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Probabilistic Seismic Hazard Maps in Dam FoundationbyHideaki Kawasaki1, Masafumi Kondo2, Akira Nakamura3, Kenji Inagaki4great impact on the site and either theoreticallyor empirically evaluating earthquake motioncaused by the hypothetical earthquake. Thebenefit of this method is that it evaluatesearthquake motion in a clear visible form of atime history wave form or response spectrum,but it lacks the general applicability needed toset hypothetical earthquakes.A probabilistic method on the other hand is amethod of evaluating the anticipated recurrencevalue of earthquake motion strength based onprobability according to statistical data ofdisastrous earthquakes. A merit of this method isthat it evaluates risk as anticipated recurrencevalue of earthquake motion that shouldessentially be treated as a risk, but it is difficultto present its results in clear visible form.ABSTRACTBecause Japan is one of the world’s mostearthquake prone countries, improving seismicresistance to guarantee safety and a sense ofsecurity is an important challenge.The Kobe Earthquake disaster in 1995 severelydamaged many infrastructures and buildings. Inresponse to this disaster, advanced research onseismic design methods, seismic diagnosis, andseismic strengthening has been carried out toreduce earthquake damage. It is difficult tocompletely prevent earthquake disasters,however in earthquake-prone Japan, earthquakedamage prediction and disaster preventionmeasures are implemented widely. In case ofdams also, it is quite important to evaluate thestrength of predicted earthquake motion, andimplement the suitable seismic design andseismic diagnosis.This paper describes the preparation of seismichazard maps in dam foundations, consideringearthquake records and earthquakes that occurcyclically on active faults and at plateboundaries, to establish a efficient method ofpredicting the earthquake motion necessary tothe seismic design of dams.This report proposes a probabilistic statisticalmethod to estimate the earthquake motionaccounting for scattering caused by theearthquake frequency and distance attenuation,for the solid rock foundation in dam sites.Further, in order to predict earthquake motionthroughout Japan, this report shows thedistribution of the earthquake motion strengthbased on earthquake prediction models.KEYWORDS: Dam Foundation, ProbabilisticSeismic Hazard Maps, Seismic Design2. PREPARATION OF AN EARTHQUAKECATALOG AND FAULT PARAMETERS1. INTRODUCTIONAn earthquake catalog and fault parameters arethe base of seismic information.Especially, an earthquake catalog model usespast earthquake data without modification.To perform seismic design or seismic diagnosis,it is very important to evaluate the earthquakehazard predicted for a dam site in order topredict earthquake damage and propose disasterprevention measures. There are two methods ofevaluating the seismic hazard: babilistic methods (earthquake hazardanalysis).A deterministic method is a method ofhypothesizing the earthquake that will have a1 Head, Water Management and Dam Division, RiverDepartment, National Institute for Land and InfrastructureManagement, Ministry of Land, Infrastructure andTransport, Tsukuba-shi, Ibaraki 305-8040, Japankawasaki-h84y6@nilim.go.jp2 Senior Researcher, dittokondou-m2cf@nilim.go.jp3 Former Director, River Department, ditto41Former Researcher, ditto

2.1 Seismic sources dataSeismic sources data are based on the UzuCatalog from 1885 to 1922, and onMeteorological Agency data from 1923 until2002. Earthquakes with magnitude of 5.0 ormore, and earthquakes with epicentral depth of200km or less are selected.Further, based on the assumption that anearthquake occurs independently, fore shocksand after shocks of major earthquakes, andearthquake swarms other than the largest one areexcluded from the catalog data. Figure 1 showsthe epicenter distribution of a total of 5,236catalog earthquakes judged to be independent.The seismic source zone model hypothesizesseismic source zones based on past earthquakedata and active fault data to model earthquakeactivity [1].The Seismic source zones are classified asfollows. Seismic source zone: Case where it is possibleto almost specify the location of earthquakesthat occur in an active fault zone or ofearthquakes such as large earthquakes that haveoccurred cyclically in the same part of a plateboundary (fault plane). Background zones: Case other than the abovewhere, even when an earthquake can bepredicted to occur within a certain range, it isdifficult to clearly specify the location inadvance. Hypocentral type: Classified into three typesbased on the category of earthquake (shallowcrustal earthquake, intra-plate earthquake, deepintra-slab earthquake).Figure 3 to Figure 6 shows examples of theclassification of seismic source zonedistributions.Because the properties of earthquakes differaccording to their type, catalog earthquakes areclassified in three types (shallow crustal,inter-plate, and deep intra-slab). An epicenter ofan inter-plate type is located in the ocean and thefocus depth is usually less than 60km. A shallowcrustal type is an earthquake that occurs in ashallow crustal dislocation. A deep intra-slabtype means what occurs in the depths, usually60km or more, although an epicenter is locatedin inland.2.2 Seismic fault parametersAs for large scale earthquakes, the widening of afault plane is considered. Therefore, faultparameters are organized for 74 earthquakes forwhich a fault model had been set based on pastearthquakes. Figure 2 shows the distribution offault planes used for the study. As in the case ofpoint epicenters, these seismic faults areclassified into three types (shallow crustal,inter-plate, and deep intra-slab).The BPT seismic source zone model is a modelusing the BPT distribution to evaluate theprobability of a large earthquake occurring fromthe present time in addition to the seismic sourcezone model.4. DISTANCE ATTENUATION FORMULATo estimate the scale of earthquake motion, weset three seismic prediction models (earthquakecatalog model, seismic source zone model, andBPT seismic source zone model).*BPT: Brownian Passage TimeTo calculate seismic motions in every meshpoint from every seismic source in Japan, thedistance attenuation formula [2] set based onearthquake observation records in foundations ofdams is adopted. There are two types of distanceattenuation formula. One is the shortest distanceequation and another is the equivalenthypocentral distance equation. The form of thedistance attenuation formula using the shortestdistance can be written as:The earthquake catalog model is model thathypothesizes that past earthquake activity duringa specified period that are provided in theearthquake catalog occur cyclically.log SA(T ) Cm (T ) M Ch (T ) Hc Cd (T ) log (R 0.334 exp (0.653 M )) Co (T )(1)3. SEISMIC PREDICTION MODELS2

Where: T is the period, SA(T) is the horizontal2-component average response spectrum, M isthe Japan Meteorological Agency magnitude, atHC H (100km), HC 100 (100km H 200km),H is the depth at the center of the fault plane,and R is the shortest distance to the fault plane.earthquake set by the fault model, the distance R(shortest distance or equivalent hypocentraldistance) is evaluated accounting for theexpanse of the fault plane, while the earthquakefor which the fault plane has not been set, thedistance from the point epicenter is evaluated.The equation using the equivalent hypocentraldistance can be written as:Similarly, in the case of the seismic source zonemodel, the hazard curve is calculated by theEq.(4) in considering the earthquake motionstrength for each mesh caused by the entirehypothesized earthquakes for each seismicsource zone.log SA(T ) Cm(T )M Ch(T ) Hc Cd (T ) Xeq log Xeq Co(T )(2)p[ A a] 1 Where: Xeq is the equivalent hypocentraldistance, and the others represent the samevalues as in the shortest distance case.5. CALCULATIONCURVEOFTHE exp ν k P[ A a M , H , R ]P[ R M , H ]P[ H M ]P[ M ]dMdHdR k (4)HAZARDWhere k is the seismic source zone, vk is thefrequency that earthquakes occur in the seismicsource zone k, and P[A α M,H,R] is theprobability that the earthquake strength willexceed a when an earthquake of magnitude Mhas occurred at hypocentral depth H at distanceR, P[M] is the probability that an earthquake ofmagnitude M will occur, P[H M] is theconditional probability that the hypocentraldepth will be H in a case where earthquake withmagnitude M has occurred, and P[R M,H] is theconditional probability that the distance will beR in a case where an earthquake with magnitudeM has occurred at hypocentral depth H.The evaluation points were set by dividing Japaninto 1,289 meshes in mesh units that are squareswith sides of 20km by 20km and the earthquakehazard was calculated for each mesh.The earthquake hazard curve is calculated usingthe seismic prediction model and the distanceattenuation equation.Using the earthquake catalog model, the hazardcurve for every earthquake in the catalog iscalculated by the Eq.(3). The occurrencefrequency for each earthquake was assumed tobe 1/T (T is the period of the data set).In the seismic source zone model, the averageoccurrence frequency over the long term wasused as the earthquake occurrence frequency toobtain the annual exceedence probabilityhypothesizing the Poison’s process. p[ A a ] 1 exp ν k P[A a M , H , R ] k (3)6. CALCULATION RESULTSWhere, k is the earthquake, vk is the number ofearthquakes k that occurs each year (if theperiod of the earthquake catalog is T it is 1/T),P[A α M,H,R] is the probability that theearthquake motion strength will exceed a in acase where earthquake k with magnitude M hasoccurred at epicenter depth H and distance R.The probability is calculated consideringscattering of the estimation equation to be alogarithmic normal distribution. For theAs examples of the earthquake hazard map,Figures 7 to 9 show the distribution of peakground acceleration (PGA) for the return periodof 100 years based on each predictive model.Figure 10 shows a PGA distribution map for thereturn period of 200 years based on theearthquake catalog model, and Figure 11compares the maps obtained by each model.3

5. There is almost no difference betweendistribution of predicted PGA with return periodof 100 years based on a model that considersBPT and a model that does not consider BPT.This is presumably a result of the fact that theinterval of shallow crustal earthquakes on activefaults ranges from several thousands of years toseveral tens of thousands of years: periods thathave little impact over a period of 100 years.7. CONCLUSIONSThis report has obtained the followingconclusions.1. A method of preparing the earthquake hazardmaps useful to set input earthquake motion isproposed.2. The PGA distribution shows that in allseismic prediction models, the hazard on thePacific Coast of Japan tends to be relatively highand the hazard on the Japan Sea Coast tends tobe relatively low.3. The PGA based on the seismic source zonemodel tends to be lower in Hokkaido and higherin other regions than the earthquake catalogmodel.4. Differences in return period have a largeeffect particularly on the accelerationdistribution on the Pacific Coast. This ispresumably a result of the fact that theinter-plate earthquakes with shorter interval thanshallow crustal earthquake on active faults occurmainly on the Pacific side.8. REFERENCES1. Annaka, T., and Yashiro, H.: TemporalDependence of Seismic Hazard in Japan, 12thWorldConferenceonEarthquakeEngineering, New Zealand, 2000.2. Matsumoto, N., Yoshida, H., Sasaki, T. andAnnaka, T.: Response Spectra of EarthquakeMotion at Dam Foundations, Proc.Twenty-first International Congress on LargeDams, 2003.Fig.1 Distribution of Earthquakes Judged to be Independent4

Fig.2 Distribution of Major Earthquake Occurrence Zones (74 planes)Fig.3 Fault Source Zones organized by Historical Earthquake Data (28 planes)5

Upper Planes of Pacific PlatePlanes of Eurasia and Okhotsk PlatePlanes of Philippine Sea PlateLower Planes of Pacific PlateFig.4 Background Seismic Source Zones along the Planes6

Shallow crustal typeInter-plate typeFig.5 Distribution of Seismic Source ZonesInter-plate typeDeep Intra-slab typeFig.6 Distribution of Background Seismic Source Zones7

45.0N40.0NEquivalent hypocentraldistance equation35.0N35.0N40.0N45.0NShortest 0[gal]140.0E145.0E45.0NShortest distanceequationEquivalent hypocentraldistance equation35.0N35.0N40.0N40.0N45.0NFig.7 Distribution of Peak Ground Acceleration (PGA) with Return Period of 100 Years(Earthquake Catalog l]145.0EFig.8 Distribution of Peak Ground Acceleration (PGA) with Return Period of 100 Years(Seismic Source Zone Model)8

45.0N45.0NEquivalent hypocentraldistance equation35.0N35.0N40.0N40.0NShortest 0140.0E[gal]145.0E45.0NShortest distanceequationEquivalent hypocentraldistance equation35.0N35.0N40.0N40.0N45.0NFig.9 Distribution of Peak Ground Acceleration (PGA) Expected to Recur Once in the next 100 Years(BPT Seismic Source Zone l]145.0EFig.10 Distribution of Peak Ground Acceleration (PGA) with Return Period of 200 Years(Earthquake Catalog Model)9

101050100130.0E135.0E‑‑100‑ ‑50‑ ‑10‑ 10‑ 50‑ 100‑ 1540[gal]145.0E(b) BPT Seismic source zone model– Seismic source zone model40.0N45.0N(a) Earthquake catalog model– Seismic source zone model35.0NFig.11. Differences between PGA based onDifferent Models(Return Period of 100 .0E‑‑100‑ ‑50‑ ‑10‑ 10‑ 50‑ 100‑ 210[gal]145.0E(c) Earthquake catalog model– BPT Seismic source zone model10

the seismic design of dams. KEYWORDS: Dam Foundation, Probabilistic Seismic Hazard Maps, Seismic Design 1. INTRODUCTION To perform seismic design or seismic diagnosis, it is very important to evaluate the earthquake hazard predicted for a dam site in order to predict earthquake damage and propose disaster prevention measures. There are two .

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