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International Journal of Earth Sciences and Engineering

DYNAMIC ANALYSIS OF NUCLEAR REACTORCONSIDERING SOIL STRUCTURE INTERACTION

O Divya1and Neelima Satyam D2

1 Post Graduate student, Earthquake Engineering Research Centre, International Institute of

Information Technology Hyderabad, Gachibowli, Hyderabad-32

2 Earthquake Engineering Research Centre, International Institute of Information Technology

Hyderabad, Gachibowli, Hyderabad-32, e-mail:neelima.satyam@iiit.ac.in

ABSTRACT

In this research paper, the dynamic analysis of complicated structures like nuclear reactorbuilding has been done by considering the site specific response analysis. Analysis is donewith and without considering the soil stiffness. First a Nuclear Reactor is considered which isresting on the ground surface and site specific ground response analysis for obtaining freefield response of soft soil site is carried out using DEEPSOIL (Youssef M.A.H, 2009). Nuclearreactor is modeled and analyzed using SAP2000 (Computers and Structures, 2007) byconsidering soil stiffness. The numerical results for the floor response spectra obtained fromSAP2000 (Computers and Structures, 2007) are presented in this paper. Secondly the effectof soil-structure interaction on the seismic response of a massive structure with foundationfinite element discretization model is used. Using the implemented model and in view of the

objective of the work, a parametric study is made. For this purpose, a reactor buildingdeeply embedded into the soil is considered. The results obtained in view of the parametersinvolved, are presented which suggest that the soil-structure interaction should beconsidered for the detailed analysis of important structures.

Keywords:Nuclear reactor, Local site effects, Response analysis, DEEPSOIL, SAP2000,Soil Structure Interaction, Finite Element Method.

INTRODUCTION

Seismic design of structures is one of themost important methods of mitigating riskof damage from future earthquakes andthe concept of seismic resistant designhave become worldwide popular. One ofthe most important challenges facingstructural engineers today is thedevelopment and implementation ofeffective techniques for minimizing thesevere and often tragic consequences ofearthquakes. To meet this challenge,future structural engineers must possess

an understanding of the dynamic responseof structures such as buildings, bridges,and towers to strong ground motion. Suchdesigns are based on the specification of

the ground motion which can be expectedin the event of an earthquake. A nuclearreactor is a device in which nuclear chainreactions are initiated, controlled andsustained at a steady rate. The mostsignificant use of nuclear reactors is as anenergy source for the generationof electrical power. Over the last fewdecades, many building structures have

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been damaged from the devastatingearthquakes. This is usually accomplishedby methods that involve using heat fromthe nuclear reaction to power steamturbines. Thus construction of nuclearreactors will increase in the near future.

For nuclear power plants it is desirable tohave a reliable site specific responseanalysis. Proper analysis should be donefor structures on soft soils since thegeometry and the properties of thesupporting soil exert large influence ontheir behavior. Dynamic analyses areperformed using the available and highlyvalidated tools which incorporateacceptable methods of combining modalresponses or with a multitude of otherfinite element programs that are eithercommercially available or developedspecifically for the analysis. In this paperdynamic analysis is performed usingSAP2000. Although recent advancementsin computer technology and software havemade this type of analysis more readilyavailable, when performing detaileddynamic analyses, a thoroughunderstanding obtained from experience,is imperative. Time history and responsespectrum methods are the two basicmethods that are commonly used for theseismic dynamic analysis. The time-

history method is relatively more timeconsuming, lengthy and costly. Theresponse spectrum method, on the otherhand, is relatively more rapid, concise andeconomical. However, time-historymethod must be employed whengeometrical and/or material non-linearityis present in the structural systems.Nowadays, its more convenient for usingtime-history method than before foradvancing of computers hardware and

software.

This study represents the seismicresponse analysis of a nuclear reactor onthick soft soils. Initially free field responseof the site is found out using DEEPSOIL(Youssef M.A.H, 2009). For this, a soilprofile of depth 32.5m is considered andground response analysis is done infrequency domain. Acceleration timehistory and frequency vs. amplitude

responses are generated. A nuclearreactor is modeled and analyzed usingSAP2000 (Computers and Structures,2007). Later soil structure interactionanalysis of embedded nuclear reactor isperformed using finite element model.

Time history response results of both themodels are shown in the paper. The effectof considering the soil structureinteraction can be understood.

METHODOLOGY ADOPTED

It has been a well established fact that adetailed dynamic analysis and design ofbuilt environment that takes into accountthe behavior of local soil deposits, reducesthe loss of life and damage toinfrastructure. Ground response analysisis an important factor that is to be takeninto consideration for evaluation andremediation of geotechnical as well asstructural seismic hazards. For sitespecific ground response analysis threebasic input parameters that are essentialare input ground motion, shear wavevelocity and dynamic soil characteristics(e.g., strain dependent modulus reductionand damping behavior and cyclic strengthcurves). Linear analysis using DEEPSOIL(Youssef M.A.H, 2009) in frequency

domain was used to compute free fieldresponse, which is very popular withpractitioners. Based on the average shearwave velocity in the top 30 m, a groundresponse analysis has been carried out forthe soft soil profile. Engineering bed rockis modeled as an elastic half space.Analyses were carried out for thestochastically simulated acceleration timehistories from local sources using in situmeasured shear wave velocities. Shearwave velocity (Vs) is one of the mostimportant input parameter to representthe stiffness of the soil layers. It ispreferable to measure Vs by in situ wavepropagation tests, however it is often noteconomically feasible to perform the testsat all locations. Hence, a reliablecorrelation between Vs and standardpenetration test blow counts (N) would bea considerable advantage. Shear wavevelocity was measured using the

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established empirical relationshipdeveloped by Neelima Satyam D and RaoK S (2009) as shown below.

VS= 61 X N0.5 (1)

where N = corrected SPT value

In the current study an earthquake ofmoment magnitude 6 was considered forthe analysis with 5% damping. A soilprofile with 8 layers is considered.Thickness (m), unit weight (kN/m3) andshear velocity (m/sec) for each layer aregiven as input as shown in table 1.Simplified complex shear modulus(Kramer, 1996) is used for the analysispurpose. A simplified form of frequencyindependent shear modulus is defined asgiven in Eq.2.

G* = G (12+ i2). (2)

Free field response for the soft soil strataconsidered is shown in Fig. 1 (a & b).

Table 1. Details of the soil strata considered

Layer

number

Thickne-

ss (m)

Unit

weight

(kN/m3)

Shear

velocity

(m/sec)

Damp

ing

ratio(%)

1 2 15.5 122 5

2 3 16.5 220 5

3 1.5 15.5 183 5

4 4 15 211 5

5 1.5 16.5 236 5

6 5.5 16 266 5

7 1.5 16.5 324 5

8 14.5 15 236 5

NUMERICAL MODELING

The validation model of the nuclearreactor with node to node joints and withplates is shown in Fig. 2 (a & b). Themodel represents a typical PressurizedHeavy Water Reactor containment

structure consisting of a primary concretecontainment. This model is an idealizationof a typical pressurized water reactor anddoes not represent an actual or existingstructure.

Figure 1(a): Acceleration time history for the soilstrata considered.

Figure 1(b): Fourier amplitude (g-sec) vs. frequency(Hz) for the soil strata considered.

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Floor slabs are simplified and includedmainly for their effect on the structuralresponse. The concrete containmentcylinder wall and dome are 300mm thick.The reactor vessel mass is included as

lumped mass in the model. The concretecontainment and internal cylindrical wallsare modeled with plate/shell elements.The foundation slab/side walls and reactorcavity are modeled with solid elements.For performance evaluation, a three-dimensional model of the dome was takenand Time history analysis was performedto evaluate the displacements at eachfloors.

Reactor model

A three-dimensional model of the domewas modeled in computer programSAP2000 and Dynamic analysis wasperformed on the structure to evaluatethe structural response. The time historyanalysis is an analysis performed in thetime domain using time history vibratoryinput. A direct integration or modalanalysis may be performed. The modelwas analyzed for earthquake groundmotion data which is obtained from theDEEPSOIL (Youssef M.A.H, 2009) results.

3D MODEL

The dimensions of the model are thestorey height is 30m, the thickness of theconcrete wall is 300mm and the radius ofthe dome is 20m.The Structural plan viewof the domed reactor is shown in Fig. 2 (a& b)

ANALYSIS

Several methods exist to input seismicexcitation when making the seismic timehistory analysis for design of nuclearpower plant such as to input thedisplacement time-history at the base(displacement method), to input theinertia loading calculated from the timehistory of support motion acceleration(acceleration method), and Large mass

Figure 2 (a): SAP2000 model of Nuclear reactor withnode to node joints

Figure 2 (b): SAP2000 model of Nuclear reactorwith plates

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method. For the linear response ofimportant structure, both amplituderesponse spectra and standardaccelerograms are used as supplements.Acceleration time history which is

developed as a free field response is givenas seismic input for the reactor model andanalysis has been carried out. The modelwas analyzed for one of the earthquakeground motion data which has peakground acceleration (PGA) of 0.053g andmoment magnitude (Mw) of 6. Model timehistory type is used in SAP 2000(Computers and Structures, 2007).Number of output time steps is taken as500 and output time step size is taken as0.02sec. This gives a total of one sec astime period. Fixed-base analyses of thereactor building were performed usingSAP 2000. The floor response spectra forthe three floor elevations of Nuclearreactor building are developed. Thespectra were generated for elevations30m, 60m and 90m for Nuclear reactorbuilding. All the response spectra weregenerated for the damping ratio of 5%.Modulus of elasticity of concrete (Ec) is30,000 N/mm2 and Poissons ratio () is0.2. The density for concrete (c) is 2500kg/m3. These values are best estimate

values used for obtaining the bestestimate values for in-structure response.The displacement time history graph andthe response spectrum curves for thethird, second and first floors of theNuclear reactor building with theconsidered earthquake ground motion isanalyzed in detail.

SEISMIC ANALYSIS CONSIDERING

SOIL STIFFNESS

A massive structure such as reactor

building is embedded in the soil and it willinteract with the surrounding and the baselevel. The seismic analysis of engineeringstructures is often based on theassumption that the foundationcorresponds to a rigid block, which issubjected to a horizontal unidirectionalacceleration. Such model constitutes anadequate representation of the physical

situation in case of average size structurefounded on a sound rock. Under suchconditions, it has been verified that thefree field motion at the rock surface, i.e.,the motion that would occur without thestructure, is barely influenced by its

presence. The hypothesis loses validitywhen the structure is founded on soildeposits, since the motion at the soilsurface without the building may besignificantly altered by the presence of thestructure (Prakesh S and S K Thakkar,2003). This detailed study has beencarried out assuming that the structureand underlying soil remain bondedthroughout the period of ground shaking,the motion at the base of foundation isassumed to be the free field groundmotion, the behavior of both soil andstructure is assumed to be linearly elasticand the side soil and base soil is modeledalong with the reactor building but havingno mass, only flexibility of soil isconsidered. Problems involving threedimensional axisymmetric solids or solidsof revolution, subjected to axisymmetricloading reduce to simple two dimensionalproblems because of the total symmetryabout the z-axis (Fig.3), with alldeformations and stresses independent ofthe rotational angle . Thus the problem

needs to be looked at as a twodimensional problem in rz. The dynamicequilibrium equations in the finite elementformulation are shown in Eq.3.

M+C+Ku=f(t) (3)

where M, K and C are harmonic dependentmass, stiffness and damping matrices,respectively, f(t) is the external forcevectors, and , are second and firstderivatives of displacements. Thehorizontal component of groundacceleration is represented as shown inEq.4 and the force is calculated usingEq.5.

a={agcos,agsin,0}. (4)

f(t)=-Ma. (5)

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z

Figure 3: Axisymmetric body and displacements incylindrical coordinates

The two-dimensional region defined by therevolving area is divided into triangular

elements, as shown in Fig 4. Though eachelement is completely represented by thearea in the rz plane, but in reality it is aring shaped solid of revolution obtained byrevolving the triangle about the z axis.Using the three shape functions N1, N2and N3 displacement is defined as shownin Eq.6.

U=Nq. (6)

The element stiffness matrix is given asbelow in Eq.7.

Ke=BTDBdu (7)

Use of finite elements for modeling thesoil structure system is the mostcomprehensive method (S L Chu, 1973).Like the elastic half space model, itpermits the radiation damping but has themajor advantage of easily allowingchanges of soil stiffness both horizontallyand vertically to be explicitly formulated.In this study two dimensional soil modelwhich was found considerable use inpractical analysis of axisymmetric system,has been used. In this model, the soilboundaries are rotationally symmetricabout the vertical axis, so that the radialand vertical coordinates are sufficient todefine the geometry of the soil system aswell as its finite element idealization.Axisymmetric structure is also rotationallysymmetric about the same vertical axis.For the purpose of study, a nuclearreactor building shown in Fig.4 has beentaken (S L Kati, 1973). The main structureis symmetrical with respect to vertical

axis. It consists of a co-axial cylindricalshell and a spherical dome resting on amassive raft foundation and all made ofreinforced concrete. The reactor structureis founded on base and surrounding soil.The material properties of structure andfounding soil used in the analysis arepresented in Table 2.

Table 2: Material properties of structure andfounding soil.

Descriptionof the

structure

Modulus ofelasticity, E,

kN/m2

Poissonsratio

Massdensity,

Kg/m3

Damp-ing

Shell, dome,

slab and raft 3x107 0.20 2.5 x 103 5%

Foundingsoil

E=2G(1+)G=*Vs*Vs

0.30 2.2 x 103 20%

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Figure 4: Finite element mesh of reactor building and founding soil

A reactor building along with foundationsoil has been idealized by finite elements,

consisting of three noded isoparametricelements shown in Fig 3. The dynamicresponse to horizontal earthquake groundmotion is obtained by time wise modesuperposition method. The time historyanalysis is carried out using Newmarks

method (Anil k Chopra, 2007) where = and = (the average accelerationmethod). The recorded El-centro

earthquake ground motion is selected forthe analysis as given in Table 3. The soilboundary is taken as viscous media.

Table 3: Typical details of earthquake dataconsidered in the analysis.

Date ofoccurrence

PGA(g)

M(w) Approximateduration (s)

EL-CentroMay 18, 1940

0.33 7.1 30.0

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In this study only horizontal earthquakemotions are considered because there isinsignificant effect of vertical groundmotion on overall seismic response ofreactor.All the lumped parameter models take

advantage of simplicity of using springdashpot and added mass have beenpopular in time history analysis of soilstructure interaction problems.

The static stiffness of the embeddedfoundations increases by increasing thedepth of the foundation (Kramer, 1996).Embedment can increase the radiationdamping considerably. Wolf (1994)developed a series of cone models inwhich stiffness of the foundation is similarto the stiffness proposed by Gazetas(1983) though it is represented in adifferent format. The spring stiffness isconsidered as shown in Eq.8.

K=8Ga/(2) (8)

Where A is Area of the foundation A= .a2, G is the Shear modulus of the soil, isthe Poissons ratio of the soil. However,the viscous damping coefficient wasassumed to be proportional to the wave

velocity in the soil and the foundation areaand is shown below in Eq.9.

C=cA0 (9)

where C is viscous damping coefficienttaking into account the the radiationdamping of the soil and foundation, issoil density, c is wave velocity (600 m/s)in the soil and A0is foundation area (Wolf,1987). It should be mentioned that thesoil has been assumed to behave as anelastic material, and therefore there wasno material damping added to the models.The finite element model is analyzed usingthe El-centro earthquake data and thedisplacement time history results for the

external nodes of the concrete nuclearreactor building are shown in Fig. 6 (a, b,c, d, e and f).

RESULTS AND DISCUSSIONS

The detailed procedure to estimate thefree field response at the site, using thisdata and the analysis of a Nuclear Reactorconstructed on thick soft soils and also theeffect of soil structure interaction ofembedded nuclear reactor building hasbeen presented in this research paper.The dynamic analysis of a Nuclear reactorbuilding resting on thick soft soil strata isperformed initially. For the analysispurpose a Pressurized heavy water reactoris considered. Free field response of thesoil strata considered is analyzed usingDEEPSOIL. Analysis of the Nuclear reactorbuilding is performed using SAP 2000.From the displacement time history of thejoints at the three floors it can be seenthat there is quite a reduction in thelateral displacements of the structuresubjected to an earthquake excitation of amoment magnitude 6. The results areshown in Fig. 5 (a, b, c, d, e and f).Secondly soil structure interaction analysisis performed using three noded finiteelement model. A Nuclear reactor building

with dome shaped concrete container isconsidered for the analysis purpose. Asimple spring dashpot model is consideredrepresenting the soil structure interaction.

Structural engineers and designers shouldmake every effort to obtain as muchinformation as possible describing theproperties of the site upon which aproposed structure is to be located.Dynamic analysis of pressurized Heavywater reactors has been performed usingthe data obtained from ground response.

In this site specific geophysical, geologicaland geotechnical characteristics of thesubstrata below the structure is verycrucial for the seismic design.

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Considering fixed base

Figure 5 (a): Displacement time history of Figure 5 (b): Response spectrum of the joint at thejoint at the 3rd floor 3rd floor

Figure 5 (c): Displacement time history of Figure 5 (d): Response spectrum of the jointthe joint at 2nd floor at the 2nd floor

Figure 5 (e): Displacement time history of Figure 5 (f): Response spectrum of the jointthe joint at 1st floor at the 1st floor

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Considering Soil Structure Interaction effect

Figure 6 (a): Displacement time history for node 43 Figure 6 (b): Displacement time history for node 37

Figure 6 (c): Displacement time history for node 35 Figure 6 (d): Displacement time history for node 33

Figure 6 (e): Displacement time history for node 31 Figure 6 (f): Displacement time history for node 26

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The maximum displacements occurring forthe fixed base reactor at the three floorsare 2.974x10-4 m, 1.925 x10-4 m and7.533 x10-5 m. From these values it isclearly observed that the reduction indisplacements moving from third floor to

first floor.

Site specific response analysis for suchimportant buildings is very necessary. Forcomplicated and important structures suchas reactor building, finite element methodis well suited for the detailed assessmentof stress and displacements. This paperalso presents the numerical results ofseismic analysis of Nuclear reactorbuilding constructed on thick soft soilstrata. When analyzing a structurefounded on a soil site due to anearthquake there are changes in motion atfoundation level leading to changes in thedynamic response of the structure. Thesechanges are all effects of dynamic soilstructure interaction. Modelling thefoundation soil and base raft mat withfinite elements gives more realistic resultsbut it is too complicated for everydayengineering applications. Totaldisplacements of the structure are largerin flexibly based structure and can bequite important for pounding of buildings.

REFERENCES

[1]DEEPSOIL. (2009), Youssef M.A.H.[2]Neelima Satyam.D and K S Rao

(2009). Estimation of peak groundAcceleration for delhi NCR usingFINSIM, a finite fault simulationtechnique. International Journal

of Geotechniques and environment,vol.1,No.2,pp 147-159.

[3]SAP2000. (2007), Computers andStructures, Inc.

[4]Steven L.Kramer. (1996)Geotechnical Earthquake

Engineering, Third edition.[5]Dr S Prakesh and Dr S K Thakkar.

(2003) Evaluation ofsoil-structureinteraction effects of a massiveembedded structure during seismicexcition. IE (i) journal-CV.

[6]S L Chu. (1973) Finite ElementTreatment of SSI Problems forNuclear Power Plants underSeismic Excitation. SMiRT-2, vol2, Paper k2/4.

[7]S L Kati. (1973) ConceptualDesign of the Modified 200 MWeReactor for Narora. Proceeding

Symposium on Nuclear Scienceand Engineering, Bhabha AtomicResearch Centre, Trombay, India.

[8]Gazetas, G. (1983). "Analysis ofmachine foundation vibrations:state of the art." Soil Dynamicsand Earthquake Engineering, 2(1),2.

[9]Anil K Chopra. (2001). Dynamicsof Structures, Theory andapplications to Earthquake

Engineering.[10] Wolf, J. P. (1987). Soil structure

interaction analysis in timedomain, Prentice hall inc.