ML20141E299

AP600 Nuclear Island Confirmatory Analysis of Soil Structure Interaction Effects

ML20141E299
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Issue date:	03/09/1997
From:	Kausel E, Roesset J MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, TEXAS, UNIV. OF, AUSTIN, TX
To:	NRC (Affiliation Not Assigned)
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AP600 NuclearIsland Confirmatory Analysis of Soil-Structure Interaction Effects by Eduardo Kausel' and Jos6 Manuel RoEsset2 Prepared for the Division of Engineeering, U.S. Nuclear Regulatory Commission 11555 Rockville Pike Rockville, MD 20852 Project Officer: Dr. Thomas M. H. Cheng .

Project FIN: J2400 Date: March 9,1997

' Professor of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 s Professor of Civil Engineering, University of Texas at Austin, Austin, TX 78712 9705200397 970516 PDR ADOCK052Og3 A '-

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Table of Contents Cover page 1 Table ofcontents 2 Introduction 3 Preliminary Comment on the SASSI-CARES model 3 New SSI software 5 Foundation model 5 Kinematic Interaction 5 Initial EKSSI model 6 Improved EKSSI model 7 Implication of results 8 AP600 and SSI effects 9 Differences in formulation between SASSI and CARES 10

'l Conclusions and Recommendation 11 Appendix: The LAYSOL, SUPELM, and EKSSI programs 12 References and Bibliography 14 Table 1: EKSSIinput file 16 i Figures 1-15 19  !

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I Introduction' <

This report presents an analysis of the seismic response of the AP600 Nuclear Island,

. including soil-structure interaction (SSI) effects, using for this purpose three new j software modules presented later on. The purpose of this SSI analysis is as follows: '

e To verify the SSI results obtained earlier with the well-known SASSI program, an objective that motivated the " confirmatory analysis" label of this report.

e To assess the reasons for the discrepancies observed in an earlier analysis for this ,

problem carried out with the CARES program, as described in the first reference. -

From the review of the CARES manual, differences in the formulation underlying the +

two programs were identified. It is concluded that the most likely cause for these discrepancies is the damping model used in CARES.

e To introduce our three new programs, namely LAYSOL, SUPELM and EKSSI, '

which allow effective yet unencumbered analyses for SSI effects. As will be seen, these new software modules provides results for this problem that are in close agreement with those obtained earlier with SASSI. These programs were used to determine the importance of various effects, and to determine which one of the j observed differences in formulation could lead to the reported differences in 1esults. -'

The AP600 Nuclear Island is a large structural complex resting on a common, massive j foundation nearly rectangular in shape that is embedded into the ground. In the SASSI

. model as well as in the model used in this report, the ." soil" is sufficiently stiff that it '

qualifies as soft rock. When this fact is taken together with the large dimensions of the foundation, one can anticipate at the outset of this study that SSI effects for the AP600 .  !

Nuclear Island are only moderate, an expectation that indeed holds true. -

Preliminary comments on the SASSI-CARES structural model The complexity of the original SASSI structural model for the AP600 Nuclear Island, as detailed in the CARES report, made the preparation of the structural models for this confirmatory study much more difficult than would have been really necessary. With reference to the CARES report, Section 5 and Appendix D, consider the following issues:

First, SASSI employed an enonnous number ofneedless nodes, such asjoints 9,98,38 and 58 in the Coupled Shield Auxiliary Building (CSAB). These nodes have virtually the same coordinates, they are connected by rigid elements, and could thus have been lumped into a single node. The same is true elsewhere in the SASSI model.

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. Second, it is not obvious why structural springs were needed in the first place. These

' could have been assimilated into the existing members, in which case the models would have been much' simpler.

3 Third, the geometric sectionproperties used for the structural members exhibit strange j

peculiarities. On the one hand, the axial stiffnesses (cross-sections) are in many cases 5

negligible, which presumably was done to compensate for the additional springs with 4

only axial stiffness. More importantly, there are a few apparent inconsistencies in the

data, namely the relationship between bending and torsional stiffnesses (moments of 1

inertia)in the following cases:

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MOMENTS OFINERTIA Section About Y About Z Torsion

[i 3 .685E7 .239E8 .160E8 4 .725E7 .256E8 .173E8 1

23 .283E5 .283E5 . 230E6 1

In general, for a closed section, one would expect the torsional moment ofinertia to be of j

the order of the sum of the two bending moments ofinertia. While it is true that an open

j. section has a torsional constant much less than the polar moment ofinertia, it is not clear

that that is the reason for the seemingly small values used for sections 3 and 4. On the other hand, it does not seem possible for the torsional moment ofinertia to be ten times l larger than either bending moment ofinertia, as occurs with section 23 used in the Steel Containment Vessel (or SCV), unless there is an error in the exponent of the bending i stiffnesses (6 rather than 5?). This potential error, however, is not expected to have i

consequences for the SSI analyses, because the overall symmetry of the SCV, for the i most part, uncouples bending and torsion. Ifit is the bending stiffnesses that are too

• small, that could obviously have an effect on the response, particularly because it occurs

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at a low elevation in the SCV, but the overall large rigidity of the lower portion of the structure is likely to mask this problem.

t Fourth, the structural damping used in CARES is bnsed on an inappropriate Rayleigh-5 damping model, which disagrees with the hystereta damping feature incorporated in both SASSI and our own software. As will be shown, this unfortunate choice in CARES will l be the principal cause of discrepancies in the results obtained.

Fife, the CARES program is unable to consider kinematic interaction effects, that is, it cannot consider the modification of effective seismic motions caused by deep embedment. While the analysis for the AP600 site was carried out for a soil of high stiffness, for which kinematic interaction effects are indeed small, in general this may not hold true, and this effect should be accounted for.

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New SSI Software

! As mentioned previously, three new pieces of software were used by us in this report to l~ aesess soil-structure interaction effects. The new SSI programs are:

! LAYSOL - to deconvolve motions in the free-field i i SUPELM - to compute foundation impedances, and obtain effective support motions i EKSSI - to compute inertial interaction effects j

3 l All three of these programs execute in a PC-DOS (or Windows) environment, and entail  ;

i relatively moderate execution times. During computation, they inform the user of current, j

ongoing operations, and provide a running estimate of the remaining processing' time. i i

These programs use dynamic storage allocation in connection with a DOS extender, so t there are no significant limitations on problem size.

g - The general characteristics of these programs are outlined in the appendix to this report.

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1 Foundation Model 4 n The foundation is assumed to be a rigid, rectangular prism of dimensions 127'x254' that i

is embedded 39.5' into the stiff ground, which is modeled as a homogeneous halfspace (Fig.1). The ground has a shear wave velocity of 3,500 ft/sec, a unit weight of 150 lb/ft', l a Poisson ratio of 0.30, and negligible material (hysteretic) damping. The foundation impedances are generated internally by EKSSI using the approximate formulae proposed by Pais & Kausel (1988). These impedances are the same as those used earlier in the CARES program.

Kinernatic Interaction Kinematic interaction refers to the motions observed in the foundation, assumed massless l and in the absence of the structure, when it is subjected to the same seismic environment 3 as the actual coupled system. This motion consists, in general, of both translations and rotations. It is well known that this is the consistent support motion that must be prescribed at the base of the soil impedances underneath the structural model (Kausel and Rousset,1974)

The motion components incorporating kinematic interaction effects are computed here I with the program SUPELM. Because this program does not include the capability of l handling prismatic foundations, a cylindrical foundation is used instead. The equivalent i radius R is chosen so as to match the contact area of the actual foundation, which can be achieved with a value ofR=100'. On the other hand, the embedment depth is chosen  !

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identical to that of the actual foundation. While SUPELM also provides the frequency-  !

dependent impedances for this cylindrical foundation, these impedances are not employed further in the confirmatory analysis since good approximations for the actual prismatic foundation are built into EKSSI, and are easier to use. More importantly, the latter were ,

the impedances actually used in the CARES annlyses. I The SUPELM foundation model is subjected to the Horizontal Input Motion in the x Direction (HI), prescribed at the free :;urface in the free field. This control motion is l identical to that one used in the analyses with CARES. For consistency of the analyses,  !

no iterations are made to account for inelastic effects in the soil, because those effects I

were not accounted for in either of the earlier models. SUPELM then provides the  !

effective translation and rotation of the foundation, measured at the intersection of the l vertical axis with the soil-foundation interface (i.e. the bottom of the foundation). As will be shown later on, the stiff soil causes the rotation component to be rather small, and the i translation component to be very similar to that observed in the free field at the elevation of the foundation. Tnis means that kinematic interaction effects are small in this case.

Initial EKSSI Model The first simplified structural model used in this report for the AP600 Nuclear Island is based on an earlier, detailed three-dimensional model presented in a document on the CARES program; that model was in turn based on an elaborate SASSI idealization l developed originally by Westinghouse. Given the complexity of the original SASSI model and the great difficulty in developing, from the available data, a soil-structure- '

interaction model fully equivalent to SASSI's, it was decided to prepare a simplified initial structural model for use in the SSI confirmatory analyses. The EKSSI model i consists of three cantilevering, close-coupled, lumped mass idealizations of the Coupled l Shield-Auxiliary Building (CSAB), the Steel Containment Vessel (SCV), and the '

Containment Intemal Structure (CIS); these stick madels are attached to a rigid, rectangular foundation embedded in a uniform elastic halfspace, as depicted in figures 1 and 2. The principal simplifications introduced in this model are the idealization of the lower elevations as a single rigid body (but with inertial properties), and the lumping of branches in each structural stick into their respective trunks (assuming the connections to the branches to be rigid elements, and using the pa allel axis theorem). The material and l

geometric properties are detailed in the self-explanatory listing of the EKSSI input file on Table 1.

Figures 3 through 5 show the three response spectra (5% damping) obtained with the simplified model referred to previously. These . spectra were cbtained for the x component of motion elicited by the H1 (or x) control motion in the free field, and kinematic interaction was fully accounted for. The spectra were obtained at the following locations:

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Top of the Coupled Shield-Auxiliary Building (CSAB).

Polar Crane Support point in the Steel Containment Vessel (SCV) e Operating Deck in the Containment Internal Structure (CIS).

Each figure shows three spectra, namely the original SASSI spectmm, the spectrum computed with the CARES software, and the spectrum obtained with EKSSI As can be seen, all spectra follow similar trends, and there is a Seneral agreement as to both amplitude and frequency content. The most important discrepancies are those exhibited by the CARES spectra, whose amplitudes are substantially less than those of SASSI or EKSSI. Nonetheless, some modest deviations are also evident in the EKSSI results, the reasons for which will be elaborated on, and ultimately removed.

Clearly, the structural models can be refined further and the agreement improved, as will indeed be done in the next section. It should be pointed out, however, that the EKSSI spectra already exhibit values in good general agreement with SASSI's; hence, one can evidently avoid obscure, complex, and error-prone structural models, and use instead fairly simple models such as EKSSI's. This observation is expected to be generally true, even in situations other than the those for the AP600 Nuclear Island, provided the general characteristics of the soil-structure system are properly accounted for.

Improved EKSSI model The most notable differences between the SASSI and EKSSI spectra are not so much in amplitude, but in the frequency of the resonant peaks. In addition, the spectrum for the CIS structure exhibits a spurious high-frequency peak that is not present in the SASSI spectrum. To some extent, these differences reflect the uncertainties that existed in mapping the SASSI structural models into EKSSI. More importantly, these deviations are undoubtedly caused by the simplifications introduced in the structural models, which effected moderate changes in the structures' resonant frequencies. Indeed, the EKSSI structural models are substantially simpler than those used in the SASSI analyses, involving far fewer nodes. The most important structural simplifications in the EKSSI model are as follows:

All three structures are modeled as close-coupled, cantilevering, discrete mass beams.

'Ihese beams have neither cross-connections nor branches. All spring elements used in SASSI/ CARES were fused into the properties of the beam members. .

The CSAB is modeled with e?ght masses and seven members, starting at elevation 180.2 (node 8 in the CARES model). The region below that elevation is assumed to be rigid, which is most certainly the cause of the shift to the right of the resonant peak in the CSAB spectrum.

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• The SCV is modeled with seventeen masses and sixteen members, staning at  ;

[ elevation 100 (node 101 in CARES). All branches are lumped into the structure, that

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is nodes 116 and 117 are part of 110, while nodes 123 through 126 are part of nodes -

106,12l,103 and 102, respectively. This change increased the effective inertia of the l

l SCV and lowered its fundamental frequency, which resulted in the shift to the left of in the spectrum (and perhaps also some changes in the modal forms).

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• The CIS is modeled with six masses and five members, starting at cleation 98.10 (node 201 in CARES). All the region below that elevation is assumed to be rigid.

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The two branches above elevation 135.3 (the operating deck) are fused into a single j one. Except for the spurious peak in the spectmm at about 15 Hz, the agreement is generally good.

l In the light of these observations, a modified structural model was prepared and used to l

compute new sets of spectra. To this effect, the ratios of the frequencies associated with the spectral peaks (i.e. the ratios of resonant structural frequencies) in the SASSI and i EKSSI models were first evaluated, and values of 1.206,0.854, and 0.87 were found for

- the CSAB, SCV and CIS buildings, respectively. Next, the stiffnesses of all members making up each of these structures were in tum adjusted by a factor so as to make coincide the resonant frequencies of each building with those of the SASSI run. Thus, the  :

frequency of the CSAB, SCV and CIS were shifted by the reciprocal of the factors above, j namely 0.83,1.17, and 1.15 respectively. The remainder of the model was left exactly as  ;

in the initial model, including the number and distribution of structural masses, the soil '

i parameters, and the effective motions. i As can be seen in Figs. 6 through 8, the agreement of the new spectra is now excellent; i the remaining small discrepancies here or there are now mostly the result of the slightly different effective seismic motions in EKSSI and SASSI. The most remarkable change occurred in the CIS: the slight increase in resonant frequency completely eliminated the ,

- spurious peak that could be seen before at about 15 Hz.  !

Implications of results The close agreement between the EKSSI and SASSI spectra obtained with the modified I model confinns, on the one hand, the validity of both programs and provides satisfaction  :

to the immediate goals of this study. At the same time, however, it demonstrates l

powerfully the sensitivity of computations in structural dynamics to small changes in the l

characteristic frequencies of a stmetural model (and to other parameters). l Consider, for example, the CIS building. It is remarkable that a mere 15% shift in its ,

resonant frequency should have completely eliminated the peak that existed before at about 15 Hz. The reason for this phenomenon can be traced to the characteristics of the {

- Fourier amplitude spectrum in the high frequency tail of the input motion. In that range, s

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the amplitude spectrum fluctuates rapidly between very small values and values that are .

less small, and depending on the exact location of the structure's resonant peak, one

' attains or not a magnification in response. By contrast, within the range where r

' earthquakes have the most energy, namely from 1 to 5 Hz, the amplitude spectrum  !

_fluctuates about much larger, non-zero values, and penurbations of structural resonant i frequencies have only moderate effects on the response.  ;

1 There are lessons to be learned from this observation that should be remembered when  :

2 assessing or conducting dynamic analyses for seismic effects for other projects or l i structural configurations. On the one hand, qualification or conf'umatory analyses should,  !

ideally, be conducted only with consistent models, since variations in structural and

! material parameters could lead to discrepancies casting needless doubt on the codes used.  !

On the other, the practice ofpeak-broadening to account for uncertainties in a structure's l resonant frequencies may merit a closer review, at least in relation to peaks occurring in i the high-frequency range of the spectrum. A possible remedy would be to carry out SSI '

j analyses with more than one set ofinput time histories, and treat statistically the results.

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' AP600 and SSI effects  !

Additional parametric studies were carried out to assess the importance of soil-structure -

interaction for the AP600 Nuclear Island. Specifically, the importance of kinematic and inertial interaction were evaluated separately from each other, and they were found to be both small.

Kinematic lateraction: First, the response spectrum for the motion in the free field at the elevation of the foundation was compared with the spectrum for the translational l component of the effective support motion (i.e. the motion accounting for kinematic i interaction. Fig. 9 shows the spectra for these two motions. As can be seen, these spectra are very similar, with only minor deviations in the high-frequency tail. Hence, the effective foundation motion and the far-field motion are very similar to each other. Next, the dynamic response was once more evaluated, but excluding the rotational component of the support motion in the input. Fig.10 through 12 compare the spectra for this situation with the response caused by both the translational and rotational components of support motion. Clearly, the differences are very small, implying that the contribution of the rotational component of seismic motion to the total response is negligible. These two observation lead to the conclusion that, at least in this project, kinematic interaction is not important, and can be neglected.

j Inertialinteraction: Once more, the analyses were repeated, assuming this time the support to be infinitely rigid (i.e. rigid soil springs). Figs.13 through 15 show a comparison of the spectra for this situation. As can be seen, the effect of the soil compliance is very small, and could have been neglected. In other words, inertial SSI is not important.

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In the light of these findings, it can be concluded that soil-structure interaction as a whole is not important for the AP600 Nuclear Island and can be neglected, at least when the

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soil is as stiff as in the configuration considered in this confirmatory analysis.

l Differences in formulation between SASSI and CARES From the review of the CARES manual, two main differences with SASSI were identified. The first one corresponded to the treatment of the kinematic interaction phenomenon. In SASSI, a complete kinematic interaction analysis is performed. This ,

implies not only a reduction for high frequencies of the amplitude of the translational I motion to be used for the analysis of the soil-structure system, but also the appearance of ,

l a rotational component of motion, which must be included in the analysis. In CARES, the l motion used as input for the dynamic analysis is that which would occur at the foundation level in the free field (a one-dimensional wave propagation solution, independent of the  !

geometry of the foundation). This motion has a variation due to the deconvolution  !

process, with substantial decrease in amplitude at the natural frequencies of the soil layer  !

above the foundation level, but no rotational component. When dealing with soft soils and important embedment, the differences between the results obtained with these two kinds ofinput can be significant. For very stiff soils, as encountered in the AP600 Nuclear Island, these differences are small, as corroborated in the previous section. l The second important difference between SASSI and CARES lies in the modeling of damping. In SASSI, the damping of both the soil and structural elements is hysteretic 'in  !

nature, which is independent of frequency. CARES, on the other hand, incorporates a l

composite damping model of the Rayleigh type. This model assumes a viscous damping matrix that is proportional to a linear combination of the stiffness and mass matrices; its coefficients are detennined by prescribing fractions of damping at two frequencies or pivots (usually the fundamental frequency of the structure together with a higher one, or i

more generally, at two arbitrary frequencies). It is well known that this procedure l produces a frequency-dependent damping law in which the effective damping is bounded within the frequency range dermed by the pivots; outside of this range, however, the effective damping grows rapidly, and attams unrealistic values. {

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l Conclusions and recommendations 1 From the analyses performed, the following conclusions can be drawn and recommendations made:

. Soil-structure interaction effects are negligible for the AP600 Nuclear Island when the shear wave velocity of the soil exceeds 3000 ft/s. The different treatment of kinematic interaction by SASSI and CARES is not responsible, therefore, for the discrepancies in the results.

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e The discrepancies in the results between SASSI and CARES would seem to be due primarily to the different kinds of damping assumed in the two programs.

The results of the dynamic analyses can be very sensitive at specific frequencies to the details of the structural model, particularly when high frequencies are involved.

4 This points to the need to use more than one input motion and treat statistically the results.

Although kinematic interaction effects were not important in this case, they may be in others. It is, therefore, recommended that an option to include properly these effects be included in CARES. An effective and particularly simple solution to this problem was proposed by Iguchi(1982).

An option to consider frequency-independent linear hysteretic damping should also be i included in CARES, particularly ifit is desired to obtain results comparable to those of SASSI. It is our understanding that this improvement either is in progress, or has stready been implemented.

J e Programs LAYSOL, SUPELM and EKSSI used for this study provide an effective additional means to conduct verifications with simple models. One should observe, however, the need to use appropriate structural models. Because EKSSI assumes a close-coupled structural system, it was not possible to use exactly the same structural 4

model used for the SASSI and CARES analyses (a modal synthesis option in EKSSI would have allowed a close or exact match, but the modes and frequencies of the SASSI stmetural models were not available). Nonetheless, simple models such as those used in EKSSI can often be used to great effect in soil-structure interaction

, studies, producing results that are in good or even excellent agreement with those obtained through more complex (and error-prone) SSI models. In general, complex  ;

models should be avoided whenever possible, provided adequate care is taken to prevent over-simplified models.

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J Appendix: The LAYSOL, SUPELM and EKSSI programs

[ 1)LAYSOL i This program computes the dynarr.:c response of viscoelastic, horizontally layered soils over elastic or rigid rock, using an efficient, but rigorous, stiffness matrix formulation

~ Kausel and Rousset,1981). The dynamic excitation may consist ofseismic waves

- propagating with any arbitrary inclination through the medium, or be applied as harmonic

, loads at some location. The following cases can be analyzed:

Seismic excitation Computes the response of the soil profile to seismic excitations. The 3

' earthquake input motions are prescribed in the form of wave amplitudes, of motion .

i amplitudes, or of time histories at some arbitrary controllayer. The control point can be j

an elevation within the soil profile, or be located on an (actual or hypothetical) j outcropping layer. The seismic environment can consist of P, SV and/or SH waves '

[ propagating at arbitrary angles with respect to the vertical, or having an arbitrary slowness (inverse ofhorizontal phase velocity). The program can optionally be used to

!' carry out iterations on the soilproperties to account for large strain, using the well known Seed-Idriss quasi linear algorithm. Agrees with the well known code SHAKE when the waves propagate vertically. The output consist of transfer functions from the F

control point to the individual layers, and 'of motion time histories at each layer interface,

if the input was prescribed in the form of time histories.

' Disk loads orStrip loads: In this option, the soil profile is excited by horizontal and .

vertical harmonic loads that may be placed at any arbitrary elevation, and that are "

distributed uniformly either over a circular area, or over a plane-strain, rectangular strip.

The solution is formulated in the frequency-wavenumber domain, and displacements are -

i computed by numerical integration over wavenumbers. The output consists of transfer functions for arbitrary points, i.e. complex responses as a function of frequency. In the plane-strain case, the program computes also the impedance matrix of a rigid strip footing i of the same width as the pres:ribed strip load. (This option was not used in the context of 4

this report). l 1

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. 1 l 2)SUPELM This program may be used to compute the dynamic response ofideally rigid cylindrical, 4

' annular, or narrowly rectangular (strip) foundations supported by horizontally layered

' . soils. The program is based on a discrete formulation that uses super-elements (hyper-elements) to model the region underneath the foundation, and consistent transmitting i

boun' daries to model the infinite lateral extent of the soil (Tassoulas and Kausel, miscell.

i ref.). Two options are available:

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l Dynamic impedances: Response to external forces and moments; this option yields the

- j dynamic stiffnesses (i.e. impedances) of the foundation, as a function of frequency, for the active degrees of freedom.

Kinematic Interaction: In this option (sometimes teferred to as the wavepassage i problem), the program computes the seismic response of the foundation resulting from P, SV and SH waves having some prescribed horizontal phase velocity.

3) EKSSI This program provides a frequency domain solution, including soil-structure interaction i effects, to a dynamically loaded structure that rests on compliant ground. EKSSI has the '

following characteristics:

1 Structure: Fully three-dimensional lumped-mass structure, with up to six degrees of I freedom per node. The stmeture can be described either as cantilevering beams assembled with linear members, or more generally, in term of the modes andfrequencies j of the structure for a rigid base condition (Kausel,1995). In the latter case, the modes

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must be computed with any appropriate program before employing EKSSI. '

Foundation: In the normal mode of operation, the user supplies any arbitrary set of frequency-dependent (or independent) impedances for some or all degrees of freedom.  ;

These impedances must have been computed with an independent program, such as  ;

SUPELM. Altematively, the program can provide intemally the impedances for cylindrical or rectangular foundations embedded in a homogeneous halfspace, which are based on approximate formulas. If desired, the support may also be rigid.

Excitation: The dynamic excita'. ion can consist either ofstructural loads applied I directly to the nodal points, or ofseismic support motions prescribed under the foundation impedances. In either case, the excitation can have up to six degrees of freedom and six independent time histories. Each time history can be scaled by any appropriate factor.

Input-Output: A significant advantage of this program is the implementation of a Program-oriented Language. Hence, the input description can be carried out in plain English, using for this purpose a set ofcommands that are easy to remember (similar in concept to the well known STRUDL program). Units can be arbitrary. A rather voluminous amount of output can be generated with th!a program in printed orplotted l format. Among the options are transfer functions, Fourier spectra, time histories', and/or Response Spectra.

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c References and Bibliography:

v CARES: Computer Analysis for Rapid Evaluation of Structures, Version 1.2, by C. i Constantino, C.A. Miller, E. Heymsfield, and A. Yang, Prepared for the Division of

] Engineering of the US-NRC, pages 5.1-5-14 and Appendix D1-D22 <

EKSSI : " Dynamic analysis of structures, including soil-structure interaction effects", a  ;

computer program by E. Kausel, Cambridge, MA 02181, version 3.11,1996 i

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~ LAYSOL: "A Program for the Dynamic Response Analysis of Layered Soils", a computer program by E. Kausel, Cainbridge, MA 02181, version 3.3,1996.

i SUPELM: " Foundations embedded in layered media: Dynamic stiffnesses and Response i to seismic waves" , a computer program by E. Kausel, Cambridge, MA 02181, version

[ 3.1,1996.

l ,

Iguchi, M (1982): "An approximate analysis of input motions for rigid embedded foundations", Trans. Arch. Inst. of Japan, , No. 315 (May), pp.61-75.

Kausel, E. and Rousset. J. M. (1974): " Soil-Structure Interaction Problems for Nuclear ,

Containment Structures", Electric Power and the Civil Engineer, Proceedings of the ASCE Power Division Conference held in Boulder, Colorado.

B b

Kausel, E. and Rousset, J. M. (1977): "Semianalytic hyperelement for layered strata", i Journalofthe EngineeringMechanics Division, ASCE,pp569-588, August 1977.

Kausel E. and Rousset J. M. (1981): " Stiffness Matrices for Layered Soils", Bulletin of the Seismological Society ofAmerica, Vol. 71, No. 6, Dec.1981, pp.1743-1761.

Kausel E. and Rousset J. M. (1984): " Soil' Amplification: Some Refinements", Soil Dynamics and Earthquake Engineering, Vol 3, No. 3, pp.116-123  :

Kausel, E. (1995): "SSI: Modal Synthesis for Stmetures with Kinematic Constraints",

Proceedings,10th Engineering Mechanics Conference, ASCE, Vol. I, pp. 269-272 Pais, A. and Kausel, E. (1985): " Stochastic Response of Foundations", MIT Research ,

. Report R85-6, Department of Civil Engineering Pais, A. and Kausel, E. (1988): " Approximate Formulas for Dynamic Stiffnesses of Rigid Foundations", Soil Dynamics and Earthquake Engineering, Vol. 7, No. 4, pp. 213-227.  ;

Pais, A. and Kausel, E. (1989): "On Rigid Foundations Subjected to Seismic Waves",

Earthquake Engineering andStructural Dynamics, Vol.19, pp. 475-489.  :

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Pais, A. and Kausel, E. (1990): " Stochastic Response of Rigid Foundations", Earthquake  !

Engineering and Structural Dynamics, Vol 19, pp. 611-622.

Schnabel, B. P., Lysmer, J., and Seed, H. B. (1972): " SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites", Report No. EERC 72-12, December 1972, Earthquake Engineering Research Center, University of California, Berkeley, CA. '

Seed, H.B., and Idriss, I.M. (1970): " Soil Moduli and Damping Factors for Dynamic Response Analysis", ReportNo. EERC 70-10, December 1970, Earthquake Engineering Research Center, University of California, Berkeley, CA.

1 Tassoulas, John L. (1981): " Elements for the numerical analysis of wave motion in layered media", MITResearch Report R-81-12, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.

Tassoulas, J.L. and Kausel, E. (1983): " Elements for the numerical analysis of wave motion in layered strata",' InternationalJournalfor Numerical Methods in Engineering, Vol.19, pp.1005 1032.

Tassoulas, J.L. and Kausel, E. (1983): "On the effect ofrigid sidewalls on the dynamic stifiness of embedded footings", Earthquake Engineering andStructural Dynamics, Vol 11, pp. 403-414.

Tassoulas, J.L. and Kausel, E. (1984): "On the dynamic stiffness of circular ring footings on 'an clastic stratum", International Journalfor Numerical and Analytical Methods in Geomechanics, Vol. 8, pp 411-426.

l l

I l

1

)

i 15

. i 1

Table 1: EKSSIinput file  !

Note: boldface type denote EK.SSI commands, text after semicolons are comments BEGIN AP600 Nuclear Island, initial model CASE seismic SUPPORT AT x=-3.0, y=-22.7, s=60.5 FMAI 50 , NTF=201, NFFT=2048 STRUCTURE ACTIVE DOF x y a rx ry rz DAMPING 0.06 JOINT COORDINATES x y a

Coupled Shield-Auxiliary Building (CSAB) 1 0. O. 306.3  ; CARES joint 16 I 2 0. O. 297.1  ; " "

15 3 0. O. 284.4  ; " "

14 4 0. O. 272.4  ; " '

13 5 0. O. 276.1  ; " "

17 6 0. O. 241.0  ; " "

11 7 0, 0. 220.0  ; " "

10 8 0. O. 200.0  ; " "

98 (9) 9 0. O. 180.2  ; a "

28 (close to it)

Steel Containment Vessel (SCV) 10 0. O. 256.3  ; CARES joint 115 11 0. O. 248.3  ; " "

114 12 0. O. 240.3  ; * "

113 13 0. O. 229.5  ; " "

112 14 0. O. 218.7  ; a "

'111 15 O. O. 205.3  ; " "

110 + 116 + 117 16 0. O. 190.0  ; a "

109 17 0 O. 170.0  ; " "

108 '

18 0. O. 162.0  ; * "

107 19 0. O. 144.5  ; " "

106 + 123 j 20 0. O. 138.6  ; " "

121 + 124 1 21 0 O. 132.3  ; " "

105 i 22 0 O. 116.9  ; * "

104 23 0. O. 112.5  ; " "

103 + 125 24 0. O. 110.5  ; * "

122 + 126 25 O. O. 104.1  ; " "

102 26 0. O. 100.0  ; " "

101 l

Containment Internal Structure (CIS) 27 12.550 31.600 158.0  ; CARES joint 207 28 1.135 33.910 148.0  ; " "

206 29 -2.363 16.120 135.3  ; " "

204 + 205 30 -4.149 4.091 107.2  ; " "

203 '

31 1.965 3.646 103.0  ; " "

202 32 -0.862 4.115 98.1  ; " "

201 1

16 j l

l

_ _ _. . . _ -_.._. _ _. ._ ,_.~._ _. _ . . _ _ _ _ _ _ _ , _ . _ _ _ _ _

4

,.( --

f .' i i JOINT alASSES m, Ja, Jy, Jh-  ; Actually, weights in Kips

• i - ,

coupled Shield-Auxiliary Building (CSAB) 1 1674. 0.287E5 0.287ES 0.574E5 2 1538.- 0.308E5 0.308E5 0.789ES, 3 3405. 0.108E6 0.100E6- 0.251E6  ;

'4 4143. '0.163E6 0.163E6 0.338E6

• [

5 4540. O. O. O.

6 6291. 0.357E6 0.357E6 0.716E6 t 4089.

7 '0.320E6 0.320E6 0.64086 '

8- 3990. 0.314E6 0.311E6 0.625E6 F 9 0. O. O. O. I

Steel Containment Vessel (SCV)

, 10- 180.7 0. O. O.

11 324.0 0.814E4 0.814E4 0.163E5 '

12 349.7 0.154E5 0.154E5 0.308E5 1

13 362.7 0.219E5 0.219E5 0.438E5 {

a 14 378.6 0.249E5 0.249E5 0.498E5  !

15 1716.7 0.577ES 0.494E6 0.551E6  ; used parallel axis for 117  ;

16 613.9 0.404E5 0.404E5 0.OO7E5 "

17 562.2 0.370E5 0.370E5 0.739ES.

18 484.4 0.318E5 0.316E5 0.637E5 '!

19 590.8 0.445E6 0.105E6 0.551E6  ; used parallel axis for 123 20- 50.6- 0.249E6 0.233E5 0.272E6  ; " " "

" 124 21 525.8 0.346ES 0.346ES 0.691E5 i 22 272.5 0.179E5 0.179ES 0.358E5 '

] 23 263.6 0.145ES 0.145ES 0.290E5 ~

24 50.6 0.249E6 0.233E5 0.272E6  ; used parallel axis for 126 25 182.7 0.120E5 0.120E5 0.240E5 26 55.9 0.363E4. 0.363E4 0.727E4 i

Containment Internal Structure (CIS)

'27 185.2' O.288E3 0.354E3 .0.642E3 20 691.7 0.242E4 0.423E4 0.665E4 {

29 8723.7 1.254E6 0.249E6 1.511E6  ; used parallel axis for 205 30 9807.0 0.210E6 0.248E6 0.606E6 ,

31 4394.0 0.355E6 0.342E6 0.352E6 32 9339.0 0.345E6 0.374E6 0.719E6 '

MIMEER PROPERTIES I

Coupled Shield-Auxiliary Building (CSAB)

stiffnesses multiplied by [g] to compensate for weights

E = 1.67E7 = 32.17*0,519E6, G= 7.14E6 = 32.17* 0.222E6)

Axial Shear-y Shear-z Torsion Bend.-y Band.-z CARES section 1.219E10 2.606E9 2.606E9 5.669E12 6.630E12 6.630E12  ; Section 14 1.38BE10 2.970E9 2.970E9' 7.111E12 8.317E12 0.317E12  ; "

13 i 1.047E08 2.799E8 2.799ES 1.364E12 1.837E11 1.837E11  ; "

10  !

1.000E14 1.00E14 1.00E14 1.000E17 1.000E17 1.000E17  ; Rigid memb 5 2.271E10 3.213E9 3.213E9 3.577E13 4.375E13 4.375E13  ; Section 9 l 2.288E10 3.284E9 3.284E9 3.556E13 4.359E13 4.359E13  ; " '

8 i

1.670E10 3.327E9 3.327E9 3.539E13 4.342E13 4.342E13  ; "

15 a

17 I

I

__ ~._ ~. _ - . _ _ _ _ _ _ _ . _ _ . . _ . . . . . _ _ . . _ _ . _ _ _ - _ . . . _ ._.. ,

1  :

l t Steel containment vessel (SCV) ~

,1

Stiffnesses multiplied by [g] to compensate for weights j-  ; E = 1.36E8 - 32.17*0.425E7, 1-G = 5.24E7 = 32.17* 0.163E7)

Axial Shear-y Shear-s Torsion Band..y. Bend.-r CARES section

I 7.072E7 '4.496ES 4.496E8 1.451212 1.890E12. 1.890E12 ; Section 29 3.155E8 1.043E9 1.043E9 4.826E12' 6.256E12 6.256E12 ; "

28 i

! .5.290E8 1.289E9 1.289E9 8.751E12 1.138E13 1.138E13. ; "

27 '

j 1.673E9 1.420E9 1.420E9 1.153E13 1.496E13 1.496E13 ; "

26 7.534E9 1.451E9 1.451E9 1.226E13 1.591E13 1.591E13 ;

• 25

8.106E9 1.562E9 1.562E9 1.320E13 1.714E13 1.714E13 ;

• 24

• 1.945E9 1.347E9 1.347E9 1.205E13 3.849E12 .3.849E12 ;

• 23 e

f  ; containment Internal Structure (CIS) i Stiffnesses multiplied by (g) to compensate for weights e

E = 1.67E7 = 32.17*0.519E6, G = 7.14E6 = 32.17* 0.222E6)  ;

j-  ; Axial Shear-y. Shear-z Torsion Bend.-y Bend.-z CARES section 3.624E9 2.8S2E8 2.892E8 7.211E10 1.141E11 1.141E11 ; Section 22 8.834E9 7.854E8 7.854EB 4.413E11 9.369E11 9.369E11 ; "

• 21 3.066E10 2.849E9 2.F49E9 4.712E12 1.463E13 1.463E13 ; "

19

(

' 9.035E10 1.571E10 1.571E10 4.605E13 6.680E13 6.680E13  ; "

18 1.222E11 2.292E10 2.292E10 6.962E13 9.703E13 9.703E13  ; "

17 i

1 EEAM 1 1 2 3 4 5 6 7 /  ;~CSAB

). 8 9 10 11 12 12 12 12 12 12 12 12 13 13 13 14 /  ; SCV l 15 16 17 18 19 / i CIS

.7 i F FOUNDATION i ACTIVE DOF x y s rx ry rs MASS m Jx Jy Js 'j 1.811E5 2.146E8 2.343E8 6.540E7 j RECTANGULAR A=127. B=254. E=39.5 G=1.837E6 MD=0.150 PO=0.3 Ur=3  ; G*g here !!!

EECITATION i ACTIVE DOF x, ry j DT = .01 INCLUDE decon ux ,

INCLUDE decon ry

't i OUTPUT PRINT PLOT =EP SPECTRA DA=0.05 F1 0.1 F2=50. NP=138 LO 1 x ta th rs 15 x ta th rs 29 x t,a th rs '

I END l

l 1

18 (

i 1

l

. i

. - . - , - . , . . - . . . - .-.- . ... . . . _ . - - - . - - . . . . . - . . . _ . . . - . . _ ~ - . . - .

1

., , q l

Fig.1. Schematic view of AP600 Foundation Plan d

b 4

/ .

a l J '

i

127' I .I 4

1 i

1 t

.  ! 254' I a

k d

i i ,

I i

2 -

I t

f .

d e

\ x ,

h r

t 19

, s

j Fig. 2 Schematic view of the soil-stmeture model

l Note: numbers refer to EKSSI nodes  !

CSAB l th SCv 2

h i

3 o 10 .

h o

() o CIS ,

a

() Iho '

o " 27 l 9g g i o o o

o h

. o o kh 1

i o Yh

! o .

o g 32 l 26 (

Common support MM  ;

Impedances 1

1 l

I Seismic input V

. I e

1 i .

! I i 20 )

i 1

. Fig.3: CSAB, initial model 5% response spectrum Coupled Shield-Auxiliary Building Top of structure, motion in x due to Hi -

8 .

i i I i

8 8 0 0 4 5 6 0

e i I t i I I

• I, -

6 ------------------  ;-------------r ,---- :--------------

, l

.._._...-- S AS SI l lln1 l c

,o EKSSI

...... .. CARES l

"j l

l

,_o. , .

g I u 1 N

4 ....................L.......... '.}. ,...'.............

l\ e 6  : \\ ,

1

. i. / \. m, .

1 8

y } '\

8t

' i

)

1. • • /

3 ....................'.......,y-lN y . . . . .\t ,,/ . . g. \_

i l1 <

l $,,,, ..y\.:y.

~. .

, ,..,, 6.1 ,

i i .

' J 4

7 's.N..e 4 ,!

I i

, 0 .___.  !

0.1 1 10 Frequency [Hz]

l l

1 l

21 i

l I

i

l .

Fig. 4: SCV, initial model 5% response spectrum Steel Containment Vessel  !

Polar Crane Support, motion in x due to HI 4 ,.

.i i.

.e .

i , ,

I i

!{ -

l I l t [' t g 3 - - - - - - - - - - - - - - - - - - ' - - - - - - - ~ ~ - - - - - ' - -l--------------

' i

... .__. SASSI e 8 EKSSI l

' f., ,i

= ........ CARES '

'l i; 6

o l l  !: l o

g i

lgg ..

2 ....................;.............-. 3 i.g..............

so < p w 6 *

, r}\ II.I  ?

e

! E ,' ;a?I \\

g p.b\ 'W Et%)l

\

I i r-.  :

l 3 ....................p..... .,, ......... ,

. . . . . . . . l. . . . . j#%..

mm.

t I

+ l I i a l i I l 8 t I i 0

0.1 1 10 Frequency [Hz]

1 l

t i

l n

22 l

l Fig. 5: CIS, initial model I

5% response spectrum

~.

Containment Internal Structure Operating Deck, motion in x due to HI 2.0 i 1

I 4

h.

0 8

4 0

j 1.5 ----'

---~--------l-------------------l

' :-~-------

y SASSI l l g ExSsi l I

.c ....... .. CARES l f- ,

y', (

i 1.0 ------"------------------,

{' kjf', '

6 , , i.

• C .

D .

gtl\

i 1

e '

M ' '

A ,

l l t^\

s i

e e.

g 0.5 ----------------~:-----------------i, ' ' ,

i

,s, 7, ,

s'/

// l e

l t

s 0

0.1 1 10 Frequency [Hz) 23

Fig. 6: CSAB, modified model 5% response spectrum Coupled Shield. Auxiliary Building Top of Structure, modified EKSSI model Motion in x due to HI 8 , ,

s l l I e i

I I i B

4 I i l q l b .

6 ------------------,b--  ;

9 i

SASSI l

{

8 EKSSI l l c . ,

e J l l

_o , ,r! ,

1 o l u

m 4 ................. ..;........... j!...

e .

....n;..............

i 6

• l!- '

8 A

u

' \!

e

{<\

yy\ i l ,-

l!

....................,l.........fY. . . . . . \.h l

2 y

. . . ;. . \........

. tv ,

• . ..y

,}l I

• w:r~;_.-

, e ,

,f a

,.L, ./ ' l 4

0 0.1 1 10 Frequency [Hz) 1 1

24

t Fig. 7: SCV, modified model 5% response spectrum Steel Containment Vessel Polar Crane Support, modified EKSSI model Motion in x due to HI 4 , ,

f f I I E

l 6

e 1 s I f 9 6

1 3 --------------------l------------------ -l--------------

8 SASSI l E' t z

8 EKSSI l Ill, ao ,

e 8

M 2 ------------------- ,'--------------

.---F-------------

, p.

l

• 6 '

o l R , v f t

(" l 4 .I  ! %, .

t v[. .. f7

~

1 3 ...................y.....j/lv{'.........$y. z...........

.+... ..

l  ;

UN . . ..._

J.f , ... .

e Y. f s / ge f p s

I I

a

,.,# I '

0 0.1 1 10 Frequency [Hz]

d 25 t

Fig. 8: CIS, modified r todel 5% response spectrum Containment Internal Structure Operating Deck, modified EKSSI model > -

Motion in x due to H1 1.5 .

I I l l 5 6 8

0 I

I I I 4 0 1.2

---

r'------------------[9------------ N sAssi l in i.y '. 6.

g 7

\.,lqi ^I 7

0.9

---

f'-----A,h,r,.','-----

q l--------

g B

,3]

I

\

! o y

6 '

I i

3 b

M 0.6

---

'j'----------------'------A.,----- c o.

'\ 'a.

l l 1

1 I

I i

............7<.!

I i l- o.3 , ,

,/, 1 1

/*- I 1

I e l

0 0,1 1 1(

Frequency (Hz)

)

)

~

l i

1 26

Fig. 9: Support motion vs. free-field motion 5% response spectrum Effective translationalinput vs.

Free field motion at foundation level (Effect ofkinematic interaction) 1.25 ,

I I i i i

,t s

. e 1 4 1.00 ------------------ ----- ~ r-------- '--------- ---

> i

.. T Effective motion 'i g l c

Free-field motion ' gr!g l

. JJ- ,

---

l'+,'-------------

0.75 - - - - ~ ~ - - - - - - - ~ ~ - - - - ' - - - - '

Tu l h}

. tfl\

f.c.

l 'l \l.

y 6

+V i b.,

.Be 0.50 ---------------------------------------l--%.---------- e

\s.

C /* ' 6 l' ! l N l / ,I l

-.i -

l

. V.u.

I j

.2

'b l 0.25 " - - - - - - - - - :.7.:::f

- - - - - - -- .e- - y - - - - - - - l, - - - - - - - - - - - - - - - - - - l, p*f 0 E 4

./a . .

"" ,.

• a i

s 1

0 0.1 1 10 Frequency [Hz) l l

l I

l i

27

Fig.10: CSAB, modified model, effect of rotational input motion 5% response spectrum Coupled Shield-Auxiliary Building Top of Structure, modified EKSSI model Effect of rotational input component 8 , ,

' s 9 I 8 6 I e I 1 0 t l e ,

8 e t #.3 t

[

6 ................................ ,,... ,,,,,,,,,,,,,,

g With rotation l l g . . .. . No rotarion l

• O i i s

a  : ,

l y4 ..---.-......-.--.'................ ..................

6 .

. t' o '

s I i

U '

I M I 4 A i

, i s

s:O e 2 --..................,t.......... ......... , ,,,,,,,,.,

.l 8

%

i:::::: c=.

9 I e I f I

I I I 6 0

O.1 ~1 10 Frequency [Hz) 1 1

I 28

Fig.11: SCV, modified model, effect of rotational input motion 5% response spectrum Steel Containment Vessel Polar Crane Support, modified EKSSI model Effect of rotational input component 4 .

t e

i i

e i I f a I 1 I i 3 .....................................f),tip !. . . . . . . . . . . . . _

~

- With rotation l l ui

' l e - - ---- No rotation f(il

,o i

'i,' ,

1.

E l

$ l J O

m 2 ----------------

--l----------------d---

u

=  ! h M e b.

A l li

! v/  !$.

3 ....................p..... ...'/'

.........p.g;3,........_

l l

s'-...:::::::

0 8

I I

e i

G t

t t i e

i i 0 0

0.1 1 10 Frequency [Hz]

< 29

9 Fig.12: CIS, modified model, effect of rotationalinput motion 5% response spectrum  ;

Containment Internal Structure Operating Deck, modified EKSSI model Effect of rotational input component 1.2 ------------------ c;------------------ I c------- -----

l i.. lvg .

l l Y'.

. Af  ?. l j l fly 9, 'A s '\,1., .

Si L4 '

\'

l 4sA

- T.$, .,)

8 z

0.8 -------------------,'----F--------------ll-----1--------

. I 2

v.

With rotation l l 1. \.

j - - -

No rotation '

l

g\

u . i

! V i y(

~ .

g c.

fl l O.4 r------------------ e----- -------

A[i i +

/

/  !,  :

f .

,f l l

,l 0 <

0.1 1 10 Frequency (Hz]

30

I l

Fig.13 CSAB, modified model, effect ofinertial interaction 5% response spectrum 1

I l

l Coupled Shield-Auxiliary Building I Top of Structure, modified EKSSI model Effect ofinertialinteraction  !

8 , ,

I

,I i

i

.i .

. . i 6 -------------------$-------------$-----b--------------

)n .

i i

g Soilimpedances  ;

,o -

Rigid support  ;

i i

- e E  ;

l v , ,

U i h 8 4 I,i - - - ------------------

=

6 o

---

,//

3 . li ,

v ,e u il a

[ i i

i llf

$;g

.i i

I ,v\ '

2 --------------------F--------,/)-l-------h,1\ ys l f;,f l

\::' .q.....::::

l .zs  :

p/j a

6 6 1 4

4 0-0.1 1 10 Frequency (Hz]

31

1 l

l Fig.14 SCV, modified model, effect ofinertialinteraction  ;

5% response spectrum 1 Steel Containment Vessel Polar Crane Support, modified EKSSI model .

Effect ofinertialinteraction Y~ l l

I a

.i .i 1

.i 0

, 1 3 -------------------------------------

I 1 c: Soilimpedances l Rigid support l l

8 co 2 -------------------l--------------- --- --------------

6  ;

m ,

e c , ,

8 . , ,

c-.  :

[  :

l

. K. ,. e.#

i .. . . . . . . . . . . . . . . . . . .,u . . . . . ,. v @. ). . . . . . . l. . w g,'. . . . . . . _

..-n.....,

i f,y! .

./ l t

4 I i i 1 4 9 I I 0

0.1 1 10 Frequency (Hz) 4 32

Fig.15 CIS, modified model, effect ofinertialintersction 5% response spectrum Containment Internal Structure Operating Deck, modified EKSSI model Effect ofinertialinteraction 1.25 .

p B

.. N{

e \

a Al l.00 --------------------l------4 a i V. W Soilimpedances y

. Rigid support l

,y #

c . l o t c

E o,y$ . . . . . . . . . . . . . . . . . . . . y . . . ,q;C...............y.....t.

9......

, t' ,

2 e s

h o e .

M l i e

'g 6 N l  %.

,i 3g 0,$o ....................'....................:...........%

c- -l l i i j e i 8

4 0.25 ------------------,,---~~~------------t I i

, e e 4 1 0 d , 4 J

0 0.1 1 10 Frequency [Hz) l I

l l

33