Department D'analyse De Surete

COMMISSARIAT A LENERGIE ATOMIQUE XA04NO298

INSTITUT DE PROTECTION ET DE SURETE NUCLEAIRE

DEPARTMENT D'ANALYSE DE SURETE

INIS-XA-N--027

RAPPORT DAS/733 MAIN FACTORS AECTING STRONG GROUND MOTION CALCULATIONS CRITICAL REVIEW AND ASESSMENT.

MOHAMMADIOUN B. PECKER A. RAPPORT DAS/733

MAIN FACTORS AECTING STRONG GROUND MOTION CALCULATIONS CRITICAL REVIEW AND ASSESSMENT.

MOHAMMADIOUN B. , PECKER A.

1990

* DAS/SASC ** Soci6t6 G6odynamique et Structure I I

MAIN FACTORS AFFECTING STRONG GROUND MOTION CALCULATIONS: CRITICAL REVIEW AND ASSESSMENT

BAGHER MOHAMMADIOUN * AND ALUN PECKER"

1. 1. INTRODUCTION

in the interests of guarding lives and property against the effects of earthquakes, building codes are frequently enforced when recting conventional structures, usually calling for simple, static calculations. Where more vulnerable facilities are involved, the failure of which, or of parts of which, could subject the environment to harmful substances, more sophisticated methods are used to compute or verify their design, often accompanied by safety margins intended to compen- sate for uncertainties encountered at various stages of the analysis that begins with input seismic data and culminates with an effective anti-seismic dsign. The forthcoming discussion will deal with what is known of the characteristics of strong ground motion, highly variable according to contM without entering into the problems raised by scismotectonic studies, which actually constitute the first aspect that must be addressed when performing such an analysis. Our conclusion will be devoted to cogent R & D work in this area.

1.2. STRONG MOTION DATA

The earliest record obtained with a strong motion accelerograph dates back to 1933 and was triggered by the Long Beach, California earthquake. Since that time, a considerable amount of data covering the western United States has been acquired thanks to an ever denser accclero- graph network. More recently, other seismic regions in the world have benefited from a similar development, notably Japan, and, in Europe, the countries of Italy, Yugoslavia, and Greece. Despite the eitistence of this data of more varied origin, seismic motion destined for engineering purposes everywhere is still inclined to rely predominantly upon the 'classic' data from California. The data naturally reflects the seismotectonic environment of that part of the world, where a certain type of strike-slip mechanism tends to prevail. But data that has become available in more recent yars s in some cases 2fforded examples of quite different source mechanisms.

1.3. PREDICTION OF SEISMIC GROUND MOTION FOR ENGINEERING PURPOSES

A common pctice among the engineering community consists in computing a spectral shape (response spectrum) which is subsequently scaled to a chosen value of peak ground acceleration (PGA). This latter value is derived from attenuation laws for ground motion versus distance based on earthquakes of varying magnitudes. When these laws are confronted with actual

Head, Bureau dEvaluation du Risque Sismique pour la SArrti Jes Installations ckfaires, ntstitut de Protection et de Sf4rrIJ4 Nudgairr,Commissariat a 'En"e Atomique Manager; Sociguf Giodynamique et Structure 2 - ECENTADVANCES IN EARTHQUAKE ENGINEEUNG & nRUMNAL DYNAWCS

values, they are often seen to be unreliable at short distances (R< 10 km); this circumstance is borne out by some noteworthy recent examples: Chile, in 1985, and Imperial Valley, in 1979 (Figure 11-1. 1). The difficulties met with when attempting'to predict earthquake motion in the ep. icentral zone can be explained by a variety of factors, prominent aong which are probably the complexity of the propagation of rupture along the fauit plane and the modification of the ground motion as it traverses superficial soil and rock formations that are likely to behave in a non-linear manner 11-1.201 under certain conditions.

Another drawback to this practice stems from the fact that the spectral shape is frequently computed from one statistical population, with a given degree of uncertainty (standard deviation a), while the PGA distribution is derived from a different population and is accordingly characterized by a different, and therefore incompatible, a-value. 17his latter problem can be overcome if a single data base is used to calculate a correlation relating the spectrum directly to magnitude and distance, thus determining shape and level of motion simultaneously I I- 1 191 11-1.23 . As to the difficulty in predicting ground motion in the near field, if the statistical approach proves inadequate, could not theoretical simulation serve as a substitute? Such would not seem to be the case, for the moment at ast. Indeed, although material progress has been accom- plished in this field over the past twenty years, simulating both source and propagation (11-1.91, the methods cannot always be properly implemented, particularly where 'high' (f> 1 Hz.) frequencies are concerned, an area of considerable importance to the engineering seismologis As matters stand, these techniques seem to be used chiefly in adjusting models by trial and error so as to arrive at a synthetic signal that resembles as closely as possible a given earthquake record. As to modelling the effects of wave propagation through the uppermost layers of earth having poor mechanical resistance and the modifications the bedrock ground motion can be xpected to undergo, the majority of computed programs work in linear elasticity, or linear equivalent, and apply monodimcnsional models of propagation.

Lastly, approches f 11-1.61 f II-1.41 that propose modeWng source and propagation in the frequency domain using a band of white noise bounded by a filtering process and sources of the type developed byJ. Brune [11-1.81 hold some promise for the future. These sources, in common use, have a spectral model termed 'w square' that is self-similar (displaying a stress drop that is constant). The comer frequency (beyond which the displacement spectrum decreases by a factor of w-2) moves towards lower frequencies as seismic moment increases (11-1-31. The aforementioned techniques,- however, if they are to be meaningful, must be implemented with input parameters that have been chosen with care.

So we must conclude that, despite their weaknesses, statistical methods for predicting ground motion for the engineer cannot as yet be readily laid aside; at best, theoretical approaches may be of assistance with some of the more trouble-some aspects. Owing to the nature of the data analyzed, the results will better characterize strike-slip mechanisms associated with an interplate context. We shall now proceed to examine certain implications of such a bias, devoting attention first to some empirical relationships concerning sources, then to problems associated with propagation.

1.4. VARIABILITYOFSOURCESPECTRAASAFUNCnONOFDYNAMIC PARAMETERS

In recent years, some strong-motion recordings have been obtained in intraplate con- tms, and although the data population is still rather sparse, correlations have been computed (i.e. [11-1.231). When compared with standard results from California data (interplatecontext), I 3

differences in spectral content are noticeable. For the former group, predominantly European in origin, high frequencies are relatively more important whereas low frequencies appear to be less so. Among examples that may be cited, a moderate-magnitude earthquake (ML = 48) was recorded on SMA-2 accelerometers in the Fessenheim nuclear power plant situated in the French portion of the Rhine valley. The first such records obtained in France, they are associated with a focal distance of about 25 km. On Figure 11-1.2 a comparison is made between response spectra at 5% damping of the horizontal components of this record and a synthetic spectrum corresponding to the same set of parameters, but based on California data. It will be noted that low frequencies have been significantly overestimated on this latter spectrum. On another example (Figurc 11-1-3) a similar effect can be observed. Here two synthetic spectra are compared, both for M=6.5 and R=80 Ian, one representing the Petrovsky correlation, the other, the California one. Lastly, Figure IMA depicts a comparison of the 1988 Armenian earthquake recorded at Gukassian with a California data synthetic spectrum. In order to be able to give credence to -the foregoing observations, a theoretical basis wl need to be sought with reference to classical models in scis- mology. The following discussion constitutes a tentative approach to explaining these differences. If we designate by ao and a,, respectively, the stresses prevailing prior to and after an earthquake, average stress can be defined by:

= (ao + a,) 2

Following [II I 15 1, the apparent stress aa can be computed by

a. = in which 7 is a constant. According to the authors cited above, a. can take on values ranging b- tween 10 and 20 bar approximately in the case of interplate earthquakes, whereas this value rises to 50 for intraplate events. If we define

&a = a-al we are accepting the following approximate relationship:

aa = Aa/2

Seismic wave energy E is related to seismic moment MO and average stress a by:

E = (MO Y?B) A (11-1.4) where u is the rigidity coefficient. When we introduce into the preceding equation the results of equations 11-1.2) and 11-1-3), we obtain:

E = (MO Aa / 2 IL

Ms magnitude, derived from surface waves, reflects seismic energy if we accept the rcia. tionship from [ II- 1. 1 1 1 :

log E = Ms I 8 4 - RECENTADVANCES IN EARYHQUAKE EVGIAEEJUNG & S7RUCrURAL DMAWCS

By combining equations (II-1.5) and 11-1.6), we obtain:

log MO = 1.5 Ms 11.8-log Aa / 2u) (II-1.7)

This latter equation demonstrates the dependence of seismic moment not only upon Ms magnitude, but also upon the stress drop AC. The source defined by Brune's acceleration spectrum is given by:

S (f) = [MO 2 7rf) / [ 1 + (f / fc 21

where f. is the comer frequency; this latter is related to the length of rupture L and the rupture velocity V, , approximately, by:

f = Vr / L .(II.1.9)

Two possible cases are to be considered, corresponding to moderate and to large erth. quakes 111-1-151 111-1-51.

1.4.1. Moderate Eartbquakes.

L = 2 NIO / &a) 13

Vr (&a)113 AC 2 N 13

&CA pIOE 113 f.A / fE = &aA / ACE 13. (MO? MOAI/3 &aEI13 , / MOA 13 (11-1.11)

11 the hypothesis is retained that ACE = 3 MPa interplate) and Aa = 10 MPa (intraplate), the following is obtained:

&CA ACE = K = 10/3 (11-1.12)

For an equivalent amount of seismic energy, the ratio of comer frequencies is'

E / fA = (I 0/3) 1/1 - 10/3 13 = (I 0/3 23 = 223

The source spectra for acceleration for the two cases in point are expressed respectively by:

Sf E MO 2 2 1 + (f/fE 2 and

SfA 0-3 MO 2 r 2 1 + [f 223 E )2 then

R SIA/ S 1 0-3 [I + (f / E 21 1 + (f / 223 f'I 2

The R values of equation 16 have been computed for different frequencies and with seven f val. ues (0-5, 1 2 4 6 , and 10 Hz) and the variations obtained are depicted on Figure 1-1.5a; for earthquakes with high stress drops, a reduction of low frequencies is observed as well as an increase in high frequencies.

11-1.4.2. LargeEartbquakes

L = 2 [MO/ (,&a.W0)]112

V, - (WO)1/2 f. 2 (&, / MO) 12 where WO represents the fault width

fA / f = ,&aA / AaE) /2 (MOE MOA) 12

fA / fE = 10/3) 1/2. 1013)112 10/3

The ratio R' for intraplate/interplate spectra is:

0.3 11 + (f / E)2]

1 + (f 333 f cE)2 (11-1 19)

Computations of R' (equation 11-1.19) were carried out as in the preceding case. The results (Figure 11-1.5b) show a reduction of low frequencies and a greater increase in high frequencies than in the case of moderate earthquakes.

In view of the fact that a large majority of strong-motion data have been obtained in interplate regions, seismic reference motions called for in various regulatory documents to be applied in anti-seismic design are doubtless strongly influenced. If the hypotheses advanced in the above paragraphs (differences in stress field) are indeed accurate, the dynamic characteristics of sources will need to be taken into account, and reference motions modified accordingly where appropriate. The Aa values furnished in our example are also capable of varying from one region to another and will therefore have to be ascertained on a case by case basis.

L 5. PATH EFFECTS

In linear elasticity, vibratory ground motion is a result of the convolution of time histories at the source (slip functions) and a function reflecting the effects of the path that has been trav- 6 - RECENTADVANCES IN EARTHQUAKE FJVGINEERrNG STRUCTURAL D"MA9CS

elled by waves propagating between the source and the observation point (Green function) We have just given a brief summary of recent dvelopments as concerns seismic sources. In the area of path effects (computing Green functions) significant progress has also been made by seismolo. gists over the past ten years. However the recording station where seismological observations are made are generally situated at the ground surf-ace, and most often on auvial deposits. Conse. quently the recorded motion reflects not only the source and path influences in competent rocks (hypothesis accepted by seismologists), but also does not rule out possible non-linear effects in. troduced by the uppermost soil layers at the recording site. The inverse problem thus set forth consists in deducing the source function from the end-product recording, The process presup- poses both large- (tens of kilometers) and small-scale (tens of meters) corrections, the former in the realm of basic seismology, the latter in that of soil dynamics. Theoretically, in classical sismology, the influence of path on the source spectrum is conveyed by a function of the type R-11 -Kl where R-11 stands for wave attenuation due to geo. metrical spreading and e-Kf for the viscoelastic attenuation of the materials through wch the waves propagate (K equalling w/2VQ, with - w being the angular frequency, V, the seismic wave velocity, and Q, the quality factor - and R being the focal distance between the source and the point of-observation). In engineering applications, this notion is requently expressed as wo, with being the equivalent damping ratio. Naturally, the waves in this case are propagating through rocky materials, where strain levels are weak. To arrive at an accurate description of path effect for use in theoretical simul 'ations a unit slip function is considered for a given point on the fault H (t) or 6 (t)], then the response is computed for the medium separating the source from the observation point. Synthetic seismograms obtained in this manner for all points on the fault are the Green functions of the medium. In theoretical seismology these functions are calculated using linear behavior laws. It is then neces. sary to know the characteristics of the layers through which the waves propagate: since engineer. ing seismology is concerned with relatively high frequencies (I to 30 Hz.), even small-scale het. erogeneities of the upper layers ould need to be dfined, which In pactice would seem proble- matical, at best. In view of these difficulties, some authors 111-1-131 111-1.281 have attempted to use micro-earthquakes in lieu of the medium's response to an elementary source in order to simu- late a large earthquake. Clearly, this approach can only be valid for materials exhibiting a linear or quasi-linear behavior over a wide range of strains. Crystalline rocks belong to that category, and soft rocks may likewise be relevant to that approach. Soils, however, can definitely not be classified as linear materials, and studies of their response to strong earthquake excitation should preferably be performed according to the approach proposed in a subsequent paragraph.

1.6. THE INFLUENCE OF SOIL AYERS ON GROUND MOTION

It has long been recognized that the nature of surficial soil deposits can significantly alter the incident ground motion (II-1.141. Recent earthquakes Mexico, 1985, Loma Prieta, 1989) have confirmed this fact. The magnitude 8.1 earthquake which struck the city of Mexico in 1985 originated some 450 Ian from the site. The ground motions recorded on the consolidated hard deposits in exico City exhibit a peak ground acceleration of 004 g, with a broad-band frequency typical of motion recorded on rock at such distances from the epicenter. On the other hand, the motions recorded on the lake deposits (SCT station), which consist In unconsolidated layers of clay, 20 to 50 m thick, showed a very strong amplification, with a peak ground acceleration of 0 17 g and a relatively selective frequency at 04 Hz. This frequency corresponds quite exactly to the fundamental frequency of vibration of the surficial soil layers [11-1 I . I - 7

Similar observations can be drawn from the 1989 Loma Prieta earthquake. This magnitude 7 earthquake resulted from a rupture of a portion of the San Andreas fault long in the San- ta Cruz Mountains, approximately 80 km south of San Francisco. Of particular interest are the records in downtown San Francisco and around the Bay area. Some stations lie atop rocky out- crops, while others are on quaternary alluvial deposits. Stations on rock expe rienced peak ground accelerations of 0. 10 g, whereas those on soil deposits exhibited values as high as 0. 33 g (San Francisco Airport) I-1.21. It is interesting to note that the same region was subjected to a moderate-magnitude earthquake (ML= 53), the epicenter of which was located 15 to 20 km west of the city. The smaller magnitude and distance to the stations gave rise to about the same peak ground accelerations on rock as for the more recent event. Motions recorded on the alluvial deposits, however, were significantly smaller than in 1989. Table II-1.6 lists peak ground accciera- tion values recorded during both events. Clearly, the surface motions are influenced to a large extent by the characteristics (i.e. thickness, mechanical properties) of the underlying layers, but also by those of the incident motion impinging the lower boundary of the soil layers.

MAXIMUM GROUND

LOCATION SOIL PROFILE ACCELERATION 1957 1989

Golden Gate Park Rock 0.13

Market Guerrero St. Rock 0.12

State Building Sand clayey sand 60 m) 0.10

Mason Pine St. Rock 0.10

Alexander Building Clayey silt sand 45 m) 0.07 0.17

Southern Pacific Building Soft clay 0.05 0.20

Rincon Hill Rock 0.10 0.09

Oakland City Hall Clay sand 30 ) 0.04 0.26 Stiff clay 270 m)

Table 16. A comparison of peak velocities recorded on strong-motion instruments in the San Francisco area for local earthquakes in 1957 and 1989.

The 1957 earthquake had a predominant period of about 025 s, whereas that of the 1989 shock was about 04 to 06 s. Since the soil deposits at the recording stations have fundamental periods of vibrations of around 06 to 0.8 seconds 40 m of alluvia with a shear-wave velocity of 200 to 250 m/s.), they amplify motions with fundamental periods in the same range 1989 earthquake) and deamptify those with smaller periods. 8 - RECFNTADVAArCES IN EAR77-IQUAKE JVGINEER[NG & STRUCH)RAL DYNAWCS

It is also interesting to note that spectral amplification ratios from ground motion at com- parable soil/rock station pairs were significantly higher for relatively weak motions from after- shocksthantheywereforthemainshock(II-1.101. Thesamplificationorfilteringeffectscanbe rendered even more complex if the non-linear soil behavior under cyclic loading is taken into account. Consequently, it is not feasible to evaluate with accuracy the ground motion at the surface of a soil deposit without a precise knowledge of the incident motion and of the soil behavior con- stituting the profile.

1.7. SOIL DYNAMICS

Results of laboratory tests conducted on remoulded or undisturbed samples reveal, with. out any doubt, that soils behave as highly non-linear material under cyclic shear stresses or strains. Results presented by various authors (i.e. [II-1.271 and II-1.121 ) show how thesecant shear modulus decreases ith Increasing shear srain. Accordingly, the energy dissipated by the material during one cycle of applied stress often, expressed as an-equivalent damping ratio, increases with an increasing strain level. These variations in modulus and damping are significant for strains of the order of those developed in a soil profile during moderate to strong earthquakes.

However, non-finearities in soil behavior are not confined to softening under. cyclic stresses. Equally important are the volumetric strains which result in the application of cycles of shear stress. If the soil is not saturated, these will induce permanent, irreversible settlement in a soil layer; if the soil is saturated, they will cause the pore water pressure to increase, eventually lead-ing to a complete loss of strength, known as liquefaction. Figure II-1.7 gives an example of the impact of ground liquefaction on the recorded surface motion; both accelerograms of Figure II-1.6 were recorded during the Loma Prieta earthquake at stations located close to each other: the upper graph, recorded on rock (Yerba Buena), exhibits a relatively high frequency content, whereas the lower one, Treasure Island, shows a low-frequency motion with vanishing accelerations caused by the liquefaction of the underlying soil.

On the strength of all these observations, geotechnical engineers now recognize that reliable computations of surface ground motions should account, in one way or another, for the non-linear behavior of sods. Various models have been developed in the past which were incor- porated into computer codes for wave propagation analysis. Probably the most widely-used model is the so-called equivalent linear model 11-1.141. In this model, soil non-linearities are appro.-dmated through a succession of linear analyses in which the soil characteristics are adjusted to be compatible with an average (during the excitation) strain level. Provided the shear strains induced are not too high (of the order of 1,3), the results procured by such a procedure have been shown to be acceptable enough for pactical purposes [II-1.201.

For higher levels of sollicitation, one must resort to more sophisticated model involving plastic yielding of the material. Many elastoplastic constitutive models have been elaborated in the past few years. Predictions of these models were checked against laboratory test results; very few comparisons, however, have been made with actual recorded motion [II-1.241. I 9

1.8. COMPUTATIONAL MODELS FOR WAVE PROPAGATION ANALYSES IN SOILS

In order to verify the accuracy of the models just discussed (equivalent linear and eWto- plastic), the authors have attempted to compare the predictions they yield with actual earthquake records. At the McGee Creek site, in the Mammoth Lakes region of astern California, 3compo- nent strong-motion accelerometers were installed in boreholes at depths of 35 and 166 m as well as at the surface [II-1.261. The surface material, approximately 30 m thick, consists in glacial mo- raine and overlies hornfels. Accelerations were recorded from two fairly large California earthquakes: Round Valley, on November 23, 1984, with a local magnitude of 5.8, and Chalfant Valley, on July 21, 1986, with a local magnitude of 64 1II- 1. 22 1. Obviously the soil type at McGee Creek and the moderate magnitude levels of the shocks could not be expected to produce significant non-finearides within the soil profile. Consequently, the seismic response of the surface deposit was computed with the equivalent linear model, using the motion at 35 rn as an input. The computer code used for the analysis is SHAKE 111-1.251, modified to accomodate waves with an inclined incidence 11-1.161. Figure 11-1.8 shows the comparison between the computed and recorded response spectr (damping 5%) at the ground surface for the Chalfant Valley earthquake. Similar results were obtained for the Round Valley event. Up to 15 Hz, both spectra show very good agreement, and it appears, from an engineering standpoint, that the one-dimensional shear-wave model, associated with the equivalent linear model for the soil behavior, is adequate under the conditions prevailing at McGee Creek.

In order to validate such models on a wider basis, the dynamic responses of ten different actual soil sites with respect to hypothetical earthquake motions were computed and compared with recorded motions. The French Commissariat ; I'Energie Atornique has developed, for the design of nuclear power plants in France, site-adapted response spectra based on a statistical analysis of actual recorded motion II-1.19]. The majority of the records used to eaborate these spectra were obtained on sites with alluvial deposits. The shear-wave velocity profiles for sven of the deposits are depicted on Figure 11-1.9. For the purpose of the analyses presented herein, four fictitious profiles have been added: they consist in dry sand layers 30, 50, 75 and 100 m thick and have characteristics assigned on the basis of results given in the literature. These ten soil profiles were subjected to incident motions representative. of moderate-magnitude earthquakes (ML = 55 to 65) for which the peak ground acceleration value on a rock outcrop was estimated at 0. 1 to 02 g at epicentral distances ranging from 15 to 50 Ian.

Figure 11-1.10 shows the comparison, for one of the cases studied, between the average response spectra computed at the ground surface and the mean and mean-plus-one standard d- viation spectra derived from the aforementioned statistical analysis. The average computed spectra are obtained for the ten sites of Figure 11-1.9, and for a given level of input motion specified at a rock outcrop and with three different values of angle of incidence (r, 150, and 300): consequently, the average curve represents the results of thirty individual calculations. The agreement is seen to be vry good in the low-frequency range (up to 2 Hz), above which (from Hz on) the computational model slightly underestimates the response. This result is in line with that obtained from the McGee Creek experiment and confirms, for moderate earthquakes, the suitability of the model for engineering purposes. Finally, in order to ascertain whether more sophisticated soil models are capable of over- coming the limitations of the equivalent linear model in the high frequency range, the response, to the same hypothetical earthquake, of 30-, 50-, and 75-meter thick sand layers were computed with an elastoplastic constitutive relationship for the soil. This relationship 11.241 is based on the concept of dnematic hardening with multi-yield surfaces of the Drucker-Prager type. Parame- ters for the model can easily be derived from conventional triaxial tests. In the present case, they I 0 - RECENTADVANCES IN EAR7HQUAKE E.VGIArEENNG SRUC7VRAL DYN"ICS

were obtained from tests performed on Hostun sand; it was established that predictions of the model under simple shear cyclic loading yielded modulus reduction and damping ratio curves versus strain similar to those previously used in the equiva lent linear analyses.

Parametric studies were carried out with increasing input acceleration levels, i.e. 0.10, 0.25, and 050 g. Results are presented in terms of computed response spectra for a 30-meter thick layer on Figures II-1.11 and II-1.12. They are compared with results obtained from a linear, and an equivalent linear analysis. It is readily apparent that, for the smaller level of acceleration (Figurell-1.11),allthreemodelsyieldthesameresults. Howeverforthehigherievelofaccelera- tion (0-5 g at the rock outcrop), although the three models continue in good agreement in the small frequency range, they differ significantly at higher frequencies: the linear model gives the highest response, the linear equivalent one, the smallest, and the non-linear model, a response closely resembling the linear equivalent model, only slightly higher. Figure 11-1-13 compares the surface accelerations for the three models and the three acceleration levels at the outcrop. The non-linear model definitely predicts a saturation in the computed surface acceleration at value of the order of 040 g; the effect is less pronounced with the equivalent linear model, and, of course, does not ist with the linear model. It is interesting to recall that observations made on actual recorded motions tend to show that surface accelerations on alluvial deposits do not ex. ceed 045 g [11-1.201. This was ascribed to the non-linear behavior of the sod and is confirmed by the theoretical calculations.

In conclusion, theoretical calculations would indicate that non-linear soil models are ca. pable of rendering the salient features of the response of a soil deposit to an incident'scismic motion; equivalent linear models are also appropriate for moderate levels of excitation and, due to their simplicity, may be preferred for such applications. Predictions of equivalent linear models have been compared to recorded motions and prove adequate from an engineering standpoint. Actual strong motions on alluvial deposits are lcking so that the validity of non-Unear models can be assessed; this his led the Commissariat 'Energy Atornique and the U. S. Nuclear Regulatory Commission to finance a project of downhole instrumentation, similar to the one conducted at McGee Creek, on a soil site in Garner Valley, southern California 11-1.211. Preliminary results from this experiment are expected to be available in the near future.

1.9. APPLYING HISTORICAL SEISMICITY DATA TO SEISMIC HAZARD DETERMINATION

A good knowledge of historical seismicity dating back as far as possible, when used as a complement to other earth science data, especially neotectonic, enables the analyst to identify source zones, which is essential to seismic hazarel assessment. Magnitudes will then need to be assigned to these historical earthquakes, most often characterized by their effects on man or his construction, in terms of macroseismic intensities. One possibility is to establish a correlation between the magnitude M, intensity I at the observation point, and the focal distance R to this latter from recent instrumental data and to use it to infer the missing magnitudes. A correlation of this type was computed on the basis of California data with the following result:

M = .55 1 + 22 log R 114 ± 04 (11-1.20)

Filling in the magnitudes for these older events and establishing a catalogue makes it pos. sible to compute magnitude distribution laws that can be applied in a probabilistic approach, but also to estimate ground motion from sting instrumental data, either local or 'imported,'. It is nevertheless necessary first to verify certain regional characteristics, important among wich are local mchanism and attenuation laws. The relationship existing between macroseismic intensity and ground motion parameters is complex in character, for an earthquakes impact on a given building, in terms of intensity, is the consequence of several factors at once duration of shaking, construction type, soil conditions), and not solely the level of PGA, as is not infrequently maintained. Macroseismic intensity furnish- es a kind of average evaluation, in a statistical sense, of damage over a relatively wide area. While it is an extremely valuable notion, it is inappropriate to attempt to equate it with any one parame- ter, be it peak acceleration or another. The statistical analysis of a set of Caftfornia data shows that a single intensity class can be represented by a wide range of spectra (5% damping) corresponding to different magnitude and distance pairs (Figure 11-1 14). Although the convergence of spectral parameters is conditioned by the constraint imposed by equation (II-1.20), the frequency at which this occurs (I to 2 Hz.) is not predetermined. It does in fact to characterize the intensity to a certain extent (the value doubles when intensity increases by one degree). Recent California earthquakes seem to display the same tendancy. In the near field R < 10 km), however, such correlations are not to be relied upon owing to the complexity of the source and rupture propagation (directivity), as well as soil effects, which may be a determining factor.

1.10. REALISTIC STRONG GROUND MOTION PREDICTION FOR ASEISMIC DESIGN PURPOSES RELYING ON AVAILABLE TECHNIQUES AND DATA

Based on the considerations developed in the preceding paragraphs, it would appear that a reliable means of computing ground motion parameters on sod deposits should make use both of available data, processed in a statistical manner, and of theoretical computational models.

In such an approach, a ock motion on a hypothetical outcrop at the site location would be determined from a data based composed of actual rock motions. Statistical treatment of this data would yield the rock motion parameters, namely the pseudo-relative velocity spectrum, as a function of magnitude and distance. It must be stressed that not only the peak ground acceleration is computed, but the whole spectrum, determined frequency by frequency. Consequently, attenuation of frequencies with distance wiH be different in different frequency ranges, and the de-rived spectrum wil] represent the correct frequency content of a rock motion at the site. As evidenced by the theoretical calculations presented above, rock motions should also tentatively be classified with respect to their focal mechanism (strike-stip, thrust, reverse, ...) and tectonic environment intraplate or interplate conditions). Once the outcrop motion is determined, actual accclerograms with the appropriate characteristics or synthetic accelerograms having response spectra that match the site response spectrum can be derived. These time histories are then used to compute, through a wave propagation analysis, the ground surface motion. Besides the input motion, the parameters needed for the analysis are the soil profile and its dynamic characteristics. These can be assessed and measured for the site. The advantages of the approach outlined above are to afford an acccurate reflection of the source effect and path-dependent characteristics of the earthquake motion travelling through the rock, as wed as the dependence of the ground surface motion on the local geotechnicam properties of the soil profile underlying the site. It has been shown on examples that the computational model correctly captures the salient features of surface motions on alluvial deposits, and it is believed that the method could, in the very near future, represent the state of the art in the prediction of strong-motion calculations for the anti-seismic design of critical structures. 12 - RECEIVTADVAIVMINEAR7HQUAKEFNGIAEERING&STRUCIVRALDYN"rCS

1. 1 1. BIBLIOGRAPHY

II- 1. 1 1 Association Franqaise de G16nie Parasismique 1985). Msme de Mexico, Rapport de mission.

111-1.21 Association Franqaise de Ginie Parasismique 1989). SkismedeLoma rieta, Rapport de mission.

I I I- 1 .31 Ald, YL and P Richards 1980). QuantitativeSeismology, W. H. Freeman, San Francisco. 11-1.41 Bnard, P. 1987). Du caract&e complexe et agressifdes sources sismiques, doctorate thesis doctorat &Ctat is sciences physiques') presented at the University of Paris V on October 1, 1987.

111-1.51 BemardP-andP.Mouroux(1987). UmodNespectraidesourcepourlecalculd'acc6- 1&ogrammes syntb4stiques et des spectres de reponse associ6es, communicated by the authors.

II 161 Boore D M. and R. Porcella 1980). 'Peak Acceleration from Strong-Motion Records: A Postscript,'BullSeism. Soc Am. 70, pp. 2295-2297.

111-1.71 Boore D M 1986). 'Short-Period P and S-Wave Radiation from Large Earthquakes: im- plication for Spectral Scaling Relation,'BuIL Seism. Soc Am. 76, pp. 43-64.

[ II-1.81 Brune, J. N. 1970). 'Tectonic Stress and the Specti of Seismic Shear Waves from Earth- quakes,'j. Geophys. Res. 75, pp. 4997-5009. [ II- 1 .91 Campillo, M. and M. Bouchon (1985). 'Numerical Modeling of Strong Ground Motions,' in G46nie Parasismique,V. Davidovici, editor, Presses de I'Ecole Nationale des Ponts & Zhauss6es, pp. II 7-129.

[II-1-101 Darragh, P, and A. Shakal 1990). 'The Site Response of the Gilroy Array, California to Strong and Weak Ground Motion,' Abstract of a communcation presented in the 85 th An- nual Meeting of the Seismological Society of America, published in SeismologicalResearch Letters 61, N' 1, P. 50.

[ II I I Gutenberg, B. and C. F. Richter 1956). 'Earthquake Magnitude, Intensity, Energy and Acceleration,"Bull. Seism. Soc. Am. 46, pp. 105-145.

( II- 1 121 Hardin, B. O.. and V. P. Drnevich (1972). 'Shear Modulus and Damping in Soils: Design Equations and Curves,'Journal of Soils Mechanics and FoundationDivision, ASCE 98 N" SM7.

11 I I 131 Hartzell, S. H. (I 978). "Earthquake Aftershocks as Green's Functions,' Geopbysical Re- search Letters 5 4 pp.

11 I- I 14 driss, 1. M. and 11. B. Seed 1968). 'Seismic Response of Horizontal Layers,"Journal of Soil Mechanics and FoundationDivision, ASCE 96, N'SM4.

III-1.151 Kanamori, H. and D. L Anderson (1975). 'Theoretical Basis of Some Empirical Rela- tions in Seismology,' Bull. Seism. Soc. Am. 65, pp. 1073-1095. 111-1-161 Kausel, E. andj. M. Roesset 1984). 'Soil Amplifications - Some Refinements,'Soil Dyn. and Eartbq. Eng 3 N" 3.

111-1.171 Keane, C. and J. H. PrEvost 1989). An Analysis of EarthquakeData Observed at te Wildlife Liquefaction Array Site, Imperial County, California,Department of Civil Engin- eering and Operations Research, Princeton University, New Jersey, personal communica. tion.

I I- 1. 181 Levret, A. and B. Mohammadioun 1988). '136termination des mouvements sismiques de r6f6rence. 116glementation dans le domaine du nucl6aire,' Compte rendu de la r6union- d6bat "Les Mouvements sismiques pour 17ng6nieur, Association Franqaise de Gtnie Para- sismique, pp. 417-428. I - 13

[II-1.191 Mohammadioun, B. and G. Mohammadioun (1980). Analyse des donn,&s sur les mouvements forts actuellement disponibles au WNISESRSIBERSSEV, Rapport Technique SESRS N 15, 41 pp. [11-1.201 Mohammadioun, B. and A. Pecker (1984). 'Low-Frequency Transfer of Seismic Energy by Superficial Soil Deposits and Soft Rocks,'Earthquake Eng. Struct D 12, pp. 737-764. III-1.211 Murphy, A. J. and B. Mohammadioun 1989). 'A Cooperative NRC/CEA Research Pro- ject on Earthquake Ground Motion on Sod Sites: Overview,'Proceedingsof te 1tb SMIRT Conference S03(K). 111-1.221 Pecker, A. and G. Mohammadioun 1989). 'McGee Creek Downhole Records Interpre- tation from an Engineering Standpoint,' Proceedings of te 10tb S)WRT Conference K, pp. 31-36 [II-1.231 Petrovski, D. 1986). ProbabilisticApproacbforEvaluationofSeismicDesignParame- ters, communication presented to the specialist meeting on earthquake ground motion and anti-seismic evaluation of nuclear power plants, Moscow, March 24-28, 1986. . II- 1. 241 Prevost, J H. 1985). 'A Simple Plasticity Theory for Cohesionless Frictional Soils,' Int. J. Soil Dyn. Eartbq. Eng. 4 N , pp. 917. [11-1.251 Schnabel, P. E., J. Lysmer, and H. B. Seed 1972). A Computer ProgramforEartbquake Response Analysis of Horizontally Layered Sites, Report EERC 72-12, Earthquake Engin- eering Research Center, University of California, Berkeley. 111-1.261 Seale, S., R. Archuleta, A. Pecker, M. Bouchon, G. Mohammadioun, A. Murphy, and B. Mohammadioun 1988). 'Strong Seismic Ground Motion Propagation,' Proceedings of te InternationalFJVSIAlVSConferenceonThermaiReactorSafety"NUCSAFE88"1pp.287-1. 111-1.271 SeedH.B.andl.M.ldriss(1970).SoilModuliandDampingFactorsforDynamicRe- sponse Analysis, Report EERC 70-10, Earthquake Engineering Research Center, University of California, Berkeley. [11-1.281 Spudich, P. A. and S. H. Hartzell (1985). 'Predicting Earthquake Ground-Motion Time- Histories,' in Evaluating Eartbquake Hazards in te Los Angeles Region - An Eartb-Sci- ence Perspective, U. S. Geological Survey Professional Paper 1360, pp. 249-26 . II- 1. 291 Wyllie, L, B. Bolt, M. Durkin, J. Gates, D. McCormick, P. Smith, N. Abrahamson, G. Cas- tro, L Escalante, R. Luft, R. Olson, and J. Vallenas 1986). 'The Chile Earthquake of March 3, 1985,' EartbquakeSpectra 2 pp. 249-513. 14 RECENTADVAN(7SINEARTHQUAKEEVGINEER[NG&STRUCTURALDYNAMICS

M=8.5

M--6.5 NO .01 0 cu 10 100 1000 = a M 0 " CL Hypocentrat Distance (Km) 2W S0

I I F I I I I M -g I I

C 1.0 0

O 0 0 Cn 0 0 O _x ajM 0 C!R =6.4 CL O 'Iq =63 0.1 0 6.1

.01 M=6.0

.001 I I I Hill 1 10 100 Gosest distance to the fautt Wm)

Figure II- 1. 1. Peak ground acceleration plotted ersus hypocentral (Chilean earthquake, 1985, part a) or closest to the fault Imperial VaHey earthquake, 1979, part b distances. I 15

lo, 8 6

4A 2 -

lo, 8 6 0 4

w CL. 2

I lo-, 2 4 6 6 10' 2 4 6 8 10' 2 4 6 10' Frequency (HZI

Figure I-1.2. Comparison of actual response spectra (horizontal components of th Kmbs earthquakc of July , 1980, ML 48 - ashed and dotted lines) with a corresponding synthetic spectrum (solid linc). 16 - RECENTADVANCES IN EARTHQUARE ENGINEENNG & SYRUCIVRAL DYNAMICS

lo, 8 6

2 O

lo, 8 6

> 2

lo,

lo-, 2 4 6 810' 2 4 6 a lo, 2 4 6 lo, Frequence (Hz)

Figure 11-1.3. Predicted spectra from California data (ML-6.5) nd from European data (ML-6.5 and 70) corresponding to a focal distance of 80 km. 7

10 0.0

-t 10.0

Gj W Q.

0.1 0.1 1.0 10.0 100.0 Frequency I Hz)

FigureII-1.4. Comparlsonofthcresponsespectnim(5%d2MPfng)obtainedfromastrong-motfonrccor-J at Gukawian of the Dcember 1988 Armenian earthqU2ke with a predicted spectrum based on California data. 00

4 hl 3

au LALu .7- 4.6 - LA Ln 5 .6

.4- .3 .3 Ln CZ .2 .4 6 2 4 6 810 20 40 100 .2 .4 6 1 2 4 6 810 20 40 100 Frequency in Hz Frequency in Hz

Figure I-1.5. Spectral ordinate ratios intmplate/interplatc) plotted versus fequency for dfferent corner- frequency values: a) moderatc-Magnitude arthquakes ) large-magnitude earthquakes. I 19

a YERBA BUENA ISLAND

Maximum acceleration 0.06g

------

0 1 2 3 4 5

b TREASURE ISLAND Maximum acceleration 0.16g

0 1 2 3 4 5 TIME IN SECONDS

Figure - 7 Recorded accelerations rom the recent Wm Prieta earthqUAe, displaying absence Yerba Buena Island, part a) and presence (17reasure Island, part b of soil liquefaction. 0.34 0.25 0.15 Cn U. 10 0 =M 006 - 0.03 - U M'002 - 0 0.01 a-14 0.0 _ 0.00 0.00 0.00

0.25 0.50 1.00 1.99 3.98 7.04 15.84 31.62 Frequency (Hz)

Figure II-L A mparison of rcorded and computed surface rsponse spectra (5% damping) the McGee Creek site. I 21

S-Wave Vel-ocity W s) 0 0 2SO SO 7

......

100 OjC3- (D C3

(D El Centro (D Cholame 2 (D Pasadena CI r

150 Santa Barbara-Court House raft- Lincoln School Wit shire Od. -Los Angeles (D Sable 30 m. Sable 50 m. Sable 75 m.

200- Sable 100 m. (D 300 m

Figurelf-1.9. ShC2r-w2vevelocitiesvetsusdepthforaselectionOfCalifOM12SItCS. 0.46 1 1 1 1 1 cl 0.25

0.12

4 0.06 2 0.03 -

0.01 -

0.12 0.25 0.50 1.00 1.99 3.98 7.94 15.84 31.62

FREQUENCY (HZ)

Figure 11-1.10. A comparison between mean and mean-plus-onc or synthetic spectra III-1.191 -fine lines - and the averag rcorded spectra for the ten sites - beavy lines. I - 23

NON INDA 0.25

0.18 LINDA LINDA

0.10 LINDA LINDA QUITALMOT

NOW LDA

0.00

0.04

0.03 MON L M

0.02 UNMAN

0.01 LINDA QUIT

0.01 - .Of

0.00 i 4_4 0. r3 0.25 0.60 1.00 2.00 3.98 7.94 ?5.85 3t.82

Figure Computed response spectra at the ground surface obtained for three assumptions of soil behavion linear, linear equivalent, and non-line2r, maximum rock acceleration as 010 g.

f.74 1.58 -

1.00 --

0.83 --

LINDA 0.40 --

LINDA RMTALZirf >. 0.25

O. le

0.08 --

0.04

A. 0 03

0 02 Frequency (112) 0. 2

0 Is 0.25 0. 0 1.00 2.00 3.98 7.94 MM 3t.62

Figure 11-1.12. Computed rsponse spectra at the ground surface obtained for three assumptions of soil behavior lnear, linc2r quivalent, and non-linear, ximum rock2CCCieration was 0.50 g. 24 - ECENTADVANCES IN EARTHQUAKE ENGIAIEERTNG & SRUCrVRAL DYNAMICS

A-

0.5

v'0.25

0.1

0.1 0.25 0.5 Rock outcrop aceieration (g)

Figure 1-1-13. Surface acceleration versus rock-outcrop accelerations for a 30-metcr thick sand layers I - 25

100

o.lcM

4A INE log lo 0.01CM

CU lg

0.1 o.1g 0.1 1 10 100 Frequency in Hz

FigureI-1.14. Response spectra corresponding to a macroscismic intensity class VI-VIII: M2gnitude/focal distance pairs ranging from 52 at 10 km to 8.1 at 200 km 111-1.191.

Octobre 1990

DESTINATAIRES

DIFFUSION CEA

M. Le Haut Commissaire M. l'Inspecteur GnC:ral pour la SQret6 Nucl6aire DCS DDSN IPSN OSSN M. GUILLEMARD DRSN M. LIVOLANT DAS/DIR DERS Cadarache SES Cadarache SERE Cadarache SESRU Cadarache SRSC Valduc SEMAR/FAR SEMAR/Cadarache DPS/FAR DPS/D0C : Mme BEAU DPT/FAR CDSN/FAR Mme PENNANEAC'H DSMN/FAR DRN Saclay DRN/DER Cadarache DRN/DEC Cadarache DRN/DMT Saclay DCC Saclay DTA/Saclay Service Documentation Saclay Mme COTTON 3 ex.) DERS/DOC Cadarache Mme REY

DIFFUSION HORS CEA

Le Secr6taire G6n6ral du Comit6 Interminist6riel de la S6curit6 Nucl6aire Conseil G6n6ral des Mines M. DE TORQUAT Service Central de Saret6 des Installations Nucl6aires M. LAVERIE 3 ex.) Service Central de SCret6 des Installations Nucl6aires FAR Monsieur le Pr-sident du G.P.d. M. GUILLAUMON'T Monsieur le Pr6sident du G.P.u. M. MUXART Direction G6n6rale de 1Energie et des Mati6res Premi6res M. LEVY FRAMATOME M. le Directeur G6n6ral NOVATOME M. le Directeur technique TECHNICATOME M. le Directeur G6n6ral TECHNICATOME Service Documentation COGEMA M. le Directeur de la Branche ENRICHISSEMENT COGEMA M. le Directeur de la Branche RETRAITEM ENT EDF : l'inspecteur gC5,n6ral de la saret6 nucl6aire : M. TANGUY EDFI/SEPTEN 2 ex.) EDF/'SPT Soci!t6 Ginirale pour les Techniques Nouvelles : M. JUSTIN Mrs Marie-Aim6e KHALIL Vienna International Centre Library 2 ex.) AIEA, Division de la SQret6 Nucl6aire, Bureau d'Information sur la Saret6 - Mme Hulrike HERWIG AEN/OCDE - Bibliothtque : Mme GODWIN Bundes Ministerium fUr Umwelt, Naturschutz und Reaktorsicherheit - BONN (RFA) - M. HOHLEFELDER - M. BREEST Bundes Ministerium fUr Forschung und Technologie, BONN (FA) M. KREWER Gesellschaft fUr Reaktorsicherheit - KOLN (RFA) - M. BIRKHOFER - M. JAHNS Octobre 1990

U.S./N.R.C. - WASHINGTON (E.U.) - M. HAUBER - USNRC, Attn : Library Commission de Contr6le de 1Energie Atomique du Canada - M. LEVESQUE - M. DIAMENSTEIN Nuclear Installations Inspectorate - LONDON (G.B.) M. J.S. MACLEOD International Collaboration Branch UKAEA - Risley WARRINGTON (G.B.) - M. J. BRANIMAN Inspector for Nuclear Safety - WARRINGTON (G.B.) M. J.G. TYROR Consejo de Seguridad Nuclear - MADRID (ESPAGNE) %I. GONZALES M. JOSE DE CARLOS D(spartement de I'Environnement, Universit& d'Aveiro (PORTUGAL) Dr C. BORREGO Studsvik Energiteknik AB, Nuclear Division, Safety and System Analysis, NYKOPING (SUEDE) M. E. HELLSTRAND Direttore Centrale della Sicurezza Nucleara e della Protezione Sanitaria. ENEA, ROMA (ITALIE) M. NASCHI Direttore relazioni esterne e informazione, ENEA, ROMA (ITALIE) M. P. VANNI National Nuclear Safety Administration (CHINE) M. LIN CHENGGE Director of the Nuclear Electricity Office - CNNC (CHINE) M. MA FUBANG MITI (JAPON) M. Hironori NAKANISHI Science and Technology Agency, Director of the Nuclear Safety Bureau (JAPON) - M. KENICHI MURAKAMI - M. HIROSHI HIROI Center of Safety Research, JAERI (JAPON) : M. FUKETA Secr6tariat G6n6ral du Minist&re de 1Energie et des Mines (MAROC) - M. Mohammed KARBID - M. Abdelmajid CAOUI I.V. Kurchatov Institute for Atomic Energy (MOSCOW): - M. Nikolal N. PONOMAREV-STEPNOI USSR Academy of Science Institute of Nuclear Safety (MOSCOW): - M. Leonid A. BOLSHOV

L'attach6 press de l'Ambassade de France aux Etats-Unis M. DE GALASSUS L'attach6 pr6s de l'Ambassade de France en URSS M. GOURDON L'attach6 "Energie" pr6s de l'Ambassade de France en Cor6e : M. DURAND L'attach6 pr6s de l'Ambassade de France au Japon : M. MORIETTE Le Conseiller nucl6aire aupr6s de l'Ambassade de France en Chine M. LALERE

COPIE (SANS P.J.) SRDE LEFH BAIN SASR SACP SAEP SGNR SAREP SAPN SASICC SASLU SASLU/VALRHO SEC SAET SAED STAS SASC SAEG SAM SPI

Le Conseiller nucl6aire pr6s de l'Ambassade de France en R.F.A. - M. GOURIEVIDIS