How Reliable are the Ground Motion Prediction Equations?

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1 20th Iteratioal Coferece o Structural Mechaics i Reactor Techology (SMiRT 20) Espoo, Filad, August 9-4, 2009 SMiRT 20-Divisio IV, Paper 662 How Reliable are the Groud Motio Predictio Equatios? Iztok Peruš a ad Peter Fajfar a a Faculty of Civil ad Geodetic Egieerig, Uiversity of Ljubljaa, Jamova 2, Sloveia, iperus@ikpir.fgg.ui-lj.si; pfajfar@ikpir.fgg.ui-lj.si Keywords: groud motio predictio, peak groud acceleratio, atteuatio, NGA project, CAE method, GMPE. ABSTRACT Recetly, several ew groud motio predictio equatios (GMPEs) have bee developed i USA (NGA project) ad elsewhere. Ufortuately, the predictios obtaied by differet models still differ cosiderably, eve if a commo database was used, as i the case of the NGA models. I this paper, a o-parametric approach (CAE method) has bee used i order to obtai some iformatio about the ifluece of differet databases ad differet fuctioal forms o the predictios. The results suggest that the predictios deped substatially o the selectio of the effective database ad o the adopted fuctioal form. Both decisios rely to some extet o judgemet. The iflueces of both subjective decisios are especially importat at short distaces from the source. The regioal differeces seem to be of the same or eve smaller magitude tha the differeces observed betwee differet models proposed for the same regio, at least at short ad moderate distaces. Aftershocks i the database geerally decrease the media values ad icrease the scatter. 2 INTRODUCTION Groud motio predictio equatios (GMPEs) are used for the estimatio of the groud motio parameters which are eeded for the desig ad evaluatio of importat structures, icludig uclear power plats (NPPs). The seismic hazard may cotribute greatly to the total risk of a NPP, therefore the selectio of appropriate GMPEs may have a substatial ifluece o the desig ad safety evaluatio. Recetly, five differet groups of US researchers developed ew groud motio models (AS Abrahamso, Silva, 2008; BA Boore, Atkiso, 2008; CB Campbell, Bozorgia, 2008; CY Chiou, Yougs, 2008; ad I Idriss, 2008) withi the NGA project (Earthquake Spectra, 2008). These models represet a sigificat advacemet i the state-of-the-art i empirical groud-motio modelig. Nevertheless, i spite of startig from the same database, usig advaced techiques ad accoutig for additioal effects, quite large differeces (from the egieerig poit of view) of the media values obtaied by differet models ca be observed. New GMPEs have bee proposed also i other parts of the world. Douglas (2008) is keepig track of the developmets worldwide. Recetly, there have bee idicatios that the models developed by usig regioal data ca be trasferred to aother regio. Stafford et al. (2008) made comparisos of recet Europea (AB Akkar, Bommer, 2007) ad NGA models. Their results idicate that, for most egieerig applicatios, the NGA models may cofidetly be applied withi Europe. A similar coclusio was made by Campbell ad Bozorgia (2006). Douglas (2007) cocluded that it is curretly more defesible to use wellcostraied models, possibly based o data from other regios, rather tha use predicted motios from local, ofte poorly costraied, models. The importace of the adopted fuctioal form, especially for the hazard at low aual probabilities importat for uclear power plats, was recetly show by Musso (2009). He demostrated that some GMPEs may yield results, which are clearly ot i accordace with commosese, if applied for probabilistic hazard purposes. For such applicatios, the stadard deviatio related to differet models is also extremely importat. The mai objective of this paper is to predict the groud motio parameters by a o-parametric empirical approach, called the CAE (Coditioal Average Estimator) method (Peruš et al. 2006), which does ot take ito accout ay a priori iformatio about the pheomeo, ad to compare the results with the results of recet Europea ad NGA GMPEs. Usig this approach, the ifluece of differet databases, as Copyright 2009 by SMIRT 20

2 well the ifluece of the pre-determied fuctioal forms, used for the developmet of GMPEs, was ivestigated. The applicability of the NGA GMPEs for Europe is also discussed i the paper. The oparametric CAE method has bee already used by the authors for groud motio predictios (Fajfar ad Peruš, 997). I recet years the available groud motio databases have bee greatly expaded, ad especially withi the NGA project, also greatly improved, compared to those available oe decade ago. So, the reliability of the CAE predictios, which strogly depeds o the quality of the database, has substatially icreased. 3 CAE METHOD FOR GROUND MOTION PREDICTIONS The CAE method is used for the estimatio of ukow quatities (e.g. peak groud acceleratio PGA ad spectral acceleratios) as a fuctio of kow data of the earthquake (e.g. magitude M ad fault characteristics) ad of the local site (e.g. the distace measure ad soil coditios). The first ad the secod set of variables are called the output ad iput variables, respectively. I order to determie ukow output variables from kow iput variables, a database cotaiig sufficiet well-distributed ad reliable empirical data is eeded. The database should iclude both measured/processed values of output variables ad the correspodig iput variables. Oe particular observatio which is icluded i the database ca be described by a sample vector, which compoets are the iput ad output variables. For example, if durig a magitude M=7 strike-slip earthquake a peak groud acceleratio PGA=0.34 g was recorded at a distace R=9 km, the the sample vector ca be defied as {M, R, F; l PGA} = {7, 9, 0.5; l(0.34)}, where F=0.5 deotes the strike-slip earthquake. The database cosists of a fiite set of such sample vectors. Accordig to the CAE method, the ukow output variable is determied i such a way that the computed vector composed of give ad estimated data is most cosistet with the sample vectors i the database. The output variables ca be estimated by the formulae N! cˆ " A # c, k " k A a " N! i" a i ad a 2 $ b b % ( &' + D l, " D exp), $ %! 2 2- w # # wd * l" 2w... l where ĉk is the k-th output variable, c k is the same output variable correspodig to the -th vector i the database, N is the umber of vectors i the database, b l is the l-th iput variable of the -th vector i the database (e.g. M or R), b l is the l-th iput variable correspodig to the vector uder cosideratio, ad D is the umber of iput variables. The parameter w l is the width of Gaussia fuctio which is called the smoothess parameter (differet values of w l correspod to differet iput variables). It determies how fast the ifluece of data i the sample space decreases with icreasig distace from the poit whose coordiates are determied by the compoets (iput variables) of the vector uder cosideratio. The larger the value of w l is, the more slowly this ifluece decreases. Large w l values exhibit a averagig effect. I the specific case, discussed i this paper, the atural logarithm of peak groud acceleratio, l PGA, was used as the oly output variable. PGA was determied as the rotatio-idepedet measure of horizotal groud motio (GMRotI50, defied by Boore et al., 2006) i the NGA database, ad as the geometric mea i the Europea database. Several studies have show that the differece betwee these two measures is very small. I order to check the dispersio of the predictio, the so-called local stadard deviatio E ˆ. k is used, which defies the dispersio of the k-th output variable ĉ k determied by eq () N! " $ cˆ, c % Eˆ. " A (2) k k k 2 E.k ˆ is comparable with the error estimates of l Y i GMPEs. For egieerig applicatios, the ratio betwee the 84 th percetile ad media is more iformative, ad is therefore used i this paper for the presetatio of the dispersio of predictios. It should be oted that the results obtaied by the CAE method correspod to media values sice a logarithmic value (l PGA) is used as the output variable. l 2 () 2 Copyright 2009 by SMIRT 20

3 The results of the CAE method deped o the choice of the values of the smoothess parameters w l. For more details see (Peruš et al, 2006). I order to obtai reasoably smooth results, the w l values were determied by a trial ad error procedure. Costat w M ad w Vs30 values were used over the whole magitude ad V s30 rage (w M =0.4 ad w Vs30 =200 m/s, respectively). A costat value (w F =0.25) was used also for the style-of-faultig. I the case of the distace measure, w R liearly decreased from w R=0 =3 km to w R=00 =3 km. 4 INPUT PARAMETERS, SCENARIO AND DATABASES USED IN THE STUDY Almost all recet GMPEs use the momet magitude, distace, style-of-faultig ad local site coditios as iput parameters. Some GMPEs use also additioal iput parameters. I the CAE approach, it is easy to take ito accout ay iput parameter, provided that a adequate database exists. I order to eable comparisos with all NGA ad recet Europea GMPEs, oly four basic iput parameters were used i our study. Two differet distace measures are used i most recet GMPEs: the closest horizotal distace to the surface projectio of the rupture plae, R JB, ad the closest distace to the rupture plae, R RUP. The relatio betwee these two measures depeds o the geometry of the fault. I this study, a vertical strike-slip fault was assumed, for which the simplest coversio betwee the two distace measures applies. The same sceario was used also by Abrahamso et al. (2008) ad by Stafford et al. (2008). The relatio betwee R JB ad R RUP depeds o the depth to the top of the rupture. The media values of this parameter from the NGA database were used: 6 km for M=5, 3 km for M=6, ad km for M=7 (Abrahamso et al., 2008). I the CAE method, a o-dimesioal parameter defies the style-of-faultig. It is related to rake agle ad has values from F=0.0 (ormal fault) to F=.0 (reverse fault). For a strike-slip fault F=0.5 applies. Local site coditios are characterized by the average shear-wave velocity i the top 30 m, V S30. The results i this paper were obtaied for V S30 = 520 m/s ( stiff soil i the case of AB model). This velocity was selected cosiderig the distributio of data ad cosiderig the rage of shear-wave velocities correspodig to the stiff-soil i the AB model. Three NGA GMPEs iclude the soil/sedimet depth as a additioal iput parameter. AS ad CY models use Z.0 which represets the depth to V S =.0 km/s. The values Z.0 =0.034 km ad Z.0 =0.024 km were used for the AS ad CY model, respectively. The CB model icludes Z 2.5 which represets the depth to V S =2.5 km/s. The value Z 2.5 =0.64 km was used. The used values for the soil depth are take from Abrahamso et al. (2008) ad are based o the values recommeded by the origial authors. The commo database, used by NGA teams, cosists of 355 publically available multi-compoet records from 73 shallow crustal earthquakes, ragig i magitudes from 4.2 to 7.9. The five NGA teams used differet criteria for establishig their ow (effective) databases which served for the developmet of GMPEs. A key differece i the databases was the treatmet of aftershocks. The AS ad CY databases iclude aftershocks, resultig i a much larger umber of recordigs tha the BA ad CB databases. The Idriss database icludes aftershocks, but it oly icludes sites with 450 m/s<v S30 <900 m/s. The Europea AB database (532 records) is cosiderably smaller tha the databases used i NGA project. The classificatio of aftershocks is ambiguous. For example, the 999 Duzce earthquake (shear-slip, M=7.2), which is icluded both i the NGA ad i the Europea database, ca be classified as a aftershock or as a mai shock. This decisio is importat because iclusio of Duzce records i a database has a very substatial impact o the CAE predictio for a M=7 shear-slip earthquake. The databases used i the preseted study were recostructed based o the data available i the literature ad/or by help ad kid co-operatio of the origial authors. I additio to the Europea ad NGA databases, ew databases were formed i this study. The large database PF-L (3550 records) icludes all records, which are icluded i ay of the other bases, ad the small database PF-S (927 records) icludes those records which appear i all five NGA databases (if V S30 is i the rage 450 m/s<v S30 <900 m/s) or i four NGA databases (all five but Idriss, if V S30 is outside of the rage 450 m/s<v S30 <900 m/s). Moreover, a reduced AS (deoted as AS-M) ad a reduced CY (deoted as CY-M) databases were formed by elimiatig the aftershocks from the origial AS ad CY databases. I both cases, the Duzce records were cosidered as aftershocks (Abrahamso ad Silva, 2008). For illustratio, parts (R JB <50 km) of four databases are show i Fig. The records which are especially relevat for the results preseted i this paper (strike-slip fault, 360m/s< V s30 / 750m/s) are highlighted. 3 Copyright 2009 by SMIRT 20

4 Figure. Data distributio for the Europea (AB) ad three NGA databases. AS-M represets the AS database with elimiated aftershocks 5 RESULTS AND DISCUSSION I this sectio the results obtaied for five NGA ad for oe Europea GMPE, as well as the results of the CAE method obtaied with differet databases, are preseted ad compared. The earthquake sceario ad other iput data are described i Chapter 4. I the case of AS ad CY models, the equatio for mai shocks is cosidered. From the egieerig poit of view, oly strog groud motio is most importat. Therefore the results are preseted for the distace rage 50 km. Because of space limitatio, the results are preseted oly for peak groud acceleratio PGA for two magitudes (M=6 ad M=7). The liear scale was used, because the logarithmic scale, geerally used for the presetatio of GMPEs, visually dimiishes substatial differeces at short distaces from the source ad may be thus misleadig. 5. Compariso of GMPEs I Fig. 2, six GMPEs are compared. Note that all the NGA GMPEs apply to mai shocks, with the exceptio of the Idriss (I) model, which does ot distiguish betwee mai shocks ad aftershocks, like the Europea AB model. (It is iterestig to ote that the AS ad CY models made a distictio betwee mai shocks ad aftershocks at the very last stage of the NGA project.) The results are preseted for the distace measure R JB (The results for R RUP, which are ot preseted here, are very similar). A cosiderable differece betwee differet NGA GMPEs ca be observed. It is a result of differet subsets of the commo database which were used by differet developig teams, ad a result of differet adopted fuctioal forms. Both iflueces will be discussed i the cotiuatio. The Europea AB model is based o a differet database. It is importat to ote that the results of the AB model are mostly i the rage of the NGA results, ear to or at the lower ed. The aftershocks icluded i the AB database may cotribute to this fact. The fuctioal form of the BA model is quite differet from the form of all other models. Mai differeces betwee differet 4 Copyright 2009 by SMIRT 20

5 GMPEs (up to a factor of.5) appear at short distaces. Note that differeces up to a factor of 3 are reported i Abrahamso et al. (2008) for spectral values ad differet iput data. Figure 2. PGA as a fuctio of R jb distace for a vertical-strike slip earthquake 5.2 Ifluece of databases As explaied i Chapter 4, the GMPEs discussed i this paper are based o differet effective databases. I order to estimate the ifluece of differet databases, groud motio predictios were made by usig the same approach, i.e. the CAE method, for all databases (CY ad CY-M are ot show i Fig. 3 because the results are very similar to AS ad AS-M, CY-M is show i Fig. 4). Figure 3. Compariso of PGA as a fuctio of R jb distace for vertical-strike slip earthquakes, obtaied by CAE method for differet databases The results show i Fig. 3 suggest that a part of differeces betwee GMPEs show i Fig. 2 is due to differeces i databases. It ca be see that the iclusio of aftershocks dimiishes the media predictios for M=6 (compare AS with aftershocks with AS-M without aftershocks, a factor of about 2 ca be observed at 50 km distace). However, ot all differeces ca be attributed to aftershocks, but also to selectio of records from the commo database based o differet, mostly subjective criteria. The Europea AB database provides quite similar results as the NGA databases with aftershocks for M=6. For M=7, the differece is larger, maily due to lack of data i this magitude rage, which does ot allow a reliable CAE predictio. The lack of relevat data is especially critical at short distaces, where a aomaly i the CAE predictio ca be see. 5 Copyright 2009 by SMIRT 20

6 Figure 4. Compariso of PGA as a fuctio of R jb distace for vertical-strike slip earthquakes, obtaied by CAE method ad by GMPEs 5.3 Ifluece of the fuctioal form The ifluece of the adopted fuctioal form ca be estimated by comparig the GMPE results with the CAE results obtaied for the same database as used i the developmet of the specific GMPE. The fuctioal forms take ito accout, i additio to data, also some physical costraits ad ievitably iclude also some judgemet. The CAE results are based etirely o data, some judgemet is ivolved oly i the choice of the smoothig parameter. Comparisos are show i Fig. 4. For M=6 the results show, geerally, a reasoable agreemet for all models with some exceptio of the BA model. For M=7, the agreemet is very good i the 6 Copyright 2009 by SMIRT 20

7 case of the CB ad AS-M models. The other models provide estimates, which are ot etirely supported by data. The differeces are substatial especially at short distaces. The comparisos suggest that high PGA values at very short distaces predicted by some of the GMPEs i the case of larger magitudes may be based o the assumed fuctioal forms. I the case of AB model the CAE predictio at very short distaces are ot i accordace with commo sese due to the lack of relevat data. 5.4 Scatter The ratios of the 84 th ad the 50 th percetile (media value) of PGA as a fuctio of distace are show i Fig. 5. This ratio is used istead of stadard deviatio i l uits sice it is more practical i egieerig applicatios. The CAE results correspod to the media values show i Fig.3. The ratios defied i the GMPEs are also show. The CAE ratios deped o the distace ad magitude. They are somewhat smaller for M=7 tha for M=6. The results suggest that the ratio (scatter) is larger for databases with icluded aftershocks (compare the ratio for AS with icluded aftershocks with AS-M). The ratio is the largest for the Europea AB database ad the smallest is for the AS-M, CB ad PF-S databases. For the larger PF-L database the ratio is cosiderably larger tha for the smaller PF-S database. Figure 5. Compariso of the ratios of the 84 th ad the 50 th percetile (media value) of PGA as a fuctio of distace for vertical-strike slip earthquakes, obtaied by GMPEs ad CAE method. Dashed lies correspod to the values defied i GMPEs. 6 CONCLUSION The aim of this study was to explore how reliable are the groud motio predictio equatios. Five NGA models ad oe recet Europea model were aalysed ad compared with the results of the o-parametric CAE method which, i cotrast to the GMPEs, does ot take ito accout ay a priori assumptio about the pheomeo. There are two mai sources of the differeces betwee various GMPEs. The first oe is the adopted database ad the secod oe is the assumed fuctioal form of the GMPEs. Both rely to some extet o judgemet. The five NGA teams used differet subsets of the origial commo NGA database. The mai source of differeces is i the treatmet of aftershocks. Those models which iclude aftershocks, use larger databases ad geerally predict smaller media values of groud motio parameters. O the other had, the iclusio of aftershocks icreases the scatter. The choice of the fuctioal form has a importat ifluece o the estimated groud motio, especially at short distaces, where the data are scarce. The results of the study shows that all ivestigated models, with oe exceptio, are i a reasoable agreemet with data i the case of M=6. I the case of M=7, some model predictios are ot etirely supported by data. A very good correlatio ca be observed i the case of the CB ad AS-M models. The Europea AB model is based o a differet database. However, the media results by the AB model are mostly i the rage of the NGA results. 7 Copyright 2009 by SMIRT 20

8 For the ivestigated sceario, the differeces betwee the AB model ad the NGA models are similar to the differeces betwee the NGA models. For the ivestigated sceario, sigificat differeces betwee the predictios of differet GMPEs ca be observed. From the egieerig poit of view, a differece i a groud motio parameter of 50% represets a substatial differece i the seismic demad with importat cosequeces for desig of a structure ad structural compoets or for the safety of a existig structure. The fact, that the NGA models differ substatially i spite of startig from the same database, suggests that the available GMPEs, although greatly improved, are ot yet fully reliable, especially at short distaces from the fault. O the other had, the fact that the media results obtaied by Europea GMPE fall i the rage of the NGA predictios, suggests that the regioal differeces do ot play a major role, at least ot i the short ad moderate distace rage. As a cosequece, the use of worldwide data i a sigle database seems to be feasible (as suggested by Stafford et al. 2008). Such a database should ot iclude aftershocks, which geerally decrease the media values ad icrease the scatter. A problem with combied databases may be the icreased scatter, which ca exert the domiat ifluece o the probabilistic seismic hazard aalysis for importat structures like NPPs. The o-parametric CAE method proved to be a simple but powerful tool, especially for research. It eables quick predictios of groud motios with differet databases ad with differet iput parameters. It is easy to add to or remove data from the database ad to check the ifluece of additioal iput parameters. Due to a large umber of accelerographs istalled worldwide, the umber of records is icreasig rapidly ad the GMPEs may become out-of-dated i a short period of time. With icreasig umber of high quality data, the o-parametric approach will become more reliable ad more attractive also for practical applicatios. Ackowledgemets. The results preseted i this paper are based o the work supported by the Sloveia Research Agecy. The iformatio ad data provided by J. Bommer, Y. Bozorgia ad R..Yougs are gratefully ackowledged. REFERENCES Abrahamso, N. A. ad Silva, W. J Summary of the Abrahamso & Silva NGA Groud-Motio Relatios. Earthquake Spectra. Vol. 24:. P Abrahamso, N., Atkiso, G., Boore, D., Bozorgia, Y., Campbell, K., Chiou, B., Idriss, I.M., Silva, W. ad Yougs, R Comparisos of the NGA Groud-Motio Relatios. Earthquake Spectra. Vol. 24:. P Akkar, S. ad Bommer, J. J Predictio of elastic displacemet respose spectra i Europe ad the Middle East. Earthquake Egieerig ad Structural Dyamics. Vol. 36:0. P Boore, D. M., Watso-Lamprey, J. ad Abrahamso, N Orietatio-idepedet measures of groud motio, Bull. Seismol. Soc. Am. Vol. 96. P: Boore, D. M. ad Atkiso, G. M Groud-motio predictio equatios for the average horizotal compoet of PGA, PGV, ad 5%-damped PSA at spectral periods betwee 0.0 s ad 0.0 s. Earthquake Spectra. Vol. 24:. P Campbell, K. W. ad Bozorgia, Y Next geeratio atteuatio (NGA) empirical groud motio models: ca they be used i Europe? First Europea Coferece o Earthquake Egieerig ad Seismology, Geeva, Switzerlad. Paper No Campbell, K. W. ad Bozorgia, Y NGA Groud motio model for the geometric mea horizotal compoet of PGA, PGV, PGD ad 5% damped liear elastic respose spectra for periods ragig from 0.0 to 0 s. Earthquake Spectra. Vol. 24:. P Chiou, B. S.-J. ad Yougs, R. R A NGA model for the average horizotal compoet of peak groud motio ad respose spectra. Earthquake Spectra. Vol. 24:. P Douglas J. (2008). O the regioal depedece of earthquake respose spectra. ISET Joural of Earthquake Techology. Vol. 44:. P Douglas J. (2008). Further errata of ad additios to Groud motio estimatio equatios , BRGM/RP-5687-FR 8 Copyright 2009 by SMIRT 20

9 Earthquake Spectra Special Issue o the Next Geeratio Atteuatio Project. Vol. 24:. P Fajfar, P. ad Peruš, I A o-parametric approach to atteuatio relatios. Joural of earthquake egieerig JEE. Vol. :2. P Idriss, I. M A NGA empirical model for estimatig the horizotal spectral values geerated by shallow crustal earthquakes. Earthquake Spectra. Vol. 24:. P Musso, R.M.W Groud motio ad probabilistic hazard. Bulleti of Earthquake Egieerig. Early View. Peruš, I., Poljašek, K. ad Fajfar, P Flexural deformatio capacity of rectagular RC colums determied by the CAE method. Earthquake Egieerig ad Structural Dyamics. Vol. 35. P Stafford, P.J., Strasser, F.O. ad Bommer, J.J A evaluatio of the applicability of the NGA models to groud-motio predictio i the Euro-Mediterraea regio. Bulleti of Earthquake Egieerig. Vol. 6. P Copyright 2009 by SMIRT 20