centrifuge modelling in earthquake geotechnical engineering

V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING V.S. Chandrasekaran Formerly of Department of Civil Engineering Indian Institute of Technology, Bombay Mumbai 400 076 INDIA Email: [email protected] ABSTRACT Simulation of earthquake geotechnical problems in centrifuge has grown significantly in the past decade and a variety of challenging problems are now being tackled in various centrifuge establishments all over the world. Considerable experience has been gained in simulating successfully earthquake effects in the centrifuge. Simulation earthquake conditions in the geotechnical centrifuge requires careful consideration of a number of factors. These include modelling of base motion, selection of model container with non-reflecting boundaries and use appropriate fluid in the soil. These aspects are discussed in this paper. A brief summary of the current activities in this field are also presented. Finally, details of the geotechnical centrifuge facility established at IIT Bombay and the preliminary details of the proposed earthquake simulator are given. INTRODUCTION Body force due to gravity plays an important role in geotechnical engineering problems. When studies are undertaken to understand the behaviour of real structures through scaled models, it is found impossible to simulate the body forces in the normal 1g field. Consequently, many phenomena of interest to the geotechnical engineer cannot be reproduced in laboratory models. It has been realised that this deficiency can be overcome with the use of centrifuge technique in which models are subjected to predetermined, high acceleration levels to produce similarity conditions satisfactorily in most situations. Centrifuge modelling is now firmly established as a dependable research tool that can provide solutions to many of the hitherto intractable problems in geotechnical engineering. Some of the important problems relating to earthdams, tunnels, offshore foundations, geo-environmental problems, problems of nuclear waste disposal, seismic studies of earth structures and foundations can be tackled using centrifuge modelling. In this paper the scaling laws are first outlined and the important aspects concerning the simulation of seismic conditions in the centrifuge modelling are then presented. The range of earthquake geotechnical problems studied in the international scene is then presented. A 4.5 m radius geotechnical centrifuge having a payload capacity of 2.5 t has been established at IIT Bombay. It is proposed to utilise this facility for carrying out research studies on earthquake geotechnical engineering. Towards this aim efforts are underway to develop an earthquake simulator for the centrifuge. The details of this centrifuge facility and the proposed earthquake simulator are presented. SCALING LAWS In the centrifuge linear dimensions are modelled by a factor 1/N and the gravitational body force is increased by a factor N. This enables stress due to the body force to be the same at homologous CPFTEGE, 23-24. December 2003

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V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

points of model and prototype. The other scaling relationships may be worked out based on these factors[1]. For example Lm = Lp /N and σm = σp

(1)

force = stress x area Fm = 1 x (1/N2)Fp = (1/N2)Fp

(2)

energy = force x distance Em = (1/N2) (1/N)Ep = (1/N3) Ep

(3)

dynamic time = (distance / acceleration)1/2 Tm = ( 1/N /N)1/2 Tm = (1/N)Tp

(4)

Based on theory of consolidation, diffusion time relationship is given by Tm= (1/N2) Tp

(5)

It is recognized that there is a conflict in the dynamic time relationship and diffusion time relationship in centrifuge modeling. In phenomena such as liquefaction where inertial effects and diffusion effects both play important role, this issue needs to be properly taken into account. This is dealt with subsequently. Various commonly used scaling relations are shown in Table 1. 1.1 Table 1. Scaling Relations Quantity Length Area Volume Velocity Acceleration Mass Force Energy Stress Strain Mass density Energy density Time (dynamic) Time (diffusion) Frequency

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Prototype

Model

N N2 N3 1 1 N3 N2 N3 1 1 1 1 N N2 1

1 1 1 1 N 1 1 1 1 1 1 1 1 1 N

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V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

MODELLING IN CENTRIFUGE MODELLING OF BASE MOTION IN CENTRIFUGE Consider the prototype base motion given by x p = a sin(ωt p )

(6)

This base motion is simulated in the centrifuge model according to the equation. Equation: xm =

tp a a sin( Nωt m ) = sin( Nω ) N N N

(7)

It is seen that time in the centrifuge is compressed by a factor N. For example, a 20 second duration prototype earthquake gets simulated in the centrifuge model rotating at 50g to 20/50 or 0.4 sec duration. If for example, there were 20 cycles of 1 second period in the prototype motion then the model motion will consist of 20 cycles of 1/50 or 0.02 sec period. The above simulation further implies that the particle velocity will be same at homologous points in the prototype structure and the centrifuge model. However, the particle acceleration in the model will be N times that of the prototype at homologous points. MODELLING THE DIFFUSION PHENOMENON IN THE CENTRIFUGE The generation of pore pressure in the soil medium depends on the nature of the soil skeleton and the dynamic stresses to which the soil skeleton is subjected to. This phenomenon may be attributed to the inertial effects caused by the earthquake. We have seen that the inertial effects in the model take place faster by a factor N in the centrifuge model. On the other-hand the dissipation of pore water pressure in the soil is governed by the phenomenon of diffusion. Diffusion takes place much faster in the model by a factor of N2. For proper matching of time scaling, between inertial and diffusion phenomena, it is necessary to delay the diffusion process by a factor equal to N [2]. This may be achieved in two ways. Firstly, we may consider reducing the permeability of the soil by a factor N by crushing the particles to a smaller size. This may not be desirable as the soil constitutive behavior may get altered in the process. The other alternative is to increase the viscosity of the fluid in the model by a factor N. This would delay the diffusion by a factor N so that there is proper matching of time scaling between inertial effect and diffusion process. The fluid in the prototype is invariably water. Several model fluids have been used successfully used in the centrifuge studies which include silicone oil, glycerol mixed with water and cellulose based water mixtures. A survey carried out indicates that silicone oil has been the preferred fluid in spite its cost and difficulty of disposal. Many experiments have been performed with water as the fluid. In those cases while interpreting the results the permeability of the soil skeleton was considered to be N times larger. Change of fluid may not be appropriate in clay soils as this may result in change of the behaviour of the soil itself. MODELLING THE SOIL EXTENT In nature, soil extends to great distance, Centrifuge containers being limited in size there will multiple reflections of stress waves affecting the soil behaviour during simulated earthquakes. In order to arrest these reflections a number of methods have been adopted. One approach is to place nonreflecting barriers near the end plates. Dux seal, silicone rubber, urethane foam are materials which have been used for this purpose. The other approach is to use specially designed containers which CPFTEGE, 23-24. December 2003

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V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

incorporate provisions to prevent reflections from the container walls. Laminar containers which are frequently used are fabricated using a number of plates stacked one above the other with a device such as ball bearing between the plates to reduce the frictional effects. There are also other approaches such as using equivalent shear beams or providing hinged plates at the ends. Current practice shows a preference towards the use of laminar boxes. GENERATION OF GROUND MOTION IN CENTRIFUGE A peak horizontal base acceleration of say a times acceleration due to gravity in the prototype implies a base acceleration of Nag in the model. If the model has a mass of 500 kg for values of a=0.2 and N=40 the reaction force exerted by the actuator system on the base of the basket will be equal to 500x0.2 x40x9.8 N or 49 kN. For example, if the prototype frequency is 1 Hz then the model frequency will be 40 Hz. It is important to ensure that this dynamic force which will have a frequency of 40 Hz does not trigger resonance conditions in any mode in the centrifuge machine. This is one of the important aspects requiring consideration in the design of the base shaking systems. Many methods have been tried for generating ground motion in the centrifuge. The first seismic modeling experiments on a centrifuge were carried out by Pokorovskii and Fiodorov [3] who designed a special suspension system in which the basket was allowed to oscillate in flight. They studied the stability of 12m high slopes in dry sand and clay loam at a scale of 1:54 at a frequency of 1 Hz. Cocked springs were used in Cambridge to shake boxes mounted on the basket by releasing a compressed spring. This allowed a damped motion of the model container at a fixed frequency. [3] The bumpy road system was employed in Cambridge to trigger earthquakes on a rotating model. The method involves motion of an extension arm from the centrifuge basket riding on a bumpy track mounted on the centrifuge wall. The motion is converted into a lateral shaking of the box placed on the basket. Two tracks were developed each giving 10 cycles at frequencies in the range of 1 to 2Hz. The method has been used in triggering hundreds of earthquakes in the Cambridge centrifuge. However the method is inflexible with respect simulating varieties of excitations. Cambridge University has now developed an actuator called as SAM (stored angular momentum) actuator. [4] This actuator can deliver sinusoidal base motions at variable frequencies and amplitude. Servo controlled electro hydraulic shakers have been installed in a number of establishments[5]. Based on the intended and the delivered shaking on the model the performance of these simulators may be considered satisfactory. Though the capability exists in such systems to deliver any earthquake signal only in limited cases such studies have been undertaken. A new electro hydraulic system [6] has been developed in which the reaction force is not transmitted to the centrifuge machine and is balanced within the shaker itself. PROBLEMS STUDIED IN GEOTECHNICAL CENTRIFUGES To understand the nature of problems that are tackled using the centrifuge a review was carried out of the papers published in this field in Centrifuge 98 conference held in Tokyo [4] in 1998. There were in all 26 papers at this conference dealing with earthquake centrifuge modeling. Of these, 19 papers addressed issues pertaining to liquefaction and liquefaction induced soil movement. The topic of caissons or gravity walls were dealt in 5 papers and pile foundations in 8 papers and dams and embankments in 5 papers. INDIAN GEOTECHNICAL CENTRIFUGE FACILITY There has been a long-felt need for the creation of centrifuge facility in India for carrying out studies on scaled models of geotechnical structures. The Department of Science and Technology with CPFTEGE, 23-24. December 2003

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V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

cooperation from DRDO and MHRD took a lead role in supporting the establishment of the geotechnical centrifuge facility at IIT Bombay. It was realised for a country like India where the accent will be on infrastructure development it would be necessary to build a large size facility. A large capacity centrifuge will allow testing of large size models making it possible to carry out studies on models of prototypes. Large model size will allow stratification of different layers and also enable extensive instrumentation. It would be easy to carry additional payload due to earthquake simulator. Also the errors associated with small machines could be considerably minimised. Keeping these requirements in perspective a geotechnical centrifuge of radius 4.5m up to the base of the basket with a payload capacity 2.5 tons at 100g has been setup at IIT Bombay. A photograph of the centrifuge is given in Fig.1. The technical details are given in Table 2.

Figure 1. Geotechnical Centrifuge at IIT Bombay Table 2. The technical details of the Geotechnical Centrifuge at IIT Bombay Radius from the axis of rotation to basket base Acceleration range at 4.25 m radius Payload at 100g Payload at 200g Soil model size Basket base dimensions (clear) Electrical slip rings Hydraulic rotary joints Run-up time

: : : : : : : : :

4.5 m 10 g to 200 g 2500 kg 625 kg 0.9 m x 1.0 m x 0.65 m or 0.7 x 0.7 x 0.8m 1000 mm x 1200 mm 112 6 6 minutes to reach 200 g

Proposed Earthquake Simulator Characteristics Plan area of model : 700mm x 500mm Model height : 400mm Shaking mass : 500 kg Peak lateral acceleration of model 30g Frequency: 0-200Hz

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V.S. Chandrasekaran CENTRIFUGE MODELLING IN EARTHQUAKE GEOTECHNICAL ENGINEERING

CONCLUDING REMARKS Centrifuge modeling of geotechnical earthquake problems has come of age. Studies on centrifuge models can provide valuable insight into the behavior soil strata and geotechnical structures during earthquakes. Experiments conducted in geotechnical centrifuge can help in understanding problems such as liquefaction, lateral spreading subsidence and soil amplification. Centrifuge studies may be undertaken to validate mitigation measures, validate numerical modeling and study the efficacy of new geotechnical structural systems. These studies can help in arriving at suitable remedial measures to protect geotechnical structures such as dams and embankments, foundations of structures against ravages of earthquakes. The National Geotechnical centrifuge Facility at IIT Bombay will be available for use in carrying out earthquake related studies for educational and research institutions and user agencies. REFERENCE [1]

V.S. Chandrasekaran : Numerical and Centrifuge Modelling in Soil Structure Interaction, Indian Geotechnical Journal, vol.31, No.1 January 2001. pp. 1-59.

[2]

H.Y. Ko : Modelling Seismic Problems in Centrifuge, Proceedings of the International Conference Centrifuge 94, Singapore, A.A. Balkema. pp. 3-12. R.V. Whitman : “Experiments with earthquake ground motion simulation” W.H. Craig, R.G. James and A.N. Schofield (Eds.) Centrifuges, Balkema, Rotterdam 1988. pp.203-216. S.P.G. Madabhushi A.N. Schofield & S. Lesley (1998) : A new stored Angular Momentum (SAM) based earthquake actuator., Proceedings of the International Conference Centrifuge 98, A.A. Balkema, Vol.1. pp.117-122. P.A. Van Laak, K Adalier, R. Dobry & A-W. Elgamal : “Design of RPI’s large servohydraulic centrifuge shaker”, Proceedings of the International Conference Centrifuge 98, Tokyo, Japan, pp.105-110. J. Perdriat, R. Phillips, J. Nicolas Font, C. Hutin : “Dynamically balanced broad frequency earthquake simulation system” Proceedings of the International Conference on Physical Modelling in Geotechniques. St. John’s, Newfoundland, Canada. July 2002.

[3] [4]

[5]

[6]

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