ML13308A634

Review of Repts on Simulation of Ground Motions

ML13308A634
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Site:	San Onofre
Issue date:	12/04/1979
From:	Bernreuter D LAWRENCE LIVERMORE NATIONAL LABORATORY
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LAWRENCE Li4MORE LABORATORY REVIEW OF REPORTS ON SIMULATION OF GROUND MOTIONS FOR THE SAN ONOFRE NUCLEAR GENERATING STATION - UNIT I By D. L. Bernreuter December 4, 1979 INTRODUCTION This report deals primarily with Del Mar Technical Associates (DELTA) report dated July 1979, Supplement I. Reference to figure numbers, page numbers etc. are from this report unless otherwise noted. I also re-reviewed DELTA's report dated May, 1978, DELTA's draft report dated August 29, 1979, Response to Proposed Task 4 and the S3 report by S. M. Day, Three-Dimensional Simulation of Rectangular Fault Dynamics, September 13, 1979.

The mesh size studies seem adequate to me and since Prof. Lucco has commented on them extensively I will not further comment on this aspect of the DELTA study.

GENERAL Overall I believe that the DELTA approach is valuable and can play a useful role in the assessment of the appropriate level for the SSE at the San Onofre site. The DELTA approach represents a significant advance in the state-of-the-art of simulating earthquake ground motion at a site. The major deficiency of the study is that the methodology has not University of California P.O. Box 808 Livermore, Calilornia 94550 E Telephone (415)422-7700 O Twx 910-38-339 UCLL LVMR

-2 been applied to enough earthquakes to eastablish reasonably conservative bounds for the key parameters of the model. These key parameters are:

(a) V = initial slip velocity (dynamic stress drop)

(b) Length and width of fault zone (c) Rupture velocity (d) Rise time (e) Final offset (average dislocation)

(f) Focusing of seismic waves (g) Q values used (h) The micro-incoherence used (i) The four macro-radomness used (j) Best "linear" model to account for any important uncertainties -- This includes geology and the representation of earth's response to loads in the model.

(k)

Rupture model The static stress drop and seismic moment must be computed from (b) and (e).

The DELTA model includes,in some manner,the physical parameters which are considered to have an important effect on the ground motion.

They fall into two types:

(1) direct physical parameters such as length and width of the fault zone, Q values etc and (2) parameters to simulate the incoherence of nature [(h) and (i)].

From the parameter variation studies made in the report it is possible to assess which are the key physical parameters relative to the specification of the SSE for San Onofre nulcear power plant. It is much more difficult to assess the random parameters introduced into the model to capture incoherence of nature and to assess the range of values assigned to the important physical parameters of their model.

The only "parameter" not dealt with is the effect of nonlinearity on the results.

-3 Clearly there is considerable uncertainty associated with each of the parameters of the model and about the simplistic rupture model used.

In order to assess how important our lack of knowledge about the key parameters of the model are it is useful to examine alternative approaches.

One approach would be to use a large finite element or difference computer program and attempt to truly model the physics of the rupture process.

This is being done in the SSS study; however, so little is known about the physics of the process and equations of state that the finite differ ence approach introduce even a more uncertain parameters than the DELTA model.

The DELTA approach represents the next "best attempt" at solving the problem from first principles. There are other simplified models that one might consider using, but such models have too many limitations to shed much additional light on the problem over the DELTA model.

Another alternative is to use some sort of semi-empirical approach.

The problem here is that there are only a few earthquakes with sufficient data to establish how to extrapolate from the bulk of the data into the very near-field. One major problem here is that two best cases have considerable controversy surrounding the key data point; namely, potential topographic amplification at the Pacoima Dam site and questions about where the energetic faulting stopped at Parkfield.

(It would have been very useful if DELTA could have continued its calculations out to 50-75 km and matched the bulk of the available data. This would have helped in the back-extrapolation process.).

As more data becomes available it may be eventually possible to back extrapolate into the very near-field. At the present time there is considerable controversy about how to do this.

It is difficult to assess from the strong motion data set what the influence of the various parameters have on the ground motion because all of the different parameters are inter mixed and for many earthquakes we do not have reliable estimates of even such important physical parameters as length and width of the rupture zone, average dislocation and seismic moment. Thus attempts to correlate ground motion with these parameters has not been very fruitful.

and ML is the most commonly used variable.

However, from studies of the available near-field data, it is apparent

-4 that the peak acceleration at a site is somewhat independent of magnitude.

By this I mean that small earthquakes can often give rise to large peak accelerations, but that it is more likely for a larger magnitude earthquake to give rise to large peak accelerations than a much smaller magnitude earthquake. Thus it is clear that some factor independent of size of the event controls the high frequency radiation of seismic energy from the fault and that this factor is quite variable. For the semi-empirical approach we have to hope that a sufficient number of earthquakes in various tectonic settings have been recorded so that we have an adequate statistical sample to define this uncertainty.

Elementary considerations suggests that focusing of seismic energy can be a problem. The available data seems to reflect some focusing -

but much weaker focusing than suggested by elementary considerations.

Potential focusing is very difficult to assess from the empirical data set, and one must rely on the hope that sufficiently varied data has been recorded to provide an adequate sample to also define the uncertainty introduced by focusing.

The alternatives to an approach such as developed by DELTA are also plagued by uncertainty as the data set is not adequate to make the necessary assessments and bound the potential uncertainty that special tectonic/

geometeric conditions might introduce.

The advantage of the DELTA model is that it is a reasonable physical model.

The model allows us to determine how the key parameters effect the ground motion at the San Onofre site. We still must use some intuition to assess key parameters, but it is at a level that is much easier to apply intuition than either directly to the data set or to simple source models.

A review of the results of the DELTA study show that the most important parameters controling the spectral level and shape in the frequency bands of interest is the parameter V.

Rise time, seismic moment, length of faulting within reasonable limits only have a small effect on frequencies greater than 2 Hz. Rupture velocity is of some importance. Are these results reasonable? I believe that they are. My reasons for believing that the results are reasonable, the uncertainty associated witth-the results and the implication of the results are discussed in the following sections of this report.

0

-5 EARTHQUAKE SIZE PARAMETERS The DELTA model incorporates a number of parameters dealing with how "large" the earthquake is:

(1) Length and width of the rupture zone, L, w.

(2) Final average dislocation, D.

(3) Rise time, tR' The seismic moment and the static stress drop can be computed.from (1) and (2), e.g., Kanamori and Anderson (1975) give the relation for strike slip faulting.

M0 =

1S-

=

c 2 L where S = Lw L = Length w = width D= Average Dislocation 0 -

1 0 = Initial Static Stress 01 = Final Static Stress 2

7r (2)

In the DELTA model L, w and 0 are the input parameters and M and Aa must be computed.

Simple source models, e.g., Brune's model would suggest that as Aa increases the peak ground velocity and acceleration would also increase.

The reason for this is that in, e.g., Brune's model a stress discontinuity of Aa is introduced at time to. In Haskell's (1964) model the dislocation is assumed to be a linear ramp of rise time tR.

The DELTA model has two

I

-6 parameters, V0 and tR. V0 models the initial rupture front and is somewhat related to Brune's Aa. The DELTA model includes Haskell's rise time, but models the ramp differently. Haskell's model is similar to the two para meter models DELTA examined. In the near-field the details of how the stress changes in time from a0 to 01 is of extreme importance. In the far-field it is of much less importance and as the seismic moment is generally computed form the far-field displacement spectrum or from field measurements by M

SDp For the high frequency content (here say >1 Hz) the details of process are very important, and infact great care must be taken to talk about the same parameter. I feel that considerable confusion exists on this point.

The 1940 Imperial Valley earthquake can be used to illustrate this confusion, e.g., Kanamori and Anderson (1975) estimate Aa for the 1940 Imperial Valley earthquake to be less than 100 bars. Trifunac (1972) used Brune's model and the strong motion data recorded at El Centro to make estimates of Aa for the various events that comprised this complex earthquake. He found that for the different events that the stress drop varied from 140 to 340 bars. He also found the characteristic length of rupture involved for each of these events to be much smaller (about 2 to 6 km) than the total rupture length of about 50 km. In the near-field, I feel, that the Ao obtained from the fitting Brune's model to the Fourier Spectrum of the ground acceleration gives a measure of the "dynamic stress drop" which corresponds to the strength of the fault gouge material and is modeled by V0 in the DELTA model.

This is based on simplified rupture models which suggest that the high frequency radiation is controled by the initial slip velocity which is related to the strength of the rupturing material.

In Brune's model the sudden stress drop of Ae gives rise to a constant slip velocity V u = -

Static stress drop is 0 m not directly computed by the DELTA model but must be computed and in fact

-7 corresponds to those estimates of static stress drop obtained from the relation Aa w

Changing the seismic moment and either fixing the rise time or making the rise time smaller will eventually have impact on the high frequency part of the spectrum as illustrated by the results of the two parameter source model.

For these cases the average dislocation was kept constant and the rise time was adjusted by t

0 where V

• was the value found by trial and error to match the peak acceleration of the stations at El Centro and Parkfield.

For their standard model DELTA used tR ' -3 sec however for the two parameter model tR < 0.5 sec. The values of tR for the two parameter model do not appear to be reasonable (much too small). It takes these very short rise time to get the constant velocity ramp high enough to radiate sufficient high frequency to match the peak accelerations recorded.

However, such a model has too much low frequency radiation. I strongly feel that the three parameter model is much more realistic, and thus changes in the seismic moment or U would have little influence on the high frequency radiation for realistic values of these parameters.

The DELTA results also show that increasing the fault length has little influence on the near-field ground motion -- at least for fault ruptures greater than 20 km. I believe that this is true. Table I Cpage 9) gives estimates for L for a number of earthquakes via fitting Brune's model to the Fourier-Spectrum of the acceleration recorded at various sites.

From this Table we see that estimates of L -- even for large magnitude events -- are less than 10 km. It appears that for long ruptures that the width of the fault zone and/or regions of higher local strength govern the low frequency fall-off of the spectrum.

-8 DYNAMIC STRESS DROP The term "dynamic stress drop" has not been generally defined in the literature. The dynamic stress drop is a measure of the large stress concentrations at the crack tip. These stresses can be much larger than the static tectonic stress existing before the tip of the rupturing fault has reached a given point on the fault surface.

As noted above, in the DELTA model it corresponds to the parameter V 0.

As expected this parameter controls the spectral levels for all frequencies of interest as can be seen from Fig. 6-25. This is clearly.

a key parameter. Its value was established by matching the data recorded at Parkfield and El Centro. Both the Parkfield Station 8 and El Centro are about the right epicentral distance. For these two earthquakes DELTA found V0 800 cm/s gave the best fit. It is assumed by DELTA that the physical process modeled by V is appraximately the same for all larger earthquakes. It is not at all evident that this is the case.

Crack mechanics indicates that the maximum slip velocity is directly controlled by material strength; hence, if V0 is constant then the variation of strength along a fault must be small.

In that case one would expect that earthquakes occurring at the same location near a site would have about the same peak acceleration recorded at the site. If one examines the data from earthquake swarms and after shock sequences, this does not appear to be the case. These were small earthquakes hence a simple modeling appears reasonable. It would appear that we can expect considerable variation (a factor of 2 or 3) in V in 0

any given region. It would seem to me that this type of randomness could be easily incorporated in DELTA's model similar to the manner in which macro-incoherence is incorporated.

It could be argued that the DELTA model replaces the variation of strength along the fault with some averaged value that gives rise to the same smoothed response spectrum at the recording station. This might be an acceptable approach if it could be shown that the value of V0 arrived at was conservative -- or truly a constant and that local random variations of material strength did not have a significant impact on the ground motion.

It seems to me that one can very approximately assess the relative variation in value of V from the available set of strong motion data by

-9 fitting Brune's (1970) model to Fourier Spectrum of the ground acceleration.

My reasons for this were discussed earlier. Trifunac (1972) has done this for El Centro, Hartzell and Brune (1978) report on an earthquake recorded at Brawley in the Imperial Valley and I have examined several earthquakes in this manner. The results are given in Table I in terms of a consistent measure --

denoted here as stress drop.

TABLE I APPROXIMATE EARTHQUAKE EPICENTRAL DISTANCE L

Aa L/2 El Centro 1A 14 5.9-6.1 177 2.3 1B 15 6.0-6.1 188 1.5 1C 16 5.7-5.8 143 1.8 2

35 6.4-6.6 349 3.2 Parkfield 5-10 5.4 228 3.0 Brawley 6

4.3 636 0.2 San Francisco (1957) 15 5.2 104 1.6 Lytle Creek 14 5.4 240 1.6 Kern Co. (Taft) 45 7.2 590 6.0 In the Brune model the "stress-drop" was related to the peak velocity and maximum Fourier Spectral level.

The model is very simple and intuitive and thus it is difficult to compare directly with the much more complex DELTA model.

Although the relation between Aa and V0 is mostly intuitive we see from Table I that we would expect little difference in the para meter V0 if we only use Parkfield and El Centro to calibrate V.

We might have reached a different conclusion if the accelerometer was located at the other end of the fault near event 2. Here it is worthwhile to note that 0.8 g's were recorded about 5 km from the fault for the most recent October 15, 1979, earthquake in the Imperial Valley. Also, 0.64 g was recorded at approximately 11 km distance from a small M = 4.9 earthquake in the same environment during the Victoria, Baja California, Mexico 5 warm of March, 1978.

-10 Focusing of Seismic Energy The gross focusing in the sense that the rupture front prop agates towards the site with a rupture velocity nearly the same as the shear wave velocity is included in the DELTA model. It seems to me that a coherent model is not realistic; therefore, I agree that DELTA needed to include-randomness in their model.

The basic sources of randomness and how they included them in their model seems reasonable.

It is, however, very difficult to evaluate the reasonableness range of values assigned to each of the parameters. Comparison of Figs. 4-4, 4-5, 4-6 and 5-23 show that the randomness is of some importance. The use of the mean and mean +1 a values (Figs. 4-7, 4-8, 4-9) seem reasonable and a good way to handie this uncertainty. Fig. 5-23 shows removing all randomness does not alter the results shown on (Figs. 4-7 to 4-9). In conclusion it seems to me that the DELTA model adequately models the focusing of seismic energy for San Onofre..- If-the site was much closer to the fault (say within 1 km).then added investigation might be required.

GEOLOGIC MODELS AND Q The DELTA model is a visco-elastic model where damping is introduced by Q. The May 1978 report shows the choice in layering is i'mportant.

I have not reviewed DELTA's model relative to the geophysical data available to determine if their choice of layering/elastic constants are adequate.

The geologic models used for El Centro and Parkfield did not attempt to resolve the upper soil layers. However, these upper layers can have considerable influence on the ground motion. Conventional widsom would say that the soils at Station 2, Parkfield, and at El Centro would have behaved nonlinearly for both the Parkfield and El Centro earthquakes. How important this is in the overall problem is hard to say. It is partly "calibrated out" because the model parameters were adjusted relative to the linear analysis. One often gets higher amplification factors in a linear model as compared to a nonlinear model.

The soil at San Onofre might be a bit stiffer and stronger than at El Centro and Parkfield. If the nonlinear behavior were accounted for there might be better agree ment at Station 2 between the computed and measured data. Refinement of the upper layers of Parkfield and El Centro might also improve the

agreement between computed and calculated spectrum in the finer details.

All of this might have some small effect on the value of V chosen but all of it is lost in the uncertainty associated with all of the parameters of the model and in particular with the parameter V.

There are a few other parameter variations studied in the report, e.g.,

rupture velocity, depth of fault rupture zone, fault top.

All of these parameters have some influence on the results which is within the variations introduced by the other parameters. The rupture top, bottom and hypocentral depth studies reflect partly the variation of the particular parameter of interest and partly a variation in the incoherence parameters. To fully assess the significance of these parameters I feel that it would be neces sary to make a number of runs with different sets of incoherence and look at the means and the coefficients of variation.

It is very difficult to assess the values of Q used for the various layers and what impact different choices would have on the results. There is significant uncertainty in the measurements of Q. The key question is what is the implication of this uncertainty of Q on the spectral estimates given in DELTA's reports. DELTA argues -- not unreasonably -- that if a different set of Q's are used for the earth's structure then this would change their choice of V.

V0 was calibrated using data from stations about the same distance from the simulated rupture surface as the San Onofre site is from the postulated rupture surface. If Q is too small, then there will be less contribution from more distance points of the fault to the observed ground motion at the site. If the DELTA model included a variation of V0 along the length of the fault in some random manner, then this could be a serious problem. The various micro and marco randomness.make some elements more efficient generators of ground motion than other elements. The potential effect of this randomness is less important for the smaller Q's used. It is somewhat difficult to sort this out with the data provided in the DELTA's draft report, Response to Proposed Task 4. For example, it is not clear why the ratio of the

-12 response spectra (Fig. 3-15) is so much different than the.ratio of the Fourier Spectra (Fig. 3-3).

However, the general trend is that Q influences the high frequencies more than the lower frequencies.

This is of some importance because it appears from Fig. 5-9 of the May, 1978 report that the peak ground acceleration at the San Onofre site is associated primarily with about a 2 Hz wave with only some smaller amount of high frequency content. If this is the case, then changing Q would only have a small influence on the peak acceleration, but a much larger influence on the high frequency part of the spectrum.

Several factors must be kept in mind when assessing all of the above.

First, the accelerograph at El Centro was located in a rather large heavy concrete structure with a basemat of 60 x 80 ft. Secondly, the building contains a very massive piece of concrete inside the building which is tied to the floor slab Cof very heavy concretel and extends into the ground about two feet. Thus we might expect that some filtering of the high frequency content of the ground motion occurred. The original record of the May, 1940 event was of poor quality and the peaks were clipped. Thirdly, the Parkfield earthquake seemed not to have generated as much. high frequency ground motion as some earthquakes. Fig. 1 shows a spectra from the MLa 6 event recorded at Helena, MLr-6.4 recorded at Pacomia Dam, ML,5. 3 recorded at Golden Gate park and the Parkfield earthquake recorded at Tremblor all normalized to 1 g and each spectral frequency divided by the Regulatory Guide Spectral level at that frequency. Fig. 2 also provides some added conformation of the fact that some earthquakes generate much. more high frequency content than others. Fig. 2 shows the spectrum from an earthquake near Brawley in the Imperial Valley not from El Centro. The spectrum is scaled to 1 g and compared to R.G. 1.60 spectrum. The peak acceleration recorded was about 0.3 g. The point of this is to suggest that it is possible that the two earthquakes used for calibration lacked high frequency content -- the Parkfield earthquake because of say the source

-13 mechanism and El Centro earthquake because of the filtering effect of the accelerograph station. Neither of these factors are in the DELTA model. Because of these special conditions it is possible that even though the,Q used is indeed too small over damping the high frequency the spectral comparisons still looked good.

In a more general case we migh expect to see more high frequency content. This is a "very what if" type of arguement, but the upper 1.4 km at the San Onofre site cause considerable damping of the higher frequencies.

The fact that as Q is changed a different value of V would be used which in turn effects the high frequency end of the spectrum makes it very difficult to sort out the significance of the uncertainty in Q with out added calculations. DELTA's results show that the variations in Q are significant. Much of the data for Q is based on the use of complex models and, in my view, must be considered unreliable.

CONCLUSIONS The DELTA model is a significant advance on the state-of-the-art and gives considerable insight into the relation between the key source parameters of an earthquake and the seismic energy radiated from the earthquake. The modeling has not been applied to enough earthquakes to assess what reasonable ranges are for the key parameters of the model.

As pointed out above there is some question about the adequacy of the events chosen to calibrate the parameters of the model.

This coupled to the sensitivity to variations in the Q values used suggest that signif icant uncertainty must be associated with the calculated spectra for the San Onofre site.

These uncertainties are not all independent but are inter-related.

The model is conservative in that maximum focusing of seismic energy is included, but this focusing might be reduced somewhat by the values of Q chosen.

If the Parkfield and El Centro (-19401 events are higher dynamic stress drop earthquakes than average, or if all large earthquakes have the same stress drop then the model is also conservative.

-14 However, if the dynamic stress drops given in Table I (page 9) are reason able then Parkfield and the El Centro earthquakes had just average dynamic stress drops and hence the predictions are not conservative but only represent a "mean" prediction. My assessment is that the calculated spectra for San Onofre are closer to the mean. Considering all of the factors discussed in the report I would -- on judgment alone -- estimate that the mean +1 a spectra would be factor of two to three times larger for all frequencies of interest.

It seems to me that the data from the most recent earthquake in the Imperial Valley could have considerable impact on these assessments.

If DELTA's arguments are correct,then they should be able to reproduce the essential features (peak-acceleration, high frequency spectral content) of the recorded ground motion with the model they have of the Imperial Valley. This would go a long way towards showing that the model was conservative and reducing the uncertainty associated with-the calculations.

REFERENCES

1. Brune, J. N. (1970), "Tectonic Stress and the.Spectra of Seismic Shear Waves From Earthquakes", JGR, 75 pp 4997-5009.

2. Hartzell, S. H. and J. N. Brune (1977), "Source Parameters for the January, 1975 Brawley-Imperial Valley Earthquake 5 Warm", PAGEOPH, 115 pp 333-355.

3. Haskell, N. A. C1964), "Total Energy and Energy Spectral Density of Elastic Wave Radiation From Propagating Faults", BSSA, 54 pp 1811-1841.

4. Trifunac, M. D. (1972),

"Tectonic Stress and Source Mechanism of the Imperial Valley Eartbquake of 1940", BSSA, 62 pp 1283-1302.

e Helena O Tremblor A

A A Golden Gate

- Pacomia Dam A

10 A *

'I 0A 00 A

A a

O O

0 e

0 0A 00 0

0 0.5.

0.1 1

10 102 Frequency -

cps Fig. 1.

Linear-log comparison of the ratio of Helena, Tremnblor, and Golden Gate response spectra to Regulatory Guide 1.60 spectra.

.cnO A A o

0 0

A A

0.

U0 1

OA C,

0 UO CO A

.0 A

CO A Mean (Dalai)

SORG 160 0.1 1--

0.1 1

10 100 Frequency 'L cps FIG. 2.

Comparison of normalized acceleration spectrum for 5% damping for an earthquake at Brawley, ML 4.3, R 6.2 km peak accel. = 0.3 g to RG 1.60.