Fig.6 show a clear attenuation of peak accelerations after first
few cycles. This event coincides with the rise of excess pore pressures indicated by
PPT’s 6260 and 6270 as seen in Figs.7 and 8. The vertical accelerometers 1572, 1925
and 5756 in Fig.9 are clearly picking up the horizontal accelerations suggesting that
they have changed their orientation following the rise of excess pore pressures. ACC
3492 did not function during this test. In general both the accelerometers and pore
pressure transducers placed along the same horizontal plane recorded very similar
accelerations and excess pore pressures confirming the uniformity of the centrifuge
model.
A small earthquake which produced a peak acceleration of 9.1 % was fired next. The
data from this earthquake are presented in Figs. 11 to 14. The magnitude of the excess
pore pressures generated during this earthquake was much smaller compared to
earthquake 1. This can be observed by comparing PPT’s 6514, 6260 and 6270 in
Figs.1 1 and 12 with corresponding traces obtained during earthquake 1. The
accelerometers 1926, 3477 and 3441 along the vertical column in the middle of the
sand bed show only a small attenuation of peak acceleration. In particular ACC 3441
near the surface of the sand bed registers all the cycles of base motion unlike in
earthquake 1. This is consistent with the smaller excess pore pressures generated
during this earthquake. There was a fault on the amplifier circuit connected to
accelerometer 3477. Also the Racal tape recorder channel connected to PPT 6270 was
faulty after earthquake 2. The correct excess pore pressures experienced by this
transducer was recorded by the Global Lab acquisition system as seen in Fig.14 This
was the case during all of the subsequent earthquakes.
11
Earthquake 3 had a strength of 14.7 %. The data from this earthquake are presented in
Figs. 15 to 18. It is interesting to note that the magnitude of excess pore pressures
generated during this earthquake are almost equal to those generated during
earthquake 1. However the accelerometer 3441 near the sand surface registers all the
cycles of base motion (see Fig. 15). Again accelerometer 3477 was faulty and remained
so during the rest of the earthquakes.
Earthquake 4 had a strength of 22.9 %. The data from this earthquake are presented in
Figs. 19 to 22. The excess pore pressures during this earthquake were almost the same
as in the previous earthquake as seen in Figs. 19 and 20. It is interesting to see the
acceleration time history recorded by ACC 3441 near the soil surface in Fig.19. After
four cycles the accelerometer registers very small accelerations suggesting that the
sand in this region has liquefied
A much stronger earthquake which produced a peak acceleration of about 30 % was
fired next. The data from this earthquake are presented in Figs.23 to 26. The
magnitude of excess pore pressures generated during this earthquake was almost the
same as in the previous two earthquakes. However accelerometer 3441 shows signs of
liquefaction after first 11/2 cycles. It does recover partially towards the end of the
earthquake when the base shaking has a lower intensity.
In the next section a more detailed analysis of the data from this centrifuge test is
presented.
155 mm
I
II
1900
3436
Fig. 6: Schematic diagram showing the placement of transducers in
Centrifuge Test MG-4
Table 1 Placement of transducers in centrifuge test MG-4
Transducer
ACC 1225
A C C 1926
A C C 1572
A C C 3492
A C C 5754
A C C 3477
A C C 3466
ACC 1925
A C C 5701
A C C 3441
A C C 1258
A C C 5756
A C C 3436
A C C 1900
PFT 3007
P P T 6514
P P T 4478
P P T 2926
P P T 6260
P P T 6784
P P T 6803
P P T 6270
P P T 3969
x (mm)
55
282
360
470
50
263
460
345
56
275
465
355
fixed to the container
fixed to the container
120
281
475
58
265
458
75
320
440
Y
(mm)
5
5
5
5
80
82
79
80
135
137
133
131
3
3
3
78
80
76
136
135
133
y :~~
.: .:.:..:..:.:.::.A: ::.:~.~.~...:..~..~.:.:.:.:.:.:.: : :_,~.,.,.,.
T
X
Table 2 Hydrostatic pore pressures in centrifuge
test MG-4
1OG
11.95
7.73
6.68
12.40
0.81
4.20
12.51
7.89
5.28
206
25.75
16.45
14.72
26.51
1.70
9.31
27.21
17.32
11.67
406
53.71
34.19
31.13
54.84
149.66
19.75
56.02
35.85
24.28
506
68.18
43.30
39.64
69.55
4.44
25.19
70.80
45.28
30.73
Table 3 Norma&d accelerations in the sand column
in centrifuge test MG-4
Location
Normalised Acceleration
At base of the sand column
At the mid depth
Near the surface of sand bed
1
0.5
0.4128
At base of the sand column
At the mid depth
Near the surface of sand bed
1
1.0106
EQ: 1
EQ: 2
0.8404
EQ: 3
At base of the sand column
At the mid depth
Near the surface of sand bed
1
-0.752
EQ: 4
At base of the sand column
At the mid depth
Near the surface of sand bed
1
--
0.3247
EQ: 5
At base of the sand column
At the mid depth
Near the surface of sand bed
1
-0.2895
Max=25.3
Mb=-26.4
Max=O.l
Mill=-0.2
Max=lO.S
Mln=-12.3
Mox=S.O
ACC344
Mill=-9.4
Max=24.9
Mln=-33.6
Maw=11.6
Mill=-10.0
Max=11.4
ACC570 1
Min=-12.4
Max=64.7
PPT65
Mln=-4.0
w
t--=1
Max=34.5
PPT6260
Mln=-1.3
I
TEST MG-4 1
M O D E L S A T 1EQ-’
FLIGHT
-1
i
I
Scales : Model
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
7
1
1267
da/b
points plotted per complete transducer record
20
ACC3436
Max=26.2
0 E
-20
Mb=-25.5
.20
Max=22.5
[msec]
/
1
PPT6270
P
2
. 10,
Mln=-1.1
110
120
130
140
150
1w
170
180
190
200
210
[msec]
.75
Mox=73.2
.50z
PPT3007
.25-
Mill=-3.6
.O
20
so
40
50
60
‘Jo
80
a0
loo
110
120
Iso
140
150
160
170
180
190
200
210
[msec]
2
Max=2.4
B
0 2
PPT2976
Mln=-2.0
-2
[msec]
.20
Mlnc=20.5
.lO 7
-0
E
PPT6803
.O
.
20
.‘.
30
40
50
fi
1~7.0
6iJ
so
loo
1;o
I
1;o
130
140
1w
160
170
190
160
200
hiin=-4.2
210
[msec]
I
.40
PPT4478
Mex=38.6
.206
z.,
.O
20
JO
40
M
60
170
00
so
loo
110
120
130
140
150
150
170
160
190
2w
Ml=-7.4
210
[msec]
Scales : Model
TEST MG-4 ~
M O D E L S A T ~ EQ-1
FLIGHT -1 I
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
8
901
da$
poirits plotted per complete transducer record
Mox=24.6
Min=-27.4
Max=ll.J
ACC 1900
0%
Mh=-6.6
Max=17.0
ACC 1572
Mln=-13.8
Mox=lS.l
(0
.I z
ACC1925
.4
Min=-4.4
Max=7.6
Mln=-6.1
h-1
. II
Min=-1.0
Max=15.6
ACC3466
ACC1258
Min=-13.6
Max=21.6
ACC1926
Scales : Model
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
9
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC3477
PPT65 14
Mln=-3.4
Max=27.7
PPT6270
b-1
Mox=44.6
PPT4478
PPT6784
Max=26
PPT3969
Min=-2.8
Scales : Model
TEST MG-4
MODEL SAT
FLIGHT
-1
i
EQ-1 ~
:
~
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
10
Min=-6.9
ACC344
Min=-10.3
Min=-6.6
Min=-9.8
Max=7.4
Min=-9.3
Mox=25.9
Mln=-2.2
Max=26.6
PPi6260
toMln=-0.8
I
TEST MG-4 ~
EQ-2
MODEL SAT
FLIGHT -1 ~
Scales : Model
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
11
1267 dab
points plotted per complete transducer record
10
M0x=8.7
ACC3436
0
20
30
40
60
60
70
60
90
loo
110
120
130
140
160
E
Mill=-9.4
-10
160
170
160
160
200
210
[msec]
.20
PPT6270
Max=21.5
7
log
Mln=-0.7
M
30
40
60
60
70
60
60
la,
110
120
130
140
160
160
170
160
1‘90
ZOO
at0
[msac]
I
1
Max=X.O
.20
PPT3007
F
-lo&
Mln=-2.2
.O
20
so
a0
too
li0
1;o
lil
140
Go
rso
1;o
GO
190
2iJO
2io
[msec]
1
-3
Max=2.7
.2
PPT?976
.lj
.O
20
30
40
60
60
70
60
90
loo
110
120
130
140
150
160
170
160
160
200
Min=-0.7
210
[msec]
I
.20
PPT6803
Mox=19.7
P
2
10
Min=-1.1
;O
20
30
40
60
60
70
60
90
100
110
120
130
140
150
160
170
160
190
200
210
[msec]
Max=2.3
2
-2
12
PPT4478
0
20
30
40
60
60
170
60
90
loo
110
120
130
140
160
160
170
160
190
200
WI=-0.4
210
[msec]
Scales : Model
I
.TEST M G - 4 I
M O D E L S A T ~E@-2
FLIGHT -1 1
I
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
12
ACC3436
Min=-4.6
ACC 1900
Yin=-4.5
ACC1572
ACC1925
Min=-6.5
Max=6.0
ACC5756
Mln=-6.6
Mox=O.6
ACC3492
Min=-0.4
ACC3466
Win=-12.5
ACC 1258
ACC1926
Min=-6.9
Scales : Prototype
TEST MG-4
MODEL SAT
FLIGHT
-1
EQ-2
:
~1
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
13
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC3477
Mox=25.4
PPT6260
Uln=-2.7
PPT6270
Uin=-3.0
PPT4478
Win=+.2
Yax=25.0
PPT6784
Min=-5.6
bhx=16.6
PPT3969
Min=-1.3
Scales : Prototype
TEST MG-4
MODEL SAT
FLIGHT -1
EQ-2
1
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
14
1267 da.10
paints plotted per complete transducer record
Mox=14.7
10
ACC3436
.o E
.-IO
20
30
40
SD
03
70
a0
w
rm
110
ml
IJO
Ma
co
100
170
Ito
IW
ml
bun=-14.5
110
[m-cl
. to
ACC 1926
Mox=lZS
OE
.-10
20
30
40
60
90
70
.v
so
ton
(10
VW
1.w
Mu
150
I(10
vm
100
Ino
¶m
Mill=-14.5
*10
[m-l
1
- ‘0
Mox=6.9
.D
ACC3477
E
Mln=-3.7
lo
30
40
0
co
70
no
w
tm
,,o
110
,m
140
180
110
110
110
1w
100
ato
b-1
Max=9.4
ACC344 1
E
.-(0
20
30
40
so
60
70
M
w
,m
110
m
IS
MO
Iso
$10
no
100
190
!2m
Mill=-14.6
no
[m-l
Mox=14.2
O E
.-to
ACC1225 -
10
30
40
$4
10
40
M
*I
wo
110
tm
h=l
Iso
wo
Ino
100
170
IW
190
m
!a0
.-20
ml=-16.2
Max=11.4
ACC5754 .-ID
20
SD
40
w
m
70
00
so
100
$10
1m
1.x
‘da
ts
MO
170
llyl
Iso
no
Min=-11.3
so
[m-cl
.o
.P E
.-0
ACC570 1
.
20
Jo
40
m
m
ny
u)
00
tm
..
,,o
..
,m
[mms]
.
,a0
140
‘so
IW
(70
I-
Iso
IOD
Max=9.4
Min=-6.7
ato
Max=BO.l
.402
.m-
PPT6514
Ml=-3.0
b-1
Max=35.6
PPT6260
ml=-0.6
20
20
90
40
[m=cl
Scales : Model
/
TEST MG-4
MODEL SAT
FLIGHT -1
wo
EQ-3
I
.._
SHORT TERM
TIME RECORDS
G Level
5 0 -
FIG.NO.
15
'
1267
da o points plotted per complete transducer record
10
ACC3436
0
Mox=14.2
z
-10
I
20
Mill=-14.s
I
30
40
50
w
170
so
90
,oo
110
120
130
140
150
180
170
110
1w
200
210
[msec]
20
PPT6270
Max=21.6
7
lo&
20
M
40
50
so
70
so
90
loo
110
120
130
140
150
160
170
160
190
Ml=-0.7
0
200
210
[msec]
Mw=59.6
PPT3007
.20Mln=-3.2
20
30
40
50
60
70
60
90
100
110
120
130
140
(50
160
170
160
190
200
210
[msec]
I
Max=3.4
2F-0
PPT2976
L
'O
20
20
30
40
Jo
30
40
50
120
1.30
140
IM
lso
170
160
190
200
Mln=-0.7
210
PPT6803
Min=-0.5
so
irn
60
90
0
loo
110
120
(30
140
150
160
170
160
190
zoo
2to
[msac]
20
Max=20.7
PPT4476
I
[msec]
Scales : Model
TEST
MG-4
’ :
EQ-3
MODEL SAT
FLIGHT
-1
;
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
16
901
ddha
points plotted per complete transducer record
ACC3436
Min=-15.2
ACC1900
“Z
r-s
ACC1572
ACC1925
Min=-3.5
Uin=-0.5
ACC3466
Yox=12.4
ACC1926
Min=-13.7
b-1
Scales : Prototype
TEST MG-4
MODEL SAT
FLIGHT
-1
EQ-3
,
1I
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
17
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC3477
h4
5.x
PPT6514
Min=-3.6
PPT6260
PPT6270
PPT4478
Mox=39.4
PPT6784
Mln=-7.8
Max=23.2
PPT3969
Minz-1.6
Scales : Model
TEST MG-4
MODEL SAT
FLIGHT -1
EQ-3,
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
18
1267
dot9
points
plotted
per
complete
transducer
record
I
Max=59.2
.aa
.20=
PPT65 14
Mill=-3.1
40
Mox=39.2
‘ii
,mz
PPT6260
ml=-0.7
&
10
Jo
,20
4a
h=l
/
TEST MG-4
MODEL SAT
FLIGHT - 1
‘70
I
I
1 :
1’
Scales : Model
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
19
126? doti points plotted per complete transducer record
ACC3436
0
20
30
40
50
60
70
60
90
loo
110
120
130
140
150
160
170
160
190
200
E
-20
Mln=-23.0
.20
Llox=21.4
210
[msac]
PPT6270
'7
. tog
Mln=-0.9
.O
20
30
40
50
60
m
80
90
100
110
120
130
140
150
16u
170
160
190
2w
210
[msec]
/
Mox=66.0
64
PPT3007
40%
.5
20
Mill=-3.7
0
20
30
40
120
50
130
140
154
160
170
164l
190
200
210
[msec]
4
PPT2976
M.xG4.3
2T
s
0
20
30
Ml
54
0'70
60
60
loo
110
120
130
140
150
160
170
160
190
200
Mill=-0.8
210
[mow]
.20
Mex=19.9
PPT6803
20
30
60
50
60
I,70
80
90
iw
110
120
150
140
15n
150
170
160
190
200
210
[msac]
I
Max=31.5
.20 B
2,
PPT4478
.O
20
30
40
50
60
70
60
90
loo
110
120
130
140
190
2w
Min=-6.1
210
[msec]
Scales : Model
I
TEST
MG-4
I ’
M O D E L S A T ! E@-4 1
FLIGHT
-1
; !
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
20
901 data points plotted per complete transducer record
,
Uox=23.0
ACC3436
-
thx=10.2
Min=-10.6
Mox=2l.6
.pD
,z
ACC1572
Yin=-14.9
Mox=14.6
(0
ACCl925
z
Mb=-4.6
Max=6.2
.e
z
.-n
ACC5756
Yin=-10.4
Mox=O.6
-0
ACC3492
.-0.6
B
Win=-0.9
Max=l7.6
uin=-21.6
uox=17.7
MIn=-17.1
I
h
A
A
P
Yox=22.6
ACC
Mln=-26.4
901
data
points
plotted
per
complete
transducer
record
ACC3436
Max=6.6
ACC3477
Max=61.9
PPT65 14
Min=-4.2
Min=-2.6
Max=37.2
PPT6270
PPT4478
Mb=-6.7
Mox=42.6
PPT6784
Mb=-5.6
Max=27.9
PPT3969
hiin=-1.5
Scales : Model
TEST MG-4
MODEL SAT
FLIGHT -1
EQ-4
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
22
1267
data
points
plotted
per
complete
transducer
record
ACC344
Min=-11.0
Min=-17.4
Max=28.0
Min=-20.8
Max=59.6
PPT65
MI=-2.8
PPT6260
Scales : Model
‘1
TEST
MG-4
I
:
M O D E L S A T i EQ-5
FLIGHT
-1
1
/
I
iI
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
23
1267 data’ points plotted per complete transducer record
Mox=32.8
20
ACC3436
6
Y
0
11
I!
l
I
A-
I
I’
'20
PPT6270
Max=21 .l
7
toz
Mill=-1.0
.O
20
30
M
60
70
80
90
100
110
120
130
140
t.50
160
170
160
190
200
210
[msec]
75
Mox=70.5
mm
B
PPT3007
25&
Mln=-2.9
0
20
30
40
60
60
70
60
90
loo
110
120
130
140
150
160
170
160
190
200
210
Max=5.3
.4
PPT2976
z
.2&
20
30
40
w
70
54
90
im
110
120
130
140
150
($0
170
160
190
2m
.o
win=-0.7
20
Max=22.5
210
[msec]
PPT6803
‘j;
log
Min=-1.9
0
20
M
40
50
70
60
60
90
1m
110
120
130
140
1w
160
170
160
190
200
210
[msec]
I
’
I
.60
Mox=61.0
.40"0
PPT4478
,205
.O
20
30
40
60
70
60
60
90
100
110
120
130
(40
160
160
(70
160
190
200
Mill=-8.0
210
[msec]
Scales : Model
I
I
TEST
MG-4
~ I ~’
M O D E L S A T j EQ-511
FLIGHT -1 ~
Ii
II
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
24
9 0 1 data
points plotted per complete transducer record
Mow=30.2
.?o
ACC3436
-
0 6
Max=26.9
Mln=-19.7
Max=lZS
Min=-4.0
,
I
ACC5756
‘0
Max=6.0
03
.-6
-
Mln=-8.0
Max=O.B
ACC3492
4
E
Mill=-1.7
Max=Z1.5
o E
ACC3466 .
,-m
Min=-26.5
Mox=20.5
Mln=-19.8
Mox=30.4
Mln=-30.0
Scales : Model
901 data points plotted per complete transducer record
Mox=30.2
ACC3436
Max=6.5
ACC3477
Mcx~61.6
PPT65 14
MI=-2.6
h-4
Max=36.3
PPT6270
Min=-2.6
Mox=65.3
PPT4478
I&x=44.7
PPT6784
hAin=-6.6
Mox=29.6
PPT3969
Min=-2.3
Scales : Model
TEST MG-4
MODEL SAT
FLIGHT - 1
I
EQ-5
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
26
13.0 Analysis of data from centrifuge test MG-4
The saturated sand bed in centrifuge model MG-4 had a height of 155 mm, The first
earthquake was a strong earthquake with a peak acceleration of about 25 %. A smaller
strength earthquake of 9.1 % was fired next. After this the strength of the earthquakes
was gradually increased in the subsequent events. The hydrostatic pore pressures
during the swing up and while increasing the centrifugal acceleration to ‘50g’ are
presented in Table 2. Note that during an earthquake event excess pore pressures are
generated over and above these hydrostatic pore pressures.
In Fig.27 the near surface accelerations recorded by ACC 3441 in all the earthquakes
are presented on the left hand side. During earthquake 1 the input acceleration was
strong and the surface accelerations attenuate significantly after first two cycles and
following the generation of excess pore pressures within the sand bed. The frequency
analysis of this trace is presented on the right hand side in Fig.27. From the frequency
analysis of this trace we can see that most of the energy is concentrated at about 100
Hz. A separate peak close to the 95 Hz frequency which is the driving frequency of the
earthquake is also seen in this figure. The peak excess pore pressures produced during
each earthquake near the base of the sand bed, at mid depth and near the surface are
plotted in Fig.28. Earthquake 2 was a small strength earthquake and magnitude of
excess pore pressures was small as seen in Fig.28. As a result all the cycles of base
shaking are present near the surface of the sand bed as well. Further the frequency
analysis of this trace shows that all the energy is now present at the driving frequency
of the earthquake which is 95 Hz (see the right hand side in Fig.27). A slightly stronger
earthquake was fired next. The excess pore pressures generated were almost equal
to
those generated during earthquake 1. The near surface accelerations show attenuation
compared to the base motion (see Table 3). All the cycles of base motion are present in
this trace. However the accelerations on the negative side have a larger amplitude
compared to the positive side. Further the frequency analysis of the near surface
accelerations during this earthquake as seen on the right hand side of Fig.27 indicate
13
that there are significant high frequency components in this trace. Earthquake 4 had a
similar strength to that of earthquake 1. After 4l/~ cycles the near surface accelerations
are significantly attenuated. The frequency analysis of this trace indicate the presence
of high frequency components (see the right hand side in Fig.27). Also the near surface
accelerations have larger peak accelerations on the negative side compared to the
positive side. During the last earthquake the attenuation of near surface accelerations
sets in after first I’/2 cycles itself. However the accelerations appear to recover
towards the end of the earthquake as noted in the previous section. The frequency
analysis of this trace indicate that most of the energy is present at the driving frequency
of the earthquake with some energy at the higher frequencies.
The column of accelerometers (see Fig.6) placed in the middle of the saturated sand
bed experienced attenuation of peak accelerations following the generation of excess
pore pressures in each earthquake. In table 3 the peak accelerations recorded by the
above column of accelerometers which are normal&d by the acceleration at the base
of the sand column during each earthquake are presented. In Fig.28 the excess pore
pressures generated in each earthquake are plotted against the strength of the
earthquake. From this figure it is clearly seen that the smaller strength earthquake 2
resulted in smaller excess pore pressures. On the converse larger strength earthquakes
all resulted in large excess pore pressures. The larger excess pore pressures also mean
lower effective stresses in the soil and hence degradation in soil stiffness. The smaller
excess pore pressures during earthquake 2 meant that there was smaller attenuation of
the base motion as it propagates towards the soil surface during this earthquake. In
sections 3,4 and 5 of this report the procedure to estimate the natural frequency of the
saturated sand bed by using the shear modulus of the soil which is corrected for the
shear strain amplitude induced during the earthquake loading and by using effective
stresses corrected for excess pore pressures induced during an earthquake is presented.
For an earthquake of given strength it is possible to relate the variation of natural
frequency with the generation of excess pore pressure. In Fig.29 the variation of
14
natural frequency of the saturated sand bed used in the centrifuge model MG-4 with
the generation of excess pore pressures is presented for earthquakes of varying
strengths from 2 % to 20 %. The soil parameters of this centrifuge model were
substituted in equations 1 to 12 and the results are plotted in Fig.29. From this figure it
is clear that for an earthquake of a particular strength the natural frequency drops with
the increase in excess pore pressure. Also stronger earthquakes results in lower natural
frequencies as larger shear strains are realised.
In Fig.30 the normal&d acceleration in table 3 is plotted against the strength of the
earthquakes fired during this centrifuge test. The near surface acceleration is
normal&d using the acceleration at the base of the sand bed and this normal&d
acceleration is plotted along the ordinate. From this figure earthquake 2 which had the
smallest strength (9.1 %) and produced relatively small excess pore pressures (see
Fig.28) results in largest normal&d acceleration. In other words earthquake 2 gave
rise to the smallest attenuation of base motion as it travelled towards the sand bed. As
the strength of the earthquake is increased the normalised acceleration is reduced as
seen in Fig.30.
This result can be explained using the theoretical variation shown in Fig.29.
Earthquake 2 had resulted in an acceleration of 9.4 % at the base of the soil column
considered in above discussion. This earthquake also resulted in the generation of
excess pore pressures of the magnitude of about 30 kPa. From Fig.29 we can obtain
the natural frequency of the saturated sand bed under these conditions as about 115
Hz. This is close to the driving frequency of the earthquake which is 96 Hz and hence
results in relatively low attenuation. From Fig.29 we can see that when the strength of
the earthquakes is larger and large excess pore pressures are generated the natural
frequency of the sand bed falls to very small values. In other words, under those
conditions there will be much larger attenuation of the base shaking as it travels
15
towards the sand surface. This is confirmed in Fig.30 which shows that stronger
earthquakes have indeed led to larger attenuations.
In Fig.31 the pore pressures recorded at the base of the sand column by the pore
pressure transducer 6514 (also see Fig.6) during each of the earthquake event is
presented. The rate of the excess pore pressure build up clearly appears to be a
function of the strength of the earthquake. During the first earthquake which had a
strength of 25.3 % the build up was rapid as seen in Fig.31. During the smaller second
earthquake not only the magnitude of the excess pore pressure generated is smaller but
the rate of build up is much more slower compared to earthquake 1. During
earthquake 3 the rate of build up is slightly faster especially towards the end of the
earthquake. The rate of pore pressure build up increases further during earthquake 4
and 5 and is comparable to that in the very first earthquake.
16
data points plotted per complete transducer record
1
0.5
0
loo
200
300
El
500
600
700
El
500
500
700
400
500
0
rw
I
1.5
1
0.5 .
I
0
I
20
40
50
80
loo
120
140
150
150
200
0
IW
200
so0
0
IW
200
3w
5no
h-1
1.5
1
22 -5
-10
0.5
-1s
.
0
20
40
50
50
1,’
1w
17.0
140
150
loo
209
[msec]
[Hz]
5
0
3
- 5
0.4 -10
I
0.2 .
-15 I
0
I
m
4i
aa
a0
lrn
lie
Ii0
IW
Ii0
loo
0
100
200
300
El
500
700
[m-l
5
0
a
-5
-10
I
0
20
40
50
50
loo
120
140
10
150
zoo
Scales : Prototype
TEST MG-4
MODEL SAT
FLIGHT
-1
FIG.NO.
Near
I
Surface
Accelerations
and Frequency Analyses
27
100
Test: MG-4
90
80
70
--q
80
v----I
50
near base
&-----------AZ
i
mid depth
i
40
30
20
10
0
I
0
I
5
I
10
I
I
15
20
I
25
1
30
I
35
Strength of the Earthquake (W G-Level)
Fig.28 Generation of excess pore pressures during the
earthquakes in centrifuge test MG-4
250
150
Natural
frequency
(Hz)
100
50
0
Excess pore pressure (Pa)
Fig.29 Theoretical relationship between excess pore
pressures and the natural frequency
0.900
5
0.800
Test MG-4
\
‘hq
\
0.700
\
0.800
\
0.500
\
kg
\
0.400
a, -----.-~
0.300
0.200
I
5
I
10
1
15
I
20
I
I
I
25
---a
I
30
S t r e n g t h o f t h e E a r t h q u a k e (% G - L e v e l )
Fig. 30 Variation of normalised acceleration
with the strength of the earthquake
I
35
data points plotted per complete transducer record
PPT 6514
EQ-2
g::.
PPT 6 5 1 4
5.
0.
0
20
40
60
80
loo
120
[mscc]
140
160
E Q - 3 zw
20.
0.
0
180
200
PPT 6 5 1 4
20
40
60
60
100
[msec
]
120
140
120
100
200
PPT 6 5 1 4
/
I
so.
40.
EQ-5
gm-
PPT 6 5 1 4
20.
10.
O0
20
40
00
00
100
120
140
120
100
200
[msac]
Scales :
TEST MG-4
MODEL SAT
FLIGHT -1
Prototype
Base Pore Pressure
TIME RECORDS
FIG.NO.
31
14.0 Centrifuge test MG-5
AS explained in Sec.6 the depth of the sand bed for this centrifuge test was 100.0 mm.
The construction of the centrifuge model was in three stages and at the end each stage
the void ratio and dry density of sand bed were estimated. The natural frequency of the
soil was computed using Eqs. 1 to 12. The final depth of sand bed required so that its
natural frequency is close to the driving frequency of the model earthquake was
determined after each stage. The schematic diagram showing the section of the
centrifuge model and placement of the instruments during this centrifuge test is
presented in Fig.32. In table 4 the exact location of each transducer during this
experiment is presented. A total of six earthquakes were fired on this centrifuge model
at 5Og. The data from these earthquakes is presented in Figs.33 to 56. The salient
features of the data are presented here while a detailed analysis of the data is presented
in next section.
As in the previous centrifuge test two data acquisition systems were used during this
centrifuge test. These systems were explained in section 11. Important transducers
were logged on both these systems so that reliable measurements can be made. In this
centrifuge test all the earthquakes were fired such that the peak acceleration induced in
each was greater than the previous earthquake. Earthquake 1 had a strength of about
12.8 %. In Figs.33 and 34 the data from all the instruments acquired using the Racal
tape recorder are presented. In Figs.35 and 36 the data obtained directly using Global
Lab data acquisition system are presented. Considering the three accelerometers 1926,
3466 and 3477 (see Fig.32) which are placed along the vertical column in the middle of
the sand bed we can see that there is significant attenuation of peak acceleration from
12.8 % at the base of the sand column to about 6.2 % at the surface of the sand bed.
Traces recorded by ACC 3477 and 3441 in Fig.33 show a clear attenuation of peak
accelerations after first few cycles. In fact the second half of the base shaking recorded
by ACC 3436 and 1926 is not at all registered by the accelerometers 3466 and 3477.
These events coincides with the rise of excess pore pressures indicated by PPT’s 6260
17
and 6270 as seen in Figs.33 and 34. The vertical accelerometers 1572, 1925 and 5756
in Fig.35 are clearly picking up the vertical accelerations unlike in the previous
centrifuge test. ACC 1572 however registers some movement of the transducer in the
vertical direction. As in the previous test, both the accelerometers and pore pressure
transducers placed along the same horizontal plane in general recorded very similar
accelerations and excess pore pressures confirming the uniformity of the centrifuge
model. PIT 3969 did not function during this earthquake.
An earthquake which produced a peak acceleration of 15.4 % was fired next. The data
from this earthquake are presented in Figs.37 to 40. The magnitude of the excess pore
pressures generated during this earthquake was almost the same as those generated
during earthquake 1. This can be observed by comparing PPT’s 6514,626O and 6270
in Figs.37 and 38 with corresponding traces obtained during earthquake 1. The
accelerometers 1926, 3466 and 3477 along the vertical column in the middle of the
sand bed show significant attenuation of peak acceleration. In particular ACC 3477
near the surface of the sand bed registers only five cycles of base motion similar to
earthquake 1. This is consistent with the excess pore pressures generated during this
earthquake. PPT 3969 did not function during this earthquake or any other subsequent
earthquake. The vertical accelerometers 1572, 1925 and 5756 all show different
response compared to the vertical acceleration recorded by ACC 1900 on the box (see
Figs.32 and 39). It appears that the vertical accelerometers are picking up a
component of the horizontal acceleration.
Earthquake 3 had a strength of 22.5 %. The data from this earthquake are presented in
Figs. 41 to 44. It is interesting to note that the magnitude of excess pore pressures
generated during this earthquake are almost equal to those generated during
earthquakes 1 and 2. Also, the accelerometer 3441 near the sand surface registers only
the first three cycles of base motion (see Fig.41).
18
Earthquake 4 had a strength of 25.2 %. The data from this earthquake are presented in
Figs. 45 to 48. The excess pore pressures during this earthquake were almost the same
as in the previous earthquakes as seen in Figs. 45 and 46. It is interesting to see the
acceleration time history recorded by ACC 3477 near the soil surface in Fig.45. After
the first 2l/2 cycles the accelerometer registers very small accelerations suggesting that
the sand in this region has liquefied.
An even stronger earthquake which produced a peak acceleration of about 27.6 % was
fired next. The data from this earthquake are presented in Figs.49 to 52. The
magnitude of excess pore pressures generated during this earthquake was almost the
same as in the previous earthquakes. However accelerometer 3477 registers signs of
liquefaction of the soil surrounding it after first 11/2 cycles. It does not recover till the
end of the earthquake unlike in the previous centrifuge test.
An even stronger earthquake which produced a peak acceleration of about 29.7 % was
fired as the last earthquake. The data from this earthquake are presented in Figs.53 to
56. The magnitude of excess pore pressures generated during this earthquake was
almost the same as in the previous earthquakes. However accelerometer 3477 registers
signs of liquefaction of the soil surrounding it after first 11/4 cycles. It does not recover
till the end of the earthquake unlike in the previous centrifuge test. From the data
obtained during this strong earthquake it was felt that by increasing the strength of the
earthquake further no useful information can be obtained.
In the next section a more detailed analysis of the data from this centrifuge test is
presented.
19
I
100 mm
1
0
3436
II
1900
Fig. 32: Schematic diagram showing the placement of transducers in
Centrifuge Test MG-5
Table 4 Placement of transducers in centrifuge test MG-5
Transducer
ACC 1225
ACC 1926
ACC 1572
ACC 5701
ACC 3441
ACC 3466
ACC 1925
ACC 5754
ACC 3457
ACC 3477
ACC 5756
ACC 1258
ACC 3436
ACC 1900
PPT 65 14
PPT 6803
PPT 4478
PFT 3969
PIT6270
PPT4481
PPT 3007
PPT 6260
PPT 6784
x (mm)
25
280
320
490
30
250
295
495
20
275
350
490
Y
(mm)
5
5
5
5
42
40
44
41
67
72
72
73
fixed to the container
fixed to the container
265
30
440.5
62
300
460
65
315
475
3
3
3
42
37
40
72
68
74
Table 5 Hydrostatic pore pressures in centrifuge
test MG-5
1
PPTNO.
PPT6514
PPT4478
PPT6803
PPT6270
PPT3969
PPT4481
PPT6260
PPT3007
PPT6784
1 1OG
206
5.31
7.65
7.78
5.37
0.52
5.83
1.67
2.62
5.13
13.56
16.38
16.92
11.55
1.11
12.43
5.47
7.52
11.10
406
31.58
35.17
35.77
24.26
2.33
25.97
13.37
17.67
23.37
506
41.26
45.57
45.95
31.19
3.00
33.17
17.24
22.68
29.85
Table 6 Normalised accelerations in the sand column
in centrifuge test MG-5
Location
Normalised Acceleration
At base of the sand column
At the mid depth
Near the surface of sand bed
1
0.9324
0.8378
At base of the sand column
At the mid depth
Near the surface of sand bed
1
1.0349
1.1047
At base of the sand columu
At the mid depth
Near the surface of sand bed
1
0.6743
0.57 14
At base of the sand column
At the mid depth
Near the surface of sand bed
1
0.5357
0.4286
At base of the sand column
At the mid depth
Near the surface of sand bed
1
0.3384
0.25
At base of the sand column
At the mid depth
Near the surface of sand bed
1
0.4086
0.2857
EQ: 1
EQ: 2
EQ: 3
EQ: 4
EQ: 5
EQ: 6
1 120 data points plotted per complete transducer record
Min=-12.2
Max=9.6
Min=-10.7
.o
A C C 1 9 2 6
.
Max=7.4
.o E
I’
Ml=-7.5
Max=6.9
Min=-6.9
Max=6.2
Min=-6.6
Max=42.6
Mill=-1.2
Mox=27.9
,a,
F
to J
PPT6270
Mln=-0.6
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-1 ~
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
33
1120
data
points
plotted
per
complete
transducer
record
10
Max=lZ.S
ACC3436
.o
I
10
20
30
40
50
60
70
60
90
loo
110
120
. -10
1
130
z
140
150
160
170
Mln=-12.4
160
[msec]
I
I
PPT6260
’
I
10
20
30
40
50
80
70
a0
90
100
110
120
130
140
150
194
170
Mln=-0.3
0
180
[msac]
40
PPT6803
Max=40.3
F
20 2
Ml=-3.6
0
10
20
30
40
50
60
70
60
90
loo
110
120
130
140
150
190
tie
li0
lie
140
lie
lie
110
120
1.30
140
170
160
[IWC]
PPT3969
10
20
30
40
50
60
m
80
90
100
170
l&J
[msec]
PPT3007
10
20
30
40
50
60
70
60
90
100
150
160
170
180
[msec]
40
PPT4476
Ma~42.4
P
20 2
Ml=-4.3
0
10
20
347
40
50
90
70
60
90
loo
110
120
130
140
150
190
170
160
[msec]
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
I
I
I
FIG.NO.
SHORT TERM
TIME RECORDS
EQ- 1
II
34
I
I
L>
901
data
points
plotted
per
complete
transducer
record
ACC3436
Uax=6.2
ACCI 926
WI=-6.5
PPT65 14
PPT6270
Min=-2.9
Max=Zl.6
PPT6260
Yin=-2.7
Max=46.7
PPT4478
Em-1
Yax=36.5
PPT448 1
Min=-3.2
Mox=33.2
PPT6784
Min=-4.6
Scales : Prototype
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-1
I
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
36
1120
data
points
plotted
per
complete
transducer
record
Min=-16.7
t&x=14.2
ACC344
Uax=13.7
MIT=-16.2
Mox=6.6
I
oE
ACC1926
-6
Mill=-7.4
Max=6.9
Min=-9.2
10
Mox=9.5
0
6
-10
Min=-10.4
L(ax=41.5
T
me
PPT65 14
Min=-0.4
Max=27.1-
PPT6270
Mill=-0.4
I
TEST MG-5
MODEL SAT
FLIGHT -1
L
I
I
I
EQ-2 ~
I
Scales : Model
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
37
1120
data
paints
plotted
per
complete
transducer
record
c/i/(y(yy-y
Max=16.6
.I0
ACC3436
z
Y
.o
I
10
20
30
40
50
50
70
60
90
(00
[msec]
110
120
130
140
150
160
170
-10
Mln=-15.5
164
.20
PPT6260
-10
Max=19.6
‘;;
B
Mill=-0.1
10
20
40
50
60
70
SO
100
$90
120
130
140
[msec]
150
160
170
la0
40
PPT6803
Max=42.7
F
20 2
Min=-3.3
D
20
10
30
40
50
60
70
60
90
100
110
120
130
140
150
110
120
130
140
Go
164
170
160
tie
l&l
[msec]
PPT3969
,o
10
20
10
20
30
40
50
60
70
60
60
100
[msec]
160
Mill=-0.3
PPT3007
Mill=-0.2
so
40
50
60
m
80
90
100
110
120
130
140
150
loo
170
160
[msec]
1
I
Max=42.5
PPT4478
x
. 2 0 ,f.,
Ml=-0.5
10
20
Jo
40
50
60
70
60
90
100
110
120
130
140
150
lso
170
180
[msec]
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT - 1
I
EQ-2
!
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
3 8
901 data points plotted per complete transducer record
ACC3436
Mox=6.6
ACCl900
Min=-6.5
ACC 1572
ACC1925
Min=-1.9
ACC5756
ACC5701
Mb=-15.6
Mox=16.1
ACC5754
Mln=-16.6
ACC1258
MI=-26.3
Max=13.6
ACC 1225
Mln=-16.5
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT
-1
I
EQ-2
/
1
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
39
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC1926
Max=42..9
PPT65 14
Wax=ZQ.D
PPT6270
PPT6260
Min=-2.9
PPT4478
Uax=37.1
PPT448 1
Min=-3.7
PPT6784
Uin=-5.6
Scales : Prototype
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-2
I
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
40
1120
data
paints
platted
per
complete
transducer
record
M.X=22.5
ACC3436
.o E
.-m
10
50
30
40
50
aa
m
00
m
too
110
120
1%
140
ma
110
170
Min=-22.7
180
[m-cl
Max=21.8
ACC 1225
0 6
.-m
m
za
so
40
so
ID
70
en
aa
Irn
[m-l
IID
110
I30
340
$60
Ia0
170
Mln=-24.2
,m
Max=18.5
ACC3441
10
m
24
4a
80
,m
70
m
w
Irn
110
m
,sn
Ma
,w
1m
(10
Ml=-18.0
--la
IID
b=l
Max=15.5
OE
ACC3457
.-lo
10
20
30
40
60
ID
m
aa
w
Irn
Ito
,a0
1s
140
150
,#a
110
Min=-22.8
,no
Cm-1
-la
Max=17.5
.I0
ACC1926
.o E
10
10
30
40
m
aa
70
IO
w
lrn
h-1
<ID
I?0
,sn
140
IYI
,m
tm
.-ID
Mill=-13.7
IO
Max=11.8
,a0
ACC3466
.o E
(0
za
so
40
aa
10
10
m
(0
100
110
120
130
140
9%
,#a
170
10
, -to
Mb=-9.4
[m=l
. to
Mox=lO.O
ACC3477
10
m
24
40
w
m
m
IO
90
102
($0
I)0
I=
(40
tDD
,a
00
Min=-9.0
r-IO
100
[m=l
Mox=42.2
6
.P&
PPT65 14
Ml=-1.3
P
#a
(00
b-4
L(ax=29.5
.7.0eB
(0
PPT6270
Mitt=-0.7
10
10
b-1
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-3 ~
/
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
41
1120 data paints plotted per complete transducer record
(A*.
.20
ACC3436
Mm=23.2
.o z
.
10
20
30
40
M
60
70
80
00
100
110
120
130
140
150
lea
170
Mill=-22.1
-20
180
[msec]
uax=17.3
PPT6260
.5
Mln=-0.3
10
20
30
40
50
50
m
50
90
loo
110
120
130
140
150
150
170
150
[msec]
Mex=47.6
.40
PPT6803
P
2
.20,
Ml=-3.5
-0
10
20
30
40
50
eo
m
50
so
100
110
120
130
140
150
150
170
150
[msec]
3
PPT3969
Mox=J.l
2,
"0
155
MIn=-0.6
0
10
20
30
40
M
60
m
50
DO
110
100
120
130
140
lea
[msec]
170
Max=25.0
PPT3007
r
10
20
30
40
50
60
m
Kl
so
loo
110
120
130
140
150
160
170
160
[msec]
.40
PPT4478
Max=45.4
6
.20&
.O
10
20
30
40
50
50
m
50
so
103
110
120
130
140
150
160
170
Mill=-3.7
160
[mscc]
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-3 ~
I
~
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
42
901
data
points
plotted
per
complete
transducer
record
ACC3436
Min=-21.6
ACCl900
M.ax=27.3
ACC 1572
ACC 1925
Min=-2.9
ACC5756
Max=23.5
ACC5701
Min=-22.0
Max=23.6
ACC5754
Min=-22.6
Max=PB.O
ACC 1250
WI=-36.7
Mcx~20.6
ACC1225
Mln=-23.4
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-3 ~
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
4 3
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC1926
kr~42.5
PPT6270
PPT6260
PPT4478
Min=-2.5
Mox=36.2
PPT448 1
Mill=-3.5
Yox=34.7
PPT6784
Mb=-4.3
Scales : Prototype
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-3
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
4 4
1120 data paints plotted per complete transducer record
ACC1225
Min=-26.4
Max=l5.6
Max=25.2
ACC1926
Min=-23.1
Min=-10.1
Max=10.6
Min=-9.0
Max=41.2
PPT65
Min=-1.3
VJ
wa
b-4
Max=29.6
.102
.10-
PPT6270
MIn=-0.6
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
SHORT TERM
E Q - 4
I
TIME RECORDS
G Level
FIG.NO.
50
45
1 120 data points plotted per complete transducer record
ACC3436
I
10
20
30
40
M
50
70
80
90
100
(IO
120
130
140
150
190
170
160
[msec]
15
Mox=l6.1
5
10
20
30
40
60
90
70
IM
90
loo
1,o
120
130
Mln=-0.5
0
140
1%
150
170
mo
[msec]
Max=42.1
PPT6803
P
.20 2
Mill=-3.6
.O
3
Mox=3.0
2
PPT3969
5
1L
0
10
20
30
40
60
60
70
50
90
loo
110
120
130
140
160
160
170
Mln=-0.5
160
[mom]
PPT3007
I
10
Max=26.6
WI=-0.6
20
30
40
50
90
70
50
90
loo
110
120
130
140
160
160
170
160
[msec]
Max=50.0
.40
PPT4478
7
2
.20-
.O
10
20
30
40
50
60
m
Ml
90
1w
110
120
130
140
150
150
170
Mln=-2.6
180
[msec]
Scales : Model
~
TEST MG-5
EQ-4
MODEL SAT
F L I G H T
- 1
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
46
901
data
points
plotted
per
complete
transducer
record
Max=26.9
ACC1572
Min=-8.6
b-1
ACC5701
Min=-25.0
Max=25.5
ACC5754
Min=-23.7
Max=23.3
ACC1225
Mln=-26.3
t-4
Scales : Model
‘TEST MG-5
MODEL SAT
FLIGHT
-1
EQ-4
1
1
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
47
901
data
points
plotted
per
complete
transducer
record
ACC3436
Max=24.2
ACC1926
Max=42.6
PPT65 14
Yox=32.5
PPT6270
Min=-2.5
PPT4478
Mox=36.7
PPT448 1
Mill=-3.0
Mox=36.4
PPT6784
Mln=-4.7
Scales : Prototype
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-4
I
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
48
1120 data paints plotted per complete transducer record
Max=27.8
ACC3436
.-lo
10
so
30
40
I
0
m
10
w
tO0
110
120
130
140
150
160
110
Min=-28.0
,a0
[m=l
Mox=29.0
ACC1225
,o E
.-10
$0
!a
lo
40
w
0
70
YI
(0
100
,,a
020
,Y)
140
Ia0
IQ
,10
ml=-29.9
,ID
h-4
.m
Max=22.1
O E
ACC344 1
10
m
so
40
P
Q
ID
IO
90
IO0
110
Ilp
,P
‘40
*so
1m
r/o
.-a
Mb=-26.5
(0
Max=16.0
,I0
b=l
ACC3457
.
.
.
+yJy)-JofiyJlJyL&>
(0
20
.m
an
60
m
10
w
m
tm
IlO
m
,a0
$40
wa
180
*?a
ma
o E
-10
-ID
Mill=-18.5
b-1
.m
kx=32.a
.o E
ACC1926
.-m
$0
20
30
40
Ea
a0
70
*I
00
100
110
m
9s
‘40
1w
IQ
Min=-32.7
tm
tm
b-4
Mox=ll.l
ACC3466
$0
20
so
40
80
0
n
w
so
Irn
[m-l
(10
110
Iso
wa
Ma
110
110
la0
.-to
.*
t&l=-9.8
Max=&2
.o E
ACC3477
.-I
to
20
m
40
m
m
IO
m
10
too
,I0
$20
130
140
Ino
110
(70
Min=-7.9
180
h-1
Maw=40.5
PPT6514
Mln=-1.1
[m-=1
Max=30*6
PPT6270
IO
Mill=-0.4
w
20
wn
h4
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
~
EQ-5 ~
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
49
1120
data
points
plotted
per
complete
transducer
record
ACC3436
I
20
10
30
40
50
80
70
60
90
100
.
-
110
120
130
140
150
160
170
,w
[msec]
PPT6260
AJ
10
20
50
40
50
90
70
60
DO
loo
(10
120
130
140
150
160
170
160
[msec]
.40
PPT6803
Max=43.0
F
.2og
Min=-3.3
.O
10
20
30
40
50
so
70
60
90
1w
110
120
130
140
150
160
170
160
[mssc]
3
Max=2.6
2
P
12
PPT3969
0
10
20
30
40
50
60
70
50
90
100
110
120
130
140
150
lso
170
Mill=-0.6
180
[msec]
30
Mox=26.6
20
PPT3007
P
2
loMb=-0.6
D
10
20
30
40
50
60
70
M
90
loo
110
120
130
140
150
lso
170
1M
[msec]
Max=50.1
.40
PPT4478
7
.2oz
.O
10
20
30
40
50
60
70
64
90
loo
1,o
120
130
140
150
160
170
Mln=-4.7
1w
[msac]
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-5 ~
1
SHORT TERM
TIME RECORDS
G Level
FIG-NO.
50
50
901
dato
points
plotted
per
complete
transducer
record
.20
ACC3436
.o E
.-zo
Min=-28.8
ACC1900
Mox=22.2
Mln=-6.6
khx=5.6
ACC 1925
Mb=-3.4
.o
ACC5756
.zo
.o E
-
Max=5.1
I -zo
Mb=-3.6
.lo
Max=30.3
.o E
ACC570 1
.-20
Mill=-28.0
Max=29.9
ACC5754
_
MI=-26.3
Max=28.2
ACC 1258
Mill=-39.0
Max=27.6
o E
.-lo
ACC1225
Mln=-29.3
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
SHORT TERM
TIME RECORDS
EQ-5
I
G Level
50
FIG.NO.
51
901
data
points
plotted
per
complete
transducer
record
ACC3436
ACC1926
PPT65 14
Max=32.5
PPT6270
Mor=19.6
PPT6260
Min=-2.9
PPT4478
Uin=-2.6
Mox=36.6
PPT448 1
Min=-4.0
Yo.=36.6
PPT6784
Uin=-5.3
Stoles
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-5
I
I
:
Prototype
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
52
1120
data points plotted per complete transducer record
,la
ACC3436
.” E
.-20
10
a0
30
40
50
m
10
u)
w
tm
Lm-4
t(Q
w.0
130
940
150
IW
170
.m
‘O E
.-10
WI
30
40
60
a0
m
m
(0
tm
110
lrn
~sn
140
150
tm
110
Min=-30.2
,a
ACC1225
$0
Max=29.7
Max=31.2
ml=-31.6
lrn
[m-=1
.E?o
ACC344 1
Maxd3.7
.o E
~Jj/y)fypy
10
?a
Y)
40
m
0
70
I
(0
too
110
v20
IJO
140
160
Ien
I70
-20
Mln=-24.6
Ian
h-4
Max=21.7
ACC3457
.o E
”
IO
!a
Jo
4a
54
(0
10
80
a0
,m
,,o
tm
1s
140
1m
l@o
,I0
.-la
Min=-21.6
.!a
Max=40.0
110
[m=l
0 3
.-m
ACC1926
10
10
SD
40
50
,a
m
au
w
Irn
(10
la
130
I40
180
I=
110
Mln=-45.5
e-m
110
h-1
TO
ACC3466
Mox=12.3
,E
Min=-8.7
10
10
so
40
s
0
7a
*I
so
rm
110
120
1s
140
160
m
170
1m
b-4
.5
ACC3477
,o E
.-n
90
20
z4
40
LQ
*
m
YI
R)
tm
b=4
110
10
,a
140
(Do
110
170
hiaX=&
Min=-6.2
mo
uax=40.7
F
.aoe,
PPT6514
Mill=-0.7
10
in
30
40
PO
10
IO
90
100
VW
h-1
Max=30.1
.ZlJ-F
0
10
PPT6270
Mb=-0.3
20
30
40
00
0
I
TEST MG-5
MODEL SAT
FLIGHT
--I
EQ-6
,
I
100
Em-1
Scales : Model
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
53
1120 data paints platted per complete transducer record
Max=30.2
20
ACC3436
r
Y
0
-20
Mb=-29.6
[msec]
- 20
Mox=17.5
1 5
PPT6260
. 10 F
-0
c
-5
10
20
30
40
60
60
70
60
SO
1W
110
120
1.30
140
150
t60
170
Min=O.Z
180
[msec]
/
Max=49.4
.40
PPT6803
P
2
.2oy
/
10
ml=-2.5
.O
20
30
40
60
60
70
60
DO
loo
110
120
1.30
140
lx)
160
170
160
[msec]
4
3
PPT3969
Max=3.7
52
2z
1
10
20
30
40
60
60
70
60
DO
100
110
120
134
140
160
164l
170
Mln=0.2
160
[meet]
M
Max=27.3
20,
PPT3007
10
T;
.?.a
Mln=-0.3
0
10
20
30
40
50
60
70
60
90
100
110
120
130
140
150
160
170
160
[msac]
I
Mox=50.6
P
2
PPT4478
. zo-
Ml=-1.2
10
20
30
40
50
60
70
60
90
1w
,,o
120
130
140
150
160
170
160
[m-l
Scales : Model
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-6
SHORT TERM
TIME RECORDS
G Level
FIG.NO.
50
54
901
data
points
plotted
per
complete
transducer
record
McJx=30.9
Min=-31.2
(0
ACClQOO
-
Mox=14.3
.D E
1
Y
Ml=-11.5
Max=21.4
‘0-z
.o
ACC 1572
Mln=-6.0
Max=5.4
ACC 1925
Min=-5.6
Max=92
ACC5756
Mln=-3.4
Mox=32.6
ACC570 1
Min=-29.6
Max=34.5
Min=-31.3
Max=34.6
Mill=-37.8
Max=JO.O
Mln=-31.5
Scales : Model
TEST MG-5
MODEi S A T
FLIGHT
-1
EQ-6
/
SHORT TERM
TIME RECORDS
G Level
50
FIG.NO.
55
901
data
points
plotted
per
complete
transducer
record
uox=so.9
ACC3436
Mln=-31.2
Max=30.1
ACC1926
Mln=-29.1
Mar=42.7
PPT65 14
Uh=-3.5
Max=32.4
PPT6270
WIT=-2.6
Max=20.4
PPT6260
Ml=-3.0
Uax=50.0
PPT4478
Uin=-2.6
Wox=36.1
PPT448 1
Mln=-3.7
[m-cl
hior=37.5
PPT6784
wn=-5.7
Scales :
TEST MG-5
MODEL SAT
FLIGHT -1
EQ-6
Prototype
SHORT TERM
TIME RECORDS
15.0 Analysis of data from centrifuge test MG-5
The saturated sand bed in centrifuge model MG-5 had a height of 100 mm. The first
earthquake was a strong earthquake with a peak acceleration of about 12.8 %. A
slightly stronger earthquake which produced a peak acceleration of 15.4 % was fired
next. After this the strength of the earthquakes was gradually increased in the
subsequent events. The hydrostatic pore pressures during the swing up and while
increasing the centrifugal acceleration to ‘5Og’ are presented in Table 5. Note that, as
in the previous centrifuge test, during an earthquake event excess pore pressures are
generated over and above these hydrostatic pore pressures.
In Fig.57 the near surface accelerations recorded by ACC 3477 in all the six
earthquakes are presented on the left hand side. During earthquake 1 the input
acceleration was about 12.8 % and the surface accelerations attenuated signifkantly
after first cycle following the generation of excess pore pressures within the sand bed.
However the surface accelerations recover after the first cycle but are again attenuated
towards the strong base shaking felt towards the end of the earthquake. The frequency
analysis of this trace is presented on the right hand side in Fig.57. From the frequency
analysis of this trace we can see that most of the energy is concentrated at about 100
Hz. The peak excess pore pressures produced during each earthquake near the base of
the sand bed, at mid depth and near the surface are plotted in Fig.58. Earthquake 2
was a slightly stronger earthquake and magnitude of excess pore pressures was the
same as in earthquake 1 and as seen in Fig.58. The first five cycles of base shaking are
present near the surface of the sand bed during this earthquake. Further the frequency
analysis of this trace shows that all the energy is present at the driving frequency of the
earthquake which is 95 Hz (see the right hand side in Fig.57). A slightly stronger
earthquake was fired next. The excess pore pressures generated were almost equal
to
those generated during earthquakes 1 and 2. The near surface accelerations show
attenuation compared to the base motion (see Table 6). The first three cycles of base
motion are present in this trace. However the accelerations on the negative side have a
20
sfightly larger amplitude compared to the positive side. Further the frequency analysis
of the near surface accelerations during this earthquake as seen on the right hand side
of Fig.57 indicate that there are significant high frequency components in this trace.
Earthquake 4 had resulted in peak accelerations of 25.2 %. After 13/4 cycles the near
surface accelerations are significantly attenuated. The frequency analysis of this trace
indicate the presence of high frequency components (see the right hand side in Fig.57).
Also the near surface accelerations have slightly larger peak accelerations on the
negative side compared to the positive side. During the fifth earthquake the attenuation
of near surface accelerations sets in after first 11/2 cycles itself. The frequency analysis
of this trace indicate that most of the energy is present at the driving frequency of the
earthquake with some energy at the higher frequencies. Earthquake 6 was even
stronger and the peak acceleration induced by this earthquake was about 29.7 % at the
base of the soil column. The near surface accelerations were attenuated after the first
11/4 cycles. The frequency analysis of this trace is presented on the right hand side of
Fig.57. By comparing the frequency analysis of all the near surface accelerations traces
in Fig.57 from earthquake 1 to earthquake 6 we can see that there is a gradual
dispersion of the energy about the driving frequency of the earthquake (which is 96
Hz) as the strength of the earthquake is increased from 12.8% to 29.7 %.
The column of accelerometers (see Fig.32) placed in the middle of the saturated sand
bed experienced attenuation of peak accelerations following the generation of excess
pore pressures in each earthquake. In table 6 the peak accelerations recorded by the
above column of accelerometers which are normalised by the acceleration at the base
of the sand column during each earthquake are presented. In Fig.58 the excess pore
pressures generated in each earthquake are plotted against the strength of the
earthquake. From this figure it is clearly seen that all the six earthquakes resulted in
more or less the same magnitude of excess pore pressures. This contrasts strongly with
the smaller excess pore pressures generated during earthquake 2 in the previous
centrifuge test MG-4. In sections 3, 4 and 5 of this report the procedure to estimate
21
the natural frequency of the saturated sand bed by using the shear modulus of the soil
which is corrected for the shear strain amplitude induced during the earthquake loading
and by using effective stresses corrected for excess pore pressures induced during an
earthquake is presented. For an earthquake of given strength it is possible to relate the
variation of natural frequency with the generation of excess pore pressure. In Fig.59
the variation of natural frequency of the saturated sand bed used in the centrifuge
model MG-5 with the generation of excess pore pressures is presented for earthquakes
of varying strengths from 2 % to 20 %. The soil parameters of this centrifuge model
were substituted in equations 1 to 12 and the results are plotted in Fig.59. The small
strain natural frequency of the sand bed in this centrifuge model was about 430 Hz
when there is no excess pore pressure generated. Also, from this figure it is clear that
for an earthquake of a particular strength the natural frequency drops with the increase
in excess pore pressure. Also stronger earthquakes results in lower natural frequencies
as larger shear strains are realised.
In Fig.60 the normal&d acceleration in table 6 is plotted against the strength of the
earthquakes fired during this centrifuge test. The near surface acceleration is
normalised using the acceleration at the base of the sand bed and this normal&d
acceleration is plotted along the ordinate. From this figure earthquake 2 which
produced a peak acceleration of 8.6 % at the base of the sand column resulted in the
largest normal&d acceleration. In other words earthquake 2 gave rise to the smallest
attenuation of base motion as it travelled towards the sand bed. As the strength of the
earthquake is increased the normal&d acceleration is reduced as seen in Fig.60.
This result can be explained using the theoretical variation shown in Fig.59. During
earthquake 1 the peak acceleration observed at the base of the sand column is 7.4 %
(see Fig.33) and the excess pore pressure generated at the base of the sand column
during this earthquake was 40 kPa. From Fig.59 we can get the natural frequency
under these conditions of the saturated sand bed in this centrifuge model as 205 Hz.
22
This frequency if far from the driving frequency of the earthquake which is at 96 Hz.
Hence there will be attenuation of base shaking as it travels to the surface of the sand
during this earthquake. Earthquake 2 had resulted in an acceleration of 8.6 % at the
base of the soil column considered in above discussion. This earthquake also resulted
in the generation of excess pore pressures of the magnitude of about 40 kPa at the base
of the sand column as seen in Fig. 58. From Fig.59 we can obtain the natural frequency
of the saturated sand bed under these conditions as about 100 Hz. This is very close to
the driving frequency of the earthquake which is 96 Hz and hence results in relative
amplification of base shaking as it travels towards the surface of the sand. From Fig.59
we can see that when the strength of the earthquakes is larger and large excess pore
pressures are generated the natural frequency of the sand bed falls to very small values.
In other words, under those conditions there will be much larger attenuation of the
base shaking as it travels towards the sand surface. This is confirmed in Fig.60 which
shows that stronger earthquakes have indeed led to larger attenuations.
In Fig.61 the pore pressures recorded at the base of the sand column by the pore
pressure transducer 6514 (also see Fig.32) during each of the earthquake event is
presented. The rate of the excess pore pressure build up clearly appears to be a
function of the strength of the earthquake. During the first earthquake which had a
strength of 12.8 % the build up was rapid as seen in Fig.61. During the stronger
second earthquake the magnitude of the excess pore pressure generated is same but the
rate of build up is much more faster compared to earthquake 1. During earthquake 3
the rate of build up is slightly faster especially towards the end of the earthquake. The
rate of pore pressure build up increases further during earthquake 4,5 and 6. From this
figure and the corresponding result in centrifuge test MG-4 we can say that the rate of
pore pressure build up increases with the increase in the strength of the earthquake.
23
data points plotted per complete transducer record
EQ-3
s 0.
-5.
I. z
I
EQ-5
B 0.
4.
”
Scales : Prototype
TEST MG-5
MODEL SAT
FLIGHT -1
Near
Surface
Accelerations
and Frequency Analyses
FIG.NO.
57
00
I
Test: MG-5
70
80
50
40
30
@.@ _ _.-. _._ _ _ _._._ * _ _ ._ _ _. _ _ -g# ._ _ . _ _ . Q . . - @
20
OC
mid depth
10
1
Y
-0
Y
near surface
0
0
5
10
15
20
25
30
35
S t r e n g t h o f t h e E a r t h q u a k e (W G - l e v e l )
Fig.58 Generation of excess pore pressures during the
earthquakes in centrifuge test MG-5
1 250
frequency
(Hz
200
150
\
i.
100
50
\
‘5.i
!
\
18
%
\
12
14
%
\
16 %
\I
\
\
yiJ
“\,
‘3;
:
:
i
\
i
‘;
:
:
:
\
rI
\
i
1
-.7-+-r
0
0
10000
20000
30000
40000
50000
60000
Excess pore pressure (Pa)
Fig.59 Theoretical relationship between the excess
pore pressures and the natural frequency
-
I . 2 0 0 -
i
/I
t
d ‘\
1.000
z
‘L
0.800
5
0.800
5
5
l
0,700
z
0
\
'i
1
u
=
i
Test MG-5
7
1.100
b.
“‘\‘.\
0.500
0.400
00.600
.300
0.200
\..,
1
1I
I
5
I
I
10
I
I
15
I
20
\
I
I
25
I
30
S t r e n g t h o f t h e E a r t h q u a k e (96 G - L e v e l )
Fig.60 Variation of the normal&d acceleration
with the strength of the earthquake
I
35
239
data
points
plotted
per
complete
transducer
record
PPT 6514
PPT 6514
PPT 651
?I
Scales :
TEST MG-5
MODEL SAT
FLIGHT -1
I
I
I
Prototype
Base Pore Pressure
TIME RECORDS
FIG.NO.
61
16.0 Conclusions
The dynamic response of a horizontal sand bed was investigated under saturated
conditions. Two centrifuge tests MG-4 and MG-5 were conducted on saturated sand
beds of different heights. Several earthquakes were fired on the centrifuge models
during each experiment. The data from these centrifuge tests is presented in this report.
This series of centrifuge tests were carried out in continuation of work done on dry
sand beds earlier, Madabhushi (1994).
The depth of the sand bed was arranged so that the small strain natural frequencies
were 250 and 450 Hz for the centrifuge models MG-4 and MG-5 respectively. When
the shear modulus of the sand bed is corrected for the shear strain amplitude the
natural frequency of the sand bed will be lower than the above values. Also when the
effective stress in the sand bed is corrected for the excess pore pressures generated
during the earthquake loading the natural frequency of the sand bed will be even
lowered.
In the first centrifuge test MG-4 a strong earthquake was fired first followed by a
smaller second earthquake. The subsequent earthquakes had increasing strengths. The
excess pore pressures generated at different heights within the sand bed followed the
strength of the earthquakes. Also the maximum amplification was observed during the
second earthquake when the excess pore pressures were small. The natural frequency
predicted by theoretical approach suggested that during earthquake 2 the natural
frequency of the saturated sand bed approaches the driving frequency of the
earthquake and hence results in relatively smaller attenuation of base motion as it
travels to the surface of the sand bed. During all other earthquakes the attenuation is
much larger as the natural frequency of the sand bed falls well below the driving
frequency. Also the data suggests that the rate of pore pressure build up is a direct
function of the strength of the earthquake.
24
In the second centrifuge test MG-5 earthquakes were fired in strictly the order of
increasing intensity. The magnitude of the excess pore pressures generated at different
heights within the sand bed remained more or less the same during all the six
earthquakes fired on this centrifuge model. The natural frequency predicted by
theoretical approach suggested that during earthquake 1 the natural frequency of the
saturated sand bed is far above the driving frequency of the earthquake and hence
results in some attenuation of base motion as it travels to the surface of the sand bed.
During the second earthquake the natural frequency is almost the same as the driving
frequency resulting in the relative amplification of base motion as it travels towards the
sand surface. During all other earthquakes the attenuation is much larger as the natural
frequency of the sand bed falls well below the driving frequency. Also the data from
this centrifuge test suggests that the rate of pore pressure build up is a direct function
of the strength of the earthquake.
REFERENCES
Hardin, B.O. and Drnevich, V.P., (1972), Shear modulus and damping in soils: design
equations and curves, Jnl. of Soil Mech. and Found. Eng.Div., ASCE, No.SM7,
pp.667-692.
Kutter, B.L., (1982), Centrifuge modelling of response of clay embankments to
earthquakes, Ph.d thesis, Cambridge University, England.
Madabhushi, S.P.G., (1994), Natural frequency of a Horizontal Soil Layer, Part I: Dry
sand bed, Technical Report, CUED/D-SOILS/TR27 1, Cambridge University, England.
Seed, H.B., Lee, K.H. and Idriss, I.M. and Makadisi, F.I(1975), The slides in the San
ASCE Jnl. of
Fernando dams during the earthquake of February 9, 1971,
Geotechnical Engineering Div., GT7, pp 651-688.
25