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SEISMIC HAZARD ANALYSISInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 1This topic addresses deterministic and probabilistic seismic hazard analysis,ground motion attenuation relationships, the U.S. Geological Survey (USGS)seismic hazard maps, the NEHRP Recommended Provisions seismic designmaps, site effects, directionality effects, and the NEHRP RecommendedProvisions response spectrum.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 1

Seismic Hazard Analysis Deterministic procedures Probabilistic procedures USGS hazard maps 2003 NEHRP Provisions design maps Site amplification NEHRP Provisions response spectrum UBC response spectrumInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 2Before pursuing this topic, study the topics that address earthquakemechanics and effects and the dynamics of single-degree-of-freedomsystems. Note that the principal references for the topic are Reiter (1990)and Kramer (1996).Although this topic is lengthy (and might not be of great interest to structuralengineers), it is necessary to proceed through the material to learn wherethe USGS seismic hazard maps come from because the NEHRPRecommended Provisions maps use the USGS maps as a “starting point.”IFEMA 451B Topic 5a NotesSeismic Hazard Analysis 2

Hazard vs RiskSeismic hazard analysisdescribes the potential for dangerous,earthquake-related natural phenomenasuch as ground shaking, fault rupture,or soil liquefaction.Seismic risk analysisassesses the probability of occurrence of losses(human, social, economic) associated withthe seismic hazards.Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 3The purpose of this slide is to clarify the differences between the terms“hazard” and “risk.” The terms are often used interchangeably, and shouldnot be. In this topic we address the hazard and do not talk about risk(except in the most general sense).For example, a hazard associated with earthquakes is ground shaking. Therisk is structural collapse and, possibly, loss of life.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 3

Approaches to Seismic Hazard AnalysisDeterministic“The earthquake hazard for the site is a peak groundacceleration of 0.35g resulting from an earthquakeof magnitude 6.0 on the Balcones Fault at a distance of12 miles from the site. ”Probabilistic“The earthquake hazard for the site is a peak groundacceleration of 0.28g with a 2 percent probability of beingexceeded in a 50-year period.”Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 4There are two basic approaches to seismic hazard analysis. Both use thesame basic body of information to determine what the “design earthquake”should be. The main difference is that the probabilistic approachsystematically examines the uncertainties and includes the likelihood of anactual earthquake exceeding the design ground motion. All of the elementsof a deterministic analysis are included in the probabilistic approach.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 4

Probabilistic Seismic Hazard AnalysisFirst addressed in 1968 by C. Allin Cornell in“Engineering Seismic Risk Analysis,” and articlein the Bulletin of the Seismological Society(Vol. 58, No. 5, October).Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 5This is the reference that first described probabilistic seismic hazardanalysis. It is not easy reading, particularly if one is not familiar withengineering probability. Cornell still teaches at Stanford.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 5

Steps in Deterministic Seismic Hazard Analysis(2) Controlling Earthquake(1) SourcesSiteF1BalconesFaultFixed distance RFixed magnitude MAreaSource(3) Ground MotionPeak AccelerationMagnitude MDistance(4) Hazard at Site“The earthquake hazard forthe site is a peak groundacceleration of 0.35 gresulting from an earthquakeof magnitude 6.0 on theBalcones Fault at a distanceof 12 miles from the site. ”Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 6These are the basic steps in the deterministic analysis. The first step is toidentify all the possible sources of ground motion. Some of these will beeasy to identify (e.g., a known active fault); others may be more difficult todescribe. Next, the controlling earthquake needs to be defined and thisinvolves engineering judgment. Do you want to design for the largestearthquake that could ever occur at the site (using perhaps an estimate ofseismic moment) or only the largest motion that has occurred, say, within thepast 200 years. Note that nothing is being said about probability ofoccurrence. As the known earthquakes will have occurred at a distance thatis not likely to be the same as the distance to the site, some correctionneeds to be made. This is done through the use of attenuation relationshipsthat have been established. In deterministic analysis, it is traditional to usethe closest distance from a source to a site. It is very important to useattenuation relationships that are characteristic to the local geology. Theresulting hazard statement is basically a scenario.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 6

Source rceSeismotectonicprovinceInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 7This slide introduces the source types. Faults were already been discussedin the topic on earthquake mechanics and effects. The other two sourcetypes are defined on the next slide.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 7

Source TypesLocalizing structure: An identifiable geologicalstructure that is assumed to generate or “localize”earthquakes. This is generally a concentration ofknown or unknown active faults.Seismotectonic province: A region where thereis a known seismic hazard but where there are noidentifiable active faults or localizing structures.Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 8Definitions of the more vague source types. The blind thrust Northridgeearthquake might be classified as being originated in a localizing structure.It is known from deep drilling that a network of such faults exists in the LosAngeles area. The New Madrid seismic zone may be classified as aseismotectonic province – that is, we know that earthquakes have occurredthere, but we are still unsure as to the source. While it may be relativelyeasy to establish magnitudes from known faults, the process is somewhatless exact when localizing structures and seismotectonic provinces areinvolved. This is particularly true when major earthquakes are infrequentand where there is not a strong instrument database.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 8

Maximum EarthquakeMaximum possible earthquake: An upper bound tosize (however unlikely) determined by earthquake processes (e.g.,maximum seismic moment).Maximum credible earthquake:The maximumreasonable earthquake size based on earthquake processes (butdoes not imply likely occurrence).Maximum historic earthquake:The maximum historicor instrumented earthquake that is often a lower bound onmaximum possible or maximum credible earthquake.Maximum considered earthquake:Describedlater.Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 9In order to establish the magnitude of the controlling earthquake, one needsto make a decision regarding the maximum earthquake. Listed here are afew possible choices in order of decreasing possible magnitude.The “maximum considered earthquake” (shown in gray) is used in theNEHRP Recommended Provisions and will be described in more detail laterin the topic. The maximum considered earthquake is more of a philosophythat it is a specific ground motion.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 9

Ground Motion ParameterGround Motion AttenuationMagnitude MReasons: Geometric spreading Absorption (damping)DistanceInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 10Attenuation has been described previously. In both deterministic andprobabilistic seismic hazard analysis (SHA), empirical attenuationrelationships are utilized. The seismologist must be careful to useattenuation relationships that are characteristic of the site. The groundmotion parameter may be anything that characterizes the shaking; peakground acceleration, spectral acceleration (at a specific period), and so on.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 10

Attenuation with DistanceInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 11Note the difference between site amplification and attenuation. These arequite different phenomena.The following two paragraphs are a paraphrase from Kramer (1996):Seismic wave attenuation can be considered of two major elements -geometric spreading and absorption (damping). Geometric spreading resultsfrom conservation of energy as waves and wave fronts occupy more area asthey spread from the seismic source. (Without absorption, waves would stillattenuate.)Absorption is controlled by loss mechanisms such as friction across cracks,internal friction, and inhomogeneities along the travel path.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 11

Comparison of Attenuation for Four EarthquakesInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 12This map shows isoseismal maps for several (nonconcurrent) earthquakes.The minimum modified Mercalli intensity (MMI) value shown on the maps isapproximately VI (boundaries of felt regions would be significantly greater).The extent of the isoseismal boundary VI is much greater in the easternUnited States than in the western states. This is because the crustal regionof the western United States, being located near a plate boundary, is muchmore internally fractured and is less homogenous than the relatively lessfractured eastern United States. A good analogy is a bell. An uncrackedbell will ring much more clearly and loudly than a cracked one.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 12

Ground Motion AttenuationSteps to Obtain Empirical Relationship1. Obtain catalog of appropriate ground motion records2. Correct for aftershocks, foreshocks3. Correct for consistent magnitude measure4. Fit data to empirical relationship of type:ln Yˆ ln b1 f1 ( M ) ln f 2 ( R ) ln f 3 ( M , R ) ln f 4 ( Pi ) ln εInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 13This is the basic form of an attenuation relationship. The equation is theresult of a regression analysis of several variables, as shown. Y overline issome parameter, such as peak ground acceleration, spectral acceleration, orsome other entity.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 13

Ground Motion AttenuationBasic Empirical Relationshipsln Yˆ ln b1 f1 ( M ) ln f 2 ( R ) ln f 3 ( M , R ) ln f 4 ( Pi ) ln εYˆ Ground motion parameter (e.g. PGA)b1 Scaling factorf1 ( M ) Function of magnitudef 2 ( R) Function of distancef 3 ( M , R) Function of magnitude and distancef 4 ( Pi ) Other variablesε Error termInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 14More detail on the “ingredients” in the regression analysis.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 14

Ground Motion AttenuationRelationships for Different Conditions Central and eastern United States Subduction zone earthquakes Shallow crustal earthquakes Near-source attenuation Extensional tectonic regions Many othersMay be developed for any desired quantity (PGA,PGV, spectral response).Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 15When performing a seismic hazard analysis, it is very important to useattenuation relationships that have been derived for the region of interest. Itwould be totally inappropriate to use a shallow crustal relationship (SanAndreas) in a subduction zone (Alaska).FEMA 451B Topic 5a NotesSeismic Hazard Analysis 15

Ground Motion AttenuationRelationshipsSeismological Research LettersVolume 68, Number 1January/February, 1997Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 16This is a edition of the Seismological Research Letters that contains writeups and coefficients for a variety of attenuation relationships. (Note that amembership in the Seismological Society of America can be had for anadditional 50 over the cost of an EERI membership. The main benefit tothe membership in SSA is a subscription to Letters.)Note that “new generation attenuations” (NGAs) have been developed overthe past year (or two) at the PEER center. The NGAs will be thepredominant relations used for the next issue of the USGS hazard maps, atleast for the regions where they apply.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 16

Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 17This is partial listing of the earthquake catalog used to determine theattenuation relationships for shallow crustal earthquakes.Note the range in magnitudes (recall differences in energy release), differenttypes of fault, and distance to epicenter. In some cases, several recordsfrom the same earthquake were used.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 17

Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 18This is a plot of moment magnitude vs distance for all earthquakes in thecatalog. There does not seem to be a strong trend (looks like a shotgunblast).FEMA 451B Topic 5a NotesSeismic Hazard Analysis 18

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 19When the catalog is separated into magnitude ranges and when a plot iscreated of a ground motion parameter (PGA here) vs distance for eachmagnitude range, patterns begin to emerge. The regression analysisproduces the lines shown on the plots. The lines then form the empiricalattenuation relationship used in the SHA.Note that as one gets to higher magnitudes (lower series of plots), thereseems to be a clearer trend in the data.It is important to emphasize the tremendous scatter in the data. Forexample, in the vicinity of 20 km, the difference between the high and lowvalues is about one order of magnitude. This aspect of deterministic analysisdoesn’t get enough discussion – even if we know the magnitude and locationof an earthquake, we are in the dark as to the amplitude of the groundmotion.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 19

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)ln( y ) C1 C2 M C3 (8.5 M ) C4 ln(rrup exp(C5 C6 M )) C7 (rrup 0.0000.0000.0000.0000.0000.0000.0000.000Table for Magnitude 6.5Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 20Once the regression analysis has been performed, the empirical attenuationrelationship is obtained from the published coefficients. Note that (asidefrom the C coefficients), the data plugged into the equation are magnitudeand distance. Hence, a single curve is obtained for a given magnitude.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 20

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)Peak Ground Acceleration, G1Magnitude0.1456780.010.0011101001000Distance, KMInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 21These curves were created in Excel by plotting the data on the previouspage for a range of magnitudes. In this case, the parameter beingdetermined at a given distance and magnitude is PGA.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 21

Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)1.0 Second Acceleration0.2 Second Acceleration10Magnitude1456780.10.010.0011.0 Sec. Spectral Acceleration, G0.2 Sec. Spectral Acceleration, G10Magnitude1456780.10.010.00111010010001Distance, KMInstructional Material Complementing FEMA 451, Design Examples101001000Distance, KMSeismic Hazard Analysis 5a - 22These curves are similar to those in the previous slide except that the itemsof interest are the 0.2 second and 1.0 second spectral acceleration.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 22

Example Deterministic Analysis (Kramer)Source 3Source 2D3D2Source 1D1SiteSource M1237.37.75.0DPGA(km) (g)23.7 0.4225.0 0.5760.0 0.02Maximum on sourceClosest distanceFrom attenuation relationshipInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 23This is a very simple example of a deterministic SHA. Three sources wereconsidered. In each case, the closest distance to the site was used. Notethe different magnitudes for the different sources. These will be consistentwith the selected “maximum earthquake.” The PGA at the site wasobtained from an appropriate attenuation relationship. The motion with thegreatest resulting PGA is chosen as the controlling earthquake. Note thatthis is NOT ENOUGH to establish risk because the effect of the motion onthe structure under consideration is not addressed. It could be that the moredistant earthquake with its lower effective PGA produces waves at afrequency that is more in sync with the structure.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 23

Steps in Probabilistic Seismic Hazard AnalysisSiteF1BalconesFaultAreaSourceLog # Quakes M(2) Recurrence(1) SourcesMagnitude M(4) Probability of ExceedanceUncertaintyM1M3DistanceM2Probability of ExceedancePeak Acceleration(3) Ground MotionInstructional Material Complementing FEMA 451, Design ExamplesGround Motion ParameterSeismic Hazard Analysis 5a - 24In a probabilistic analysis, the recurrence relationship (e.g., frequency ofearthquakes above a certain magnitude) is introduced as is the uncertaintyin each step of the process. Each of the uncertainties are included in aprobabilistic analysis, and the result is a seismic hazard curve that relatesthe design motion parameter to the probability of exceedance. Hence, if adesigner wished to design a dam for the ground motion that had only a 2%probability of being exceeded in a 50 year period, the ground motionparameter (e.g., PGA) would be taken from the seismic hazard curve.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 24

λmEmpirical Gutenberg-RichterRecurrence Relationship1000log λm a bmMean Annual Rate of Exceedance100λm1010.1 mean rate ofrecurrence(events/year)1 / λm 0.01return period0.0010.00010246Magnitude810a and b to be determined from dataInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 25The relationship between magnitude and likelihood of occurrence is called a“recurrence relationship.” The relationships are determined for regressionanalysis of historic ground motions.In the original Gutenberg Richter relation, the vertical axis was the number ofoccurrences per unit of time per unit of area. The linear relation (log scale)works well for large areas but it does not necessarily work so well for smallareas or single sources.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 25

Bounded vs UnboundedRecurrence RelationshipMean Annual Rate of 00010.000010.0000010246810MagnitudeInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 26The bounded relationship corrects for the fact that faults are capable ofgenerating earthquakes of a maximum magnitude.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 26

Uncertainties Included inProbabilistic AnalysisAttenuation lawsRecurrence relationshipDistance to siteNS NM NRλ y* vi P[Y y * m j , rk ] P[ M m j ] P[ R rk ]i 1 j 1 k 1Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 27This is the basic probability equation. Keep in mind the components and theparticular uncertainties that are involved.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 27

Example Probabilistic Analysis (Kramer)Source 3Source 2D3D2 ?D1 ?Source 1Source 3SiteM3 ?A3 ?Source 1SiteSource 2M2 ?A2 ?M1 ?A1 ?Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 28This slide emphasizes the uncertainties incorporated in probabilistic seismichazard analysis. They include distance to site (all possible distances areincluded), magnitude, and attenuation. Deterministic SHA uses the closestdistance, one particular definition of maximum earthquake (and itsassociated magnitude), and one set of attenuation relationships (tied to thegiven magnitude).FEMA 451B Topic 5a NotesSeismic Hazard Analysis 28

Result of Probabilistic Hazard AnalysisSource 1SiteSource 2Mean Annual Rate of ExceedanceSource 3SEISMIC HAZARD CURVE10-110-010-1All Source Zones10-210-3Source 210-410-5Source 1Source 310-610-710-80.00.20.40.60.8Peak Horizontal Acceleration (g)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 29The result of the probabilistic seismic hazard analysis is the seismic hazardcurve. One of these curves (red line) is produced for each source, and thesum (blue line) is the seismic hazard curve for the site. Note that the verticalaxis gives the (desired) level of probability, and the horizontal axis is someground motion parameter such as peak ground acceleration. The desiredparameter could also be a 5% damped spectral acceleration at T 1second.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 29

Relationship Between Return Period, Period of Interest,and Probability of ExceedanceReturn period -T/ln(1-P(Z z))10000R e turn Pe riod (y e 00Period of Interest (years)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 30This slide illustrates the relationship between return period, period ofinterest, and probability of exceedance. A 2% probability of being exceededin 50 years has a return period of 2475 years. A 10 percent probability ofexceedance in 50 years has a 474-year return period. For building design, a50-year base line is used as this is estimated as the service life of a typicalbuilding. For structures such as dams, a longer return period may be moreappropriate as the required service life might be much longer. While returnperiod stands alone, the probability of exceedance must be tied to a periodof interest. For example, an earthquake with a 2% probability of beingexceeded in 100 years has a return period of –100/ln(1-.02) 4950 years.]Note that the precision of knowledge of the phenomenon is such that thereturn periods should be rounded so that the number of significant digits isnot out of whack with the initial criteria – thus, the computation of 2475 yearsshould be rounded to 2500 years for most purposes.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 30

Acceleration, g10% probability in 50 yearsReturn period 475 yearsRate of exceedance 1/475 0.00210.80.610% in 50 yearelastic responsespectrumMean Annual Rate of ExceedanceUse of PGA Seismic Hazard CurveSEISMIC HAZARD 20.40.60.8Peak Horizontal Acceleration (g)0.4PGA 0.33g0.20.00.51.01.5Period, T (sec)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 31If a series of seismic hazard curves is developed for a range of differentparameters (e.g., PGA, 1 sec spectral acceleration, 0.2 sec spectralacceleration) and values are extracted for a certain constant probability (saya 10% in 50 year probability of exceedance), then a design responsespectrum may be created by plotting the parameter magnitudes vs period.The plot at the lower left shows the first point on such a spectrum -- in thiscase, the PGA with a 10% probability of being exceeded.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 31

Mean Annual Rate of ExceedanceUse of 0.2 Sec. Seismic Hazard CurveAcceleration, g10% probability in 50 yearsReturn period 475 yearsrate of exceedance 1/475 0.00210.80.610% in 50 yearElastic ResponseSpectrumSEISMIC HAZARD 20.40.60.80.2 Sec Spectral Acceleration (g)0.4PGA 0.55g0.20.00.51.01.5Period, T (sec)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 32A point representing the 0.2 second (5% damped) spectral ordinate with a10% probability of being exceeded in 50 years is plotted on the responsespectrum.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 32

10% in 50 Year ElasticResponse Spectrum0.8Acceleration, g0.60.40.20.00.51.01.5Period, T (sec)Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 33If the process is continued, the result is a complete response spectrum. It iscalled a uniform hazard spectrum (UHS) because each point on thespectrum has the same probability of being exceeded in the given period.These spectra could then be used in a response spectrum analysis of thestructure.Note that the information from the analysis may instead be used to assist inthe development of ground motion time histories. To do this, the groundmotion amplitudes (and possibly frequency content) is scaled such that thespectrum of the scaled ground motion closely matches the UHS. There issome danger in doing this, however, because the UHS is a composite ofhundreds if not thousands of earthquakes, any two of which are highlyunlikely to occur simultaneously.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 33

Uniform Hazard SpectrumResponseUniform hazard spectrumLarge distantearthquakeSmall nearbyearthquakePeriodInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 34This slide illustrates the previous point. It should be possible to generate arealistic earthquake ground motion that matches the small or largeearthquake. However, a generated earthquake that matches the UHS wouldbe unrealistic (and possibly too demanding).FEMA 451B Topic 5a NotesSeismic Hazard Analysis 34

Uniform Hazard SpectrumDeveloped from probabilistic analysisAll ordinates have equal probability of exceedanceRepresents contributions from small local,large distant earthquakesMay be overly conservative for modal responsespectrum analysisMay not be appropriate for artificial ground motiongenerationInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 35This is a summary of the previous points. Note that in certain regions of thewestern United States, the NEHRP Recommended Provisions spectrum isnot a true UHS because of the deterministic cap (discussed later). Thespectrum generated from the USGS maps is a true UHS.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 35

Probabilistic vs DeterministicSeismic Hazard Analysis“The deterministic approach provides a clear andtrackable method of computing seismic hazard whoseassumptions are easily discerned. It providesunderstandable scenarios that can be related to theproblem at hand.”“However, it has no way for accounting for uncertainty.Conclusions based on deterministic analysis can easilybe upset by the occurrence of new earthquakes.”Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 36Self explanatory. The quote is from Reiter.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 36

Probabilistic vs DeterministicSeismic Hazard Analysis“The probabilistic approach is capable of integratinga wide range of information and uncertainties intoa flexible framework.”“Unfortunately, its highly integrated framework canobscure those elements which drive the results, and itshighly quantitative nature can lead to false impressionsof accuracy.”Instructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 37Self explanatory. The quote is from Reiter.The best solution is often a mix of DSHA and PSHA. The DSHA may beused for the “maximum expected earthquake” and a PSHA used for themore frequent operational basis earthquake.The important thing to recognize is that the two methods are simply tools tobe used to assist in decision making. One method is not better than theother; rather, the methods are complimentary.FEMA 451B Topic 5a NotesSeismic Hazard Analysis 37

USGS Probabilistic Hazard Maps (Project 97)Spectral Response Acceleration (g)2.52.01.51.00.50.000.511.522.5Period (sec)2% in 50 yearsHAZARD MAP10% in 50 yearsRESPONSE SPECTRAInstructional Material Complementing FEMA 451, Design ExamplesSeismic Hazard Analysis 5a - 38The maps in the 1997, 2000, and 2003 NEHRP Recommended Provisionsare based on a set of probabilistic maps developed by Frankel, et al., of theUSGS. See the references for more details. Note that it is these maps thatare reflected in the IBC and ASCE 7.By using the maps it is possible to develop 5% damped response spe

seismic hazard maps, the NEHRP Recommended Provisions seismic design maps, site effects, directionality effects, and the NEHRP Recommended Provisions response spectrum. FEMA 451B Topic 5a Notes Seismic Hazard Analysis 2 Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 2

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