Seismic design of nuclear power plants—where are we now?

Nuclear Engineering and Design 182 (1998) 3–15

Seismic design of nuclear power plants—where are we now?

J.M. Roesset *Department of Ci6il Engineering, ECJ 4.6, Uni6ersity of Texas at Austin, Austin, TX 78712, USA

Received 1 September 1997; accepted 30 September 1997

Abstract

The lack of any significant activity in the design and construction of new nuclear power plants over the last 10 yearshas resulted in a corresponding lull in the basic academic research carried out in this field. Whilst some work is stillgoing on related to the evaluation of existing plants or to litigation over some of them (including some that neverbecame operational) most of it is of a very applied nature and little basic research is being conducted at present.However, research on earthquake engineering in general, as applied to buildings, bridges, lifelines, dams and otherconstructed facilities has continued. This paper attempts to look at some of the areas where there were majoruncertainties in the seismic design of nuclear power plants (selection of the design earthquake and its characteristics,evaluation of soil effects and soil structure interactions, dynamic analysis and design of the structures), the progressthat has been made in these areas, and the remaining issues in need of further research. © 1998 Published by ElsevierScience S.A. All rights reserved.

1. Introduction

The importance of nuclear power plants andthe consequences of a nuclear accident requiredthat they be designed to safely withstand the mostsevere environmental conditions that could rea-sonably be expected to affect them during theirlifetime. This led, during the 1960s and 1970s toan extraordinary amount of basic and appliedresearch on their seismic analysis and design, re-search which benefited not only the nuclear indus-try but also the area of earthquake engineering ingeneral. Many significant advances in this field area direct result of these research efforts and thenuclear industry can be proud of their contribu-

tion. Yet the desire to apply new knowledge asfast as it was being generated and the pressure touse the latest state of the art procedures withoutan adequate amount of time for reflection andvalidation had some undesirable consequences:further analyses and re-analyses were required insome cases without any real justification based onconclusions or results from papers which ad-dressed very particular cases of limited scope;methodologies that were incomplete and at timesincorrect (incorrect for some practical situations)were accepted or even endorsed at one time andthen disavowed entirely; and criticism of estab-lished and commonly used procedures pointingout their limitations was occasionally consideredtreacherous and detrimental to the good of theindustry. All this resulted in a significant amount* Tel.: +1 512 4714927; fax: +1 512 4718477.

0029-5493/98/$19.00 © 1998 Published by Elsevier Science S.A. All rights reserved.

PII S0029-5493(97)00277-X

J.M. Roesset / Nuclear Engineering and Design 182 (1998) 3–154

of controversy. This controversy and the adver-sarial relationships which existed at one time be-tween the owner/designer/manufacturer team, theregulatory agencies and their consultants and thepublic at large, who justifiably demanded answersto a number of important questions and access toinformation, hurt the nuclear industry and re-sulted eventually in a near complete halt in newdesigns and construction as well as research. Un-fortunately, the conflict has not stopped. It hascontinued with the adversaries becoming the reac-tor manufacturers, the architect engineeringteams, and the owners who try to recover theextra costs associated with the lack of completeknowledge at the time the design of their plantswas initiated and was being carried out, the needfor research and development of new methodolo-gies which existed at the time, and the requiredreanalyses and design modifications.

The reduction in activity within an area withthe corresponding decrease in the pressure to findinstant solutions to new problems for which thereis very limited experience provides, or shouldprovide, the opportunity to compare and validatemethodologies, to better define their ranges ofapplicability, to identify areas where additionalresearch is necessary, and to reach a consensus,perhaps, on acceptable solutions and procedures.It is also the time for industry to regroup andprepare itself to be ready when the need for newdesigns arises again, trying to avoid future contro-versies. Unfortunately, in the seismic design ofnuclear power plants this kind of activity has beenrather limited, although significant work has beendone in Japan by a number of companies (Ka-jima, Mitsubishi, Ohbayashi, Toshiba) and in theUS by the Electric Power Research Institute(EPRI, 1993) and government organizations suchas the Nuclear Regulatory Commission or theDepartment of Energy, amongst others. Most ofthis work is, however, of an applied rather than abasic nature and some controversial issues remainunresolved. Research on earthquake engineeringhas continued, on the other hand, with applica-tions to building structures, bridges, hospitals,dams, lifelines, and other facilities, using in manycases the methodologies developed for nuclearpower plants and extending them.

The purpose of this paper is to review some ofthe major sources of uncertainties which existed inthe seismic design of nuclear power plants, discussbriefly some of the work that has been done inthese areas, and point out remaining topics inneed of further research. The three main areas tobe addressed are the definition of the design earth-quake (or earthquakes), the effects of the soil (soilamplification and soil structure interaction), andthe dynamic structural analysis.

2. Definition of design earthquake

The determination of the design earthquake (orearthquakes) for a nuclear power plant was nor-mally based on a series of extensive seismologicaland geological studies. Potential active faults wereidentified. Rates of occurrence of earthquakes ofdifferent magnitudes were assigned to all knownfaults or areas where epicenters of past earth-quakes had been located. Finally, attenuationlaws were developed which could provide peakvalues of the ground motions parameters (acceler-ation, velocity or displacement) for a given earth-quake as a function of magnitude and distance.However, the results of all these studies wereexpressed in terms of a single parameter, theeffective peak ground acceleration. The designearthquake was then specified in terms of thisacceleration as a scaling factor and a standard setof response spectra for various values of damping.

This process could be improved considerably bygenerating design motions on the basis of physicalconsiderations, accounting for the effects of mag-nitude, focal mechanism, distance, topography,and soil conditions, not only on the value of thepeak or effective ground acceleration but also onthe frequency content and duration of the earth-quake. A detailed modelling of a fault with thecomplete length of rupture and the geologicalfeatures of the terrain over dimensions of manykilometres may be far too expensive even forpresent day supercomputers, particularly for prac-tical applications. Studies with less detailed mod-els but accounting for information from actualrecords can provide, however, valuable insight onthe general characteristics of the expected motions

J.M. Roesset / Nuclear Engineering and Design 182 (1998) 3–15 5

at the site (duration and frequency content) fordifferent magnitudes and distances.

Many are the researchers who have contributedto this area and no attempt will be made here totrace their individual efforts. One should mention,however, the studies conducted by EPRI (1986)and by the Lawrence Livermore Laboratory(Bernreuter et al., 1985, 1987, 1989) for the east-ern United States and more recently the workconducted at the National Center for EarthquakeEngineering Research of the State University ofNew York in Buffalo (Jacob, 1994). Clearly morework remains to be done and there are still uncer-tainties that cannot be accounted for fully. Inspite of the remaining issues, and the fact that theinterpretation of the same data by different re-searchers may lead to different conclusions, it ispossible today to prescribe design motions consis-tent with a desired return period (or probability ofoccurrence) in terms no longer of a single parame-ter but accounting for duration and frequencycontent as well as peak ground acceleration. Thisis a major step forward.

A second improvement would be the consider-ation of more than one design motion for thesame return period, corresponding perhaps to dif-ferent distances and magnitudes (one could havefor instance a small, or relatively smaller, but veryclose earthquake and a stronger but more distantone). When the motions are specified in terms ofdesign response spectra or, even better, in termsof a power spectral density that could be useddirectly for probabilistic dynamic analyses, this isall that is needed. When using actual earthquakerecords with characteristics similar to those of thedesign motions or synthetic accelerograms match-ing the design spectra it would be necessary toconsider several samples for each designearthquake.

The next major point of concern in the defini-tion of the seismic input is the location where thedesign or control motion is specified. This was asubject of considerable debate for many years andalthough some promising trends are observed it isnot yet clear whether the matter has been fullyresolved. As has been often stated (Roesset andKim, 1987), there are five possible choices:� the free surface of the soil deposit at the site,

� a hypothetical outcropping of rock,� bedrock when there is rock at some finite depth

at the site,� the elevation of the foundation in the free field

(soil deposit without any structure or excava-tion,° directly at the foundation.If the characteristics of the design motions cor-

respond to some average firm ground conditionsand the soil at the site can be classified as such,specification of the earthquake at the free surfaceof the soil deposit would be the logical choice.This would also be the case if the seismic hazardanalyses had already incorporated the effect ofthe local soil conditions. A more general solutionwould be to specify the motion at a hypotheticaloutcropping of rock, accounting for earthquakemechanism and distance but not for local soilconditions. If the site has a well-defined transitionbetween soil and much stiffer rock at a finitedepth the specification of the motion at bedrockwould be very similar to the specification at rockoutcropping. Otherwise this alternative is not verymeaningful since the characteristics of the motionat one level within the soil deposit will be afunction of the properties of the soil above andbelow that level. Specification of the design mo-tion at the foundation level in the free field, asrequired at one time, is the least advisable optionand leads to a number of serious inconsistencies ifthere are various structures with their foundationsat different levels. Specifying the control motiondirectly at the foundation is equivalent to ignoringkinematic interaction effects.

One of the main problems in deciding the loca-tion of the control motion was an apparent confu-sion for embedded foundations between itsspecification at the level of the foundation in thefree field and the direct specification at the foun-dation. This confusion was aggravated by a num-ber of papers and studies that attempted to justifythe reduction in the levels of acceleration withfoundation depth by looking at the motionsrecorded at different depths in boreholes. Asource of concern was the fact that the motionthat would be obtained at a given depth in thefree field would exhibit a very sharp valley in itsspectrum at the natural frequency of the overlyingsoil mass. This concern would be eliminated by


the use of more than one earthquake record assuggested above and primarily by the use of morethan one set of soil properties (as has always beendone). More importantly, the compatible motionsat the foundation level accounting for the excava-tion will exhibit a clear reduction in the highfrequency components of motion but much lesssensitivity to specific frequencies than the one-di-mensional deconvolution solution.

A sixth alternative which has not been includedin the above list is the specification of the motionnot at the foundation but directly at the base ofthe structure ignoring therefore not only kine-matic but also inertial interaction. This is ofcourse what was traditionally done for regularbuildings.

3. Effect of local soil conditions

The effect of the local soil conditions on thecharacteristics of the earthquake motions at thesite (soil amplification studies or determination ofsite specific spectra) is normally carried out as-suming a horizontally stratified soil deposit andvertically propagating seismic waves. The solutionof this problem, whether using a continuous for-mulation based on one-dimensional wave propa-gation theory (Roesset and Whitman, 1969), or adiscrete model (finite differences, finite elementsor a physical discretization of lumped masses andsprings) as suggested by Seed and Idriss (1969), isvery simple and well-known. It can be efficientlyperformed on a personal computer. When themotion is specified at a hypothetical outcroppingof rock (the ideal location) or at bedrock thepurpose of the analysis is to compute the consis-tent motions at the free surface of the soil depositor at any other elevation in the free field, as wellas compatible motions and stresses at other pointswithin the soil profile. If the motion is specifieddirectly at the free surface of the soil deposit butthe soil structure interaction studies are going tobe conducted using a finite element discretizationamplification studies must again be conducted toobtain now compatible motions at the bottomboundary of the domain as well as at otherpoints.

These analyses are normally performed in thefrequency domain assuming therefore linear elas-tic material behavior. It has long been recognized,however, that soil is a highly nonlinear materialand that the design seismic motions are likely toinduce large strains. Nonlinear soil behavior isnormally accounted for in convolution or decon-volution analyses using an iterative linear proce-dure where the values of the shear moduli and thesoil material damping are adjusted at the end ofeach cycle of analysis based on the strains com-puted in the previous cycle and curves of modulusand damping versus shear strain characteristic ofthe material (Schnabel et al., 1972). This proce-dure is well-established and unfortunately gener-ally accepted. However, the accuracy of theresults is open to question, particularly when deal-ing with soft and deep soil deposits. When themotions are followed from the bottom (or rockoutcropping) to the free surface the procedurefilters out excessively the high frequency compo-nents. In fact if this procedure were correct, itwould imply that earthquake motions recorded ontop of very deep or soft soil deposits should haveno energy above 8 or 10 Hz. This simply is notthe case. In deconvolution analyses high fre-quency components increase with depth and thesolution eventually becomes unstable. The mainreason for these errors is the assumption of alinear hysteretic damping which is independent offrequency although the amplitudes of the differentfrequency components are quite different (Roessetet al., 1995). A large number of studies have beenconducted through the years to assess the validityof the iterative linearization (Constantopoulos,1973; Dames and Moore, 1978; D’ Appolonia,1979). Nonlinear analyses in the time domain,which would avoid these problems, can be per-formed very economically and also on a personalcomputer, for the one-dimensional convolutionproblem. For the deconvolution problem the pro-cess is at times ill conditioned. A procedure toperform true nonlinear deconvolution analyses us-ing the theory of characteristics has been recentlysuggested by Yamada et al. (1995). If this methodis robust even for deep deposits it would representa significant improvement and it should beadopted to replace the iterative linearizationscheme.


There are a number of areas in which addi-tional research is necessary to resolve outstandingquestions in the computation of soil specific mo-tions. The main source of uncertainties is related,however, to the soil properties. To perform soilamplification studies, as well as the soil structureinteraction analyses discussed later, it is necessaryto know the soil properties in situ, under theexisting state of stresses, as well as their variationwith levels of strain (variations of modulus anddamping with strain for one-dimensional studiesand more complete nonlinear constitutive modelsfor more general two- or three-dimensional statesof stresses). Traditionally, soil properties weredetermined through laboratory tests on so-called‘undisturbed’ samples. Yet, when measurementswere carried out in the field the values of theelastic moduli obtained for very low levels ofstrain in situ and in the laboratory could differ byfactors of 2–4. This is again one of the areaswhere significant progress has been achieved inthe last 15 years. In addition to the downhole andcrosshole method, which have been in use forsome time and can be very reliable (particularlythe crosshole test), but are expensive due to theneed to have boreholes, the spectral analysis ofsurface waves (SASW) method, which has evolvedfrom the Rayleigh wave technique, provides anaccurate, fast and relatively economical way ofdetermining the soil properties in situ and theirvariation with depth over an extended area.

To account for the uncertainties in soil proper-ties, it was common in the seismic design ofnuclear power plants to perform analyses with thebest estimate of the soil properties and with thesevalues multiplied and divided by a factor. Thesefactors were applied simultaneously to all thelayers. When the properties of the different strataare relatively homogeneous in the horizontal di-rections and in situ measurements are availableover an extended area, more realistic, and proba-bly smaller, variations can be justified from thedata. For soils where the variations in propertiesin both horizontal and vertical directions are large(such as alluvial deposits), the application of afactor to all the layers simultaneously may notprovide an adequate range of variation in the finalresults, as pointed out by J. Lysmer (personalcommunication, 1994).

A second source of uncertainty is the angle ofincidence of the incoming seismic waves in theunderlying rock, as a function of frequency, andthe relative amplitudes of the different types ofwaves (SH, SV, P) propagating through the soildeposit. The formulation to study the amplifica-tion of any type of waves by a horizontally lay-ered soil deposit has been available for a longtime and the solution of this problem is not morecomplicated than that of vertically propagatingwaves (Jones and Roesset, 1970). The maindifficulty in considering other types of waves liesin the selection of the appropriate type and this isan area where seismologists can again providevaluable information.

In many cases soil profiles are not horizontallystratified: soil layers can be dipping at differentangles or have arbitrary geometries with soilproperties changing in both the horizontal andvertical directions. In other cases some of thestructures may be built at different levels on em-bankments or small hills with two- or three-di-mensional geometries. Amplification studiesconsidering simple two-dimensional geometries (asloping bottom layer, elliptical sedimentary val-leys, etc.) have been carried out for some time(Aki, 1988; Bard and Bouchon, 1980, 1985;Dravinski, 1982, 1983; Papageorgiou and Kim,1992; Sanchez Sesma, 1983). The studies con-ducted on simple geometries have provided con-siderable insight into the nature and importanceof two-dimensional amplification effects for shal-low rectangular (or trapezoidal) valleys as well asdeep triangular canyons, but most of these studieshave assumed homogeneous and linear soil prop-erties for the valley or canyon. Two- or three-di-mensional amplification analyses are clearly moreexpensive and time-consuming than the simpleone-dimensional solutions and their use in actualpractice (rather than for research purposes) isgoing to be limited. Even so, when the geometryat the site is clearly two- or three-dimensional,some studies of this kind should be conducted toassess the potential importance of geometriceffects.

The approximate iterative linear analyses de-scribed earlier become even more questionablewhen dealing with two- or three-dimensional


states of stresses. To assess their applicability andto answer some of the lingering questions, itwould be necessary to conduct true nonlinearanalyses with appropriate nonlinear constitutivemodels for the soil. A considerable amount ofwork has been done on the development of plas-ticity-type models for soils but this is one of theareas where relatively little improvement has beenachieved in practical studies and much more re-mains to be done. Nonlinear two- and three-di-mensional analyses are again expensive andrequire the use of powerful workstations or evensupercomputers (particularly for the three-dimen-sional case). Their use in practical design applica-tions is further limited by the uncertainties in thesoil properties and the cost and labor associatedwith extracting a sufficient number of undisturbedcore samples over an area with large horizontaland vertical dimensions to determine the modelparameters. This is an area in which supercom-puters can contribute significantly to basic re-search in order to validate simpler approximateprocedures which can be used in practice.

Another problem closely related to the effectsof local soil conditions on the seismic motions isthe assessment of the liquefaction potential for asite and the estimation of the effects of suchliquefaction on settlements and the behavior ofthe foundations. Although a substantial amountof work has been conducted, and is still going onin this area, most of it has been concerned withestablishing correlations between the occurrenceof liquefaction (observed in past earthquakes) anda number of different soil parameters. The resultsof these studies are supposed to provide a mecha-nism to determine for a given site and a specificlevel of earthquake whether liquefaction is likelyto occur or not. The more important question ofwhat are the extent and consequences of the po-tential liquefaction would again require true non-linear analyses with an appropriate two-phaseconstitutive model. This is another area in whichsome significant progress has been achieved dur-ing the last years (Dobry, 1995), even if this workhas not been associated with the design of nuclearpower plants. The application of these more so-phisticated nonlinear dynamic analyses in prac-tice, considering three-dimensional geometries and

states of stress, may be again impractical, not justbecause of the cost of the analyses but primarilybecause of the lack of detailed information on thesoil parameters over an extended volume. How-ever, these type of studies for research purposesare necessary in order to validate simpler approx-imate procedures which can be used for designpurposes. Probabilistic formulations are alsoneeded (and are beginning to be developed) inorder to account in a rational way for the manyuncertainties.

4. Soil structure interaction analyses

The degree of sophistication of soil structureinteraction analyses for nuclear power plants in-creased continuously with the development of newformulations and computer programs and the im-provements in memory capacity and speed ofcomputation. However, it appears that in the last10 or 15 years, in spite of the continued improve-ments in computational capabilities, the trend inresearch has been towards ignoring the more rig-orous methodologies already available in order todevelop new, alternative, simplified procedureswith different degrees of reliability.

Soil structure interaction analyses were initiallyconducted replacing the foundation by a series ofsprings and dashpots (and sometimes lumpedmasses) with their values computed with availableformulae for circular foundations on the surfaceof an elastic, homogeneous and isotropic halfspace. The viscous dashpots were intended toreproduce the loss of energy by radiation of wavesaway from the foundation, while the lumpedmasses, when used, were meant to reproduce thevariation of the stiffnesses with frequency. Thistype of model was known (rather improperly) asthe foundation impedance approach. It was in-tended to reproduce the internal interaction ef-fects. Kinematic interaction was ignored. Whenapplying this model it was common to imposearbitrary bounds on the effective damping of thecombined soil structure system particularly inmodal analyses, because the nature and magni-tude of radiation damping were not well under-stood. In some cases, however, the limitations


were not imposed if the solution was performed inthe frequency domain (indicating again a lack ofunderstanding). The practical advantage of thisapproach was that most of the computer pro-grams developed for general dynamic analysis ofstructures allowed one to incorporate these con-stant masses, springs and dashpots or at least themasses and springs. When a modal analysis wasconducted the combined structure-foundation sys-tem would not have normal modes in the classicalsense (real modes) when the dashpots were in-cluded and it was then necessary for a modalspectral analysis to compute equivalent values ofmodal damping using approximate formulae. Allthese problems disappeared when performing theanalyses in the frequency domain. Unfortunatelythe normal structural analysis programs did notallow this type of solution.

With increasing research (Veletsos and Wei,1971; Veletsos and Verbic, 1974; Luco, 1974;Kausel, 1974), it became clear that the dynamicstiffnesses of a mat foundation are functions offrequency and that the parabolic variation impliedby the use of constant springs and masses is onlyvalid over a very small range of frequencies. Thefrequency dependence of the foundation stiff-nesses is affected by the variation of soil proper-ties with depth. The existence of a much stiffer,rocklike material at some depth (and particularlyat shallow depths) gives rise to marked oscilla-tions around the half space solution correspond-ing to the natural frequencies of the soil deposit.More importantly, below the fundamental fre-quency of the soil there is no radiation of wavesin the lateral direction and correspondingly noradiation damping. To account more realisticallyfor all these effects as well as for the effect offoundation embedment (both on the stiffnessesand on the kinematic interaction) a number ofcomputer programs specially conceived for dy-namic analysis in the frequency domain were de-veloped. Most of these programs performed theanalyses assuming linear elastic behavior althoughsome of them applied the iterative linearization tosimulate nonlinear material behavior with two-di-mensional states of strain. Only a small number ofprograms carried out the solution in the timedomain with nonlinear constitutive equations forthe soil.

Two main approaches evolved from this re-search work: the analysis in a single step of thecomplete soil structure system, often referred to asthe direct approach, and a three step or substruc-ture approach (Kausel and Roesset, 1974). Thethree steps are:

determination of compatible seismic motionsfor the foundation (kinematic interactionanalysis);determination of the foundation stiffness;dynamic analysis of the structure supported ona continuum represented by the dynamic stiff-ness matrix of the foundation, and subjected tothe motions computed in the first step.When each one of these steps is carried out in

the frequency domain, the results are in terms oftransfer functions. In the last step, if one uses adetailed model of the structure, one can furtherseparate the effect of the structure from that ofthe foundation through a modal synthesis or asimple condensation procedure. One can obtain inthis way a dynamic stiffness matrix relating forcesand displacements at the base of the structurewhich can be coupled directly to the dynamicstiffness matrix of the foundation.

In the direct approach the structure is normallymodeled through a combination of finite elementsand linear members. The soil is discretized usingfinite elements or finite differences. Since a dis-crete model is used to reproduce a semi-infinitedomain, special attention must be paid to themesh size and to the boundary conditions im-posed at the edges of the domain. The mainadvantage of this approach is that it would permita true nonlinear analysis with the complete inter-action effects. A rigorous solution would require,however, a fully three-dimensional model and anappropriate set of nonlinear constitutive equa-tions for the soil. In practice these requirementsare rarely met. The first programs developed fordirect soil structure interaction analyses used atwo-dimensional plane strain model with elemen-tary, viscous-type boundary conditions at the ver-tical edges to simulate radiation effects (forinstance the program LUSH) (Lysmer et al.,1974). Program FLUSH (Lysmer et al., 1975)incorporated consistent lateral boundaries whichcould be placed directly at the edges of the foun-


dation for a linear solution, and allowed to placedashpots on the sides of a finite width soil slice tosimulate three-dimensional behavior. For struc-tures with axisymmetric geometry and horizon-tally layered soil deposits, a true three-dimensional solution assuming linear behaviorcould be obtained formulating the problem incylindrical coordinates and solving separately forvertical and torsional excitations on one hand andhorizontal and rocking motions on the other.True nonlinear solutions in the time domain usingthe cap model were implemented in programssuch as TRANAL (Baylor et al., 1974) and FLEX(Vaughan, 1983). In these cases the lateralboundaries of the finite element region must beplaced at a sufficient distance from the foundationto guarantee that the reflected waves have a verysmall amplitude when reaching back to the coreregion.

In the substructure approach the foundationmotions and the dynamic stiffness can be ob-tained using a discrete model with finite elementsand a consistent boundary or using the boundaryintegral equation (or boundary element) method.Programs such as TRIAX, developed by Stoneand Webster Corporation, used the first approachfor structures with axisymmetric geometrywhereas CLASSI, developed by J.E. Luco, usedthe second (indirect boundary element method).In the boundary element solutions the Greenfunctions can be obtained from a continuum for-mulation, evaluating numerically the integrals inthe wave number domain, or from a discreteformulation (Kausel, 1981; Kausel and Peek,1982).

All the above mentioned programs were devel-oped in the middle and late 1970s and the early1980s. They could be run in the mainframes avail-able in those times with some limitations on themaximum number of layers or finite elements.With the advent of supercomputers or even withthe present workstations the capabilities of theseprograms can be tremendously expanded. Newand more powerful programs such as SASSI(Lysmer, 1988) have been developed. These pro-grams allow one to consider truly three-dimen-sional effects with a linear elastic solution. Truenonlinear effects such as the nonlinear soil behav-

ior under three-dimensional states of strain andwith an appropriate constitutive model, or separa-tion effects (sliding and uplifting of the founda-tion) are still not included in these powerfulprograms and require a solution in the domain.Nonlinear soil behavior is normally accounted forconsidering only the nonlinearities associated withthe soil amplification problem (using the equiva-lent properties resulting from the last cycle of theiterative procedure) or implementing the interac-tive scheme with a two- or three-dimensionalmodel (which makes its validity much more ques-tionable). Separation effects tend to be beneficial,reducing the base shear and overturning moment,but they may increase vertical accelerations nearthe axis of the structure and produce additionalstresses in the mat (Wolf, 1976, 1977; Roesset andScaletti, 1979). These effects are also stronglydependent on the properties and initial state ofstresses in the soil. The proper consideration ofnonlinear effects is the area where the majorcontributions to the soil structure interactionproblem remain to be done.

Most of the research work on seismic soil struc-ture interaction has been concerned with rigid,and in most cases circular, mats resting on orembedded in a horizontally layered soil deposit.This is due to the fact that this is the type offoundation most commonly encountered in nu-clear power plants. A number of studies havebeen conducted to determine the dynamic stiffnessand motions of rectangular foundations usingboundary elements (Dominguez, 1978a,b). Thesestudies have led to a number of simplified proce-dures to obtain their stiffness from those of anequivalent circular mat or to approximate formu-lae to compute them directly (Dobry and Gazetas,1985). It should be noted, however, that theseapproximate procedures are intended to matchprimarily the static values of the stiffness and thattheir frequency variation may not be as well re-produced. This is particularly so when dealingwith a layered soil deposit where the propertiesvary with depth rather than an elastic half space(normally considered in these studies). A substan-tial amount of work has also been done on pilefoundations including group effects. A number ofrigorous formulations assuming a linear elastic


soil and perfect bonding between the pile and thesurrounding soil have been developed (Blaney etal., 1976). Group effects can be accounted forwith some approximations such as enforcing thecompatibility of displacements along the axis ofthe pile rather than along its perimeter for thestudy of two piles, and enforcing interaction atthe pile heads only for large groups (Kaynia andKausel, 1982; Sanchez Salinero, 1983). These as-sumptions are no longer valid when consideringclosely spaced piles or very large numbers of piles,but are reasonable for many other cases, particu-larly if the layering of the soil is taken intoaccount properly. Simplified procedures based onan elastic half space again raise questions whenextrapolated to realistic soil profiles. The mainlimitation in the analysis of pile foundations isagain the linear assumption. The behavior of thesoil around a pile and particularly near the pilehead is highly nonlinear. Approximations basedon the assumption of a concentric annular cylin-der with reduced soil properties are of value toprovide a qualitative picture of the phenomenonbut cannot provide accurate quantitative results.The alternative is the use of P-y and T-z curves,as employed in the offshore industry, which re-produce the nonlinear soil behavior under staticloads (particularly monotonic loads) but which donot account for dynamic effects (Matlock andReese, 1960; Matlock, 1970). Clearly much morework remains to be done on this type offoundation.

Nuclear power plants are structures for whichsoil structure interaction effects may be importantand normally beneficial when designing forsmooth broad band response spectra. As a resulta considerable amount of research was performedin this area in the 1960s and 1970s under thesponsorship of the nuclear industry, and a consid-erable amount of knowledge was acquiredthrough this research. Much of the recent workon dynamic or seismic soil structure interactionhas dealt with the derivation of alternative proce-dures to solve problems for which results arealready available with emphasis on obtainingmore elegant formulations which can be moreeconomical for the same degree of accuracy thanthe existing ones (boundary element solutions in

the time or frequency domains for instance) orsimplified models which are more economical butskill provide a reasonable approximation, at leastfor the particular cases studied. In the best casesthese alternative formulations have provided abetter insight into the problem or the relativeimportance of various effects. In a number ofcases the studies have shown on the other hand alack of understanding of the phenomenon withmodels which accounted (sometimes incorrectly)for the real part of the foundation stiffnesses butneglected the radiation damping, or with values ofthe soil and structural parameters which weretotally unrealistic.

A serious controversy existed for a long timebetween the two general approaches to soil struc-ture interaction analysis. The substructure ap-proach referred to as the impedance approach wasnot allowed at one time because it was erro-neously associated with the use of frequency inde-pendent springs and dashpots based on the staticsolution for an elastic half space. The direct ap-proach which had been the recommended onelater became unpopular because of the two-di-mensional nature of the solution. It appears thatat the present time, both might be acceptable butthere seems to be a trend towards the simplestpossible solutions. Simplified solutions are ofgreat value to gain insight into the behavior of thephysical process, to identify key parameters andunderstand their effects and relative importance,to obtain preliminary estimates of the response, toassess whether effects can be important and moresophisticated analyses are necessary, and toprovide checks to the results of more complicatedmodels. There is, however, a risk of over simplifi-cation. When effects are found to be importantand when dealing with structures such as nuclearpower plants one should always try to use themost accurate models available at least for alimited number of studies rather than relying ex-clusively on simple models.

5. Structural models

The buildings encountered in a nuclear powerplant are typically very stiff, massive and ex-


tremely complex structures, including many dif-ferent structural types (thick shells for the con-tainment, frames, trusses, heavy shear walls, thickslabs, etc.). A detailed modeling of any one ofthese structures requires a large number of de-grees of freedom, and these models have beenoften used. In many cases, however, the seismicanalyses were carried out using highly simplifiedmodels consisting of close-coupled systems ofmasses and springs (or equivalent stiffness ma-trices). These were referred to as ‘stack’ models.Each element connecting two adjoining masses, orits stiffness matrix, was intended to reproduce thecombined effects of all the members and wallsbetween the two floor levels where the masseswere lumped. The stiffness matrices were oftencomputed with the implicit assumption that thefloor slabs were infinitely rigid not only as di-aphragms in their own plane but also in bending.The use of simplified models with a reduced num-ber of degrees of freedom is of course common tomany structures and not just nuclear power plantsbut the degree of simplification that was used attimes in nuclear structures was unusually large.Thus, while these models could be reasonablyaccurate to estimate the general, or global, fea-tures of the dynamic response, such as accelera-tions at various floor levels, some questions couldbe raised as to their ability to reproduce localresponse parameters such as stresses or deforma-tions in individual members. The main objectiveof the seismic analyses of nuclear power plantsconducted with these models was in fact in manycases the derivation of floor response spectra forthe design of equipment rather than a detailedstress analysis of the structure.

The structural models could be more crude forsoil structure interaction analyses where, ironi-cally, a considerable amount of effort might bedevoted to the appropriate modeling of the soilwhile the structure was idealized as a stick withonly a few masses or a solid block discretized withfinite elements. This situation was more likely tobe encountered when the complete analysis wasperformed in a single step (direct approach) thanwhen using the three step or substructure ap-proach (particularly if the modal synthesis proce-dure described earlier to reduce the structure to

forces and displacements at its base wasimplemented).

Even when the derivation of floor responsespectra is the main objective of the analysis thestick models can introduce some significant er-rors. This is so, for instance when considering thevertical accelerations at various points on thefloor without accounting properly for the flexibil-ity and dynamic response of the slab. The errorwould become more significant as the flexibility ofthe floors increased. It is also common to ignorethe equipment entirely in the derivation of thestructural model. Uncoupling the equipment fromthe structure is justified in most cases because themass of the former is very small compared to thatof the latter. The exception is when the naturalfrequency of the equipment is very close to that ofthe structure and its mass is not negligible. How-ever, it is interesting to note that accountingproperly for the coupling between equipment andthe structure in a rigorous way is relatively easyand not as laborious or expensive as often be-lieved, particularly for analyses in the frequencydomain using the substructure approach.

A considerable amount of time and effort wasnormally spent on the analysis and design ofpiping and pipe supports. A source of difficulty inthese analyses was the fact that the structuralmodel was not detailed enough in most cases toproperly define the motions of the different sup-ports. An even more serious problem in this casetended to be, however, the lack of consistency andup-to-date files with information on the as-builtconditions or the latest modifications and the factthat analyses and redesigns were often performedby different persons with little communication.

All these comments point out the desirability ofhaving a large data base where complete informa-tion on the nuclear power plant at any time, themodels of the different structures and the soil, theseismic motions used for input, and intermediateresults such as transfer functions of different ef-fects, can be stored and retrieved as needed. Thiswould not only affect the consistency and reliabil-ity of the seismic analyses but facilitate consider-ably the evaluation of potential changes and theireffects, future redesigns or just checks requestedat a later date. These points can become particu-


larly important when the plant has reached itsdesign life but it is desired to maintain it opera-tional and therefore extend its service life.

A variety of methods have been used in the pastto perform the dynamic analysis of the structuralor soil structure models. They ranged from tradi-tional modal spectral analyses directly using thesmooth design spectra and performing the combi-nation of the modal maxima through a number ofdifferent expressions (accounting or not approxi-mately for correlation between the modal re-sponses), to standard modal analyses in the timedomain combining the time histories of the re-sponses in each mode, direct integration of theequations of motion in the time domain or solu-tions in the frequency domain. For the secondand third options it is necessary to have availableearthquake time histories, whether correspondingto actual earthquake records or generated syn-thetically to match the target spectra; for the lastoption one can start with these time histories andobtain their Fourier transform or directly with theFourier spectrum (or in some cases the powerspectrum) of the desired motion. It was not un-common to have different parts of the plant ordifferent portions of the analyses carried out withdifferent approaches using several of these meth-ods simultaneously with very little consistency.The fact that different groups within the designteam were in charge of different sections of theanalysis explains in part the diversity in ap-proaches and lack of consistency.

By opposition to regular buildings which aredesigned on the assumption that they will undergolarge inelastic deformations under a severe earth-quake the structures in a nuclear power plantwere always designed to remain linearly elasticeven under the safe shutdown earthquake. A verysmall amount of inelastic behavior was implicitlyassumed in allowing larger values of materialdamping for the safe shutdown than for the oper-ating basis earthquake but it was supposed to bevery small. The use of reduction factors based ona vaguely defined and often meaningless systemductility customary in the seismic design of regu-lar buildings had been, however, wisely avoided.

Three new and significant trends have beenevolving during the last 15 or 20 years in the

seismic design of structures: the design for perfor-mance criteria rather than simply for a desiredfactor of safety (or equivalent load and resistancefactors); the incorporation of probabilistic con-cepts to perform a complete seismic risk analysisaccounting for the uncertainties in all the differentphases; and the use of reduction factors based onsystem ductility following procedures similar tothose used for conventional buildings (althoughthe allowable reduction factors are smaller). Thefirst two trends represent a desire to obtain moreaccurate and realistic estimates of the effects ofpotential earthquakes on the behavior of thestructures. The third trend is somewhat contradic-tory to the others, and in the opinion of thewriter, an undesirable step backwards.

6. Summary and final considerations

The major uncertainties in the seismic design ofnuclear power plants have always been associatedwith the selection and characterization of thedesign earthquake(s), the soil properties to beused consistent with the in situ state of stresses,the accuracy of the structural and soil structuremodels and methods of analysis, and the generaltreatment of nonlinear effects (nonlinear soil be-havior, liquefaction potential, separation effectsbetween the foundation and the soil, and to alimited extent only nonlinear structural response).In spite of the considerable reduction in the re-search effort related to nuclear power plants overthe last 15 years substantial progress has beendone in some of these areas.

Thanks to the research conducted over the lastyears it is possible now to define the earthquakeor earthquakes associated with a desired level ofhazard, or probability of occurrence, in a muchmore realistic way than before, accounting for theeffects of magnitude, source mechanism and dis-tance not only on a single parameter such as thepeak ground acceleration, or an effective accelera-tion, but also on the duration and frequencycontent. This represents a major breakthroughand an important departure from the traditionalobsession with the use of only one variable.


Much progress has also been achieved in thedetermination of soil properties in situ over anextended volume but only for low levels of strain.For one-dimensional situations the nonlinear soilbehavior can then be inferred from the curvesrelating modulus and damping to level of strain.

The techniques used to perform linear one-di-mensional soil amplification studies have beenwell-known for a long time. Major advances havebeen made in the consideration of two- and three-dimensional geometries, as often encountered inpractice.

The assessment of the liquefaction potential ata site and the evaluation of the consequences ofliquefaction is another area where the state of theart has improved considerably in the last years,with a much better understanding (after years ofcontroversy) of the physical phenomenon, muchmore statistical data to validate numerical predic-tions, experimental data from centrifuge tests, andcomputational models capable of accounting forpore pressure buildup, nonlinear soil behaviorand large deformations and displacements.

There are now a number of rigorous formula-tions available to perform linear soil structureinteraction analyses including all major effects.There is also an ever increasing inventory ofsimplified models and procedures which can beused for preliminary design purposes, to estimatethe potential importance of various effects or tocheck the order of magnitude of the results frommore sophisticated models. With present daycomputational capabilities, however, there can beno justification for the use of these simplifiedmodels in the final analyses instead of the morerigorous techniques which are available.

The final area in which very significant progresshas been achieved is the development of method-ologies for complete seismic risk analyses. This isthe only rational way to account for the uncer-tainties that will always be present and to reachdecisions related to safety and performance. Itshould be noted, on the other hand, that thesemethodologies by themselves will not be of realvalue unless accurate models and data are avail-able to predict the structural performance. This isnot yet the case in practice.

It is clear that more work remains to be done ineach one of these areas. The success achieved overthe last years should encourage the industry andother funding sources to continue these lines ofresearch if it is desired to avoid unnecessary con-troversies when the design of new nuclear powerplants becomes a need. The area in which lessprogress has been done and a considerableamount of research is needed is the evaluation ofnonlinear effects.

As important as the improvement in the accu-racy of the models and the analysis procedures isthe maintenance of up-to-date files with informa-tion on the status of the plant, the analyses,intermediate results, modifications introduced,etc. The computer capabilities now availablemake it particularly easy to develop modern databases where this information can be stored.

References

Aki, K., 1988. Local site effects on ground motion. State ofthe art report. Recent advances in ground motion evalua-tion. Geotechnical Special Publication, ASCE 20.

Bard, P.Y., Bouchon, M.A., 1980. The seismic response ofsediment filled valleys, parts I–II. Bull. Seismol. Soc. Am.70.

Bard, P.Y., Bouchon, M.A., 1985. The two-dimensional reso-nance of sediment filled valleys. Bull. Seismol. Soc. Am. 75.

Baylor, J., Bienieck, M., Wright, J., 1974. TRANAL: A 3Dfinite element code for transient nonlinear analysis. DNA3501F. Weidlinger Associates.

Bernreuter, D.L., Savy, J.B., Mensing, R.W., Chen, J.C.,Davis, B.C., 1985. Seismic hazard and characterization ofthe eastern United States, vols. 1–2. LLNL-UCID 20421.

Bernreuter, D.L., Savy, J.B., Mensing, R.W., 1987. Seismichazard of the eastern US. Comparative evaluation of theLLNL and EPRI studies. USNRC report NUREG/CR-4885.

Berareuter, D.L., Savy, J.B., Mensing, R.W., Chen, J.C., 1989.Seismic hazard characterization of 69 plant sites east of theRocky Mountains, vols. 1–8. LLNL, USNRC reportNUREG/CR-5250, UCID-21517.

Blaney, G.W., Kausel, E., Roesset, J.M., 1976. Dynamic stiff-ness of piles. In: Proceedings of the Second InternationalConference on Numerical Methods in Geomechanics,ASCE.

Constantopoulos, I.V., 1973. Amplification studies for a non-linear hysteretic soil model. Report R73-46. Civil Engineer-ing Department, MIT, MA, USA.

Dames, Moore, 1978. Study of nonlinear effects on one-di-mensional earthquake response. EPRI Report NP-865.


D’Appolonia Consulting Engineers, 1979. Seismic input andsoil structure interaction. Report prepared for the USNuclear Regulatory Commission. NUREG/CR-0693.

Dobry, R., Gazetas, G., 1985. Stiffness and damping of arbi-trary shaped machine foundations. J. Geotech. Eng.,ASCE.

Dobry, R., 1995. Liquefaction and deformation of soils andfoundations under seismic conditions. State of the artpaper. In: The Third International Conference on RecentAdvances in Geotechnical Earthquake Engineering andSoil Dynamics, vol. 3, St. Louis, MO, USA.

Dominguez, J., 1978a. Dynamic stiffness of rectangular foun-dation. Report R78-20. Civil Engineering Department,MIT, MA, USA.

Dominguez, J., 1978b. Response of embedded foundations totravelling waves. Report R78-24. Civil Engineering Depart-ment, MIT, MA, USA.

Dravinski, M., 1982. Scattering of elastic waves by an alluvialvalley. J. Eng. Mech. Div., ASCE, 108.

Dravinski, M., 1983. Amplification of P, SV and Rayleighwaves by two alluvial valleys. Soil Dyn. Earthq. Eng., 2.

EPRI, 1986. Seismic hazard and methodology for the centraland eastern United States, vols. 1–11. Technical ReportNP-4726A.

EPRI, 1993. Guidelines for determining design basis groundmotions. Technical Report TR-102293.

Jacob, K., 1994. Quantifying seismic hazard and providingrealistic ground motions for engineering applications pri-marily in the eastern United States. Research 1986–1994accomplishments. NCEER.

Jones, T.J., Roesset, J.M., 1970. Soil amplification of SV andP waves. Report R70-3. Civil Engineering Department,MIT, MA, USA.

Kausel, E., 1974. Forced vibrations of circular foundations onlayered media. Report R74-11. Civil Engineering Depart-ment, MIT, MA, USA.

Kausel, E., Roesset, J.M., 1974. Soil structure interaction fornuclear containment structures. Proceedings of the ASCEPower Division Specialty Conference, Boulder, CO, USA.

Kausel, E., 1981. An explicit solution for the Green functionsfor dynamic loads in layered media. Report R81-13. CivilEngineering Department, MIT, MA, USA.

Kausel, E., Peek, R., 1982. Boundary integral method forstratified soils. Report R82-50. Civil Engineering Depart-ment, MIT, MA, USA.

Kaynia, A.M., Kausel, E., 1982. Dynamic stiffness and seismicresponse of pile groups. Report R82-03. Civil EngineeringDepartment, MIT, MA, USA.

Luco, J.E., 1974. Impedance functions for a rigid foundationon a layered medium. Nucl. Eng. Des.

Lysmer, J., Udaka, T., Seed, H.B., Hwang, R.N., 1974.LUSH. A computer program for complete response analy-sis of soil structure systems. Report EERC 74-4. Universityof California, Berkeley, CA, USA.

Lysmer, J., Udaka, T., Tsai, C.F., Seed, H.B., 1975. FLUSH.A computer program for approximate 3D analysis of soilstructure interaction problems. Report EERC 75-30. Uni-versity of California, Berkeley, CA, USA.

Lysmer, J., 1988. SASSI. A computer program for dynamicsoil structure interaction analysis. Report UCB/GT81-02.University of California, Berkeley, CA, USA.

Matlock, H., Reese, L.C., 1960. Generalized solutions forlaterally loaded piles. J. Soil Mechan. Found. Div., ASCE86 SM-J.

Matlock, H., 1970. Correlations for design of laterally loadedpiles in soft clays. In: Proceedings of the Second OffshoreTechnology Conference. Paper OTC 1205.

Papageorgiou, A., Kim, J., 1992. Propagation and amplifica-tion of seismic waves in 2D valleys excited by obliquelyincident SV and P waves. Earthquake Eng. Struct. Dyn.22.

Roesset, J.M., Whitman, R.V., 1969. Theoretical backgroundfor amplification studies. Report R69-15. Civil EngineeringDepartment, MIT, MA, USA.

Roesset, J.M., Scaletti, H., 1979. Nonlinear effects in dynamicsoil structure interaction. In: The Third International Con-ference on Numerical Methods in Geomechanics, Aachen,Germany.

Roesset, J.M., Kim, Y.S., 1987. Specification of control mo-tions for embedded foundations. In: The Proceedings ofthe Fifth Canadian Conference on EarthquakeEngineering.

Roesset, J.M., Huerta, C., Stokoe, K.H., 1995. Effect ofmagnitude and type of damping on soil amplification. In:The third International Conference on Recent Advances inGeotechnical Earthquake Engineering and Soil Dynamics,St. Louis, MO, USA.

Sanchez Salinero, I., 1983. Dynamic stiffness of pile groups:approximate solutions. Report GR83-5. Civil EngineeringDepartment, The University of Texas at Austin, TX, USA.

Sanchez Sesma, F.J., 1983. Diffraction of elastic waves bythree dimensional surface irregularities. Bull. Seismol. Soc.Am. 73.

Schnabel, P.B., Lysmer, J., Seed, H.B., 1972. SHAKE. Acomputer program for earthquake response analysis ofhorizontally layered sites. Report EERC 72-12. Universityof California, Berkeley, CA, USA.

Seed, H.B., Idriss, I.M., 1969. Influence of soil conditions onground motions during earthquakes. J. Soil Mech. Found.Div., ASCE.

Vaughan, D., 1983. FLEX User’s guide. Document UG8298.Weidlinger Associates

Veletsos, A.S., Wei, Y.T., 1971. Lateral and rocking vibrationsof footings. J. Soil Mech. Found. Div., ASCE, 97.

Veletsos, A.S., Verbic, B., 1974. Basic response functions forelastic foundations. J. Eng. Mech. Div., ASCE, 100.

Wolf, J.P., 1976. Soil structure interaction with separation ofbase mat from soil (lifting off). Nucl. Eng. Des. 38.

Wolf, J.P., 1977. Seismic response due to travelling shearwaves including soil structure interaction with base matuplift. Earthquake Eng. Struct. Dyn. 5.

Yamada, A., Miura, K., Kobori, T., 1995. Nonlinear analysismethod for prediction of base motion. In: The ThirdInternational Conference on Recent Advances in Geotech-nical Earthquake Engineering and Soil Dynamics, St.Louis, MO, USA.

Documents

Seismic design of nuclear power plants—where are we now?