Earthquake Resist Design
Earthquake Resist Design CIVL 7119
University of Memphis
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CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker SECTION 1 ENGINEERING CHARACTERIZATION OF EARTHQUAKES 1 1 Introduction u This section presents information on and 39 39 39 39 39 of earthquakes The key references for this module are Bolt 1988 FEMA 2000 and Kramer 1996 The objective is to introduce the reader to gt Sources and effects of earthquakes gt Basic concepts and terminology gt Factors that in uence earthquake shaking at a site gt Characterization of earthquakes for structural engineers gt Attenuation relationships gt Seismic hazard analysis gt Generation of earthquake histories The following section in this module provides an overview of hazard characterization per the 2000 NEHRP Recommended Provisions FEMA 2000 so that the reader is familiar with the stateofpractice in the United States 12 Sources and Effects of Earthquakes Earthquakes are generated by natural and manmade sources including I Tectonic movement gt Plate boundaries eg San Andreas fault termed interplate earthquakes gt Mid continent eg New Madrid fault termed intraplate earthquakes gt Midocean ridge Volcanoes eg Mammoth Lakes Sierra Nevada mountain range California Reservoir induced Nuclear explosions eg Nevada Test Site Earthquakes can damage the built environment a number of ways including Module 02 Page 1 CIE 619 Earthquake Engineering and Structuml Dynamics 11 Instructor Andrew Whittaker o Earthquake shaking Fault rupture Liquefaction or soil failure Tsunami sea or seiche lake Flooding 0 Fire Some examples of earthquakeinduced damage are presented below Earthquake shaking Izmit Turkey 1999 Earthquake shaking Izmit Turkey 1999 Module 02 Page 2 CIE 619 Earth uake E ineeri and Structuml D namics 11 Instructor Andrew Whittaker Tsunami Alaska USA 1964 Flooding Izmit Turkey 1999 Fire Izmit Turkey 1999 Landslide Northridge USA 1994 Liquefaction Kobe Japan 1995 Module 02 Page 3 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker 13 Basic Concepts in Seismology 13 Elastic Rebound Theory The elastic rebound theory proposes that as two plates move relative to the other along a fault segment elastic strain energy develops in the rock along the plate boundaries and that rupture occurs once the shear stresses in the rock exceed the shear strength of the rock This is illustrated in the figure below from Bolt 1988 Because fault planes are generally highly fractured substantial strain energy can be stored before rupture If the shear strength of the plate boundary is known the length of the fault is known the rate at which the plates are moving relative to one another termed the slip rate is known the time required to build up sufficient strain energy to produce an earthquake and the probable magnitude of that earthquake can be estimated The illustration of Bolt is of a road running at right angles to the fault Immediately following construction of the road the line ADB is straight After time the line bends with the left side moving with respect to the right side with the deformation constrained to a relatively narrow width 10s to 100s of meters Once the strength threshold of the interface is reached the fault ruptures and each side of the fault rebounds that is point D moves to D1 on the lefthandside of the fault and D2 on the righthand side of the fault E E White line on road Fault Displaced white line VI Module 02 Page 4 CIE 619 F 39 39 F 39 39 and Structural Dynamics II lnstructor39 Andrew Whittaker The gure below shows the effect of fault rupture on a farm fence following the 1906 San Francisco earthquake 132 Faulting Following Bolt fault displacements can be classi ed into one of two types Strike slip and dip slip The gure below from Bolt illustrates strike slip and dipslip normal and reverse faulting Faulting is often a combination of strikeslip and dipslip 0 Strike slip gt Faulting that produces only horizontal displacements along the strike of the fault The direction from north of the line of the plane of the fault at the surface is termed the strike The arrows on the strikeslip fault below show leftlateral faulting To determine whether the fault is left lateral or right lateral imagine that you are standing on one side of the fault line looking across the fault If the offset on the other side of the fault line is from right to left the faulting is left lateral Viceversa for the other direction 0 Dip slip gt Faulting that produces vertical displacements along the strike of the fault I 90quot dip is vertical Module 02 Page 5 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker gt Two types of dipslip faults normal fault and reverse fault gt Normal fault when the rock on that side of the fault hanging over fracture the hanging wall plane slips downward gt Reverse fault when the hanging wall moves upwards over the footwall I A thrust fault is a special type of reverse fault in which the dip of the fault is small shallow Subduction zones eg Cascadia in the Paci c North West are the sites of many thrust earthquakes Additional information is presented in the gure at the bottom of the page Strikeslip fault Reverse fault Normal fault Faults can rupture over substantial lengths and generate large magnitude earthquakes Sample data are presented below for selected earthquakes The reader should complete the table Earthquake Magnitude Rupture Length miles Horizontal Offset ft 1857 Fort Tejon 49 1906 San Francisco 83 250 21 1960 Chile 95 600 1964 Alaska 92 1971 San Fernando 15 3 1999 Izmit 7 4 1999 ChiChi 76 Module 02 Page 6 CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker The bestknown fault in the United States is the San Andreas fault in California Information on the fault is available at a number of web sites including SCEC at httpwww srerdr srer 39 html and the USGS at httpearthguakeusgsgov Consider the image below from the USGS web site that shows the eXtent of the San Andreas fault This fault is composed of many segments or combinations o9f segments 14 by the count of USGS with various slip rates maXimum moment magnitudes and return shezpshakin 39 htm for details u periods See httpwwwconsr m Paci c plate sliding against North American plate Fault type is Length of 1200 km Fault zone width up to 1 km Part of plate motion is compressional gt Los Angeles basin Last major ruptures gt January 1857 Mojave segment gt April 1906 Northern segment Slip rate 20 to 35 mm per year Intervals between ruptures gt 140 years on Mojave segment Probable magnitudes MW 68 to 80 The distance from the site of a building or recording station to the fault or fault projection is described by a number of terms which are illustrated below All of these terms should be used with care Surface trace Site of fault S B A Epicenter S T C Surface trace of fault Module 02 Page 7 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker SA Epicentral distance SB Distance to fault trace SD Hypocentral distance or slant distance SC Distance to rupture 133 Factors In uencing Earthquake Shaking at a Site The key factors that in uence the characteristics of earthquake shaking at a site are 0 Seismicity 0 Source mechanism 0 Travel path source to site 0 Local soil conditions 0 Soilstructure interaction Seismicity gt Tectonic features Good site as or bad I Maximum magnitude function of fault length gt Recorded events I Frequency of occurrence characteristic earthquakes Source mechanism Surface trace of ault 0 Type of fault strikeslip normal reverse 0 Rupture process gt Continuous and regular or multiple and irregular series of dislocations Module 02 Page 8 CIE 619 Earthquake Engineering and Structural Dynamics II o Directivity effects Instructor Andrew Whittaker gt Consider the gure below from Singh 1985 which models the rupture as a series of point dislocations 0 1 2 3 4 5 and assume that the velocity of rupture vr is nearly as large as the shear wave velocity vs 2500 ftsec to 5000 ftsec for most rock Module 02 00 0Q U be N Compression of the wavefront in the direction of propagation I Large intensity short duration shaking in the forward azimuth direction I Modest intensity long duration shaking in the backward azimuth direction Omscnm Of PROPACAIION MM 19 0mm AWAV non moo W0 SUUANI39 IN ontoow Of mum Page 9 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker gt See the gure below from SomerVille et al 1997 that illustrates the differences in ground motion velocity histories in the forward and backward azimuth directions Data are from the 1992 Landers earthquake in Southern California forward directivity region Luceme I36 cmsec 345 r quot F l mpm 1 propaganon epicenter 39 Joshua Tree 1 43 cmsec T 34 L i quoti backward directivity region 0 Km 30 1225 f 20 sec 1 1 1 n 1 165 1 16 Module 02 Page 10 CIE 619 Earthquake Engineering and Structural Dynamics 11 Module 02 Instructor Andrew Whittaker See the gures below from SomerVille et al 1997 that further illustrates the differences in ground motion in the faultstrike normal and faultparallel directions Data are from the 1992 Landers earthquake 39139 Faultnormal doublesided velocity pulse small no permanent displacement 139 Faultparallel singlesided velocity pulse large permanent displacements 1 Differences in spectral displacements Strike Normal Strike Parallel 69962 Ma s 78389 cals 3 Acceleration 39 13604 M 7026 cms 7 Velocity J 18379cm r p quot Displacement lIOsecI 229 77 cm 1 150 I a I l r39 M73Landers 92 i R1l km Spectal Displacement cm 50 39 i 00 I 2 3 4 5 Period sec Strike Normal Strike Parallel Page 11 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Travel Path 0 Seismic wave propagation gt Body waves Module 02 I P waves compression waves generally not damaging a below from Kramer I S waves shear waves cause damage to structures b below from Kramer 1 SV waves in the vertical plane SH waves in the horizontal plane I Geologic materials stiffest in compression P waves travel faster than S waves and arrive rst at a site 1 P waves velocity 5 kmsec in hard rock 15 kmsec in water 1 S waves velocity 3 kmsec in hard rock 0 kmsec in water no shear stiffness Undisturbed medium Comptosslons I Rarefactions H gtI Wavelength Undisturbed medium H gtl Wavelength Surface waves I Result from interaction between the body waves and the surface and sur cial layers of the earth I Travel along the earths surface with amplitudes that decrease with depth I Can dominate peak ground motions at distances greater than about twice the crust thickness 50 to 80 kms from the epicenter 139 Important I Raleigh waves and Love waves Page 12 CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker I Sourcetosite travel gt As distance from source to site increases I Intensity of shaking is reduced attenuation I Duration of shaking increases I Predominant period of shaking increases Local Soil Effects I Soil acts like a dynamic oscillator and greatly affects the ground motions that a structure atop the soil column experiences Equivalent to M Rock AW Softer and deeper soils will have shorter longer predominant frequency content Rock PS a g Firm soil Soft soil Period seconds Module 02 Page 13 CE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Soil Structure Interaction Kinematic Effect gt Flexibility of the soil in uences the overall response of the soilstructure system gt Affects exible light buildings on soft soil sites Examples Inertial Effect gt Mass of the structure in uences the overall response of the soilstructure system gt Affects stiff heavy buildings on soft soil sites Examples 134 Characterizing Earthquake Size Using Engineering Parameters The size of an earthquake can be described in terms of intensity magnitude and energy release Each of these descriptors is introduced below Intens im Earthquake intensity is a qualitative and thus subjective descriptor of the size of the earthquake and serves to record the level of damage and the response ofpeople to the earthquake shaking I Oldest measure of earthquake size I Function of the distance from the epicenter or rupture plane I Intensity measures cannot be used for design The modified Mercalli scale MIII is widely used in Englishspeaking countries the scale ranges from I not felt to XII total damage Intermediate points include III felt by people and X major damage MIVII data are presented as isoseismal maps as shown below for the 1994 Northridge earthquake39 such maps show the distribution of damage following an earthquake Module 02 Page 14 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Other intensity scales are used in Japan JMA leII and Central and Eastern Europe MSK lzXII A comparison of the scales is presented in Kramer Section 29 Magnitude Instruments such as the seismograph and accelerometer have made it possible to accurately measure earthquake ground motions Several magnitude scales are used to report earthquakes but the best scale for scienti c and engineering purposes is the moment magnitude The commonly used scales are listed below Kramer provides much additional information M Richter Log of the pendulum displacement of a WoodAnderson seismometer L magnitude located 100 km from the epicenter Traditional measure of magnitude Based on the seismic moment M O and is a measure of the work done by M Moment the rupture MW 2 log10 MO l5 107 where M0 yAD and y is the magnitUde rupture strength of the material along the fault A is the rupture area and D is the average amount of slip M Surface wave Amplitude of Raleigh waves with a period of 20 seconds Used for distant S magnitude earthquakes gt1000 km M Body wave Based on the amplitude of the rst few cycles of P waves Used for deep b magnitude focus earthquakes Groundshaking characteristics do not proportionally increase with the total amount of energy released during an earthquake 0 Saturation Only moment magnitude does not saturate See the gure below from Kramer QTIlllll39lljlr I l 1 r Magnltudo 39 l x l 1 3 ru 2 391 l I l I l l 1 ll I l l l 2 3 4 5 6 7 8 9 10 WW Module 02 Page 15 CIE 619 E 39 39 E 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker Wells and Coppersmith 1994 proposed an equation to estimate the earthquake potential of a fault of a given length namely MW a blogSRL where SRL is the surface rupture length in kilometers and Fault type a b Strike slip 516 112 Normal 486 132 Reverse 500 122 All 508 116 Wells and Coppersmith also developed equations to relate magnitude and average displacement maXimum displacement rupture area and subsurface rupture length Energy The total seismic energy released during an earthquake is often estimated using the following equation that applies also to moment magnitude loglOE11815MS where E is measured in ergs o A unit increase in magnitude corresponds to a 101395 or 32fold increase in seismic energy 0 Energy release from a M7 event is 1000 times greater than that from a M5 event 135 Characterizing Earthquake Histories Using Engineering Parameters An earthquake history can be described using amplitude frequency content and duration Each of these descriptors is introduced below Much additional information is presented in Kramer Amplitude The most common measures of amplitude are 0 Peak ground acceleration PGA ZPA PHA PVA 0 Effective peak acceleration EPA Newmark and Hall 1982 ATC306 1978 Module 02 Page 16 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Spectral velocity 01 i 05 391 5 10 50 Period sec 0 Peak ground velocity PGV PHV PVV Effective peak velocity EPV Peak ground displacement PGD Frequency Content The frequency content of an earthquake history is often described using Fourier Spectra Power spectra and response spectra Details on the derivation of these spectra can be found in Kramer Fourier Spectra A periodic function for which an earthquake history with a tail of zeros is an approximation can be written as 00 xt 2 co 2 en s1nant Q n l where cn and n are the amplitude and phase angle respectively of the nth harmonic in the Fourier series The Fourier amplitude spectrum is a plot of en versus an and shows how the amplitude of the motion varies with frequency Module 02 Page 17 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker 8 Garey No 1 rock N O A O Fourier amplitude g sec 0 or m o h 01 a s on Gllroy No2 soil 39 Fourier amplitude 9 sec Narrow band implies a dominant frequency or period smooth sinusoidaltype motion Broad band rich broad frequency content 8 g Q g 5 2 g V Period The Fourier phase spectrum is a plot of n versus a n 0 Phase angles control the times at Which the peaks of harmonic motion occur Fourier phase spectrum in uences the variation of ground motion With time o No characteristic shapes from earthquake histories Module 02 Page 18 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Power Spectrum The power spectrum density PSD function is de ned by the following equation and is closely related to the Fourier amplitude spectrum Ga c a where T a is the duration of the ground motion The power spectrum is a plot of Ga versus a The PSD function is used to characterize an earthquake history as a random process The PSD by itself can describe a stationary random process that is a process whose statistical parameters do not change with time An earthquake history is not such a process because the intensity builds to a maXimum value remains constant for a period and then decreases from the maXimum value a nonstationary random process Response Spectrum Response spectra are widely used in earthquake engineering Procedures for calculating spectral quantities were discussed in CIE 519 and are not repeated here The response spectrum describes the maXimum response of a SDOF oscillator to a particular input motion as a function of frequency and damping ratio Consider the spectra below from two sites one rock and the other soil 0 What are the key differences Gilroy No1 rock Gllroy No 2 soil 8 1 39 sa 9 05 a 05 0 o 1 E 3 100 100 Squot 50 quot 8quot cmsec cmsec 0 o 1 3 20 r 20 6 10 Sc 10 an W cm 0 39 39 L 0 Z 39 i 0 1 2 3 O 1 2 3 Period Tsec Period Tsec Module 02 Page 19 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker Other descriptors that describe both amplitude and frequency content are used to describe earthquake histories Kramer provides much information on some of these descriptors including RMS acceleration Arias Intensity and Housner Intensity RMSAcceleration The RMS acceleration is given by T l d 2 F aw dt 10 d 0 where at is the acceleration history T d is the duration of the ground motion and 20 is the average intensity or meansquared acceleration Arias Intensity The Arias Intensity is closely related to the RMS acceleration and is de ned as 77 GO 2 I 7 a t dt 2g 1 Housner Intensity The Housner or responsespectrum intensity was proposed as a measure of the damage potential of an earthquake recognizing that most structures have a fundamental period in the range from 01 to 25 seconds 25 515 IPSVT dT 01 where PS Vis the pseudovelocity response spectrum 0 Why pseudovelocity Duration The duration of an earthquake history is somewhat dependent on the magnitude of the earthquake Consider the gure below from Kramer that shows accelerograms from siX earthquakes off the Paci c coast of MeXico The epicentral distance was the same for all siX earthquakes o What do you conclude Module 02 Page 20 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker M 31 Acceleration I 100 8 0 E 8 C 9 E 9 0 8 lt 0 10 20 30 40 50 Time sec Two de nitions of strongmotion duration are widely used in earthquake engineering Bracketed duration the time between the rst and last crossing of a threshold acceleration say 005 g the gure below provides some information on how this duration is calculated Proposed by Bolt Interval between the times when 5 and 95 of the total energy is recorded Proposed by Trifunac and Brady 0395 r a s is 2 First 33 exceedance 0359 c 1 g n Hquot in upquot A a E O l lidIt39d I lt 1 Last 1 0059 exceedance o5 L i 3 4 O 5 1O 15 29 25 30 35 40 Time sec 05 l i 7 5 b Acceleration 9 39 o 5 o is 20 is 30 35 40 Module 02 Page 21 CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor Andrew Whittaker 14 Attenuation Relationships 14 Introduction Attenuation relationships relate ground motion parameters to the magnitude of an earthquake and the distance away from the fault rupture Relationships have been established for many ground motion parameters including 0 Peak ground acceleration 0 Peak ground velocity 0 Peak ground displacement 0 Spectral quantities Attenuation relationships are developed by statistical evaluation of a large set of ground motion data 0 Relationships developed for different regions and fault types strikeslip versus subduction and interplate versus intraplate 0 Relationships only as good as the data set upon which they are based 0 The greater the size of the data set the more robust the relationship Abrahamson and Shedlock 1997 provide a most useful summary of key attenuation relationships Some of the relationships are listed in the table below that is based in part on the notes of Mahin 1999 Ranges Model Calculatedl Slie vanables Conditions 2 Tquot r M secs km W Western North America PHA PVA Rock M rm 0 Abrahamson and S11va 1997 Sah Sav Deep Soil F HW 05 100 48 Boore Joyner Fumal 1997 PHASah V mupper M rjbF 02 080 539539 30m 75 PHA PVA Hard rock M r 0 Campbell 1997 PHV PVV Soft rock m 04 100 49 5 Sah Sav Soil F D Module 02 Page 22 CIE619 39 39 F and Structural Dynamics II lnstructor39 Andrew Whittaker Ranges Model Calculatedl Slie vanables Conditions 2 Tquot r M secs km W Rock My rmpy 0 Sadigh et al 1997 PHA Sah Deep Soil F HW 04 100 48 PHA PHV Rock 0 y y y M Sadigh and Egan 1998 PHD Soil y rmp NA 100 4 8 Central and Eastern North America Atkinson amp Boore 1997 PHA Sah Rock My rhypo 02 495 Toro et al 1997 PHA Sah Rock My rjb 02 1100 58 Subduction Zones M S or Anderson 1997 PHA Rock M NA NA NA by rmp PHA PHV 10 7 7 M Atkinson amp Boore 1997 Sah Rock y rhypo 0 2 400 4 95 Rock My mpy 0 Youngs et al 1997 PHA Sah Soil F H 04 100 495 horizontal ground velocity PVV peak vertical ground velocity Sah horizontal spectral acceleration Sav vertical spectral acceleration 2r WP projection of the rupture rh yPO rupture zone M magnitude F fault type H hanging wall closest distance to the rupture surface rjb closest horizontal distance to the vertical hypocentral distance rim closest distance to the seismogenic PHA peak horizontal ground acceleration PHV peak vertical ground acceleration PHV peak A selected subset of these attenuation relationships is presented below Much additional information is presented in the literature Module 02 Page 23 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker 142 Western North America Shallow Crustal Earthquakes Abrahamson and Silva The ground motion estimation equation of Abrahamson and Silva is InSag f1Mrmp Ff3M HWf4Mrmp Sf5ggamck where Sag is the spectral acceleration in g M is the moment magnitude rmp is the closest distance to the rupture plane in km F is the fault type 1 for reverse 05 for reverseoblique and 0 otherwise H W is the dummy variable for hanging wall sites 1 for sites over the hanging wall and 0 otherwise and S is a dummy variable for the site class 0 for rock or shallow soil and l for deep soil The function f1Mrmp is the basic functional form of the attenuation for strikeslip events on rock sites The function f3M allows for a magnitude and period dependence of the styleoffaulting factor The function f4Mrm is used to model differences in the motion on the hanging wall and foot wall of dipping faults Nonlinear soil response is captured by f5ggamck Information on these functions and values for the coefficients are presented in the paper of Abrahamson and Silva Some information can be found at httpoverlordengbuffaloeduClassHomePagescie6l9LecturesAbrahamSilvaAttenpdf Boore Joyner and Fumal The ground motion estimation equation of Boore Joyner and Fumal is 2 VS InYb1b2M76b3M76 bSInrb Inf V where 7 I 2 2 r 7 rjb h and b1 b1 SS for str1ke slrp earthquakes ble for reverseslip earthquakes and b1 ALL otherwrse In the above equation Y is the ground motion parameter in g and the predictor variables are M is the moment magnitude rb is distance in km VS is the average shear wave velocity to 30 m and h is a ctitious depth that is determined by the regression The paper of Boore et al provides a table of values for the coefficients required to solve for Y Some information can be found at the class home page namely httnn erlnrd em hanzln Pd ClassHomePa es cie6l 9 m A quot ndf Recommended values for the average shear wave velocity are 1070 msec NEHRP B 520 msec NEHRP C 250 msec NEHRP D 620 msec rock and 310 msec soil Module 02 Page 24 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker 143 Central andEasterrt North America Toro Abrahamson and Schneider The ground motion estimation equation of Toro et al is LM InY C1C2M76C3M762 7C4InRM 705 7C4max1n100 07C6RM 82 8 where 712 2 RM7 ijC7 and Y is the spectral acceleration or peak ground acceleration M is either Moment magnitude or Richter magnitude and ij is the closest horizontal distance to the earthquake rupture km C1 through C7 are coef cients that are tabulated in Toro et al and 82 is the epistemic uncertainty uncertainty due to lack of knowledge and ea is the aleatoric uncertainty uncertainty due to variability The uncertainties are assumed to follow normal distributions with mean zero The paper of Toro et al provides a table of values for the coefficients required to solve for Y Some information can be found at the class home page namely htt overlorden buffaloeduClassHomePa escie619LecturesToroAtten df 144 7quot 139quot 39 of 39 n 1 39 quotI forRuptureDirectivily Rupture directivity causes spatial variations in the amplitude and duration of ground motions around faults Propagation of rupture towards a site produces larger amplitudes of shaking at periods longer than 06 second and shorter strongmotion durations than for average directivity conditions Somerville et al 1997 developed modi cations to the empirical attenuation relations of Abrahamson and Silva 1997 to account for these variations The study of Sommerville et al is summarized below Consider rst the gure to the right from 3 I Somerville that shows simulations of strike or M72quot Dis39me0 km 5 79ka faultnormal and strikeparallel motions Simulation directly above a M7 2 strikeslip earthquake it llquot and a comparison of their average horizontal I 39 Em pin 5 d M odd motions with the empirical model of 2 39 Average Abrahamson and Silva What are the key observations Average simulation versus average from the empirical model Spectral Acceleration g Fault normal versus average 0 Fault parallel versus average n l Module 02 Perio m A g CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Fault rupture directivity parameters 9 and X for strikeslip faults and and Y for dip slip faults and the region off the ends of a dipslip fault that are excluded from the model are shown below from the paper by Somerville Somerville considered three ground motion parameters 1 Amplitude factor bias in average horizontal response spectrum acceleration with respect to Abrahamson and Silva 1997 2 Duration factor bias in duration of acceleration with respect to Abrahamson and Silva 3 StrikenormaZAvemge amplitude ratio of strike normal to average directivity horizontal response spectrum acceleration Vertical Section Plan View Module 02 Strike Slip fault V hypocenter site ofmptmearea site I epicenter ltxl amp1 17 Page 26 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker Somerville et al set bounds on the range of applicability of the directivity model namely Parameter Description Range of Applicability 65 to 75 for 1 and 2 above M Moment magn1tude 60 to 75 for 3 above 0 to 50 km for 1 and 3 above rmp Rupture d1stance 0 to 20 km for 2 above X Length ratio for strikeslip faults 0 to 10 Y Width ratio for dipslip faults 0 to 10 6 Azimuth angle between fault plane and ray 0 to 90 degrees for 1 and 2 abOVe path to site for strikeSlip faults O to 45 degrees for 3 above Zenith angle between fault plane and ray 019 90 degrees for 1 and 2 abOVe path to site for dipSlip faults O to 45 degrees for 3 above 3 quotI The empirical model of Somerville that g 39 I x s 1 shows the spectral amplification factor parameter 1 above is shown below for 8 2 39 39 strikeslip and dipslip faults At a period 3 03975 of 2 seconds for a strikeslip fault the g 1 I 05 maximum directivity response is approx E 025 18 times the average response and the g 00 minimum directivity response is approx m 39 J u I u I 06 times the average response 0901 01 l 10 period sec These factors should be used as 39 multipliers to the spectral ordinates of Abrahamson and Silva 1997 to calculate H 3 r 1 quotI 91981 I 1 spectral ordinates for maximum average g I directivity L I g 2 a Somerville et al 1997 extended the E hawk presentation on directivity effects to Ea 039 further consider the ratio of strikenormal lt 1 05 to average directivity motions Two E 3335 equations relating strikenormal and g J l I A average directivity motions were 901 01 1 f Period sec Module 02 Page 27 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker developed one including magnitude and closest distance rmp but excluding consideration of the azimuth and zenith angles ignoring the location of the site With respect to the epicenter and one including magnitude closest distance and aXimuth and zenith angles Each formulation is presented below Magnitude and Closest Distance Dependence Period 800 61100081 0 Dist 0 Mam y 2 C1 C2 11109249 1 C3M 6 05 0 000 0 000 0 000 06 0048 0012 0000 Where y is the natural logarithm of the strike 5 07 0079 41019 0000 normal to average directivity ratio at a given 03975 039093 43902 039000 d h d k M h 08 0108 0026 0000 perio rmp 1st e rupture 1stance1n m 1st e 3 0124 4030 0000 moment magnitude and C1 through C3 are 10 0139 43033 0000 perioddependent coef cients Values for the 15 0192 0046 0000 coef cients are given in the table to the right 30 0304 0075 0025 To calculate the str1kenormal spectral ord1nate 35 0331 41084 0045 multiply the average directivity ordinate from 40 0351 0096 50063 above by ey To calculate the strike parallel ord1nate d1v1de the average d1rect1v1ty ord1nate by 60 0375 4113 0106 ey Magnitude Closest Distance and Direction Dependence Madam CConst mum c0439 2CCI 1CM 6 y cos a 1 2 rmp 3 H 05 0000 00000 0000 06 0027 00069 0000 Where 5 is 6 for strikeslip and for dip slip and 07 0050 00127 7 0000 all other terms are de ned above Values for the 39 39 03975 0061 40155 O39ooo 08 0070 00178 0000 coef c1ents are given in the table to the right 0 9 0 088 o 0220 0 000 1 0 0104 00255 0000 To calculate the strikenormal spectral ordinate 15 0154 40490 0034 multiply the average directivity ordinate from above 20 0207 00613 0059 by ey To calculate the strike parallel ordinate 2395 0280 390390816 mm 30 0353 01007 0093 d1v1de the average d1rect1v1ty ord1nate by ey 35 0415 411172 0106 40 0456 01282 01 1 8 45 0462 01307 0128 50 0450 01269 0137 60 0424 01223 0152 Module 02 Page 28 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker 15 Seismic Hazard Analysis 15 Introduction Seismic hazard analysis takes one of two forms Deterministic Seismic Hazard Analysis DSHA and Probabilistic Seismic Hazard Analysis PSHA Each type of analysis is described below Much additional information is provided in Kramer 1996 152 Deterministic Seismic Hazard Analysis DSHA DSHA preceded PSHA as the prevalent form of hazard assessment for maXimum worst case earthquake shaking It involves development of a seismic scenario and characterization of that scenario Kramer describes DHSA as a simple fourstep process as enumerated and depicted below The schematic is from Kramer Source 1 Source 3 Site M1 0 M3 Source 2 i STEP 1 STEP 2 A C 8 gt Y1 0 Controlling S g Ma earthquake Y Y2 5 M1 9 3 39 93quot Lquot F72 51 Distance STEP 4 STEP 3 l Identi and characterize geometry and potential MW all earthquake sources capable of generating signi cant shaking at the site See the gure below in which three sources are shown surrounding the site 2 Calculate the sourcetasite distance for each source identi ed in step 1 Distance measures can include epicentral distance and hypocentral distance depending on the distance measure adopted in the predictive attenuation relationship Step 2 in the gure below illustrates the calculation Module 02 Page 29 CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker 3 Select the controlling earthquake that is the earthquake that generates the greatest shaking effect typically acceleration at the site using attenuation relationships Step 3 of the gure illustrates the process for the three sources and distances The controlling earthquake is described in terms of its magnitude and distance from the site eg M W 7 at 10 km 4 De ne the hazard at the site by the controlling earthquake spectral ordinates maXimum ground acceleration maXimum ground velocity maXimum ground displacement Positive features of DHSA I Simple to apply I Often conservative where the tectonic features are well de ned line sources I San Andreas fault Hayward fault I Maximum earthquake assumed to occur at point on fault closest to the site Negative features of DHSA I Dif cult to apply to distributed sources close to the site gt What distance to use gt How about distributed sources far from the site Does not treat uncertainty well gt Incorporate rudimentary statistics into the calculation by taking one standard deviation above the mean at every step in the process magnitude PGA etc I Produces a big and perhaps unrealistic answer No information on the likelihood of the controlling earthquake No information on the level of shaking that might be experienced in the lifespan of the structure at the site Module 02 Page 30 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker One example of DHSA that is developed in Kramer is shown below to illustrate the process The site shown in Figure E42 is located in the vicinity of three independent seismic sources represented by source zones 1 2 and 3 Using a deterministic seismic hazard analysis compute the peak acceleration Mum 50 20 78 10078 Source 3 O 0 60 Source 1 MW 77 0 0 Mmax 73 D 2018 10018 Site 5075 15 A r Figure 3342 Solution Taking the site as the center of a local x y coordinate system the coordinates of the source zone boundaries in kilometers are given in parentheses Source zone 1 is a Illkm long linear source zone that can produce a maximum magnitude of 73 at any point along its length Source zone 2 is an areal source zone of 4800 km2 capable of generating a magnitude 77 earthquake anywhere within its boundaries Source zone 3 is a point source that can produce a maximum magnitude of 50 Following the fourstep procedure described earlier 1 The problem statement provides the location and maximum magnitude of each source zone In real DSHAs this is often an extremely complex and difficult task 2 The sourcetosite distance can be represented by the minimum between the site and any part of each source zone On that basis the distances are Distance R Source Zone km I 237 2 250 3 600 3 If the level of shaking is assumed to be adequately characterized by the peak horizontal acceleration an appropriate attenuation relationship can be used to select the controlling earthquake Using the relationship of Cornell et al 1979 developed with data from M 30 to 77 earthquakes at distances of 20 to 200 km in the western United States lnPHA gals 674 0859M 180111 R 25 Source Zone M R km PHA 1 73 237 0423 2 77 250 am 3 50 600 002g On this basis the source zone 2 event would be selected as the controlling earthquake Note Though currently out of date the Cornell et al relationship is used here because of its simplicity which will make a subsequent example on probabilistic seismic hazard analysis much easier to understand 4 The hazard would be taken as that which would result from a magnitude 77 earthquake occurring at a distance of 25 km This motion would produce a peak acceleration of 0573 other ground motion parameters could be obtained from the predictive relation ships described in Chapter 3 Module 02 Page 31 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker 153 Probabilistic Seismic Hazard Analysis PSHA PSHA recti es a number of the problems inherent in DSHA by quantifying uncertainty and the probability of earthquake occurrence As noted by Kramer PHSA follows similar steps to DSHA but uncertainty is quanti ed by a probability distribution at every step in the process Probability distributions are determined for the magnitude of each earthquake on each source fM m the location of the earthquake in or along each source fR r and the prediction of the response parameter of interest P pga gt pga39 The schematic is from Kramer mr Kramer describes PHSA as a fourstep process as enumerated and depicted below Source1 Sourcea A l E i 1 h quot 2 Site 0 g R R a a 39 1 t a 39 G I I39393 5 Source 2 7 H Magmtude x STEP 1 STEP 2 gt g A A o E 9 239quot 7 2 r g a 2 3 2 A L z o W 39 Distance R Parameter value y39 STEP 3 STEP 4 1 Identify and characterize geometry and potential MW all earthquake sources capable of generating signi cant shaking at the site See the gure above in which three sources are shown surrounding the site For each source develop the probability distribution of rupture locations within the source A uniform probability distribution is generally chosen which means that earthquakes are equally likely of occurring at any point along or in the source Combine these distributions with the source geometry to obtain the probability distribution of sourcetosite distance Contrast this with DSHA that assumes that the probability of occurrence is l at the points in each source zone closest to the site and 0 elsewhere 2 Develop a seismicity or temporal distribution of earthquake occurrence A recurrence relationship which speci es the average rate at which an earthquake of some size will be exceeded is used to characterize the seismicity of each source zone The recurrence relationship may accommodate the maXimum earthquake but is not limited to that earthquake as DSHA often doesj Module 02 Page 32 CIE 619 Earthquake Engineering and Structural Dynamics II Instructor Andrew Whittaker 3 The ground motion produced at the site by earthquakes of any possible size magnitude occurring at any possible point in each source zone must be determined with the use of predictive attenuation relationships The uncertainty inherent in the attenuation relationship is also considered explicitly in PSHA unlike DSHA 4 The uncertainties in earthquake location size and ground motion prediction are combined to obtain the probability that the ground motion parameter e g PHA spectral acceleration will be exceeded in a particular time period say 10 in 50 years A detailed treatment of PSHA is beyond the scope of this course Refer to Kramer for a detailed presentation on the subject 16 Design Earthquakes 16 1 Response Spectra and Earthquake Histories The presentations of the previous sections facilitate the determination of maximum earthquake ground motion characteristics acceleration velocity displacement and spectral response quantities Maximum ground motion characteristics are of interest but of little use to the earthquake engineer earthquake ground motion histories and spectra are needed for analysis of structures An elastic response spectrum presents the relationship between maximum responses of elastic single degreeoffreedom oscillators of differing frequencies to one earthquake history The shape of a single spectrum is often jagged and of little use in analysis and design Generalized smoothed spectra are needed Response spectra from recorded ground motions and design spectra are shown in the gures below from Chopra 2000 The generation and use of inelastic response spectra are presented in later modules in this class I 6 3 quot S I 0 13 n 439 V l e I 3 23 w 1968 2 1 fa Module 02 Page 33 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker The smoothed spectrum similar to what appears in codes of practice and design guidelines is often termed 0 Design spectrum 0 Target spectrum Earthquake groundmotion histories are often selected to match or t the elastic design target spectrum Such histories provide a full description of the earthquake motion 0 Amplitude 0 Frequency content 0 Duration Earthquake histories are used for analysis and evaluation but not design The number of histories to be used for analysis of a structure is somewhat codedependent but the number generally ranges between 0 Three maXimum of maXimum values of response used for checking 0 Seven average of maXimum values of response used for checking 162 Selection ofEarihquake History Records Ground motions proposed for the responsehistory analysis of a structure should be selected to adequately represent potential ground motions at the site Consideration should be given to magnitude source mechanism sourcetosite distance local soil conditions and directivity among others Archives such as httppeerberkeleyedusmcat can be searched online for historical records In many cases suf cient and appropriate historical records are unavailable and arti cial earthquake histories must be generated Module 02 Page 34 CIE 619 F 39 39 F 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker There are several methods or techniques for generating arti cial or synthetic earthquake histories including o Modifying eXisting records by gt Amplitude scaling gt Frequency scaling gt Addition of records 0 Time domain procedures gt Filtered White noise gt Wavelet addition by Abrahamson gt ARMA autoregressive moving average methods 0 Frequency domain procedures A discussion of these methods is beyond the scope of this course Module 02 Page 35 CIE 619 P 39 39 P 39 39 and Structural Dynamics II Instructor39 Andrew Whittaker SECTION 2 HAZARD CHARACTERIZATION PER THE 2000 NEHRP PROVISIONS 2 1 Introduction The 2000 NEHRP Recommended Provisions provides a simple strategy for estimating the maXimum and design earthquake hazard Standard spectral shapes and mapped values of spectral acceleration at 02 second and 10 second are used to characterize the elastic design response spectrum Summary details are presented below 22 General Procedure for Characterizing the Maximum Earthquake The general procedure for characterizing the maXimum earthquake is straightforward Maximum earthquake shaking is de ned for a uniform probability of exceedance of 2 in 50 years a return period of about 2500 years The maXimum earthquake is characterized rst for a rock site and then modi ed to account for local soil effects The rocksite characterization is based on spectral accelerations at 02 second S S and 10 second SI These accelerations are made available through maps prepared by the USGS The USGS web site httpgeohazardscrusgsgoveq contains the requisite information The maXimum earthquake spectral response accelerations for short periods S MS and at 1 second SMl adjusted for site effects are calculated as SMSFaSS and SMIES1 where site coef cients Fa and Fv are de ned in Tables 4124a and b respectively of 2000 NEHRP Values of these coefficients vary as a function of S S and S1 and soil type A through F 0 Why 0 Range of soil multipliers o Deterministic limit see Section 4132 23 General Procedure for Characterizing the Design Earthquake In past editions of the NEHRP Recommended Provisions the design earthquake was characterized by a return period of 475 years This characterization has changed in the 2000 NEHRP Provisions wherein the design earthquake spectral ordinates are determined as follows unless a sitespeci c hazard analysis is undertaken as described in the previous section of this module In the 2000 NEHRP Provisions the design earthquake response accelerations are determined as follows S SMSFaSS and S SM1FvSl DS 15 15 D1 15 15 The gure on page 38 shows the shape of the design earthquake spectrum Module 02 Page 36 CIE 619 Earth auake Engineering and Structural Dynamics H Instructor Andrew Whittaker USGSNational Seismic Hazard Mapping Project Page 1 of1 7quotquot a bit fora myme r SEIRM39IC burgh Drsrrtw NIAPS A Gridded Values s Hazard by Zip Code IBC mags Hazard by LatLon IRC mags Deaggregations 2 quot mermwe De re amquot Fromm 391 Nru Uncertainties V I l I Y HAMRD Mm Info forthe Layman Genera Information Current Earthquake Info Na on What39s New CalifomiaNevada W P e G l 1 CennaiEastem Us LEWquot amji Mailing List Alaska in GET I ERAI Additional Maps Anon mous FTP GIS data Publications Orders Publication Orders Intemtive Maps Software 7 Damage Photos a M91 Related Links e D ocumentation quota c ogs Seismicity Rates Rnquot ED 5 Fault parameters Earth uake Hazards Pro ram i Earthquake Information Center Geologic Hazards Ground Motion MIC HAZARD MAPPING PRf ECT GOLDEN CILORJampJG 7x Geological Survey allure of the 75 De mm a the Interior URL thMgeahaaudxmnuxgxgaveqindexJ ml Emai w v Laleadx newly Jammy 22 m 1738 P I l Maintained Izy Nmuy Hickman mth cumin tsunami USGS P vm smmmi uncutmm mm iAccexxibm39 39 939 i v 7 401 This page is madman g httpgeohazardscrusgsgoveq 262002 Page 37 Module 02