Natural Frequency of a Horizontal Soil Layer Part II ... Frequency of a Horizontal Soil Layer Part...

Natural Frequency of a Horizontal Soil LayerPart 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 conductingtwo centrifuge tests. The depth of the sand bed in each of these centrifuge tests wasarranged such that the small strain natural frequency of the sand bed was very highcompared to the driving frequency of the earthquake. When the correct naturalfrequency of the sand bed was estimated using the shear modulus corrected for shearstrain amplitude induced by the earthquake loading and taking into account thereduced effective stresses within the sand bed following the generation of excess porepressures, the natural frequencies of the sand beds were much lower and close to thedriving frequency of the earthquakes.

In the first centrifuge test a strong earthquake was fired first followed by a smallersecond earthquake. All the subsequent earthquakes had increasing intensity. Smallerexcess pore pressures were generated during the smaller second earthquake and allother earthquakes resulted in large excess pore pressures. Also during the secondearthquake the attenuation of base shaking was small as it travelled towards the sandsurface. Calculation of the natural frequency of the sand bed during earthquake 2 hasshown that it is indeed close to the driving frequency of the earthquake there byresulting in the smallest attenuation. In all other earthquakes the driving frequency wasfar from the natural frequency causing significant attenuation of base shaking as ittravelled towards the sand surface. Also the data suggested that the rate of excess porepressure build up is a function of the strength of the earthquake.

In the second centrifuge test all the earthquakes had increasing intensity. Also all theearthquakes resulted in more or less the same magnitude of excess pore pressureswithin the sand bed. During the second earthquake the attenuation of base shaking wassmall as it travelled towards the sand surface. Calculation of the natural frequency ofthe sand bed during earthquake 2 has shown that it is indeed close to the drivingfrequency of the earthquake there by resulting in the smallest attenuation. In the firstearthquake it was shown that the natural frequency is far above the driving frequencyand in all other earthquakes the driving frequency was far below the natural frequencycausing 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 porepressure 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 .

bAXIAL STRAIN

7

AXIAL STRAIN

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

5

I

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 + $Vsa, =

h. . . . . . . (6)

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

ZmaxYr = - . . . . . . . . . . (9)

G max

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= =GmZt+

. . . . . . . . . . (12)

r

Knowing 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 generation of

6

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

11.4. .* -c .

0.600.25

f-+ 5.8

T’ *-

I

-

B

/-‘Filterkrmmic)

Tulbn tubaoutsiclo dia 2.37

, Idl,,r:4l CU~IIW~lIUI~ /Rod Supply Poritivrho SUP~Y nrwiwYolbw Output poiitivrGreen Output rwgatk0

unit: mm

mass: 0.004kg

Fig.4 Typical dimensions of a pore pressure transducer

i” = ylz....(2)

4 bBase shaking Bed rock

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 (l+ 2Ko) ’0, =

3 cb---- (4)

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

-100

.

. I

I

0 500 1000 t500 2000 2500

Fig.5 Filter Characteristics

I

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.

1 1

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.


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 II3436 1900

Fig. 6: Schematic diagram showing the placement of transducers inCentrifuge Test MG-4

Table 1 Placement of transducers in centrifuge test MG-4

TransducerACC 1225A C C 1926A C C 1572A C C 3492A C C 5754A C C 3477A C C 3466A C C 1 9 2 5A C C 5701A C C 3441A C C 1258A C C 5756A C C 3436A C C 1900PFT 3007P P T 6514P P T 4478P P T 2926P P T 6260P P T 6784P P T 6803P P T 6270P P T 3969

x (mm)5 5

28236047050

2 6 34603 4 556

2754653 5 5

fixed to the containerfixed to the container

1 2 02 8 14755 8

26545875320440

Y (mm)5555

808279801 3 51 3 71 3 31 3 1

333

7880761 3 61 3 51 3 3

y :~~T

. . . . . . :::A:.: . . . . . :.:.:.:.:.:.::::::~::::::.:..:..:.::::~.~.~.:.~.~ _,.,.,.,.X

Table 2 Hydrostatic pore pressures in centrifugetest MG-4

1OG11.957.736.6812.400.814.2012.517.895.28

20625.7516.4514.7226.511.709.3127.2117.3211.67

40653.7134.1931.1354.84149.6619.7556.0235.8524.28

50668.1843.3039.6469.554.4425.1970.8045.2830.73

Table 3 Norma&d accelerations in the sand columnin centrifuge test MG-4

Location

EQ: 1At base of the sand column

At the mid depthNear the surface of sand bed









Normalised Acceleration

10.5

0.4128

11.01060.8404

1- -

0.752

1--

0.3247

1- -

0.2895

ACC344

ACC570 1

PPT65

wt--=1

PPT6260

Max=25.3

Mb=-26.4

Max=O.l

Mill=-0.2

Max=lO.S

Mln=-12.3

Mox=S.O

Mill=-9.4

Max=24.9

Mln=-33.6

Maw=11.6

Mill=-10.0

Max=11.4

Min=-12.4

Max=64.7

Mln=-4.0

Max=34.5

Mln=-1.3

I

T E S T M G - 4 1M O D E L S A T 1 EQ-’FLIGHT -1 i

I

Scales : Model

SHORT TERMTIME RECORDS

G Level FIG.NO.5 0 7

1

1267 da/b points plotted per complete transducer record

20 Max=26.2

ACC34360 E

-20 Mb=-25.5

[msec]

/

1

.20 Max=22.5

PPT6270 P2. 10,

Mln=-1.1

110 120 130 140 150 1w 170 180 190 200 210[msec]

.75Mox=73.2

PPT3007 .50-z

.25-

Mill=-3.6.O

20 so 40 50 60 ‘Jo 80 a0 loo 1 1 0 120 Iso 140 150 160 170 180 190 200 210

[msec]

2 Max=2.4

PPT2976 B0 2

Mln=-2.0- 2

[msec]

.20Mlnc=20.5

PPT6803 .lO -07E

.O hiin=-4.2

. .‘.20 30 40 50 fi 1~7.0 6iJ so loo 1;o 1;o 130 140 1w 160 170 160 190 200 210

I [msec]

I

.40Mex=38.6

PPT4478 .206z.,

.O Ml=-7.4

20 JO 40 M 60 170 00 so loo 1 1 0 120 130 140 150 1 5 0 170 160 190 2w 210

[msec]

Scales : Model

T E S T M G - 4 ~ SHORT TERM G L e v e l FIG.NO.M O D E L S A T ~ EQ-1 5 0 8FLIGHT -1 I

TIME RECORDS

901 da$ poirits plotted per complete transducer record

ACC 1900 0%

ACC 1572

(0

ACC1925 .I z

. 4

h-1. II

ACC3466

ACC1258

ACC1926

Scales : Model

Mox=24.6

Min=-27.4

Max=ll.J

Mh=-6.6

Max=17.0

Mln=-13.8

Mox=lS.l

Min=-4.4

Max=7.6

Mln=-6.1

Min=-1.0

Max=15.6

Min=-13.6

Max=21.6


G Level

5 0FIG.NO.

9

ACC3436

ACC3477

PPT65 14

PPT6270

PPT4478

PPT6784

PPT3969

901 data points plotted per complete transducer record

b-1

Mln=-3.4

Max=27.7

Mox=44.6

M a x = 2 6

Min=-2.8

Scales : Model

T E S T M G - 4 i

MODEL SAT E Q - 1 ~FLIGHT -1 : ~


G Level

50

FIG.NO.1 0

ACC344

PPi6260 to-

I Scales : Model

Min=-6.9

Min=-10.3

Min=-6.6

Min=-9.8

Max=7.4

Min=-9.3

Mox=25.9

Mln=-2.2

Max=26.6

Mln=-0.8

T E S T M G - 4 ~ G Level FIG.NO.MODEL SATFLIGHT -1 ~

EQ-2 SHORT TERMTIME RECORDS 50 1 1

1267 dab points plotted per complete transducer record

10

M0x=8.7

ACC34360 E

Mill=-9.4

20 30 40 60 60 70 60 90 loo-10

110 120 130 140 160 160 170 160 160 200 210[msec]

.20 Max=21.5

PPT6270 7log

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]

I1

Max=X.O

PPT3007.20

F-lo&

.OMln=-2.2

20 so a0 too li0 1;o lil 140 Go rso 1;o GO 190 2iJO 2io[msec]

1-3

Max=2.7

PPT?976.2

.lj

.OMin=-0.7

20 30 40 60 60 70 60 90 loo 110 120 130 140 150 160 170 160 160 200 210

[msec]

I

.20Mox=19.7

PPT6803 P10 2

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]

2 Max=2.3

PPT4478 -212

0 WI=-0.4

20 30 40 60 60 170 60 90 loo 110 120 130 140 160 160 170 160 190 200 210

[msec]

Scales : Model

.TEST M G - 4 I ISHORT TERM G Level FIG.NO.

M O D E L S A T ~ E@-2 5 0 12FLIGHT -1 1 TIME RECORDS

I

ACC3436

ACC 1900

ACC1572

ACC1925

ACC5756

ACC3492

ACC3466

ACC 1258

ACC1926

Scales : Prototype

Min=-4.6

Yin=-4.5

Min=-6.5

Max=6.0

Mln=-6.6

Mox=O.6

Min=-0.4

Win=-12.5

Min=-6.9

T E S T M G - 4MODEL SAT EQ-2FLIGHT -1 : ~1


G Level

5 0

FIG.NO.13

ACC3436

ACC3477

PPT6260

PPT6270

PPT4478

PPT6784

PPT3969


Scales : Prototype

Mox=25.4

Uln=-2.7

Uin=-3.0

Win=+.2

Yax=25.0

Min=-5.6

bhx=16.6

Min=-1.3

T E S T M G - 4 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 2 14

F L I G H T - 1 TIME RECORDS 5 01

1267 da.10 paints plotted per complete transducer record

10 Mox=14.7

ACC3436 .o E.-IO

bun=-14.5

20 30 40 SD 03 70 a0 w rm 110 ml IJO Ma co 100 170 Ito IW ml 110[m-cl

. to Mox=lZS

ACC 1926 OE.-10

Mill=-14.5

20 30 40 60 90 70 .v so ton (10 VW 1.w Mu 150 I(10 vm 100 Ino ¶m *10[m-l

1 - ‘0Mox=6.9

ACC3477.D

E

Mln=-3.7

lo 30 40 co 0 70 no w tm ,,o 110 ,m 140 180 110 110 110 1w 100 atob-1

Max=9.4

ACC344 1 E.-(0

Mill=-14.6

20 30 40 so 60 70 M w ,m 110 m IS MO Iso $10 no 100 190 !2m no[m-l

Mox=14.2

ACC1225 - O E.-to

ml=-16.2 '.-20

10 30 40 $4 40 10 M *I wo 110 tm Iso wo Ino 100 170 IW 190 m !a0h=l

Max=11.4

ACC5754 -

.-ID Min=-11.3

20 SD 40 w m 70 00 so 100 $10 1m 1.x ‘da ts MO 170 llyl Iso no so[m-cl

Max=9.4.o

ACC570 1 .P E.-0

. . . . . . Min=-6.7

20 Jo 40 m m ny u) 00 tm ,,o ,m ,a0 140 ‘so IW (70 I- Iso IOD ato[mms]

Max=BO.l

PPT6514.40-

2.m-

Ml=-3.0

b-1

Max=35.6

PPT6260

ml=-0.6

20 20 40 90 wo[m=cl

Scales : Model/

T E S T M G - 4 SHORT TERM G Level FIG.NO.MODEL SAT EQ-3 .._

TIME RECORDS 5 0 - 15

F L I G H T - 1 I

ACC3436

PPT6270

PPT3007

PPT2976

PPT6803

PPT4476

1267 da o points plotted per complete transducer record

10 Mox=14.2

0 z

-10Mill=-14.s

I I20 30 40 50 w 170 so 90 ,oo 110 120 130 140 150 180 170 110 1w 200 210

[msec]

20 M 40 50 so 70 so 90 loo 110 120 130 140 150 160 170 160 190 200 210[msec]

20 Max=21.6

7lo&

Ml=-0.70

Mw=59.6

.20-

Mln=-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-0L

'O Mln=-0.7

20 30 40 Jo 120 1.30 140 IM lso 170 160 190 200 210

Min=-0.50

20 30 40 50 so irn 60 90 loo 110 120 (30 140 150 160 170 160 190 zoo 2to

[msac]

20Max=20.7

I [msec]

Scales : Model

TEST MG-4 ’ :E Q - 3MODEL SAT

FLIGHT -1 ;


G Level5 0

FIG.NO.1 6

901 ddha points plotted per complete transducer record

ACC3436

ACC1900 “Z

r-s

ACC1572

ACC1925

ACC3466

ACC1926

b-1

Min=-15.2

Min=-3.5

Uin=-0.5

Yox=12.4

Min=-13.7

Scales : Prototype

T E S T M G - 4MODEL SAT E Q - 3FLIGHT -1 , 1I


G Level5 0

FIG.NO.1 7

ACC3436

ACC3477

PPT6514

PPT6260

PPT6270

PPT4478

PPT6784

PPT3969


5.x

h4

Min=-3.6

Mox=39.4

Mln=-7.8

Max=23.2

Minz-1.6

Scales : Model

T E S T M G - 4 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 3 ,

TIME RECORDS 5 0 18F L I G H T - 1

1267 dot9 points plotted per complete transducer record

IMax=59.2

.a-PPT65 14 a

.20=Mill=-3.1

40 Mox=39.2

‘iiPPT6260 ,mz

ml=-0.7

&10 Jo 4a ,20 ‘70

h=l

/ I

T E S T M G - 4I

MODEL SATFLIGHT - 1 1 : 1’

Scales : Model


G Level5 0

FIG.NO.1 9

ACC3436

PPT6270

PPT3007

PPT2976

PPT6803

PPT4478

126? doti points plotted per complete transducer record

0 E

-20 Mln=-23.0

20 30 40 50 60 70 60 90 loo 110 120 130 140 150 160 170 160 190 200 210[msac]

.20 Llox=21.4

'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]

/

20 30 40 5 0 120 130 140 154 160 170 164l 190 200 210[msec]

64

40%.5

20

0

Mox=66.0

Mill=-3.7

4 M.xG4.3

2Ts

0 M i l l = - 0 . 8

20 30 Ml 54 0'70 60 60 loo 110 120 130 140 150 160 170 160 190 200 210

[mow]

.20Mex=19.9

20 30 60 50 60 I,70 80 90 iw 1 1 0 120 150 140 15n 150 170 160 190 200 210

[msac]

IMax=31.5

.20 -B2,

.O Min=-6.1

20 30 40 50 60 7 0 60 90 loo 1 1 0 1 2 0 1 3 0 140 1 9 0 2w 210

[msec]

Scales : Model

I

TEST MG-4 I ’M O D E L S A T ! E@-4 1FLIGHT -1 ; !



901 data points plotted per complete transducer record,

A C C 3 4 3 6 -

.pD

ACC1572 ,z

(0

A C C l 9 2 5 z

.eACC5756 z.-n

-0ACC3492 B

.-0.6

I h A A P

A C C

Uox=23.0

thx=10.2

Min=-10.6

Mox=2l.6

Yin=-14.9

Mox=14.6

Mb=-4.6

Max=6.2

Yin=-10.4

Mox=O.6

Win=-0.9

Max=l7.6

uin=-21.6

uox=17.7

MIn=-17.1

Yox=22.6

Mln=-26.4

ACC3436

ACC3477

PPT65 14

PPT6270

PPT4478

PPT6784

PPT3969


Max=6.6

Max=61.9

Min=-4.2

Min=-2.6

Max=37.2

Mb=-6.7

Scales : Model

Mox=42.6

Mb=-5.6

Max=27.9

hiin=-1.5

T E S T M G - 4E Q - 4 SHORT TERM G Level FIG.NO.

MODEL SAT TIME RECORDS 5 0 2 2

F L I G H T - 1


ACC344

PPT65

PPT6260

Min=-11.0

Min=-17.4

Max=28.0

Min=-20.8

Max=59.6

MI=-2.8

Scales : Model

TEST MG-4 I :I

M O D E L S A T i EQ-5‘1

FLIGHT -1 1

SHORT TERM

T I M E R E C O R D S

G Leve l

5 0FIG.NO.

23

/ i I

1267 data’ points plotted per complete transducer record

ACC343620 Mox=32.8

60 Y

I

1 1

A -l

I !

PPT6270I I’

20 30 M 60 70 80 90 100 110 120 130 140 t.50 160 170 160 190 200 210

PPT3007

[msec]

20 30 40 60 60 70 60 90 loo 110 120 130 140 150 160 170 160 190 200 210

'20 Max=21 .l

7toz

Mill=-1.0.O

75Mox=70.5

mmB

25&

Mln=-2.90

Max=5.3

PPT2976 .4

z.2&

.o win=-0.7

20 30 40 w 70 54 90 im 110 120 130 140 150 ($0 170 160 190 2m 210[msec]

PPT6803

20 M 40 50 60 70 60 90 1m 110 120 130 140 1w 160 170 160 190 200 210

[msec]

20 Max=22.5

‘j;log

0Min=-1.9

PPT4478

I

’ I .60Mox=61.0

.40-"0

,205

.O Mill=-8.0

20 30 40 60 60 70 60 90 100 110 120 130 (40 160 160 (70 160 190 200 210

[msec]

Scales : Model

I I

TEST MG-4 ~ I ~’M O D E L S A T j EQ-511FLIGHT -1 ~ Ii

II



9 0 1 data p o i n t s p l o t t e d p e r c o m p l e t e t r a n s d u c e r r e c o r d

.?o

A C C 3 4 3 6 - 0 6

,

I ‘0

A C C 5 7 5 6 - 03.-6

ACC3492 E4

A C C 3 4 6 6 . o E

,-m

S c a l e s : M o d e l

Mow=30.2

Max=26.9

Mln=-19.7

Max=lZS

Min=-4.0

Max=6.0

Mln=-8.0

Max=O.B

Mill=-1.7

Max=Z1.5

Min=-26.5

Mox=20.5

Mln=-19.8

Mox=30.4

Mln=-30.0

ACC3436

ACC3477

PPT65 14

PPT6270

PPT4478

PPT6784

PPT3969


h-4

Mox=30.2

Max=6.5

Mcx~61.6

MI=-2.6

Max=36.3

Min=-2.6

Mox=65.3

I&x=44.7

hAin=-6.6

Mox=29.6

Min=-2.3

Scales : Model

IT E S T M G - 4 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 5

TIME RECORDS 5 0 26

FLIGHT - 1

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

I I

0 20 40 50 80 loo 120 140 150 150 200

h-1

22 -5

- 1 0

-1s . 1,’

0 20 40 50 50 1w 17.0 140 150 loo 209

[msec]

5

0

3 - 5

-10

I

I

-15 I

1

0.5

0 loo 200 300 El 500 600 700

TEST MG-4MODEL SATFLIGHT -1 I

Near Surface Accelerations

and Frequency Analyses

FIG.NO.

27

0 m 4i aa a0 lrn lie Ii0 IW Ii0 loo

[m-l

5

0

a

-5

-10

I0 20 40 50 50 loo 12 0 1 4 0 10 150 zoo

I1 . 5

1

0 . 5 .

0 IW 200 so0 El 500 500 700 5no

1 . 5

1

0.5

0 IW 200 3w 400 500 0 rw

[Hz]

0.4 -

0.2 .

0 100 200 300 El 500 700

Scales : Prototype

100

90

80

70

80

50

40

30

20

10

0

Test: MG-4

v-----

--q near base&-----------AZ

I

i

i mid depth

I I I I I I 1 I

0 5 10 15 20 25 30 35

Strength of the Earthquake (W G-Level)

Fig.28 Generation of excess pore pressures during theearthquakes in centrifuge test MG-4

Naturalfrequency

(Hz)

250

150

100

50

0

Excess pore pressure (Pa)

Fig.29 Theoretical relationship between excess porepressures and the natural frequency

0 . 9 0 0

0 . 8 0 0

0 . 7 0 0

0 . 8 0 0

0 . 5 0 0

0 . 4 0 0

0 . 3 0 0

0 . 2 0 0

5

\Test MG-4

‘hq

\\

\

\kg\a, -----.-~

---a

I I 1 I I I I I I

5 1 0 1 5 2 0 2 5 3 0 3 5

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 accelerationwith the strength of the earthquake


P P T 6 5 1 4

EQ-2 g::.

5.

0.

PPT 6 5 1 4

0 20 40 60 80 loo 120 140 160 180 200[mscc]

E Q - 3 zw20. PPT 6 5 1 4

0.0 20 40 60 60 1 0 0 1 2 0 1 4 0 120 100 200

[msec ]

PPT 6 5 1 4

/ I

so.

40.

EQ-5 gm-

20.

10.

PPT 6 5 1 4

O-

0 20 40 00 00 100 120 1 4 0 120 100 200[msac]

Scales : Prototype

T E S T M G - 4MODEL SATFLIGHT -1

Base Pore PressureTIME 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.


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


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

I100 mm

10 II3436 1900

Fig. 32: Schematic diagram showing the placement of transducers inCentrifuge Test MG-5

Table 4 Placement of transducers in centrifuge test MG-5

TransducerACC 1225ACC 1926ACC 1572ACC 5701ACC 3441ACC 3466ACC 1925ACC 5754ACC 3457ACC 3477ACC 5756ACC 1258ACC 3436ACC 1900PPT 65 14PPT 6803PPT 4478PFT 3969PIT 6270PPT4481PPT 3007PPT 6260PPT 6784

x (mm)25

28032049030

25029549520

275350490

fixed to the containerfixed to the container

26530

440.562

30046065

315475

Y (mm)5555

424 0444167727273

333

423740726874

Table 5 Hydrostatic pore pressures in centrifugetest MG-5

1 PPTNO. 1 1OGPPT6514PPT4478PPT6803PPT6270PPT3969PPT4481PPT6260PPT3007PPT6784

5.317.657.785.370.525.831.672.625.13

20613.5616.3816.9211.551.1112.435.477.5211.10

40631.5835.1735.7724.262.3325.9713.3717.6723.37

50641.2645.5745.9531.193.0033.1717.2422.6829.85

Table 6 Normalised accelerations in the sand columnin centrifuge test MG-5

Location





EQ: 3At base of the sand columu








Normalised Acceleration

10.93240.8378

11.03491.1047

10.67430.57 14

10.53570.4286

10.3384

0.25

10.40860.2857

1 120 data points plotted per complete transducer record

.o

A C C 1 9 2 6 . .o E

I’

,a,PPT6270 FJto

Scales : Model

Min=-12.2

Max=9.6

Min=-10.7

Max=7.4

Ml=-7.5

Max=6.9

Min=-6.9

Max=6.2

Min=-6.6

Max=42.6

Mill=-1.2

Mox=27.9

Mln=-0.6

T E S T M G - 5E Q - 1 ~ SHORT TERM G Level FIG.NO.

MODEL SAT TIME RECORDS 5 0 33

FLIGHT -1


1 0 Max=lZ.S

ACC3436.o z

.I 1 -10 Mln=-12.4

1 0 20 30 40 50 60 70 60 90 loo 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 160[msec]

II

PPT6260 ’I

1 0 20 3 0 40 50 8 0 70 a0 90 1 0 0 1 1 0 1 2 0 1 3 0 140 1 5 0 194 1 7 0 180[msac]

PPT6803

1 0 2 0 30 40 50 60 70 60 90 loo 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 9 0 1 7 0 1 6 0[IWC]

PPT3969

1 0 20 30 40 50 60 m 80 90 100 tie li0 lie 140 lie lie 1 7 0 l&J[msec]

Mln=-0.30

40

F20 2

0

Max=40.3

Ml=-3.6

PPT3007

10 20 3 0 40 50 60 70 60 90 1 0 0 1 1 0 1 2 0 1.30 1 4 0 1 5 0 1 6 0 1 7 0 180[msec]

PPT4476

1 0 2 0 347 40 5 0 90 7 0 60 90 loo 1 1 0 1 2 0 1 3 0 140 1 5 0 1 9 0 1 7 0 1 6 0

[msec]

Scales : Model

40 Ma~42.4

P20 2

0 Ml=-4.3

T E S T M G - 5EQ- 1 SHORT TERM

MODEL SATFLIGHT -1 TIME RECORDS

I

FIG.NO.34

I I I I I I L>


ACC3436

ACCI 926

PPT65 14

PPT6270

PPT6260

PPT4478

PPT448 1

PPT6784

Em-1

Scales : Prototype

Uax=6.2

WI=-6.5

Min=-2.9

Max=Zl.6

Yin=-2.7

Max=46.7

Yax=36.5

Min=-3.2

Mox=33.2

Min=-4.6

T E S T M G - 5 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 1 3 6

FLIGHT -1 TIME RECORDS 5 0I


ACC344

I

ACC1926 oE

-6

10

0 6

-10

PPT65 14 Tme

PPT6270

I Scales : Model

Min=-16.7

t&x=14.2

Uax=13.7

MIT=-16.2

Mox=6.6

Mill=-7.4

Max=6.9

Min=-9.2

Mox=9.5

Min=-10.4

L(ax=41.5

Min=-0.4

Max=27.1-

Mill=-0.4

I I

T E S T M G - 5 IE Q - 2 ~ SHORT TERM G Level FIG.NO.

MODEL SAT TIME RECORDS 5 0 3 7

F L I G H T - 1 IL

1120 data paints plotted per complete transducer record

.I0c/i/(y(yy-y Max=16.6ACC3436

z.o Y

-10I Mln=-15.5

10 20 30 40 50 50 70 6 0 90 (00 1 1 0 1 2 0 130 140 1 5 0 160 1 7 0 164[msec]

.20Max=19.6

PPT6260‘;;

-10 B

Mill=-0.1

1 0 20 40 50 60 70 S O 1 0 0 $90 1 2 0 1 3 0 1 4 0 1 5 0 160 1 7 0 la0[msec]

PPT6803

10 20 30 40 50 60 70 6 0 90 1 0 0 1 1 0 120 130 1 4 0 1 5 0 164 1 7 0 1 6 0[msec]

4 0 Max=42.7

F20 2

D Min=-3.3

PPT3969

,o Mill=-0.3

1 0 20 30 40 50 60 70 6 0 60 1 0 0 1 1 0 1 2 0 130 1 4 0 Go 1 6 0 tie l&l[msec]

PPT3007

Mill=-0.2

1 0 20 so 40 50 60 m 80 90 100 1 1 0 1 2 0 1 3 0 140 150 loo 1 7 0 160[msec]

PPT4478

1I

Max=42.5

x. 2 0 ,f.,

Ml=-0.5

1 0 20 Jo 40 50 60 70 60 90 1 0 0 1 1 0 1 2 0 130 1 4 0 1 5 0 lso 1 7 0 180[msec]

Scales : Model

I

T E S T M G - 5 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 2

TIME RECORDS 5 0 3 8

FLIGHT - 1 !

ACC3436

ACCl900

ACC 1572

ACC1925

ACC5756

ACC5701

ACC5754

ACC1258

ACC 1225


Mox=6.6

Min=-6.5

Min=-1.9

Mb=-15.6

Mox=16.1

Mln=-16.6

MI=-26.3

Max=13.6

Mln=-16.5

Scales : ModelI

T E S T M G - 5MODEL SAT E Q - 2FLIGHT -1 / 1


G Level

5 0FIG.NO.

39

ACC3436

ACC1926

PPT65 14

PPT6270

PPT6260

PPT4478

PPT448 1

PPT6784


Scales : Prototype

Max=42..9

Wax=ZQ.D

Min=-2.9

Uax=37.1

Min=-3.7

Uin=-5.6

T E S T M G - 5MODEL SAT E Q - 2 SHORT TERM G Level FIG.NO.

TIME RECORDS 5 0 40

FLIGHT -1 I

1120 data paints platted per complete transducer record

M.X=22.5

ACC3436 .o E

.-m Min=-22.710 50 30 40 50 aa m 00 m too 110 120 1% 140 ma 110 170 180

[m-cl

Max=21.8

ACC 1225 0 6

.-m Mln=-24.2m za so 40 so ID 70 en aa Irn IID 110 I30 340 $60 Ia0 170 ,m

[m-l

Max=18.5

ACC3441

Ml=-18.0

10 m 24 4a 80 ,m 70 m w Irn--la

110 m ,sn Ma ,w 1m (10 IIDb=l

Max=15.5

ACC3457 OE

.-lo Min=-22.8

10 20 30 40 60 ID m aa w Irn Ito ,a0 1s 140 150 ,#a 110 ,noCm-1

-laMax=17.5

.I0ACC1926 .o E

.-ID Mill=-13.7

10 10 30 40 m aa 70 IO w lrn <ID I?0 ,sn 140 IYI ,m tm ,a0h-1

I O Max=11.8

ACC3466 .o E

Mb=-9.4, -to

(0 za so 40 aa 10 10 m (0 100 110 120 130 140 9% ,#a 170 10[m=l

. toMox=lO.O

ACC3477

Min=-9.0r-IO

10 m 24 40 w m m IO 90 102 ($0 I)0 I= (40 tDD ,a 00 100[m=l

Mox=42.2

PPT65 14 6.P&

Ml=-1.3

P #a (00b-4

L(ax=29.5

PPT6270.7.0-

eB(0Mitt=-0.7

10 10b-1

Scales : Model

T E S T M G - 5 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 3 ~

TIME RECORDS 5 0 4 1F L I G H T - 1 /


.20(A*. Mm=23.2

ACC3436.o z

. -20 Mill=-22.1

10 20 30 40 M 60 70 80 00 100 110 120 130 140 150 lea 170 180[msec]

uax=17.3

PPT6260

.5Mln=-0.3

10 20 30 40 50 50 m 50 90 loo 110 120 130 140 150 150 170 150[msec]

.40Mex=47.6

PPT6803 P2.20,

Ml=-3.5-0

1 0 20 30 40 50 eo m 50 s o 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 5 0 170 150[msec]

3Mox=J.l

PPT3969 2,"0

155

0 MIn=-0.6

10 20 30 40 M 60 m 50 DO 100 110 120 130 140 lea 170[msec]

Max=25.0

PPT3007

r10 20 30 40 50 60 m Kl s o loo 110 120 130 140 150 160 170 160

[msec]

.40 Max=45.4

PPT4478 6.20&

.OMill=-3.7

10 20 30 40 50 50 m 50 so 103 110 120 130 140 150 160 170 160

[mscc]

Scales : Model

T E S T M G - 5MODEL SAT E Q - 3 ~

SHORT TERM G Leve l FIG.NO.

TIME RECORDS 5 0 42

F L I G H T - 1 I ~

ACC3436

ACCl900

ACC 1572

ACC 1925

ACC5756

ACC5701

ACC5754

ACC 1250

ACC1225


Min=-21.6

M.ax=27.3

M i n = - 2 . 9

Max=23.5

M i n = - 2 2 . 0

Max=23.6

Min=-22.6

Max=PB.O

WI=-36.7

Mcx~20.6

Mln=-23.4

Scales : Model

T E S T M G - 5 SHORT TERM G L e v e lE Q - 3 ~

FIG.NO.MODEL SAT TIME RECORDS 5 0 4 3

FLIGHT -1

ACC3436

ACC1926

PPT6270

PPT6260

PPT4478

PPT448 1

PPT6784


T E S T M G - 5MODEL SAT E Q - 3 SHORT TERM G Level FIG.NO.

5 0 4 4

FLIGHT -1 TIME RECORDS

Scales : Prototype

kr~42.5

Min=-2.5

Mox=36.2

Mill=-3.5

Yox=34.7

Mb=-4.3

1 1 2 0 d a t a p a i n t s p l o t t e d p e r c o m p l e t e t r a n s d u c e r r e c o r d

ACC1225

ACC1926

PPT65

VJ wab-4

.10-PPT6270 2

.10-

Min=-26.4

Max=l5.6

Max=25.2

Min=-23.1

Min=-10.1

Max=10.6

Min=-9.0

Max=41.2

Min=-1.3

Max=29.6

MIn=-0.6

S c a l e s : M o d e l

T E S T M G - 5 SHORT TERMG Leve l

E Q - 4FIG.NO.

MODEL SAT T I M E R E C O R D S 5 0 45

F L I G H T - 1 I

1 120 data points plotted per complete transducer record

ACC3436

I10 20 30 40 M 50 70 80 90 100 (IO 120 130 140 150 190 170 160

[msec]

10 20 30 40 60 90 70 IM 90 loo 1,o 120 130 140 1% 150 170 mo[msec]

15 Mox=l6.1

5

Mln=-0.50

Max=42.1

PPT6803 P.20 2

.OMill=-3.6

PPT3969

10 20 30 40 60 60 70 50 90 loo 110 120 130 140 160 160 170 160[mom]

PPT3007

PPT4478

3Mox=3.0

2

51L

0 Mln=-0.5

I10 20 30 40 50 90 70 50 90 loo 110 120 130 140 160 160 170 160

[msec]

Max=26.6

WI=-0.6

Max=50.0.40

72

.20-

Mln=-2.6.O

10 20 30 40 50 60 m Ml 90 1w 110 120 130 140 150 150 170 180

[msec]

Scales : Model

T E S T M G - 5 ~

MODEL SAT E Q - 4F L I G H T - 1


G Level

5 0FIG.NO.

46


ACC1572

b-1

ACC5701

ACC5754

ACC1225

t-4

Max=26.9

Min=-8.6

Min=-25.0

Max=25.5

M i n = - 2 3 . 7

Max=23.3

Mln=-26.3

Scales : Model

‘ T E S T M G - 5E Q - 4MODEL SAT

FLIGHT -1 1 1


G Level

5 0FIG.NO.

47


ACC3436

ACC1926

PPT65 14

PPT6270

PPT4478

PPT448 1

PPT6784

Max=24.2

Max=42.6

Yox=32.5

Min=-2.5

Mox=36.7

Mill=-3.0

Mox=36.4

Mln=-4.7

Scales : Prototype

T E S T M G - 5 G Level FIG.NO.

MODEL SAT E Q - 4 SHORT TERMTIME RECORDS 5 0 48

FLIGHT -1 I


Max=27.8

ACC3436

.-loMin=-28.0

10 so 30 40 I 0 m 10 w tO0 110 120 130 140 150 160 110 ,a0[m=l

Mox=29.0

ACC1225 ,o E.-10

ml=-29.9

$0 !a lo 40 w 0 70 YI (0 100 ,,a 020 ,Y) 140 Ia0 IQ ,10 ,IDh-4

.m Max=22.1

ACC344 1 O E

.-a Mb=-26.5

10 m so 40 P Q ID IO 90 IO0 110 Ilp ,P ‘40 *so 1m r/o ,I0

b=l

+yJy)-JofiyJlJyL&>

(0 Max=16.0

ACC3457 o E-10

. . . Mill=-18.5-ID

(0 20 .m an 60 m 10 w m tm IlO m ,a0 $40 wa 180 *?a mab-1

kx=32.a.m

ACC1926 .o E

.-mMin=-32.7

$0 20 30 40 Ea a0 70 *I 00 100 110 m 9s ‘40 1w IQ tm tm

b-4

Mox=ll.l

ACC3466

.-to t&l=-9.8

$0 20 so 40 80 0 n w so Irn (10 110 Iso wa Ma 110 110 la0[m-l

Max=&2.*

ACC3477 .o E

.-IMin=-7.9

to 20 m 40 m m IO m 10 too ,I0 $20 130 140 Ino 110 (70 180

h-1

Maw=40.5

PPT6514

Mln=-1.1

[m-=1

Max=30*6

PPT6270 IOMill=-0.4

20 w wnh4

Scales : Model

~T E S T M G - 5 SHORT TERM G Level FIG.NO.MODEL SAT E Q - 5 ~

TIME RECORDS 5 0 4 9

F L I G H T - 1


ACC3436

I . -

10 2 0 30 40 50 80 70 60 90 100 110 120 130 140 150 160 170 ,w[msec]

PPT6260

AJ10 20 50 40 50 90 70 60 DO loo (10 120 130 140 150 160 170 160

[msec]

.40 Max=43.0

PPT6803 F.2og

.OMin=-3.3

10 20 30 40 50 so 70 60 90 1w 110 120 130 140 150 160 170 160

[mssc]

PPT3969

10 20 30 40 50 60 70 50 90 100 110 120 130 140 150 lso 170 180

[msec ]

PPT3007

10 20 30 40 50 60 70 M 90 loo 110 120 130 140 150 lso 170 1M

[msec]

3Max=2.6

2P

12

0Mill=-0.6

30

Mox=26.6

20P2

lo-

Mb=-0.6D

Max=50.1.40

PPT4478 7.2oz

.O Mln=-4.7

10 20 30 40 50 60 70 64 90 loo 1,o 120 130 140 150 160 170 1w

[msac]

Scales : Model

T E S T M G - 5E Q - 5 ~

SHORT TERM G Level FIG-NO.MODEL SATF L I G H T - 1 TIME RECORDS 5 0 5 0

1

901 dato points plotted per complete transducer record

.20

A C C 3 4 3 6 .o E

.-zo

ACC1900

ACC 1925

.o

.zoA C C 5 7 5 6 - .o E

I -zo

.lo

ACC570 1 .o E

.-20

A C C 5 7 5 4 _

ACC 1258

ACC1225 o E.-lo

Min=-28.8

Mox=22.2

Mln=-6.6

khx=5.6

Mb=-3.4

Max=5.1

Mb=-3.6

Max=30.3

Mill=-28.0

Max=29.9

MI=-26.3

Max=28.2

Mill=-39.0

Max=27.6

Mln=-29.3

Scales : Model

T E S T M G - 5E Q - 5

SHORT TERM G Level FIG.NO.MODEL SAT TIME RECORDS 5 0 51F L I G H T - 1

I

ACC3436

ACC1926

PPT65 14

PPT6270

PPT6260

PPT4478

PPT448 1

PPT6784


T E S T M G - 5 G Level FIG.NO.E Q - 5 SHORT TERM

MODEL SAT 52

FLIGHT -1 TIME RECORDS 5 0II

Stoles : Prototype

Max=32.5

Mor=19.6

Min=-2.9

Uin=-2.6

Mox=36.6

Min=-4.0

Yo.=36.6

Uin=-5.3


,la Max=29.7

ACC3436 .” E.-20 Min=-30.2

10 a0 30 40 50 m 10 u) w tm t(Q w.0 130 940 150 IW 170 ,aLm-4

.m Max=31.2

ACC1225 ‘O E.-10

ml=-31.6$0 WI 30 40 60 a0 m m (0 tm 110 lrn ~sn 140 150 tm 110 lrn

[m-=1

~Jj/y)fypy

.E?o Maxd3.7

ACC344 1 .o E

-20 Mln=-24.610 ?a Y) 40 m 0 70 I (0 too 110 v20 IJO 140 160 Ien I70 Ian

h-4

Max=21.7

ACC3457 .o E

” .-la Min=-21.6

IO !a Jo 4a 54 (0 10 80 a0 ,m ,,o tm 1s 140 1m l@o ,I0 110[m=l

.!a Max=40.0

ACC1926 0 3.-m

Mln=-45.510 10 SD 40 50 ,a m au w Irn (10 la 130 I40 180 I= 110

e-m110

h-1

TO Mox=12.3

ACC3466 ,E

Min=-8.7

10 10 so 40 s 0 7a *I so rm 110 120 1s 140 160 m 170 1mb-4

hiaX=&.5

ACC3477 ,o E.-n

Min=-6.2

90 20 z4 40 LQ * m Y I R) tm 110 10 ,a 140 (Do 110 170 mob=4

uax=40.7

PPT6514 .aoe,F

Mill=-0.7

10 in 30 40 PO 10 IO 90 100 VWh-1

Max=30.1

PPT6270.ZlJ-

0F10

Mb=-0.3

20 30 40 00 0 100Em-1

Scales : ModelI


TIME RECORDS 5 0 53

FLIGHT --I ,I

1120 data paints platted per complete transducer record

20 Max=30.2

ACC34360 Yr

-20Mb=-29.6

[msec]

- 20Mox=17.5

PPT62601 5

F. 10 -0c

-5Min=O.Z

10 20 30 40 60 60 70 60 SO 1W 110 120 1.30 140 150 t60 170 180

[msec]

/

Max=49.4.40

PPT6803 P2

.2oy

ml=-2.5

/ .O

10 20 30 40 60 60 70 60 DO loo 110 120 1.30 140 lx) 160 170 160

[msec]

4

Max=3.7

PPT39693

522z

1Mln=0.2

10 20 30 40 60 60 70 60 DO 100 110 120 134 140 160 164l 170 160

[meet]

M

Max=27.3

PPT3007 20,T;.?.a

1 0

Mln=-0.3

010 20 30 40 50 60 70 60 90 100 1 1 0 120 130 140 150 160 170 160

[msac]

I

Mox=50.6

PPT4478 P2

. 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


TIME RECORDS 5 0 54

FLIGHT -1


(0

ACClQOO - .D E

1 Y

ACC 1572 ‘0-z.o

ACC 1925

ACC5756

ACC570 1

McJx=30.9

Min=-31.2

Mox=14.3

Ml=-11.5

Max=21.4

Mln=-6.0

Max=5.4

Min=-5.6

Max=92

Mln=-3.4

Mox=32.6

Min=-29.6

Max=34.5

Min=-31.3

Max=34.6

Mill=-37.8

Max=JO.O

Mln=-31.5

Scales : Model

T E S T M G - 5MODEi S A T E Q - 6FLIGHT -1 /



ACC3436

ACC1926

PPT65 14

PPT6270

PPT6260

PPT4478

PPT448 1

PPT6784


T E S T M G - 5E Q - 6 SHORT TERM

MODEL SATF L I G H T - 1 TIME RECORDS

[m-cl

Scales : Prototype

uox=so.9

Mln=-31.2

Max=30.1

Mln=-29.1

Mar=42.7

Uh=-3.5

Max=32.4

WIT=-2.6

Max=20.4

Ml=-3.0

Uax=50.0

Uin=-2.6

Wox=36.1

Mln=-3.7

hior=37.5

wn=-5.7

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


E Q - 3

s 0.

-5.

II. z E Q - 5

B 0.

4.”

Scales : Prototype

TEST MG-5MODEL SATFLIGHT -1

Near Surface Accelerations

and Frequency Analyses

FIG.NO.

57

00I

7 0

80

5 0

40

30

2 0

10

0

Test: MG-5

@.@ ___.-... _.._______._._ * ______._______.______ -g# .____...____... Q . . ..- @mid depth

1 OCY Y -0

near surface

0 5 10 15 2 0 2 5

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 )

30 3 5

Fig.58 Generation of excess pore pressures during theearthquakes in centrifuge test MG-5

1 250

frequency(Hz

200

150

100

50

0

i.\

‘5. \

\ \ 12 yiJ “\,

\

i14 % ‘3; ‘;

16 % \: :: ::

\i

r

!\

18 % I i

\ \ \I

i

1-.7-+-r

0 10000 20000 30000 40000 50000 60000

Excess pore pressure (Pa)

Fig.59 Theoretical relationship between the excesspore pressures and the natural frequency

I . 2 0 0 - -

1 . 1 0 0

1 . 0 0 0

z 0 . 8 0 0‘L

l

5 0 . 8 0 0

55 0 , 7 0 0

1u

0

-

0.600

=

i 0.500

z0 . 4 0 0

0 . 3 0 0 1

1

7 Test MG-5

i/I

td ‘\

\

'ib.“‘\‘.\

\..,\

0 . 2 0 0 II I I I I I I I I I

5 10 1 5 2 0 2 5 3 0 35

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 accelerationwith the strength of the earthquake


P P T 6 5 1 4

P P T 6 5 1 4

PPT 651?I

Scales : Prototype

T E S T M G - 5MODEL SATFLIGHT -1

Base Pore PressureFIG.NO.

6 1TIME RECORDSII I

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.

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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: designequations 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 toearthquakes, Ph.d thesis, Cambridge University, England.

Madabhushi, S.P.G., (1994), Natural frequency of a Horizontal Soil Layer, Part I: Drysand 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 SanFernando dams during the earthquake of February 9, 1971, ASCE Jnl. ofGeotechnical Engineering Div., GT7, pp 651-688.

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