PRELIMINARY CENTRIFUGE TESTS USINGTHE STORED ANGULAR MOMENTUM (SAM)

EARTHQUAKE ACTUATOR - PHASE I

S.P.Gopal Madabhushi

CUED/D-SOILSiTR298 (1996)

PRELIMINARY CENTRIFUGE TESTS USINGTHE STORED ANGULAR MOMENTUM (SAM)

EARTHQUAKE ACTUATOR

S P Gopal MadabhushiResearch Fellow (Wolfson College),Cambridge University and

Lecturer, University of Edinburgh, Edinburgh

Synopsis

A new earthquake actuator based on the principle of Stored Angular Momentum(SAM) was developed at Cambridge University. This report concerns itself with theperformance of this new actuator under ‘high g’ centrifuge tests. The concept of theSAM actuator is explained. Results from the initial tests with the SAM actuator arepresented. Based on the results from these initial tests, further improvementsnecessary to the actuator are discussed.

Introduction

Modelling of earthquake events using a geotechnical centrifuge has established as a

powerful technique over the past decade. At Cambridge University many boundary

value problems were studied using a mechanical actuator called the Bumpy Road

actuator, Kutter (1982). Schofield (1980,1981) discusses the scaling laws which relate

the dynamic behaviour of the centrifuge model to the prototype behaviour. Bumpy

Road actuator generates an essentially single frequency ground motion with fixed

duration. This actuator was extremely successful as strong earthquakes could be fired

using this system on payloads of upto 287 kg in a 80g centrifuge test. Using this

system earthquake induced liquefaction problems were studied, for example,

Schofield and Lee (1988) studied the decoupling of sand islands following

liquefaction of the foundation soil, Zeng and Steedman (1993) have investigated the

dynamic behaviour of quay walls with saturated back-tills, Madabhushi and Schofield

(1993) have investigated the behaviour of tower structures on saturated soils subjected

to earthquake perturbations. Large excess pore pressures were observed in the

saturated soils following an earthquake event which resulted in a lowering of the

effective stress. When the magnitude of these pore pressures reaches a value close to

the effective stress it said that the soil has suffered complete liquefaction. Based on

the experience of the studies at Cambridge University, it was proposed that the onset

of partial liquefaction may induce significant damage on high frequency soil-structure

systems as they are drawn towards the resonance frequency, well before full

liquefaction of soil has resulted. In the work by Madabhushi and Schofield (1995) it

was observed that there is a need for an earthquake actuator which can fne successive

earthquakes at different discrete frequencies at any one ‘g’ level. Also the duration of

the earthquake needs to be variable. With such a system it will be possible to study the

behaviour of any soil-structure system near to or away from resonance.

At Cambridge University an earthquake actuator which can fire earthquakes at any

one desired frequency was developed. Successive earthquakes can be fired at different

frequencies irrespective of the ‘g level’. Also the duration of earthquakes is variable.

A brief description of the principle of this new earthquake actuator is presented next.

Stored Angular Momentum (SAM) actuator

Very high levels of energy can be stored in a fly wheel spinning at high angular

velocities. The energy stored in the fly wheel may be used to subject a centrifuge

model to earthquakes. The angular velocity of the fly wheel determines the frequency

of the earthquake. The duration of the earthquake is controlled by a fast acting clutch

which starts and ends the earthquake. A schematic diagram of the Stored Angular

Momentum (SAM) earthquake actuator is shown in Fig.1. A set of fly wheels

mounted on a central shaft are spun at the required speed by a three phase electric

motor. The central shaft of the fly wheels turns an eccentrically mounted crank which

in turn drives a reciprocating rod through a cross head. The reciprocating rod can be

connected to a lever at the desired moment via a fast acting clutch. This starts the

earthquake and subjects the model container to a lateral shaking. The earthquake is

stopped by disengaging the clutch. The strength of the earthquake can be controlled

by altering the pivot point of the lever. In Fig.1 the soil model is shaken in the

direction of centrifuge flight and the fly wheels rotate in the plane of rotation of the

centrifuge arm: alternatively the system could have the soil model sh&en

perpendicular to the plane of rotation of the centrifuge. A more detailed description of

the SAM actuator will be presented elsewhere, Madabhushi and Lesley (1996). The

salient features of the SAM actuator are outlined here.

i) frequency of choice: the earthquake can be fired at a desired frequency or may

sweep through a range of frequencies, for example from 0 Hz to 150 Hz.

ii) ‘g’ level of choice: earthquakes can be fired at different ‘g’ levels. The system is

designed for centrifuge tests conducted at upto 1 OOg.

iii) earthquake strength of choice: it is hoped that the actuator can impart a small

strength earthquake with swept sine wave input motion or a large earthquake at one

frequency (a tone burst). The strength of the earthquake will be changeable.

iv) duration of choice: Another feature is that the duration of the earthquake can be

changed. A possible range of earthquake duration may be from 50 ms to 500 ms.

* The present version of SAM actuator at Cambridge uses BumpyRoad actuator’s Blue face plate to convert reciprocating rod motion

to lateral shaking of the model

1 motor &

11 Timing

Soilmodelto be

shaken

Directionof shaking

Fig. 1 Schematic diagram* showing the plan view ofStored Angular Momentum (SAM) shaker

tDirection

of rotation ofthe centrifuge

Initial Centrifuge Tests

This preliminary report presents the data from the first few centrifuge tests conducted

aboard the 10m beam centrifuge at Cambridge University using the new Stored

Angular Momentum (SAM) actuator. The aim of these initial experiments was to

verify the working principles of the SAM actuator and to prove that strong

earthquakes can be generated using this new actuator.

It was decided that the initial centrifuge tests will be conducted at 40g and the g level

will be increased in each of the subsequent tests. In this report data fi-om a centrifuge

test conducted at 60g are presented. Experiments are currently underway to increase

the working envelope of the SAM actuator to a further level of 90g.

Model Preparation and Test Configuration

A simple horizontal sand bed was chosen as the centrifuge model to be used in the

in&l centrifuge tests. The sand used in these experiments was LB 100/l 70 grade fine

sand. A uniform sand bed was prepared by raining sand from a hopper into an

Equivalent Shear Beam (ESB) box from a predetermined height to give a medium

dense soil sample. The dry density of the sample was calculated as 1614.5 kg/m3.

This gives a void ratio of 0.64 from which the relative density of the sample is

calculated as 80.6%.

A schematic section of the model showing the position of the accelerometers is

presented in Fig.2.

The ESB box (Schofield and Zeng, 1992) was designed to simulate semi-infinite

boundaries at 5Og as the stiffness of sand layer at that g level will match the stiffness

of the end walls. This will enable the wall to undergo the same deformation pattern as

the shear deformation in soil during earthquake loading. Also thin, inextensible shear

sheets are used to generate the complementary shear stresses. Madabhushi, Schofield

and Zeng (1993) describe the efficacy of the shear sheets in generating the

complementary shear stresses. It must be pointed out that use of this ESB box at ‘g’

levels other than 5Og will induce an error as the increased soil stiffhess due to increase

in ‘g’ level is not matched by the end walls. This effect is ignored for the present tests

but new ESB box will be designed for use in future experiments in which this error is

eliminated.

ElACC 3477

ACC 3478 0

ACC 1925

ACC 3441 0

LB 100/170Sand

ACC 3457

0

ACC 5754 ,ACC 1572

0 ACC 1926 on theFast Acting Clutch 0of SAM Actuator

0 ACC 5756 measuresthe lateral accelerationof the rack below themodel container

II

3466ACC 1932 measures radialaccelerations on the Beam Centrifuge(main rotor)

ACC 3436 measures verticalaccelerations on the Beam Centrifuge(main rotor)

Fig.2 Schematic section of the centrifbge model SAM-4and placement of the accelerometers in this test

Earthquake Firing Procedure

The following procedure was adopted before firing an earthquake. The three phase

motor is switched on and the speed of the three phase motor is increased until the

main flywheels are spinning at the with the same angular velocity as the desired

frequency of the earthquake. This is done by using a three phase inverter installed in

the centrifuge control room. Once the required angular velocity of the fly wheels is

achieved the required offset on the blue face plate (refer to Kutter, 1982) is driven by

using a second smaller three phase motor. The timing sequence to operate the

pneumatic valves which open the high pressure hydraulic fluid to the clutch is

engaged. This automatically fires the earthquake after a pre-set duration. Also the

clutch is vented to atmosphere automatically by the timing sequence at the end of the

earthquake duration. After the earthquake is finished the timing circuit is switched off

and the three phase motor is stopped bringing the fly wheels to a gradual halt.

Earthquake 1

The speed of the centrifuge was increased gradually so that the centrifuge model was

at 60g. Earthquake 1 was fired by dialling a modest offset to generate a medium sized

earthquake. The speed of the three phase motor was increased gradually so that the

angular velocity of flywheels was 50 Hz. This is expected to generate an earthquake

which has a predominant frequency of 50 Hz.

The data recorded from the accelerometers shown in Fig.2 are presented in Figs.3 and

4. As is customary, the magnitude of the accelerations are expressed as a percentage

of the centrifugal acceleration (60g).

In Fig.3 it can be seen that the SAM has produced an earthquake almost sinusoidal

motion. All the horizontal acceleration traces recorded in this earthquake are

presented in this figure. ACC 1926 fixed to the fast acting clutch registered a peak

acceleration of 27.3%. This is translated to the rack underneath the model container

via the main shaft of the blue face plate. The peak rack acceleration was about 12.6%

as recorded by ACC 5756. The horizontal acceleration of the model container was

recorded by ACC 3466 as 13.7 %. Within the sand model the accelerometers at the

base of the model ACC’s 3492 and 5754 measure peak accelerations of 14.7% and

15.3% respectively. The accelerometers at the mid depth of the sand model ACC’s

3441 and 3457 record peak accelerations of 17.5% and 21.3%. The accelerometer just

below the ground surface ACC 3477 recorded a peak ground acceleration of 20.5%.

Considering the traces ACC 3492,344l and 3477 it may be concluded that there is an

amplification of accelerations as the stress waves travel from the base of the model to

the soil surface. ACC 3478 did not function in this test.

In Fig.4 the vertical accelerations recorded in the sand model during this earthquake

are presented. Also the beam centrifuge itself was monitored in two directions to see

if the SAM actuator causes any undue vibrations of the main centrifuge rotor. This

data is also presented in this figure. ACC1926 is reproduced at the top in this figure.

The vertical accelerometers at the base of the sand model ACC’s 1900 and 1572

recorded a peak vertical acceleration of 2.9% and 2.5% respectively. This vertical

acceleration is also amplified as the stress waves travel to the soil surface. This is

recorded by ACC 1572 which recorded a peak vertical acceleration of 3.4%.

ACC 1932 which records the radial acceleration did not measure any significant radial

acceleration of the beam centrifuge. The peak accelerations was only about 0.3%.

ACC3436 which measures the vertical acceleration of the beam recorded a peak

vertical acceleration of 1.3%. Also the trace indicates high frequency vibration. These

two accelerometers suggest that the SAM actuator is not causing any undue vibrations

in the main rotor arm of the centrifuge during the earthquake.

In Fig. 5 the frequency analysis of the acceleration-time histories of three

accelerometers ACC 3492, 3441 and 3477 are presented. The frequency analysis of

ACC 3492 suggests that the predominant frequency of the earthquake was indeed 50

HZ. Also some energy is present at higher harmonics namely 150 Hz and 250 Hz. A

similar observation can be made in the case of the frequency analyses of ACC’s 3441

and 3477. However, it is interesting to note that the high frequency Components Of

150 HZ and 250 HZ are amplified more as the stress waves are travelling from the base

of the model (ACC3492) to the soil surface (ACC3477).

798 data points #tteiJ per complete transducer record

ACC 19260

ACC3466

ACC3492

.m

ACC3477

Lo5

ACC3478 0

Uox=27.3

Uin=-27.2

Uin=-10.8

Mb=-11.8

Mb=-12.4

Uin=-15.3

Max=20.5

Min=-14.4

Max=O.l

Uin=-0.1

Stoles : Prototype

T E S T S A M - 4M O D E L D R Y E Q - 1FLIGHT - 1 ,.,. ,i

SHORT TERM G L e v e l FIG.NO.j 1.

TIME RECORDS 6 0 3

I ih

7$8 data points plotfed per c&nplete transducer record

ACC 1926

ACC1 5 7 2

ACC1900

ACC 1925

ACC1932

ACC3436

[ m s e c ]

I13w 1 3 2 0 1340 1 3 6 0 ,360 1400 1 4 2 0 1 4 4 0 I.60 1460 1 5 0 0 1 5 2 0 1540 1 5 6 0 1560 1 6 0 0 1 6 2 0 1 6 4 0 1 6 6 0 1 6 6 0

I

[msec]

0 1 3 2 0 13W 1 3 6 0 1 3 6 0 1400 1420 l&O W(Y) 1480 t500 1 5 2 0 1540 1 5 6 0 1580 1600 1 6 2 0 1640 1 6 6 0 1 6 6 0

[ m s e c ]

2Mox=2.9

E0

Mill=-1.9- 2

2Max=2.5

0F

- 2

Min=-3.8-4

2Mox=3.4

0s

- 2M i n = - 3 . 3

,300 ,320 ,540 1360 1 3 6 0 1,OO 1 4 2 0 1440 1460 ,480 I W O 1 5 2 0 1 5 4 0 1 5 6 0 1560 16W 1 6 2 0 1 6 4 0 1 6 6 0 1 6 6 0

[ m s e c ]

1 3 0 0 1 3 2 0 1 3 4 0 1360 1 3 6 0 14W 1 4 2 0 1 4 4 0 1460 1 4 6 0 lso0 1520 1540 1 5 6 0 1 6 6 0 1 6 0 0 1 6 2 0 1 6 4 0 1 6 6 0 1680

[ m s e c ]

0 . 3Max=O.J

0 . 2

60 . 1 -

0 Min=-0.1

1 uax=1.3

60-

Min=-0.9- 1

I1 3 0 0 1 3 2 0 13.0 , 3 6 0 , 3 6 0 ,,OO 1 4 2 0 l,,O 14W 1460 1 5 0 0 1 5 2 0 1 5 4 0 1 5 6 0 1560 1600 1 6 2 0 1 6 4 0 1 6 6 0 1 6 6 0

[msec]

Scales : Prototype

T E S T S A M - 4 SHORT TERM G L e v e l FIG.NO.

. MODEL DRY iQ,- 1TIME RECORDS. 4 6 0 4

FLIGHT * 1 .Y .?, ‘I .,~ :._

798 data points plotted per complete transducer record

10

n0, 0

- 1 0

- 2 0

A C C 3 4 9 2

1300

20

-0, 0U

- 2 0

1400 1500 1600

[msec]

A C C 3 4 4 1

I- ’

1300 1400 1500 1600

[‘msec]

20

7s 0

- 2 0

A C C 3 4 7 7

1300 1400 1500

[ msec]

1600 0 100 200

Ml

Scales : Prototype

T E S T S A M - 4 FIG.NO.S H O R T - T E R M

M O D E L D R Y I T I M E R E C O R D S 609 5FLIGHT - 1

Earthquake 2

Earthquake 2 was fired by dialling a modest offset to generate a strong earthquake.

The speed of the three phase motor was increased gradually so that the angular

velocity of flywheels was 50 Hz. This is expected to generate an earthquake which has

a predominant frequency of 50 Hz.

The data recorded Ii-om the accelerometers shown in Fig.2 are presented in Figs.6 and

7. As is customary, the magnitude of the accelerations are expressed as a percentage

of the centrifugal acceleration (60g).

In Fig.6 it can be seen that the SAM has produced an earthquake almost sinusoidal

motion. All the horizontal acceleration traces recorded in this earthquake are

presented in this figure. ACC 1926 fixed to the fast acting clutch registered a peak

acceleration of 26.5%. This is translated to the rack underneath the model container

via the main shaft of the blue face plate. The peak rack acceleration was about 26.4%

as recorded by ACC 5756. The horizontal acceleration of the model container was

recorded by ACC 3466 as 26.9 %. Within the sand model the accelerometers at the

base of the model ACC’s 3492 and 5754 measure peak accelerations of 28.9% and

27.8% respectively. The accelerometers at the mid depth of the sand model ACC’s

3441 and 3457 record peak accelerations of 31.9% and 33.3%. The accelerometer just

below the ground surface ACC 3477 recorded a peak ground acceleration of 33.3%.

This second earthquake has indeed resulted in much stronger accelerations compared

to Earthquake 1. This is due to the larger offset driven in the blue face plate. Also,

considering the traces ACC 3492,344l and 3477, it may be concluded that there is an

amplification of accelerations as the stress waves travel from the base of the model to

the soil surface. ACC 3478 did not function in this test.

In Fig.7 the vertical accelerations recorded in the sand model during this earthquake

are presented. Also the beam centrifuge itself was monitored in two directions to see

if the SAM actuator causes any undue vibrations of the main centrifuge rotor. This

data is also presented in this figure. ACC1926 is reproduced at the top in this figure.

The vertical accelerometers at the base of the sand model ACC’s 1900 and 1572

recorded a peak vertical acceleration of 5.2% and 4.6% respectively. This vertical

acceleration is also amplified as the stress waves travel to the soil surface. This is

recorded by ACC 1572 which recorded a peak vertical acceleration of 4.7%. It

appears that during this earthquake the vertical acceleration traces include higher

frequency components.

ACC 1932 which records the radial acceleration did not measure any significant radial

acceleration of the beam centrifuge. The peak accelerations was only about 0.3%.

ACC3436 which measures the vertical acceleration of the beam recorded a peak

vertical acceleration of 1.8%. Also the trace indicates high frequency vibration. These

two accelerometers reinforce the fact that the SAM actuator is not causing any undue

vibrations in the main rotor arm of the centrifuge during the earthquake.

In Fig. 8 the frequency analysis of the acceleration-time histories of three

accelerometers ACC 3492, 3441 and 3477 are presented. The frequency analysis of

ACC 3492 suggests that the predominant frequency of the earthquake was indeed 50

Hz. Also some energy is present at higher harmonics namely 150 Hz and 250 Hz. A

similar observation can be made in the case of the frequency analyses of ACC’s 3441

and 3477. However, it is interesting to note that the high frequency components of

150 Hz and 250 Hz are amplified more as the stress waves are travelling from the base

of the model (ACC3492) to the soil surface (ACC3477).

Conclusions

Based on the data recorded in the two earthquakes of this centrifuge test SAM-4 it is

concluded that the Stored Angular Momentum (SAM) actuator is viable device to

generate strong earthquakes of desired frequency and duration. This is considered to

be a major development in research position from the Bumpy Road actuator as the

SAM actuator is relatively cheap to construct and does not sufl?er from many of the

limitations of the Bumpy Road like the fixed frequency earthquakes or fixed duration

earthquakes. Also it is possible to design future versions of the SAM actuator which

8&1 data paints f5khd per completi transducer record

t-74

.m.,ACC3466 .o E

.’$ .a0

ACC3492 D E

A C C 3 4 4 1

Mox=26.5

Min=-27.2

Max=26.4

Min=-16.9

Max=X.9

thin=-21.4

Max=28.9

hiin=-20.4

Max=27.8

Mb=-22.7

t&n=-25.7

Min=-27.0

Min=-28.0

Mox=O.2

Mb-t=-0.6

Scales : P r o t o t y p e

T E S T S A M - 4 SHORT TERM G L e v e l FIG.NO.

M O D E L D R Y E Q - 2 6 0 6

F L I G H T -1 ‘91” jl T I M E RECORD3 “i

ACC 1926

: :8198 data points @laitetd per complete transducer record

20 Max=25.9

0 z

- 2 0Mill=-27.9

2

[msec]

ACC1900

A C C 1 5 7 2

A C C 1 9 2 5

ACC1932

ACC3436

6Max=5.2

2.5

0 E

- 2 . 5 Min=-3.6

2aW 2825 2850 2875 2900 2925 2950 2975 3Yoo 3025 3050 3075 31w 3125 3150 3175 3200 3225 3250[msec]

- 5Min=-7.0

!000 2825 2850 2875 2900 2925 2950 2975 3WO 3025 5054 3075 3100 3125 3150 3175 3200 3225 3254l[msec]

OZ

I. I Mln=-5.0

-52eW 2825 2550 2075 2SW 2825 2950 2975 3ooo 3025 3050 xl75 3lQo 3125 3150 3175 3200 3225 3200

[msec]

Max=O.J0 . 2

E

0uinc-0.1

2aw 2825 2850 2875 2900 2925 2950 2975 mail 3025 MM 3075 3100 3125 3150 3175 32W 3225 3250[msec]

I2aW 2825 2a50 2.975 2900 2925 2950 2975 moo 3025 3054 5075 3100 3125 3150 3175 32W 3225 :

[msec]

2Max=l.0

03

-2 ml=-2.1

, O

Scales : Prototype

TEST SAM-4 SHORT TERM G Level FIG.NO.

MODEL DRY E Q - 2 7FLIGHT -1, TIME RECORDS ” ‘. ”

’1 ,!,. .i

7% data points plotted per complete transducer record

2 0 6-

T;;: 0 4-

- 2 0 2-

- 4 02 8 0 0 2 9 0 0 3 0 0 0 3 1 0 0 3 2 0 0 0 1 0 0 2 0 0 3 0 0

[msec J D-M

4 0

2 0 6-

T;;: 0 4.

- 2 0 2 -

- 4 02 8 0 0 2 9 0 0 3 0 0 0 3 1 0 0 3 2 0 0 0 1 0 0 2 0 0 3 0 0

[ msec] 0-M

2 0 6

r;;: 0 4

- 2 0 2

- 4 0 1 - I2 8 0 0 2 9 0 0 3 0 0 0 3 1 0 0 3 2 0 0 0 1 0 0 2 0 0 3 0 0

[ m s e c ] v-4

Scales : Prototype

T E S T S A M - 4 l=lG.NO.E Q - 2 SHORT-TERM

MODEL DRY 609 8F L I G H T - 1 TIME RECORDS

can work in even higher ‘g’ environments as the device relies on extremely simple

components for examples fly wheels, bearings, three phase motor and a fast acting

clutch.

Future Work

It is anticipated that in coming weeks the working of the SAM actuator will be

extended from 60g to 90g at first and then to the designed ‘g’ level of 1OOg. This

would need some changes to the existing three phase motor. A stronger motor with a

larger starting torque is need to start the flywheels at 1OOg. Also the present system is

working with pneumatic valves which start and stop the earthquake. The response of

the system can be improved by using servo-hydraulic valves. Initial attempts of using

servo-hydraulic valves were not successful due to the failure of the later to work in

high ‘g’ environments. Better servo-hydraulic valves are currently being looked into

to further improve the response of the fast acting clutch.

ACKNOWLEDGEMENTS

The author wishes to express his sincere thanks to Mr. Chris Collison and Mr. Paul

Ford for all the help rendered in the commissioning of the SAM actuator on the 10m

beam centrifuge. Thanks are also due to Mr. Navin Pieries for helping with the initial

experiments. The constant encouragement of Prof. Andrew Schofield and Dr.Malcolm

Bolton, without whose support this work would not have been possible, is gratefully

acknowledged.

REFERENCES

1. Kutter, B.L., (1982), Centrifugal modelling of response of clay embankments toearthquakes, Ph.d thesis, Cambridge University, England.

2. Madabhushi, S.P.G and Lesley, S., (1996), Design and construction of a StoredAngular Momentum (SAM) based of earthquake actuator, CUED report (underpreparation), Cambridge University.

3. Madabhushi, S.P.G. and Schofield A.N., (1993), Response of tower structuressubjected to earthquake perturbations, Geotechnique, Vo1.43, No.4.

4. Madabhushi, S.P.G. and Schofield, A.N., (1995), Simulation of earthquakes in ageotechnical centrifuge, I Intl. Conf. on Earthquake Geotechnical Engineering, IS-Tokyo’95, Tokyo, Japan.

5. Madabhushi, S.P.G., Schofield, A.N. and Zeng, X., (1994), Complementary ShearStresses in Dynamic Centrifuge Modelling, Dynamic Geotechnical Testing:Second Volume, ASTM STP1213, Ronald I. Ebelhar, Vincent P. Drnevich andBruce L. Kutter, Eds., American Society for Testing and Materials, Philadelphia.

6. Schofield, A.N.,( 1980), Cambrid eGeotechnique, Vo1.25., No.4, pp 743- 7 61.

geotechnical centrifuge operations,

7. Schofield, A.N.,(1981), Dynamic and Earthquake geotechnical centrifugemodelling, Proc. Recent Advances in Geotech. Earthquake Eng. Soil dynamicsand earthquake eng., Univ. of Missouri-Rolla, Rolla.

8. Schofield, A.N. and Lee, F.H., (1988), Centrifuge modelling of sand embankmentsand islands in earthquakes, Geotechnique, Vo1.38, No. 1.

9. Schofield, A.N. and Zeng, X., (1992), Design and performance of an equivalent-shear-beam (ESB) container for earthquake centrifuge modelling, TechnicalReport, CUED/D-SoilslTR245, Cambridge University, UK.

10. Zeng, X. and Steedman, R.S., (1993), On behaviour of quay walls in earthquakes,Geotechnique, Vo1.43, No.3, pp 417-43 1.