INTEGRATED DATA FLOW AND RISK AGGREGATION FOR CONSEQUENCE-BASED RISK MANAGEMENT OF SEISMIC REGIONAL LOSSES

Transcription

1 INTEGRATED DATA FLOW AND RISK AGGREGATION FOR CONSEQUENCE-BASED RISK MANAGEMENT OF SEISMIC REGIONAL LOSSES Joshua Steelman, Junho Song, and Jerome F. Hajjar A Report of the 1241 Newmark Cvl Engneerng Laboratory 205 North Mathews Avenue Unversty of Illnos at Urbana-Champagn Urbana, Illnos January 2007

2 ACKNOWLEDGEMENTS Ths research was supported by the, headquartered at the Unversty of Illnos at Urbana-Champagn, under NSF Grant No. EEC , and by the Unversty of Illnos at Urbana-Champagn. The authors would lke to thank the researchers throughout the MAE Center who have provded gudance and nformaton for ths research. In partcular, Mr. Ray Foltz s recognzed for hs contrbutons conductng extensve research nto avalable lfelne fragltes from varous lterature resources. 2

3 TABLE OF CONTENTS ACKNOWLEDGEMENTS 2 1. INTRODUCTION 6 2. Inventory database MAEVz Implementaton Prompt user to map nventory to fragltes mmedately after loadng nventory Buldng Stock Inventory Transportaton Lfelne Inventory Utlty Lfelne Inventory Modfy nventory databases to store perod for ndvdual tems after mappng to fragltes Buldng Stock Inventory Utlty Lfelne Inventory Partton total value of nventory tems nto component values Buldng Stock Inventory Utlty Lfelne Inventory Prompt user for level of buldng stock structure type uncertanty to consder Buldng Stock Transportaton Systems Utlty Systems Inventory Data HAZARD DEFINITION MAEVz Implementaton Wthn the Embayment, calculate hazard approprate to specfc nventory tems (user opton) Buldng Stock Hazard Transportaton Lfelne Hazard Utlty Lfelne Hazard Implement MAEC lquefacton hazard estmaton algorthm (Memphs) Implement typcal USGS CEUS attenuaton combnatons Implement typcal USGS WUS attenuaton combnatons Implement Toro and Slva sol amplfcaton factors Background Hazard Defnton Overvew Sesmc Source Defnton Ground Moton Attenuaton Attenuaton to Locatons Insde the Msssspp Embayment USGS Attenuaton to Locatons Insde the CEUS but Outsde the Msssspp Embayment Toro and Slva ste factors (84ºW to 96ºW, 36ºN to 40ºN) MAEC Attenuaton to Locatons Insde the CEUS but Outsde the Msssspp Embayment USGS Attenuaton to WUS Locatons Attenuaton to Locatons outsde the US 72 3

4 3.2.4 Implementaton of Scenaro-Based Ground Shakng Hazard Models Implementaton of Probablstc Ground Shakng Hazard Models Ground Falure Hazard (Lquefacton) Engneerng engnes (fraglty curves) MAEVz Implementaton Implement Parametrc Fragltes Propagate hazard uncertanty effects through evaluaton of vulnerablty Implement generalzed () nonstructural buldng fragltes Combne ground shakng and ground falure probabltes of damage Implement transportaton lfelne fragltes Implement utlty lfelne fragltes Background Buldng structures Buldng Structural Damage Buldng Nonstructural and Contents Damage Parametrc fraglty curves Transportaton systems Utlty Lfelne Fragltes Bured Ppelnes Water Tanks Tunnels Electrc System Combned Damage from Ground Shakng and Ground Falure Socal and economc LOSSES MAEVz Implementaton Implement Buldng Structural Damage Factors and Compute Loss of Structural Value Implement Damage Factors and Compute Losses of Buldng Nonstructural and Contents Implement Brdge Repar Factors and Calculate Expected Economc Loss for Brdges Implement utlty lfelne damage factors Adjust Loss Calculatons to Consder Inventory Uncertanty Scale losses to account for nflaton Aggregate Losses of Inventory wthn Study Regon Calculate Fscal Losses (Property Tax Revenue) Background Economc Loss for Buldng structures Buldng Structural Damage Buldng Nonstructural and Contents losses Socal Impacts NETWORK MODELING SYSTEM INTERDEPENDENCIES 160 4

5 8. Decson Support Conclusons 161 REFERENCES 162 APPENDIX A SUPPLEMENTARY INVENTORY INFORMATION 167 A Utlty Component Mappng Data 167 APPENDIX B SUPPLEMENTARY HAZARD INFORMATION 174 B Attenuaton to Locatons Insde the Msssspp Embayment 174 B Estmatng Probablty of Lquefacton-Induced Ground Falure 175 APPENDIX C SUPPLEMENTARY Fraglty INFORMATION 180 C4.2.1 Supplementary Fraglty Data 180 Appendx D drect economc loss example for buldngs Error! Bookmark not defned. 5

6 1. INTRODUCTION Ths report documents the ntegrated flow of data wthn the Consequence-based Rsk Management (CRM) framework establshed wthn the Md-Amerca Earthquake (MAE) Center for sesmc regonal loss assessment. Ths data flow s beng mplemented n MAEvz, the rsk management software of the MAE Center. The report also provdes an effcent framework for ncorporatng the uncertantes systematcally nto each key contrbuton to the loss assessment process. Supplementary documents to ths report provde detaled examples of the quanttatve data flow and assocated aggregaton of uncertanty. Ths report frst dentfes the algorthmc methodologes and nputs/outputs (I/O) used n the MAE Center research efforts on sesmc hazard, nventory, structural damage, and socal and economc losses, from source to socety. Ths helps dentfy possble ncompatbltes between I/O s and mssng nformaton, and enables gaps n the data threads to be dentfed. Ths report then provdes recommendatons for fllng of several of these dentfed gaps n the CRM data threads. Based on these results and the CRM framework encompassed wthn the MAE Center, ths report also suggests a method to systematcally ncorporate aleatory and epstemc uncertantes dentfed by MAE Center research efforts nto MAEvz. In the sectons that follow, the general flow of the document s ntended to frst outlne suggested modfcatons to MAEVz, accompaned by examples, then proceed nto a more detaled descrpton of the nformaton avalable for use n MAEVz. The examples focus on applcatons for the Memphs Testbed. 6

7 2. INVENTORY DATABASE 2.1 MAEVz Implementaton Inventory s the collectve group of enttes that are subject to a projected hazard n a partcular rsk assessment. Inventory s ncorporated nto MAEVz as pont-wse data for buldngs, brdges, and utlty facltes, and lne-type data for utlty ppelnes. The followng upgrades are recommended for MAEVz handlng of nventory: Prompt user to map nventory to fragltes mmedately after loadng nventory. o Buldng stock o Brdges o Components of electrc generaton facltes and substatons o Water tanks Modfy nventory databases to store perod for ndvdual tems after mappng to fragltes. o Buldng stock o Components of electrc generaton facltes Partton total value of nventory tems nto component values. o Buldng stock o Components of electrc generaton facltes and substatons Prompt user for level of buldng stock nventory uncertanty to consder. 7

8 2.1.1 Prompt user to map nventory to fragltes mmedately after loadng nventory Buldng Stock Inventory Algorthm Inputs: structure type, occupancy, number of stores, year bult from buldng stock nventory database. Parametrc fragltes by Jeong and Elnasha also requre sol type (Uplands or Lowlands), tme-hstory source/ste (7.5 Blythevlle/Memphs, 6.5 Marked Tree/Memphs, 5.5 Memphs/Memphs), hazard uncertanty ncluson (50 th and 84 th percentle), and hazard parameter (PGA, 0.2 sec Sa, or 1.0 sec Sa) nputs. Process: use Table C wth Inputs to assgn fragltes to ndvdual nventory tems. Prompt user to accept default mappng or modfy by creatng new mappng checks or changng exstng mappng checks. Outputs: modfed buldng stock nventory database wth each entty keyed to buldng fraglty database Example Three buldngs were selected at random from the avalable buldng stock nventory for Memphs and Shelby County, TN. The example wll use the followng three buldngs: Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Table Example Buldng Inventory Data Structural Occupancy Year Apprased Stores type Class Constructed Value ($) Lattude Longtude C1 Industral , N W URM Retal Trade , N W URM Industral , N W The data presented n Table s obtaned drectly from the nventory database. Fragltes can be mapped to the nventory tems usng ether the default mappng scheme provded n Table C or n accordance wth a user-specfed mappng scheme. For ths example, nventory tem I1 wll be evaluated usng fragltes developed by the MAE Center for evaluatng damage to gravty load desgned concrete frames (Concrete Frame, Bracc Gravty Desgned, Fraglty ID : SF_C1_10), and nventory tems I2 and I3 wll be evaluated usng MAE Center URM fragltes (Unrenforced Masonry, Wen and L, Fraglty ID : SF_URM_41). Note that the URM mappngs are not consstent wth the default mappng shown n Appendx C, as shown n Table , snce the example preceded the development of the mappng scheme. 8

9 Table Example Buldng Mappng Default Mapped Fraglty Default Fraglty ID Overrde Fraglty Overrde Fraglty ID Inventory 1 (I1) Concrete Frame Bracc Gravty Desgned SF_C1_10 Concrete Frame Bracc Gravty Desgned SF_C1_10 Inventory 2 (I2) Adapted Pre- URML SF_URM_1 Unrenforced Masonry Wen and L SF_URM_41 Inventory 3 (I3) Adapted Pre- URML SF_URM_1 Unrenforced Masonry Wen and L SF_URM_41 9

10 Transportaton Lfelne Inventory Algorthm Inputs: brdge structure type from brdge nventory database. Process: Prompt user to map fragltes for brdge structure types based on descrptons n Table Outputs: modfed brdge nventory database wth each entty keyed to brdge fraglty database Example Descrptons of brdge fragltes avalable from the MAE Center are shown n Table Table Avalable Brdge Fraglty Descrptons MAE Center Fraglty Descrpton Retrofts MSC_Concrete Mult-Span Contnuous Concrete Grder Brdge None MSC_Steel Mult-Span Contnuous Steel Grder Brdge None MSC_Slab Mult-Span Contnuous Concrete Slab None MSC_Conc Box Mult-Span Contnuous Concrete Box Grder None MSSS_Concrete Mult-Span Smply Supported Concrete Grder Brdge None MSSS_Steel Mult-Span Smply Supported Steel Grder Brdge None MSSS_Slab Mult-Span Smply Supported Concrete Slab None MSSS_Conc Box Mult-Span Smply Supported Concrete Box Grder None SS_Concrete Sngle-Span Concrete Grder Brdge None SS_Steel Sngle-Span Steel Grder Brdge None MSC_Concrete Mult-Span Contnuous Concrete Grder Brdge Elastomerc Bearng MSC_Steel Mult-Span Contnuous Steel Grder Brdge Elastomerc Bearng MSSS_Concrete Mult-Span Smply Supported Concrete Grder Brdge Elastomerc Bearng MSSS_Steel Mult-Span Smply Supported Steel Grder Brdge Elastomerc Bearng Other Other Elastomerc Bearng SS_Concrete Sngle-Span Concrete Grder Brdge Elastomerc Bearng SS_Steel Sngle-Span Steel Grder Brdge Elastomerc Bearng 10

11 MAE Center Fraglty Descrpton Retrofts MSC_Concrete Mult-Span Contnuous Concrete Grder Brdge Restraner Cables MSC_Steel Mult-Span Contnuous Steel Grder Brdge Restraner Cables MSSS_Concrete Mult-Span Smply Supported Concrete Grder Brdge Restraner Cables MSSS_Steel Mult-Span Smply Supported Steel Grder Brdge Restraner Cables Other Other Restraner Cables SS_Concrete Sngle-Span Concrete Grder Brdge Restraner Cables SS_Steel Sngle-Span Steel Grder Brdge Restraner Cables Three brdges were selected at random from the avalable nventory for Memphs and Shelby County, TN. The example wll use the followng three brdges shown n Table Table Brdge Inventory Data Classfcaton Spans Structure Length (ft) Deck Wdth (ft) Lattude Longtude Brdge 1 SS-PSC N W Brdge 2 MSC-PSC N W Brdge 3 MSC-SG N W The brdges can be mapped to approprate fragltes as shown n Table By default, brdges are not assumed to have retrofts nstalled. Table Brdge Inventory to Fraglty Mappng Classfcaton Descrpton MAE Center Fraglty Brdge 1 SS-PSC Sngle-Span Concrete Grder Brdge SS_Concrete Brdge 2 MSC-PSC Mult-Span Contnuous Concrete Grder Brdge MSC_Concrete Brdge 3 MSC-SG Mult-Span Contnuous Steel Grder Brdge MSC_Steel 11

12 Utlty Lfelne Inventory Electrc Power Plants Algorthm Inputs: electrc power plant nventory database (no partcular felds). Process: Prompt user to map fragltes for ndvdual components n Table Provde user wth opton to add new component(s). Outputs: modfed electrc power plant nventory database wth each component of power plants keyed to electrc utlty fraglty database(s). Modfed nventory database has an entry for each component of each power plant, nstead of a sngle entry for each power plant, as n the Input. Example A detaled roster of components can be lsted and mapped to fragltes gven n Tables through , as shown n Table Table Default Mappng for Power Plant Components Component Fraglty Fraglty ID Bolers + Steam Generators Bolers and Pressure Vessels EPP_MC_2 Turbnes Turbne EPP_EC_7 Flat Bottom Tanks N/A Large Horzontal Tanks Large horzontal vessels EPP_MC_3 Small to medum Hz. tanks Small to medum horzontal vessels EPP_MC_4 Vertcal pumps Large vertcal pumps EPP_MC_5 Horzontal pumps Motor Drven pumps EPP_MC_6 Large motor operated valves Large Motor Operated Valves EPP_MC_7 Large hydraulc, ar valves Large Hydraulc and Ar Actuated Valves EPP_MC_8 Large relef, manual and relef valves Large Relef, Manual and Check Valves EPP_MC_9 Small valves Small Motor Operated Valves EPP_MC_10 Desel Generators Desel Generators EPP_EC_1 12

13 Component Fraglty Fraglty ID Batteres Battery Racks EPP_EC_2 Instrument racks and panels Instrument Racks and Panels EPP_EC_4 Control Panels Control Panels EPP_EC_5 Swtchgear Swtchgear EPP_EC_3 Motor control centers Aux. Relay Cabnets / MCCs / Crcut Breakers EPP_EC_6 Inverters Aux. Relay Cabnets / MCCs / Crcut Breakers EPP_EC_6 Cable trays and raceways Cable Trays EPP_OTH_1 HVAC ductng HVAC Ductng EPP_OTH_2 HVAC equpment HVAC Equpment Fans EPP_OTH_3 Swtchyard Mscellaneous N/A N/A Three power plants were selected at random from the avalable nventory for Memphs and Shelby County, TN. The example wll use the followng three power plants shown n Table , where EPP s a generc name for Electrc Power Plant. Table Electrc Power Plant Inventory Data Capacty (MWe) Fuel Lattude Longtude EPP1 4.3 NG N W EPP NG N W EPP NG N W All components wll be mapped accordng to the defaults shown n Table

14 Electrc Substatons Algorthm Inputs: Max Voltage electrc substaton nventory database. Process: Classfy each substaton as VHV, HV, or MHV, usng Max Voltage and Table Prompt user to map fragltes for ndvdual components n Tables through Provde user wth opton to add new component(s). Outputs: modfed electrc substaton nventory database wth each component of substatons keyed to electrc utlty fraglty database(s). Modfed nventory database has an entry for each component of each substaton, nstead of a sngle entry for each substaton, as n the Input. Example Substatons are classfed as Very Hgh Voltage (VHV), Hgh Voltage (HV), or Moderately Hgh Voltage (MHV). The classfcatons correspond to a maxmum voltage ranges shown n Table Table Electrc Substaton Classfcaton Classfcaton Max Voltage (kv) Moderately Hgh Voltage (MHV) <= 165 Hgh Voltage (HV) 165 < & <= 350 Very Hgh Voltage (VHV) 350 < 14

15 A detaled roster of components can be lsted and mapped to fragltes gven n Tables through based on classfcaton (VHV, HV, or MHV), as shown n Table through Table Table Default Mappng for VHV Substaton Components Component Fraglty Fraglty ID Transformer - Anchored Transformer - Anchored ESS_VHV_1 Transformer - Unanchored Transformer - Unanchored ESS_VHV_2 Lve Tank Crcut Breaker - Standard Lve Tank Crcut Breaker - Standard ESS_VHV_3 Lve Tank Crcut Breaker - Sesmc Lve Tank Crcut Breaker - Sesmc ESS_VHV_4 Dead Tank Crcut Breaker - Standard Dead Tank Crcut Breaker - Standard ESS_VHV_5 Dsconnect Swtch - Rgd Bus Dsconnect Swtch - Rgd Bus ESS_VHV_6 Dsconnect Swtch - Flexble Bus Dsconnect Swtch - Flexble Bus ESS_VHV_7 Lghtnng Arrestor Lghtnng Arrestor ESS_VHV_8 CCVT - Cantlevered CCVT - Cantlevered ESS_VHV_9 CCVT - Suspended CCVT - Suspended ESS_VHV_10 Current Transformer (gasketed) Current Transformer (gasketed) ESS_VHV_11 Current Transformer (flanged) Current Transformer (flanged) ESS_VHV_12 Wave Trap - Cantlevered Wave Trap - Cantlevered ESS_VHV_13 Wave Trap - Suspended Wave Trap - Suspended ESS_VHV_14 Bus Structure - Rgd Bus Structure - Rgd ESS_VHV_15 Bus Structure - Flexble Bus Structure - Flexble ESS_VHV_16 Other Yard Equpment Other Yard Equpment ESS_VHV_17 15

16 Component Table Default Mappng for HV Substaton Components Fraglty Fraglty ID Transformer - Anchored Transformer - Anchored ESS_HV_1 Transformer - Unanchored Transformer - Unanchored ESS_HV_2 Lve Tank Crcut Breaker - Standard Lve Tank Crcut Breaker - Standard ESS_HV_3 Lve Tank Crcut Breaker - Sesmc Lve Tank Crcut Breaker - Sesmc ESS_HV_4 Dead Tank Crcut Breaker - Standard Dead Tank Crcut Breaker - Standard ESS_HV_5 Dsconnect Swtch - Rgd Bus Dsconnect Swtch - Rgd Bus ESS_HV_6 Dsconnect Swtch - Flexble Bus Dsconnect Swtch - Flexble Bus ESS_HV_7 Lghtnng Arrestor Lghtnng Arrestor ESS_HV_8 CCVT CCVT ESS_HV_9 Current Transformer (gasketed) Current Transformer (gasketed) ESS_HV_10 Wave Trap - Cantlevered Wave Trap - Cantlevered ESS_HV_11 Wave Trap - Suspended Wave Trap - Suspended ESS_HV_12 Bus Structure - Rgd Bus Structure - Rgd ESS_HV_13 Bus Structure - Flexble Bus Structure - Flexble ESS_HV_14 Other Yard Equpment Other Yard Equpment ESS_HV_15 16

17 Table Default Mappng for MHV Substaton Components Component Fraglty Fraglty ID Transformer - Anchored Transformer - Anchored ESS_MHV_1 Transformer - Unanchored Transformer - Unanchored ESS_MHV_2 Lve Tank Crcut Breaker - Standard Lve Tank Crcut Breaker - Standard ESS_MHV_3 Lve Tank Crcut Breaker - Sesmc Lve Tank Crcut Breaker - Sesmc ESS_MHV_4 Dead Tank Crcut Breaker - Standard Dead Tank Crcut Breaker - Standard ESS_MHV_5 Dsconnect Swtch - Rgd Bus Dsconnect Swtch - Rgd Bus ESS_MHV_6 Dsconnect Swtch - Flexble Bus Dsconnect Swtch - Flexble Bus ESS_MHV_7 Lghtnng Arrestor Lghtnng Arrestor ESS_MHV_8 CCVT CCVT ESS_MHV_9 Current Transformer (gasketed) Current Transformer (gasketed) ESS_MHV_10 Wave Trap - Cantlevered Wave Trap - Cantlevered ESS_MHV_11 Wave Trap - Suspended Wave Trap - Suspended ESS_MHV_12 Bus Structure - Rgd Bus Structure - Rgd ESS_MHV_13 Bus Structure - Flexble Bus Structure - Flexble ESS_MHV_14 Other Yard Equpment Other Yard Equpment ESS_MHV_15 17

18 Three electrc substatons were selected at random from the avalable nventory for Memphs and Shelby County, TN. The example wll use the followng three substatons shown n Table , where ESS s a generc name for Electrc Substaton. Table Electrc Substaton Inventory Data Max Voltage (kv) Lattude Longtude ESS N W ESS N W ESS N W The sample substatons wll be classfed accordng to Max Voltage and the scheme shown n Table as shown n Table Table Electrc Substaton Inventory Classfcaton Max Voltage (kv) Classfcaton ESS1 161 MHV ESS 2 0 MHV ESS VHV All components wll be mapped to fragltes wth the default mappng scheme n Tables through

19 Water Tanks Algorthm Inputs: Possbly (Fll, Anchorage, Heght, Dameter, H/D). Process: Prompt user to choose between mappngs based on Fll, Anchorage, or H/D rato. If user selects to map based on Fll, use default mappng as shown n Table If user selects to map based on Anchorage, use default mappng as shown n Table If user selects to map based on H/D rato, use default mappng as shown n Table Assume the user wll provde Heght and Dameter data separately, and calculate H/D by default. Also provde an opton for the user to specfy H/D drectly. Provde user wth to accept default mappng scheme or modfy. Allow users to modfy mappng parameters or map to new fragltes. Outputs: modfed water tank nventory database wth each entty keyed to water tank fraglty database. Example If the user selects to map based on Fll, use the default mappng scheme shown n Table to map to fragltes shown n Table The All Tanks fraglty s not ntended to appear n the default mappng. Note that Default values shown are n percent fll. If Fll data s not provded, use the Ednger Fll >= 50% fraglty. Table Water Tank Mappng Scheme for Fll Fll (percent) Fraglty < 50 Ednger Fll < 50% 50 <= & < 60 Ednger Fll >= 50% 60 <= & < 90 Ednger Fll >= 60% 90 <= Ednger Fll >= 90% 19

20 If the user selects to map based on Anchorage, use the default mappng scheme shown n Table to map to fragltes shown n Table Table Water Tank Mappng Scheme for Anchorage Anchored Y N Unknown Fraglty Ednger Anchored Ednger Unanchored Ednger Anchorage Unknown If the user selects to map based on H/D rato, use the default mappng scheme shown n Table to map to fragltes shown n Table The All Tanks fraglty s not ntended to appear n the default mappng. Note that Default values shown are n percent fll. Table Water Tank Mappng Scheme for H/D rato Fll (percent) H/D Fraglty 50 < O Rourke and So Fll > 50% < <= O Rourke and So H/D >= 0.7 < 50 < 70 O Rourke and So H/D < 0.7 Sample water tank nventory data s lsted n Table Table Sample Water Tank Inventory Data Fll (percent) Anchored Heght Dameter Lattude Longtude Water Tank 1 Water Tank 2 Water Tank 3 40 N N W 55 Y N W 80 Y N W Users may provde all, some, or none of the data felds (locaton s always expected to be provded) specfed n Table As a default opton f the user has no data other than locatons of water tanks, the frst fraglty lsted n Table may be used. 20

21 Bured Ppelnes Algorthm Inputs: Possbly (ppelne materal, ppelne dameter, jont type, sol condton). Process: Prompt user to choose between mappngs based on Researcher. The mappng of attrbutes from the ppelne dataset to MAEvz-recognzed feld types wll depend on whch Researcher s selected. Set the default Researcher to Ednger (2004). Prompt the user to select default attrbutes, dependng on whch Researcher s selected. If the user selects Ednger (2001) (or keeps the default), prompt the user for default ppe materal, jont type, sols, and dameter mappngs. Set the defaults to Cast Iron, Cement, All, and Small, respectvely. Note that only certan combnatons are avalable. Check f the selected parameters are avalable and dsplay an error f they are not. For example, f the user has selected Welded Steel, Lap Arc Welded, Corrosve, Small, the parameters are vald. If the user then changes the dameter to Large, there s no sols parameter avalable besdes All, so havng Corrosve selected should generate an error. If the user selects O Rourke, M. and Ayala (1993), prompt the user for default ppe materal mappng. Set the default to Cast Iron. If the user selects O Rourke, T. and Jeon (1999), prompt the user for default ppe materal and dameter mappngs. Set the defaults to Cast Iron and 8 nches, respectvely. Note that only certan combnatons are avalable. If the user selects Asbestos Cement Ppe, they must also choose between specfyng PGV or dameter. By default, use PGV. Outputs: modfed ppelne nventory database wth each entty keyed to ppelne fraglty database. Example Consder the ppe segment shown n Fgure Very lttle nformaton s avalable to ad n assgnng fragltes. If the user accepts the default Researcher, Ednger (2001), and selects a mappng for dameter -> DIAMETER, MAEvz should then assume that all ppes are Cast Iron materal, have Cement jont types, and have an unknown sol type (ALL s approprate). 21

22 MAEvz would then perform a check for each ppe segment to determne f the ppe dameter s Large (>12 nches) or Small (<= 12 nches), and assgn fragltes approprately. In ths case, a fraglty for Large ppes s not provded, so the default fraglty for Small ppes would be used regardless of ppe dameter. If the user selects the O Rourke, M. and Ayala (1993) fragltes, the default fraglty would be assgned for all ppes, dependng on the default materal selected by the user for ppe materal. If the user selects O Rourke, T. and Jeon (1999) fragltes, the default fraglty wll be assgned for all ppes. Fgure Sample Ppe Segment. 22

23 2.1.2 Modfy nventory databases to store perod for ndvdual tems after mappng to fragltes Buldng Stock Inventory Algorthm Inputs: Fraglty assocated wth each entty n buldng stock nventory database. Go to fraglty database for T Eqn Type and T Eqn ParamX parameters, where X can be 0, 1, and 2 (See Fraglty Database Documentaton n Appendx C.4.2.1). Number of stores from buldng stock nventory. Process: Apply equatons gven n the Fraglty Database Documentaton secton of Appendx C to evaluate perods based on fragltes and the number of stores obtaned from the buldng stock nventory. Provde user wth opton to accept default perod calculatons or modfy. Allow users to modfy mappng parameters or specfy perods drectly for partcular fragltes. NOTE: If structure type uncertanty s consdered, allow users the opton to calculate a perod for each structure type avalable n the nventory. Ths s expected to be very computatonally ntensve and should NOT be performed by default. Outputs: modfed buldng stock nventory database wth perod calculated for each buldng. Example The default MAEVz buldng stock fraglty database and accompanyng documentaton ncludes data to calculate approxmate perods for each fraglty set. The mapped fraglty for the concrete frame buldng has T Eqn Type = 3. Usng the equaton suppled n the Fraglty Database Documentaton wth the default values gven n the fraglty database yelds a perod of 0.95 seconds, as shown below, where the fraglty database documentaton ndcates when T Eqn Type = 3 T 1 = b And where ( a NO _ STORIES) c a = T Eqn Param0 = 13 b = T Eqn Param1 = c = T Eqn Param2 = Therefore, T ( 13 ) = = 0.95 seconds 23

24 Lkewse, the fundamental perod for URM structures may be estmated from data suppled n the fraglty database and documentaton. The nventory database wthn MAEVz would then be augmented to nclude the followng data n Table Table Example Buldng Perods Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Structural type Perod C URM 0.6 URM

25 Utlty Lfelne Inventory Electrc Power Plants Algorthm Inputs: Component name n electrc power plant database. Process: Assgn perods to components lsted n Tables through wth Hazard Parameter of Sa. Provde user wth opton to accept default perods or modfy. Allow users to specfy perods drectly for partcular fragltes. Outputs: modfed electrc power plant nventory database wth perod assgned to each component, as requred. Example Electrc power plants typcally nclude some components wth fragltes calbrated to peak ground acceleraton, and others calbrated to spectral acceleraton. When components are calbrated to spectral acceleraton, the nventory database should be modfed to assgn a perod to the partcular component, smlar to the treatment of buldng nventory. The process for electrc power plants s less complcated, though, because t s always a smple assgnment, wth no calculatons requred. The typcal power plant components are shown n Tables through , along wth Component ID s to match wth the data gven n Table for reference. Table Electrc Power Plant Equpment - Electrcal Components - Well Anchored Component ID Component Hazard Parameter Perod (sec) EPP_EC_1 Desel Generators Sa EPP_EC_2 Battery Racks Sa EPP_EC_3 Swtchgear Sa EPP_EC_4 Instrument Racks and Panels Sa EPP_EC_5 Control Panels Sa EPP_EC_6 Aux. Relay Cabnets / MCCs / Crcut Breakers Sa EPP_EC_7 Turbne PGA

26 Table Electrc Power Plant Equpment - Mechancal Equpment - Well Anchored Component ID Component Hazard Parameter Perod (sec) EPP_MC_1 Large vertcal vessels wth formed heads Sa EPP_MC_2 Bolers and Pressure Vessels Sa EPP_MC_3 Large horzontal vessels Sa EPP_MC_4 Small to medum horzontal vessels Sa EPP_MC_5 Large vertcal pumps Sa EPP_MC_6 Motor Drven pumps Sa EPP_MC_7 Large Motor Operated Valves Sa EPP_MC_8 Large Hydraulc and Ar Actuated Valves Sa EPP_MC_9 Large Relef, Manual and Check Valves Sa EPP_MC_10 Small Motor Operated Valves Sa Table Electrc Power Plant Equpment - Other Equpment Component ID Component Hazard Parameter Perod (sec) EPP_OTH_1 Cable Trays PGA EPP_OTH_2 HVAC Ductng Sa EPP_OTH_3 HVAC Equpment Fans Sa

27 2.1.3 Partton total value of nventory tems nto component values Buldng Stock Inventory Algorthm Inputs: Apprased Value, Buldng Use, Essental Faclty from buldng stock nventory database. Process: Use Table to map Verson 3 buldng use and essental faclty status to /Verson 4 occupancy. Allow users to modfy parameters used for mappng or select alternate /Verson 4 mapped occupances. Use Table to map /Verson 4 occupancy to percentages of component value for structural, acceleraton-senstve nonstructural, and drft-senstve nonstructural components. Allow users to specfy alternate percentages of component values. Multply Apprased Value by the percentages obtaned from Table to obtan values for each component of each buldng stock entty. Outputs: modfed buldng stock nventory database wth calculated values for components. Example Augment the nventory wthn MAEVz to partton total apprased value nto structural, acceleraton-senstve nonstructural (AS NS), and drft-senstve nonstructural (DS NS). The total apprased value of the sample buldngs gven n Table s parttoned nto structural, AS NS, and DS NS values as shown n Table Table Example Buldng Value Parttonng Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Occupancy Verson 4 Apprased % Struc Structural % AS NS AS NS % DS NS DS NS Class Occupancy Value Value, α SD Value Value, α NA Value Value, α ND Value Industral IND1 $136, $21, $98, $16,095 Retal Trade COM1 $415, $122, $179, $114,233 Industral IND1 $811, $127, $588, $95,739 27

28 Utlty Lfelne Inventory Electrc Power Plants Algorthm Inputs: Value (drectly n user suppled data) OR Fuel and Capacty from electrc power plant nventory database. Process: IF Value s NOT obtaned drectly n user suppled data, use Table to map value per unt output of power plants to nventory. Use values for Gas Fred for unknown Fuel types. Allow users to modfy parameters used for mappng or specfy alternate values per unt output. Multply value per unt output tmes Capacty tme nflaton adjustment factor of 1.4 to obtan total power plant value. Use Table to partton total power plant value nto component values. Use Notes 1 and 2 gven for Table to estmate ppng at each power plant. Allow users to specfy alternate percentages of component values or ppng multplers. Outputs: modfed electrc power plant nventory database wth calculated values for components and ppng estmates. Example Default values of power plants per unt output are gven n Table

29 Table Default Electrc Power Plant Value Fuel Capacty (MWe) Value per MWe $1,250,000 Coal Fred $1,500, $1,750, $1,000,000 Gas Fred $1,500, $1,750, $1,750, $1,250,000 Ol Fred $1,500, $1,750, $1,750,000 Nuclear All $2,500,000 Total value for the sample electrc power plants gven n Table s presented n Table The Fuel type, NG, corresponds to natural gas, so the Gas Fred values are used from Table Table Sample Electrc Power Plant Values Capacty (MWe) Fuel Mapped Fuel Type 1994 Value per MWe 1994 to 2006 nflaton Value EPP1 4.3 NG Gas Fred $ 1,000, $ 6,020,000 EPP NG Gas Fred $ 1,500, $ 151,830,000 EPP NG Gas Fred $ 1,000, $ 35,000,000 The default parttonng scheme to break total value of power plants down nto components s gven n Table Component names correspond to the names gven n Where ID s are marked N/A, ether the loss s already assessed elsewhere n an analyss, or there s no data currently avalable to model damage to the partcular component. 29

30 Table Default Mappng for Values of Power Plant Components Component % of total value Boler Buldng 10 Turbne Buldng 8 Admnstraton Buldng 2 Bured Ppe* 1 Elevated Ppe** 12 Bolers + Steam Generators 11 Turbnes 5 Flat Bottom Tanks 3 Large Horzontal Tanks 4 Small to medum Hz. tanks 4 Vertcal pumps 2 Horzontal pumps 3 Large motor operated valves 3 Large hydraulc, ar valves 1 Large relef, manual and relef valves 1 Small valves 1 Desel Generators 2 Batteres 2 Instrument racks and panels 1 Control Panels 1 Swtchgear 1 Motor control centers 3 Inverters 1 Cable trays and raceways 3 HVAC ductng 1 30

31 Component % of total value HVAC equpment 2 Swtchyard n.a. Mscellaneous 12 Note 1: 6,000 feet of bured ppe s assumed per 100 MWe. Note 2: 40,000 feet of elevated ppe s assumed per 100 MWe. Table shows data for the estmated amounts of ppng at each sample power plant, and also shows the sample value of bolers and steam generators as an example of parttoned component value. Table Sample Electrc Power Plant Component Data Capacty (MWe) Bured Ppe (thousands of feet) Elevated Ppe (thousands of feet) Boler and Steam Generator Value ($) EPP ,200 EPP ,701,300 EPP ,850,000 31

32 Electrc Substatons Algorthm Inputs: Value (f avalable drectly n user suppled data), substaton classfcaton (MHV, HV, VHV), and Sesmc Zone desgn level (assume 0 as default f not specfed) from electrc substaton nventory database. Process: IF Value s NOT obtaned drectly n user suppled data, use Table to map total value to nventory for each substaton. Allow users to specfy alternate values for substatons. Based on substaton classfcaton and Sesmc Zone desgn level, use Table or smlar tables n Appendx A to partton total substaton value nto component values. Allow users to specfy alternate percentages of component values. Outputs: modfed electrc substaton nventory database wth calculated values for components. Example Default values of substatons are gven n Table Table Assumed Values of Electrc Substatons Transformer Capacty (kv) Transformers per Substaton MHV HV VHV Value per Transformer (1994) Inflaton Multpler (2006) Total Value (2006 $) For electrc substatons, parttonng total value nto component value s a two-step process. Frst, the general type of component values are parttoned from total value, then more specfc parttonng s appled to break down the general component values. Parttonng schemes are based on the substaton classfcaton (MHV, HV, VHV) and whether the substaton specfc components are lkely to nclude elements desgned to resst sesmc effects. Mappng tables are provded n Appendx A. A sample parttonng scheme from Appendx A s provded n Table for a VHV substaton whch has elements that are not lkely to have been desgned for sesmc effects 32

33 (Sesmc Zone desgn level = 0 to 2). The Overall Multpler should be appled drectly to total value to calculate value for the specfc component,.e., anchored transformers account for 0.1 * Total Value of the substaton. Ths s equvalent to 40% (general component parttonng factor) * 25% (specfc component parttonng factor) = 10% = 0.1. The overall multplers do not sum to 1 because ether the damage s expected to be accounted for elsewhere n the analyss or damage estmaton algorthms are not avalable for partcular components. Table Sample Electrc Substaton Subcomponent Value Parttonng (VHV Substaton, not desgned for sesmc) Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_VHV_1 Transformer - Unanchored ESS_VHV_2 Lve Tank Crcut Breaker - Standard ESS_VHV_3 Lve Tank Crcut Breaker - Sesmc ESS_VHV_4 Dead Tank Crcut Breaker - Standard ESS_VHV_5 Dsconnect Swtch - Rgd Bus ESS_VHV_6 Dsconnect Swtch - Flexble Bus ESS_VHV_7 Lghtnng Arrestor ESS_VHV_8 CCVT - Cantlevered ESS_VHV_9 CCVT - Suspended ESS_VHV_10 Current Transformer (gasketed) ESS_VHV_11 Current Transformer (flanged) ESS_VHV_12 Wave Trap - Cantlevered ESS_VHV_13 Wave Trap - Suspended ESS_VHV_14 Bus Structure - Rgd ESS_VHV_15 Bus Structure - Flexble ESS_VHV_16 Other Yard Equpment ESS_VHV_17 33

34 Sample specfc component data s provded for each of the sample substatons n Table Table Electrc Substaton Sample Component Inventory Data Classfcaton Total Value Specfc Component Overall Multpler Component Value Fraglty ID ESS1 MHV ESS 2 MHV ESS 3 VHV Transformer - Anchored Transformer - Unanchored Lve Tank Crcut Breaker - Standard ESS_MHV_ ESS_MHV_ ESS_VHV_3 34

35 2.1.4 Prompt user for level of buldng stock structure type uncertanty to consder. Algorthm Inputs: None. Process: Prompt user to specfy level of buldng stock structure type uncertanty. Set default to 0% (perfect accuracy no uncertanty). Provde button to vew metadata for buldng stock nventory (lnk to Excel spreadsheet provded by MAEC for nventory database). If a non-zero uncertanty s specfed, assgn fragltes to each buldng based on the mappng for each type of structure n the nventory. Outputs: User defned buldng stock structure type uncertanty. Example If a user were to use the button to vew metadata for the buldng stock nventory database, they would have access to the confuson matrx shown n Table They would also have access to buldng counts, and so they mght make a somewhat arbtrary selecton of uncertanty based on both the confuson matrx and knowledge of buldng counts as descrbed n Secton Assume the user selects to consder a 15% overall uncertanty n the buldng stock. Also, for smplcty, the example wll consder the three sample buldngs to be the extents of the nventory. Therefore, the Concrete Frame buldng only needs to be assgned an alternate URM fraglty, and the URM only needs to be assgned an alternate Concrete Frame fraglty. For the full nventory of Memphs, an alternate fraglty would need to be assgned for EACH avalable structure type. 35

36 2.2 Background Buldng Stock The majorty of buldng stock data s generated by the MAE Center through use of census data, mage synthess data, and a seres of regresson and neural network algorthms (French and Muthukumar, 2006; French and Muthukumar, 2006). The process ncludes an ntal data gatherng exercse to acqure baselne data and subsequent calbraton exercses to refne the model (French and Muthukumar, 2006). Inventory data for fre statons and schools have also been obtaned ndependently (Patterson, 2006). To produce relable predctons of damage and potental losses, MAEVz should estmate hazard approprately for each nventory tem. For buldng stock, structural perod must be known n order to estmate an approprate spectral acceleraton hazard. To estmate structural perod, fragltes must be mapped to nventory tems. Therefore, the frst step n a MAEVz analyss (pror to hazard estmaton) should be ngeston of nventory, mmedately followed by mappng of nventory to fragltes, and ther assocated perod expressons, based on partcular data felds n the nventory database. For the present, consderaton of perod when estmatng hazard for each structure should be avalable as a user opton, but not requred. Valdty of the model s not assured n geographcal regons other than where data s gathered. Uncertanty exsts for each nventory parameter, but the prmary sources of uncertanty for buldng stock are n the predcted structure type and, to a lesser extent, the predcted occupancy type. Uncertanty n structure type can be represented by a confuson matrx for a partcular sample of the buldng stock nventory, as shown n Table The confuson matrx shows how many of each structure type are predcted by the neural network, and of those predcted for each structure type, how many actually belong to each structure type. Table Sample Confuson Matrx for Memphs Buldng Stock There are two proposed methods ntended to account for uncertanty n the structure type. For the frst method, the confuson matrx wll be used to develop adjusted probable damage factors for each structural type. The uncertanty has an effect on both the hazard and the fraglty, snce dfferent structure types wll have dfferent natural perods, and therefore dfferent demand 36

37 spectral acceleratons. For a partcular nventory tem, therefore, the frst step s to consder whch structure types are lkely, then compute approprate hazard parameters at the locaton of the nventory tem based on the natural perods of the probable structure types. Pendng senstvty analyses to analytcally defne a crtcal threshold, the effect of ndvdual structure types whch represent 5% or less of the actual structure types wthn each predcted structural type wll be neglected. For the confuson matrx shown n Table , ths approach takes nto account a mnmum of 85% of the actual structures contrbutng to the response of any gven predcted structure type. The next step s to pass the hazard parameters nto the approprate fraglty functons and obtan probable damage factors for each probable structure type. The fnal step s to compute a weghted average of probable damage factors, wth the weghts calculated based on the confuson matrx. An alternate method, whch may be useful when a confuson matrx s not avalable, s to assume all structure types have an equal probablty of accuracy. Based on the confuson matrx shown for Memphs, ths value may be taken as approxmately 70%. Then, for the 30% naccuracy, losses wll be determned by a weghted average of expected losses for all structure types. The weghtng of expected losses for each structure type s determned drectly on the bass of how many of each structure type are beleved to be n the nventory (that s, the more of a structure type there are, the more lkely t wll be naccurately predcted to be some other buldng type, based on a random samplng approach). Ths alternate approach would use the nformaton that s presumed to be naccurate to develop a means of mtgatng that same naccuracy, but t also offers a method of approxmately accountng for the fact that the structure type s uncertan n the event that a confuson matrx s not provded. It should also be noted that the selecton of the value used for probablty of accuracy s somewhat arbtrary, snce usng the value of 70% obtaned from the surveys of 416 structures s only vald for that partcular sample. Also, t should be noted that wood frame buldngs only accounted for 86 of the 416 buldngs that were surveyed, and each tme a buldng was predcted to be wood frame, the predcton was correct. For the full set of buldng nventory n Shelby County, wood frame buldngs wll account for more than 90% of structures, and the probablty of accuracy for the full buldng nventory wll be sgnfcantly hgher than 70%, probably closer to 85% at a mnmum. Two sets of databases have been provded by the MAE Center for Memphs nventory data. The sets are generally referred to as verson 3 and verson 4. Verson 4 nventory data has been provded n a format that more closely matches, prmarly n terms of occupancy classfcatons. Most MAE Center researchers are expected to be more famlar wth verson 3 rather than verson 4 format, so ths document wll focus on the use of verson 3 data. The followng s a lst of the buldng stock nventory data that has been obtaned wthn the MAE Center to date (verson 3): Data overvew Memphs Testbed buldng stock nventory data. 37

38 Locaton: Shelby County, Tennessee. Source: Shelby county Tax Assessor s database. Database 1: Shelby_Bldg_ver3: 287,057 buldng records. Database 2: Shelby_noSF_ver3: 21,903 buldng records (excludng sngle famly resdental structures). These databases each have 16 parameters, as shown n Table Table Buldng Stock Inventory Parameters ID Descrpton Categores* STRUCT_TYP Structure type 10 types Number of stores n structure SQ_FOOT Square footage of entre structure YEAR_BUILT Year that the structure was constructed BLDG_USE Occupancy class for the structure 9 classes APPR_BLDG Apprased value of the structure CONT_VAL Value of contents contaned wth the structure 10 use-specfc multplers DWELL_UNIT Number of dwellng unts n structure EFACILITY Descrpton of essental faclty status of structure 6 statuses BFOOTPRINT Buldng footprnt confguraton 7 types BMASSING Buldng confguraton n three-dmensons ADDRESS Address of the parcel n whch structure s contaned SP_XCOORD X-coordnate of structure locaton n feet SP_YCOORD Y-coordnate of structure locaton n feet LAT Lattude of structure locaton LON Longtude of structure locaton * See Categores for detals. The followng category nformaton s used n the buldng stock nventory of the MAE Center: Categores a) Structure types (10) Wood Frame (W) Steel Moment Resstng Frame (S1) Lght Metal Frame (S3) Concrete Moment Resstng Frame (C1) Concrete Frame wth Concrete Shear Wall (C2) Concrete Tlt-Up (PC1) 38

39 Precast Concrete Frame (PC2) Renforced Masonry (RM) Unrenforced Masonry (URM) Unknown Please note, as of verson 4 of the buldng stock nventory database, the Unknown type s no longer used. Wood frames are also broken down nto W1 and W2 subcategores, whch now correspond to structure types found n. b) Occupancy classes (9) Resdental_SF (Sngle Famly) Resdental_MF (Mult Famly) Retal Trade Wholesale Trade Offce Health Care Parkng Industral Lght Industral Please note, as of verson 4 of the buldng stock nventory database, occupancy classes are beng assgned n a manner consstent wth. Based on documentaton suppled for verson 4 nventory data, a default mappng scheme has been establshed between Memphs verson 3 nventory occupancy classes and (and verson 4) occupancy classes, as shown n Table Ths mappng s expected to be accurate (to the greatest degree currently possble) for all occupancy classes except Offce. Accordng to the documentaton provded wth verson 4, Offce s comprsed of COM3, COM4, COM5, and COM9 by about 42%, 12%, 32%, and 10%, respectvely. Further refnement of the mappng scheme may be requred f verson 3 data wll be used extensvely n developng MAE Center algorthms. Table Occupancy Mappng between Verson 3 and (Verson 4) Verson 3 Occupancy & Essental Faclty Buldng Use : Resdental_SF Buldng Use : Resdental_MF Buldng Use : Retal Trade Buldng Use : Wholesale Trade (and Verson 4) Occupancy Sngle Famly Dwellng (House) (RES1) Mult Famly Dwellng (Apt/Condomnum) (RES3) Retal Trade (Store) (COM1) Wholesale Trade (Warehouse) (COM2) 39

40 Verson 3 Occupancy & Essental Faclty (and Verson 4) Occupancy Buldng Use : Offce Professonal/Techncal Servces (Offces) (COM3) Buldng Use : HealthCare Hosptal (COM6) Buldng Use : Parkng Parkng (Garages) (COM10) Buldng Use : Industral Heavy (Factory) (IND1) Buldng Use : Industral_Lght Lght (Factory) (IND2) Essental Faclty : School (EFS1) Grade Schools (EDU1) Essental Faclty : Fre Staton (EFFS) Emergency Response (Polce/Fre Staton/EOC) (GOV2) Essental Faclty : Polce Staton (EFPS) Emergency Response (Polce/Fre Staton/EOC) (GOV2) c) Use-specfc multplers for value of contents (10) Table Ratos of Contents to Apprased Value Occupancy or Essental Faclty Status Percent apprased value, α CL Resdental (SF and MF) 50% Retal Trade 100% Wholesale Trade 100% Offce 100% Health Care 150% Parkng 50% Industral 150% Lght Industral 150% Schools (EFS1) 100% Fre Statons and Polce 150% Statons (EFFS, EFPS) The values shown n Table are dentcal to those gven n the Techncal Manual, and have already been appled to the apprased values before the nventory databases are suppled from the MAE Center. d) Essental faclty status (6) All nventory suppled by the MAE Center s provded wth an accompanyng essental faclty flag, as shown n Table Table Essental faclty types 40

41 EFACILITY (Strng) EFS1 EFHL EFHM EFFS EFPS None Faclty Schools Low-rse hosptals Md- and Hgh-rse hosptals Fre statons Polce statons Not essental The essental faclty classfcatons gven n Table correlate closely to essental faclty classfcatons used by. e) Buldng footprnt confguratons (7) Square Rectangular T-Shaped L-Shaped I- or H-Shaped C-Shaped Irregular The apprased value of an nventory tem s not the same as the replacement cost, but t can serve as a reasonable estmate of buldng value for a loss assessment (French, 2006). Buldng fragltes suppled by the MAE Center estmate damage to structural value only. There s no nformaton currently avalable n the MAE Center regardng how to partton the total value of an nventory tem nto structural and nonstructural values. In leu of such nformaton, structural and nonstructural values wll be parttoned from total value usng damage ratos gven n Tables 15.2 through 15.4 of the -MH MR2 Techncal Manual (NIBS, 2006). Accordng to those tables n the Techncal Manual, Complete damage corresponds to the followng percentages of buldng total replacement cost, as shown n Table The α SD, α NA, and α ND headers for each column n Table represent percentages of structural, acceleraton-senstve nonstructural, and drft-senstve nonstructural values, respectvely. Table Percentages of component value based on /Verson 4 Occupancy Occupancy α SD α NA α ND RES RES RES3a-f

42 Occupancy α SD α NA α ND RES RES RES COM COM COM COM COM COM COM COM COM COM IND IND IND IND IND IND AGR REL GOV GOV EDU EDU Archtectural and MEP (Nonstructural) The MAE Center has provded nonstructural fragltes to estmate damage to specfc nonstructural components for the MLGW Project, but the fragltes are only useful when nventory data for specfc nonstructural components s also suppled. In most cases, specfc nonstructural nventory data are not avalable, and a representaton of nonstructural assets (value) wll be adapted from as an nterm measure. does not consder specfc nonstructural nventory tems, but rather breaks nonstructural nventory nto two subsets: drftsenstve and acceleraton-senstve. Fractons of total value for each subset of nonstructural nventory are shown n Table Transportaton Systems 42

43 The MAE Center has provded brdge data obtaned from the Natonal Brdge Inventory for Memphs, Tennessee and Charleston, South Carolna (DesRoches, 2006; FHWA, 1995). Road data has been provded for both locatons as well (French and Muthukumar, 2006; Patterson, 2006). Uncertanty s not characterzed for the attrbutes of ths nventory data Utlty Systems Water system nventory data, ncludng ppelnes and tanks, has been provded for Shelby County (French, 2006). Data for the cast ron ppe network carryng natural gas and the electrc power network has been provded by muncpal contacts (MLGW, 2005). Addtonal hgh fdelty Shelby County utlty nventory data wll also be made avalable to MAEVz developers as t s suppled by muncpal contacts for other networks n addton to natural gas. An addtonal source of lfelne nventory s the Homeland Securty Infrastructure Program (HSIP) GOLD Dataset (PMH, 2006). A small porton of the HSIP was made avalable to the MAE Center by FEMA through a sample fle for an eght state study regon n Md-Amerca. The subset of HSIP utlty nventory data was lmted to natural gas and ol ppelnes, and t had also been modfed from ts orgnal form for use n. The MAE Center has recently acqured the full release verson of the HSIP and s currently nvestgatng how the data mght be used wthn MAEVz. Uncertanty s not characterzed for the attrbutes of utlty nventory data. The majorty of data beng used to estmate breakdowns of total value to component values for electrc power plants and substatons s based on the work of Ednger (G & E Engneerng Systems, Inc., 1994) Inventory Data buldng stock nventory s aggregated to the census block level for default nventory. The data has been extracted drectly from databases n, but t has not yet been manpulated so that MAEVz could use t to perform analyses. In order for MAEVz to use the buldng stock nventory data, the aggregated census tract nventory wll need to be converted to equvalent buldngs. Ths process wll requre the followng steps for each census block: Compute total value of buldngs for each specfc occupancy usng the approxmate dollar exposure of each occupancy ($/ft 2 ) publshed n the Techncal Manual and the total floor area for each occupancy extracted from databases. Partton buldng value for each occupancy nto equvalent buldngs by structure type (e.g., W1, S1, C1) by usng occupancy mappng schemes n. Ths approach wll result n a maxmum of (33 specfc occupances) x (36 specfc structure types) = 1188 equvalent buldngs for each census block. Assets other than general buldng stock are treated as pont-wse enttes by. Note that uncertanty s not characterzed for the attrbutes of ths nventory data. 43

44 3. HAZARD DEFINITION 3.1 MAEVz Implementaton MAEVz can currently estmate sesmc hazard n terms of spectral acceleraton, peak ground acceleraton, peak ground velocty, and peak ground dsplacement wthn the Msssspp Embayment usng a collecton of ndvdual attenuaton functons collectvely referred to as the Rx-Fernandez attenuatons (Fernandez and Rx, 2006). MAEVz can also estmate spectral acceleraton and PGA outsde of the Embayment by usng the standard attenuatons n use by USGS wth NEHRP sol amplfcaton factors, although MAEVz currently only evaluates one USGS attenuaton for an analyss outsde of the Embayment. The followng modfcatons are recommended for MAEVz hazard estmaton: Wthn the Embayment, calculate hazard approprate to specfc nventory tems (user opton). o Buldng stock o Brdges o Utlty lfelnes In the Memphs area, mplement the lquefacton hazard estmaton algorthm provded by the MAE Center. When estmatng hazard outsde of the Embayment, but wthn the Central and Eastern Unted States (CEUS), use a weghted combnaton of USGS attenuaton functons by default, where the weghts are taken from Table Implement Western Unted States (WUS) attenuaton functons, wth weghts as shown n Table Implement Toro and Slva sol amplfcaton factors for use outsde the Embayment but wthn the CEUS. 44

45 3.1.1 Wthn the Embayment, calculate hazard approprate to specfc nventory tems (user opton) Buldng Stock Hazard Algorthm Inputs: Fraglty assocated wth each entty n buldng stock nventory database. Go to fraglty database for hazard type (typcally Sa) assocated wth fraglty. Perod, T, for each buldng as calculated n Secton Locaton of buldng from buldng nventory. Underlyng sol type and depth for each buldng based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate spectral acceleraton at the approprate perod for each nventory tem. NOTE: If structure type uncertanty s consdered, and users select the opton to calculate a perod for each structure type avalable n the nventory, compute approprate hazard for each structure type n the nventory, based on perod. Outputs: mean and standard devaton of estmated hazard for each nventory tem at approprate perod Example Hazard wll be estmated for each of the three sample nventory tems based on dstances from a specfed epcenter locaton and a magntude assumed for the scenaro. For ths example, consder the default maxmum magntude event gven for Memphs, TN n Table (M w = 7.9 at Blythevlle, AR). Note that the spectral acceleratons shown n Table were calculated for approprate structural perods from Table

46 Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Table Example Ground Shakng Hazard Data Lattude Longtude Perod Mean, λ S a ln S a Standard devaton, N W N W N W β S a 46

47 Transportaton Lfelne Hazard Algorthm Inputs: Fraglty assocated wth each entty n brdge nventory database. Go to fraglty database for hazard type (typcally PGA) assocated wth fraglty. Locaton of brdge from buldng nventory. Underlyng sol type and depth for each brdge based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate spectral acceleraton at the approprate perod for each nventory tem. Outputs: mean and standard devaton of estmated hazard for each nventory tem Example Brdge fragltes are calbrated to PGA. The calculated hazard for each of the three sample brdges s shown n Table Table Example Brdge Ground Shakng Hazard Data ln PGA Lattude Longtude Mean, λ PGA Standard devaton, β PGA Brdge N W Brdge N W Brdge N W

48 Utlty Lfelne Hazard Electrc Power Plants Algorthm Inputs: Fraglty assocated wth each entty n electrc power plant nventory database. Go to fraglty database for hazard type (typcally Sa or PGA) assocated wth fraglty. Perod, T, for each component (from Secton ). Locaton of power plant from nventory database. Underlyng sol type and depth for each power plant based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate spectral acceleraton at the approprate perod or PGA for each component as approprate, based on fraglty. Outputs: mean and standard devaton of estmated hazard for each component at approprate perod Example Hazard should be calculated for each component of electrc power plants, based on component perods. Note that multple components may have the same perod, and therefore requre only a sngle hazard calculaton. Sample hazard data n terms of PGA and spectral acceleraton are shown n Tables and , respectvely. Table Example Electrc Power Plant PGA Data ln PGA Lattude Longtude Mean, λ PGA Standard devaton, β PGA EPP N W EPP N W EPP N W

49 Table Example Electrc Power Plant Spectral Acceleraton Data ln S a Sample Component Perod Standard devaton, Mean, EPP 1 Bolers + Steam Generators EPP 2 Bolers + Steam Generators EPP 3 Bolers + Steam Generators λ S a β S a 49

50 Electrc Substatons Algorthm Inputs: Fraglty assocated wth each entty n electrc substaton nventory database. Go to fraglty database for hazard type (typcally PGA) assocated wth fraglty. Perod, T, for each component wth fraglty calbrated to Sa. Locaton of substaton from nventory database. Underlyng sol type and depth for each power plant based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate spectral acceleraton at the approprate perod or PGA for each component as approprate, based on fraglty. Outputs: mean and standard devaton of estmated hazard for each component at approprate perod Example Hazard should be calculated for each component of electrc substatons, based on component perods. Currently, all components of substatons are descrbed by fragltes calbrated to PGA. Therefore, only PGA s currently requred to be calculated for substatons. Sample hazard data n terms of PGA s shown n Table Table Example Electrc Substaton PGA Data ln PGA Lattude Longtude Mean, λ PGA Standard devaton, β PGA ESS N W ESS N W ESS N W

51 Water Tanks Algorthm Inputs: Fraglty assocated wth each entty n water tank nventory database. Go to fraglty database for hazard type (typcally PGA) assocated wth fraglty. Perod, T, for each component wth fraglty calbrated to Sa. Locaton of water tank from nventory database. Underlyng sol type and depth for each power plant based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate spectral acceleraton at the approprate perod or PGA for each component as approprate, based on fraglty. Outputs: mean and standard devaton of estmated hazard for each component at approprate perod Example Water tanks are descrbed by fragltes calbrated to PGA. Sample hazard data n terms of PGA s shown n Table Table Example Ground Shakng Hazard Data ln PGA Lattude Longtude Mean, λ PGA Standard devaton, β PGA Water Tank N W Water Tank N W Water Tank N W

52 Bured Ppelnes Algorthm Inputs: Locaton of end nodes (calculated nternally or read from nventory database). Underlyng sol type and depth at the mdpont between end nodes for each ppelne based on locaton. Sesmc source magntude and locaton. Process: Use Rx-Fernandez attenuatons to estmate PGV for each ppelne. Outputs: mean and standard devaton of estmated hazard for each ppelne Example A representatve hazard for a ppelne segment can be determned by evaluatng the governng attenuaton equatons at the mdpont between the end nodes of the segment. For the example segment, the end nodes are located at ( ºN, ºW) and ( ºN, ºW). The Rx-Fernandez attenuatons can then be appled to obtan the lognormal mean and standard devaton of peak ground velocty, PGV, at the average locaton of the two end nodes as shown n Table Table Example Bured Ppelne PGV Data Approx. Lattude of Mdpont Approx. Longtude of λ Mdpont Mean, PGV ln PGV Standard devaton, β PGV Segment N W

53 3.1.2 Implement MAEC lquefacton hazard estmaton algorthm (Memphs). Algorthm Inputs: Locaton of nventory. Underlyng sol type for each nventory tem based on locaton (Note sol types for lquefacton are dfferent than sol types for Rx-Fernandez attenuatons). Computed PGA for each tem. Sesmc source magntude and locaton. Process: Calculate magntude scalng factor from Table B based on magntude of source event. Then for each tem: Calculate duraton-adjusted PGA from Equaton (B ). Look up coeffcents for LPI value of 15 n Table B based on sol type. Set w 1 and w 2 equal to 1/3 and 2/3 by default, unless all coeffcents n a row of Table B are zeros. When all coeffcents for a row are zeros, set the weghtng factor for the row populated wth zeros equal to 0 and the weghtng factor for the row wth nonzero coeffcents equal to 1. Allow the user to adjust default weghtng factors. Substtute coeffcents and weghtng factors nto Equaton (B ) to obtan probablty of major lquefacton. Outputs: probablty of major lquefacton, P[LPI >15] Example To compute lquefacton hazard, PGA must be computed for nventory tems. PGA values must also be scaled relatve to the magntude of the source event to account for duraton effects. A Magntude Scalng Factor (MSF) may be nterpolated from Table B as 0.95 for an Mw = 7.9 source event. The maxmum adjusted PGA s then checked to ensure t does not exceed a lmtng value of 0.55 g. PGA PGAmax. adj = < 0. 55g

54 Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Table Example Ground Falure Hazard Data Rx-Fernandez Structural PGA, g = Lattude Longtude Output, type exp(ln(pga)) ln(pga) PGA maxadj, g C N W URM N W URM N W Usng a shapefle suppled by the MAE Center (see Fgure B n Appendx B), the sample buldngs may be determned to st atop the geologc unts noted n Table Each sol unt has been mapped to coeffcents as shown n Table B The coeffcents may then be used n an equaton provded by the MAE Center to estmate probablty of exceedng one of two LPI lmts. Use the coeffcents for evaluatng probablty of exceedence of LPI = 15 when estmatng damage to nventory. The standard weghtng factors of 1/3 for CPT coeffcents and 2/3 for SPT coeffcents were NOT used for the example because coeffcents for CPT tests are all zeros for Ql sol and coeffcents for SPT tests are all zeros for af sol. Weghtng factors of 0 for the CPT coeffcents and 1 for the SPT coeffcents were used for the URM sample buldngs. Also, snce nventory tem I1 s n an artfcal fll zone, weghtng factors of 1 for the CPT coeffcents and 0 for the SPT coeffcents were used. Table Sol Unts and Coeffcents Sol Unt w 1 w 2 Type of Test a b c Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) af 1 0 CPT Ql 0 1 SPT Ql 0 1 SPT The general equaton to evaluate lquefacton hazard s a P[LPI > x] = w b 1 exp c 1 a max.adjusted [ ( )] + w 2 a 2 [ 1+ b 2 exp( c 2 a max.adjusted )] So the equaton to estmate hazard for tem I2, for example, becomes 54

55 P [ LPI > 15] = ( 0) 1 [ 1+ b exp( c a )] 1 a 1 max. adjusted () 1 [ exp( 15.89* 0.165) ] P [ LPI > 15] = Table Probabltes of Ground Falure Sol Unt P[LPI>15] Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) af Ql Ql

56 3.1.3 Implement typcal USGS CEUS attenuaton combnatons. Algorthm Inputs: Locatons throughout study regon where hazard must be estmated. Underlyng sol type (NEHRP) based on locaton (assume D by default). Sesmc source magntude and locaton. Process: Prompt user to choose from a lst ( Select Attenuaton(s) ) ncludng Characterstc Event (default), Non-Characterstc Event, or User Specfed, for whch the user manually enters weghts. Compute hazard for all attenuatons requred for combnaton as lsted n Table For all attenuatons EXCEPT Frankel et al. (1996), convert lognormal mean hazard values to standard mean values, multply by the factors gven n Table , then convert back to lognormal values. Combne results usng the weghtng factors shown n Table Convert hazard from combned attenuatons to standard mean values and multply by NEHRP sol factors. Outputs: mean of estmated hazard n terms of PGA, 0.2 sec Sa, and 1.0 sec Sa. Example Table Default CEUS Attenuaton Functons and Weghts (outsde Msssspp Embayment) Applcable Regon / Event Attenuaton Functon Weght Atknson and Boore (1995) CEUS Characterstc Event Toro et al (1997) (New Madrd and Frankel et al (1996) Charleston) outsde Campbell (2002) Msssspp Embayment Sommervlle et al (2002) Atknson and Boore (1995) CEUS source (not Toro et al (1997) characterstc) outsde Frankel et al (1996) Msssspp Embayment Campbell (2002)

57 Table Correcton Factors to Convert Ste Class A Motons to B/C Motons Perod Factor PGA sec sec sec 1.34 > 1 sec 1.34 If a ste s located at ºN, 90.05ºW, the expected ground motons resultng from an M w =7.7 CEUS Characterstc event may be determned as follows: Table Intal Calculatons of lny (log10 for Atknson and Boore) PGA 0.2 sec Sa 1 sec Sa Atknson and Boore Toro et al Frankel et al Campbell Sommervlle et al Next, convert all Y hazards from lognormal, except Frankel et al. Note that Atknson and Boore values must be converted from base 10, and also from cm/s 2 to g s. Table Values converted from lognormal PGA 0.2 sec Sa 1 sec Sa Atknson and Boore Toro et al Campbell Sommervlle et al Then, convert Ste Class A motons to Ste Class B/C motons, usng values from Table

58 Table Values converted from Ste Class A to B/C PGA 0.2 sec Sa 1 sec Sa Atknson and Boore Toro et al Campbell Sommervlle et al Fnally, convert values back to lognormal (all n terms of natural log) Table Fnal values of lny PGA 0.2 sec Sa 1 sec Sa Atknson and Boore Toro et al Frankel et al Campbell Sommervlle et al The values gven n Table can be used to determne medan lognormal hazard and epstemc varance smlarly to the Rx-Fernandez equatons. Medan PGA, 0.2 sec Sa, and 1 sec Sa are 0.486g, 0.840g, and 0.275g, respectvely, for B/C motons. Fa and Fv can be determned n accordance wth NEHRP to be 1.16 and 1.85 for Ste Class D. 0.2 sec Sa then becomes * 1.16 = 0.977g, and 1 sec Sa becomes * 1.85 = 0.508g. Lognormal medan acceleratons are , , for PGA, 0.2 sec Sa, and 1 sec Sa. The epstemc standard devatons of lognormal acceleratons are 0.245, 0.144, and Aleatory standard devatons are fxed for all attenuatons except Campbell. Campbell requres the coeffcents gven n Table Table Campbell Aleatory Standard Devaton Coeffcents C 11 C 12 C 13 PGA sec Sa sec Sa The values n Table may then be used n Equatons and σ M when M w < M 1 ( ) a, lny = c11 + c12 w 58

59 σ when M w M 1 ( ) a, lny = c13 where M 1 = Lognormal aleatory standard devatons are gven n Table Table Aleatory standard devatons of lny PGA 0.2 sec Sa 1 sec Sa Atknson and Boore Toro et al Frankel et al Campbell Sommervlle et al The lognormal aleatory standard devatons can be squared to obtan varances, then combned wth weghtng factors smlarly to the approach used for the Rx-Fernandez equatons. Combned aleatory standard devatons are 0.665, 0.664, and for PGA, 0.2 sec Sa, and 1 sec Sa, respectvely. 59

60 3.1.4 Implement typcal USGS WUS attenuaton combnatons. Algorthm Inputs: Locatons throughout study regon where hazard must be estmated. Underlyng sol type (NEHRP) based on locaton (assume D by default). Sesmc source magntude and locaton, type and orentaton of fault rupture. Process: Prompt user to choose whch combnaton shown n Table s approprate. Compute hazard for all attenuatons requred for combnaton as lsted n Table Combne results usng the weghtng factors shown n Table Convert hazard from combned attenuatons to standard mean values and multply by NEHRP sol factors. Outputs: mean of estmated hazard n terms of PGA, 0.2 sec Sa, and 1.0 sec Sa. Example Table Default WUS Attenuaton Functons and Weghts Applcable Regon / Event Attenuaton Functon Weght Abrahamson and Slva (1997): Hangng Wall Sadgh, Chang, Egan, Makds, and Young WUS Shallow Crustal Event - Extensonal (1997) Boore, Joyner and Fumal (1997) Spudch et al. (1999) Campbell & Bozorgna (2003) Abrahamson and Slva (1997): Hangng Wall WUS Shallow Crustal Event Non-Extensonal Sadgh, Chang, Egan, Makds, and Young (1997) Boore, Joyner and Fumal (1997) WUS Cascada Subducton Event WUS Deep Event ( > 35 km n depth) Campbell & Bozorgna (2003) Youngs, Chou, Slva and Humphrey (1997) Sadgh, Chang, Egan, Makds, and Young (1997) Youngs, Chou, Slva and Humphrey (1997) Atknson and Boore (2002) - Global

61 Atknson and Boore (2002) - Cascada [example data not currently avalable] 61

62 3.1.5 Implement Toro and Slva sol amplfcaton factors. Algorthm Inputs: Locatons throughout study regon where hazard must be estmated. Underlyng sol type and depth based on locaton (only currently avalable between 84ºW and 96ºW, and between 36ºN and 40ºN). Sesmc source magntude and locaton. Process: Prompt user to choose whether or not the sesmc source s a Characterstc Event (default to yes). Compute hazard for all attenuatons requred for combnaton as lsted n Table For only the Frankel et al. (1996) attenuaton, convert lognormal mean hazard values to standard mean values, dvde by the factors gven n Table , then convert back to lognormal values. Combne results usng the weghtng factors shown n Table Convert hazard from combned attenuatons to standard mean values. Use PGA, sol type, and sol depth to determne Toro and Slva sol factors. Multply standard mean values of PGA, 0.2 sec Sa, and 1.0 sec Sa by Toro and Slva sol factors. Outputs: mean of estmated hazard n terms of PGA, 0.2 sec Sa, and 1.0 sec Sa. Example Use Toro and Slva sol amplfcaton factors rather than NEHRP sol factors for stes located between 84ºW and 96ºW, and between 36ºN and 40ºN where the sol s underlan by ether Ozark Uplands or Glacal Tll (e.g., St. Lous, MO), as shown n Fgure

63 Fgure Regon of applcablty for Toro and Slva amplfcaton factors. Hazard estmaton s dentcal to Secton except for two characterstcs: Ground motons from attenuaton functons must be calbrated to ste A motons for Toro and Slva amplfcaton factors, so dvde the results of Frankel et al. (1996) by the factors shown n Table Compute Toro and Slva amplfcaton factors to be appled to standard normal mean of ground moton based on sol type, sol depth, and PGA. (Shape factors are avalable from the MAE Center for sol type and sol type n the regon of applcablty). [example data not currently avalable] 63

64 3.1.6 Implement lquefacton hazard estmaton algorthms. Algorthm Inputs: Map of lquefacton susceptbltes. Map of PGA hazard. Sesmc source magntude (f possble, record Mw used for generatng PGA map and use as default value). Map of groundwater depth (default to assumpton of 5 ft). Process: Calculate probabltes of lquefacton throughout the study regon usng Equaton ( ). Calculate expected value of lateral spreadng usng Equaton ( ). Calculate expected value of ground settlement by multplyng the result of Equaton ( ) by the approprate value n Table ( ). Outputs: Probablty of lquefacton for each buldng. Expected lateral spreadng for each buldng. Expected ground settlement for each buldng. Example For use as a general approach when nformaton s not suffcent to apply MAEC lquefacton algorthms (when sol condtons are sgnfcantly dfferent than Memphs, TN), mplement the lquefacton hazard algorthms. The frst step n the lquefacton methodology s to quanttatvely estmate lquefacton susceptblty usng qualtatve maps, accordng to Equaton ( ). The maps have sx levels of lquefacton susceptblty, rangng from None to Very Hgh. P [ Lquefacton ] where SC P [ Lquefacton PGA a] = [ Lquefacton PGA = a] K M SC K w P ml ( ) P SC = s determned as a functon of both PGA and lquefacton susceptblty category, accordng to Table

65 Table Lquefacton probablty functons Assume a sample buldng sts on sol wth a Very Hgh Susceptblty Category, and a PGA of 0.3g. Substtutng a = 0.3 nto the equaton shown n Table for Very Hgh results n the maxmum value of 1.0. The terms n the denomnator of Equaton ( ) calbrate the susceptblty functon to account for the magntude of the sesmc source event and the nfluence of the groundwater table. They can be determned accordng to 3 2 K M = M M M ( ) and K 0.022d ( ) w = w where M s the moment magntude of the sesmc source and d w s the depth of the groundwater table. If the moment magntude of the source event s 7.9, K M = If the groundwater depth s 5 ft, K w = Fnally, the P ml coeffcents may be obtaned from Table Table Map calbraton factors The P ml coeffcent for Very Hgh s Probablty of lquefacton can then be calculated as 1 P [ Lquefacton SC ] = 0.25 = ( ) Next, calculate expected lateral spreadng usng Equaton ( ). 65

66 E SC ( ) PLSC PGA [ PGD ] = K Δ E PGD = a PGA Where E PGD = a s determned usng a normalzed PGA accountng for the PLSC threshold value of PGA requred to nduce lquefacton, as shown n Fgure Fgure Expected lateral spreadng wth respect to normalzed PGA [from NIBS (2006)] The values of PGA(t) may be obtaned from Table Table Threshold PGA requred to nduce lquefacton The normalzed PGA/PGA(t) for the sample buldng s 0.3/0.09 = Usng ths value n Fgure yelds an unadjusted expected lateral spreadng of 70* = 53 nches. The K Δ term can be evaluated usng Equaton ( ). 3 2 K = M M M ( ) Δ 66

67 where M s the moment magntude of the source event. Usng M = 7.9 as before, K Δ = The adjusted expected lateral spreadng s then 1.26 * 53 = 67 nches. Ground settlement can be calculated by multplyng the result of ( ) by the approprate value from Table dependng on mapped susceptblty category. Table Expected ground settlement For the sample buldng, the expected ground settlement s 0.25 * 12 = 3 nches. 67

68 3.2 Background Hazard Defnton Overvew The sesmc hazard models of MAEvz wll be prmarly based on project HD-1 1 on synthetc ground motons for regonal hazard analyses (wth epstemc uncertantes quantfed) (Fernandez and Rx, 2006; Romero and Rx, 2005; Park and Hashash, 2005). Project HD-3 on sesmc path modelng of earthquakes n md-amerca has provded results that are already ncorporated nto project HD-1. Project HD-4 on ste modelng establshed procedures for conductng ste-specfc hazard analyses when detaled knowledge of local ste condtons are avalable. Projects HD-2 on ntraplate ground moton and HD-5 on verfcaton of ste response paradgms do not have results to be mplemented now, but the upcomng fndngs n these projects may mprove the hazard models n MAEvz n the future. Project HD-2 has started to yeld crtcal nformaton that wll help constran recurrence ntervals for large earthquakes n the New Madrd Sesmc Zone (NMSZ). Project HD-5 s ntended to valdate the ground moton models used for the Msssspp Embayment regon Sesmc Source Defnton The New Madrd fault s roughly composed of three prmary segments: New Madrd North, Reelfoot, and Cottonwood Grove, also called the Blythevlle Arch. Prmary (.e., default) sesmc sources for the New Madrd Sesmc Zone have been defned by the Hazard Defnton (HD) thrust for use n MAEVz wth pared data ndcatng the magntude and locaton of scenaro events. The source events orgnate on the Blythevlle Arch for Memphs, Tennessee, and on the New Madrd North fault for St. Lous, Mssour and Caro, Illnos. The Memphs source events are located wth a maxmum magntude event near the center of the Blythevlle Arch (at Blythevlle, Arkansas) and wth a lesser magntude event near the southern tp of the Blythevlle Arch, at Marked Tree, Arkansas. The source events that are consdered crtcal for St. Lous and Caro happen to be the same locaton, and are both located at Caro, Illnos. The Wabash Valley Sesmc Zone also poses a sgnfcant threat to Md-Amerca, and St. Lous, Mssour n partcular. A Wabash Valley sesmc source was proposed by the team workng on a project for the Illnos Emergency Management Agency wthn the MAE Center, ncludng members of the HD thrust. MAEVz wll nclude these sources as default choces for Md- Amerca. Default magntude and locaton data are shown n Table Table Default Scenaro Event Sesmc Sources for Md-Amerca Sesmc Zone Crtcal Cty Magntude Lattude Longtude New Madrd Memphs, TN N W New Madrd Memphs, TN N W 1 Throughout the report, specfc projects wthn the MAE Center are dentfed whle hghlghtng specfc contrbutons from those projects. 68

69 New Madrd St. Lous, MO N 89.12W New Madrd St. Lous, MO N 89.12W New Madrd Caro, IL N 89.12W New Madrd Caro, IL N 89.12W Wabash Valley St. Lous, MO N 88.17W The sources provded by the HD thrust represent deaggregaton of USGS probablstc sesmc hazard maps to determne lkely combnatons of earthquake magntude and locaton, but also ncorporate expert opnon of multple team members n establshng the fnal locatons. MAEVz also offer users the opton of specfyng a magntude and locaton of ther choosng. For a scenaro event, there s a presumpton of the occurrence of a partcular event, and thus there s no quantfed uncertanty assocated wth the choce of the source event. Smlarly, the descrpton of a source event cannot be framed wthn the context of a constant recurrence nterval Ground Moton Attenuaton Ground moton s determned at nventory locatons as a functon of the magntude and dstance of a sesmc event and sol data. Multple attenuaton functons process ths data and output local ground motons, whch are then weghted and combned to arrve at a sngular set of ground moton data (PGA, PGV, PGD, S a, S v, S d ) Attenuaton to Locatons Insde the Msssspp Embayment Part of the HD thrust was devoted to developng more approprate attenuaton models for the Msssspp Embayment than those currently n use by USGS. Memphs, TN and Caro, IL are both located wthn the Msssspp Embayment. Fgure , from Fernandez and Rx (2006), shows the extents of the Embayment. 69

70 Fgure Extents of Msssspp Embayment [from Fernandez and Rx (2006)] Fernandez and Rx (2006) used one-corner-frequency (Frankel et al and Slva et al. 2003) and two-corner frequency (Atknson and Boore, 1995) pont source models for establshng the attenuaton relatons assocated wth pont epcenters. Three values of medan stress drop are used for each of the one-corner-frequency models, resultng n a total of seven attenuaton relatons (see Table B ). The effects of nonlnear sol were also ncluded n each attenuaton relaton, usng the equvalent lnear method (separate from the work conducted for Project HD-4 on response of nelastc sol). Each attenuaton relatonshp predcts ground motons and spectral values as a functon of magntude, dstance, sol type (Uplands or Lowlands), and sol depth. See Appendx secton B for more nformaton. Sol maps contanng default data (sol type and depth) for the Msssspp Embayment have been ncorporated nto MAEVz. The default sol values can be modfed by the user to adjust sol type (Uplands vs. Lowlands) or sol depth n accordance wth more detaled ste nformaton, when avalable, by substtutng a revsed shape fle when MAEVz reads n sol data (all terran and hazard nformaton are typcally to be stored wthn a GIS database). Magntude, dstance to epcenter, and sol data are passed nto the seven Msssspp Embayment attenuaton functons, and the functon outputs are weghted and combned to arrve at fnal peak ground motons and spectral values. The attenuaton functons are also capable of provdng spectral values for 298 perods between 0.01 and 10 seconds. Aleatory uncertanty was ncluded by the HD team wth respect to source (e.g. stress drop, depth), path, and ste response parameters, as well as random modelng errors, when developng the attenuaton functons for the Msssspp Embayment. See Appendx B for more nformaton. 70

71 USGS Attenuaton to Locatons Insde the CEUS but Outsde the Msssspp Embayment When the regon of nterest s outsde of the Msssspp Embayment, the attenuaton functons used by USGS n developng ts probablstc maps are more approprate than those developed wthn the MAE Center specfcally to address the geology of the Msssspp Embayment. The USGS attenuaton functons, unlke those developed wthn the MAE Center for the Msssspp Embayment, do not nclude the effects of local sol amplfcaton. Therefore, obtanng ground motons outsde of the Msssspp Embayment s a two-step process. Probablstc bedrock moton s determned at a locaton of nterest based on the typcal USGS CEUS attenuaton functons n the frst step, and determnstc ste-specfc sol amplfcaton effects from NEHRP are ncluded n the second step to determne peak ground surface response and spectral values. MAEVz currently assumes ste class D at all locatons outsde the Msssspp Embayment, unless the user provdes more detaled nformaton. Most USGS CEUS attenuaton relatons are for ste class A (hard rock) ste motons, but the ste amplfcaton factors n NEHRP are for B/C motons. Wherever the approach of usng the determnstc NEHRP factors s employed, correcton factors are requred to provde more accurate hazard results. Only the Frankel et al. (1996) model provdes B/C motons. The spectral acceleraton results of the remanng four CEUS attenuaton relatons must be corrected by the followng factors lsted n Table (Fernandez, 2006). Values may be lnearly nterpolated for perods between those lsted n the Table. Note that these factors should be appled to actual acceleraton values, not the lognormal outputs that are commonly obtaned as drect outputs from the attenuaton functons. Functons descrbng the uncertanty assocated wth the CEUS relatons used by USGS are avalable and ready for mplementaton n MAEVz Toro and Slva ste factors (84ºW to 96ºW, 36ºN to 40ºN) The NEHRP ste factors were developed for the geology of the WUS (see Borcherdt, 1994 and Dobry et al., 2000 for dscusson on NEHRP sol factors). Hazard estmaton for the CEUS outsde of the Msssspp Embayment can be mproved by usng generalzed sol amplfcaton factors developed by Toro and Slva (2001) for the Central U.S. rather than the NEHRP sol factors. Ths method provdes a more accurate hazard estmate for the CEUS outsde of the Msssspp Embayment, relatve to usng NEHRP factors, both n terms of geologc effects on sesmc response and also n terms of provdng nsght nto the range of uncertanty that should be expected for sol amplfcaton MAEC Attenuaton to Locatons Insde the CEUS but Outsde the Msssspp Embayment 71

72 For the long term future, an approach to computng weghted attenuaton n the CEUS outsde the Msssspp Embayment s beng developed for mplementaton smlar to the approach used wthn the Msssspp Embayment as descrbed n Secton USGS Attenuaton to WUS Locatons See Secton 3.1 and Table The MAEC s not currently developng attenuaton models for the WUS Attenuaton to Locatons outsde the US The MAEC s not currently developng attenuaton models outsde the US Implementaton of Scenaro-Based Ground Shakng Hazard Models Scenaro-based ground shakng hazard models are approprate for loss assessment studes of many nventory tems and nterconnected systems over a broad regon. In order to obtan the ground shakng hazard for a partcular scenaro, a magntude and locaton of the source event must be specfed, as outlned n Secton 3.2.2, and approprate attenuaton functons must be selected, as outlned n Secton To mprove the accuracy of the hazard estmaton, sol data may be updated to better reflect actual condtons when they are known. Weghtng factors on attenuaton functons may also be adjusted to emphasze certan features of the study regon. The epstemc uncertanty assocated wth the use of attenuaton functons can by quantfed by calculatng the varance of the functon outputs about the mean. For example, the attenuaton functons provded by the HD thrust output the natural logarthm of hazard parameters (e.g., ln(pga), ln(s a )), and the weghtng factors provded for the functons used n the Msssspp Embayment are applcable to the natural logarthm values. Epstemc uncertanty s computed as follows: n 7 ( ) ln( ) = = ln y w y ( ) = 1 2 e n 7 = = 1 ( ( ) ( )) 2 ln y ln y β = w ( ) n = 7 = 1 w = 1.0 ( ) Where ( ) ln y s expected value of a ground moton hazard parameter for attenuaton functon based on Monte Carlo smulatons consderng aleatory uncertantes. The weghtng factor, w, 72

73 s the weghtng factor assocated wth attenuaton relatonshp, and there are n=7 attenuaton relatonshps used nsde the Msssspp Embayment, as shown n Table B The aleatory uncertanty for each attenuaton functon s computed along wth sesmc hazard parameters usng equatons provded by the HD team (see Equaton (B )). The expressons used to compute aleatory uncertanty were derved based on performng Monte Carlo smulatons varyng the aleatory parameters, such as stress drop, depth to source, path to ste, and ste response parameters lke shear wave velocty profle. Aleatory uncertanty for multple attenuaton functons can be combned mathematcally by usng the followng formula: n 7 2 = = 2 β a wβ a, ( ) = 1 Where β a, s the standard devaton representng aleatory uncertanty for an ndvdual attenuaton relatonshp and the weghtng factors, w, sum to 1.0 as they dd when calculatng epstemc uncertanty. Note that the expressons provded for calculatng β a, actually provde the natural log of hazard parameters. Fnally, aleatory and epstemc uncertantes can be combned to fnd the total uncertanty usng β = β + β ( ) 2 total 2 e 2 a Implementaton of Probablstc Ground Shakng Hazard Models Probablstc hazard maps are approprate for estmatng rsk, framed wthn a tme nterval, across a study regon. The probablstc hazard represents the consderaton of the effects of multple possble events, and as such, provdes an estmaton of the probablty of exceedng a specfed hazard wthn a certan perod of tme at a partcular locaton. Snce the effects of all consdered events are represented for each mapped locaton, evaluatons of system nterdependences wll produce unrealstcally hgh rsk estmates. Consderatons of system nterdependences for probablstc scenaros must ncorporate a deaggregaton of the probablstc hazard nto the orgnal source events to obtan realstc results. Quantfable uncertanty n probablstc hazard suppled by the MAE Center s lmted to epstemc uncertantes. Aleatory uncertantes are ncorporated drectly n calculatons of the probablstc sesmc hazard curve plottng hazard magntude versus probablty of exceedence. Epstemc uncertantes may be computed as follows: n w = 1 ln λ = ln λ ( ) ( ) 2 ln λ ln n 2 2 total = σ e = w λ = 1 σ ( ) 73

74 where λ s the annual frequency of exceedance for a gven level of ground moton derved usng the th attenuaton relatonshp. Mean, mean + sgma, and mean sgma maps for the Msssspp Embayment have been provded by the HD thrust. If hazard at some fracton of sgma other than +/- 1 s desred, t may be determned as follows. Note that sgma s actually a logarthmc standard devaton. So, to fnd probablstc hazard for cases other than mean and mean +/- sgma, use the followng steps: 1. Isolate the logstandard devaton of ground moton. Ths may be done by takng ln(sgma) = ln(mean + sgma) ln(mean). 2. Apply whatever fracton of sgma s desred, x, to the value that was calculated n step Sum ln(mean) and x tmes ln(sgma) (from step 2). 4. Obtan hazard n terms of g by rasng e, the base of a natural logarthm, to the power of the value calculated n step 3. As an example, consder hazard level at 3 logstandard devatons (.e., x = 3 n step 2). The spectral acceleraton, Sa, for mean + 3 sgma would be e ^ ( ln(mean Sa) + 3*ln(sgma) ), where e s the base of a natural logarthm Ground Falure Hazard (Lquefacton) The development of lquefacton maps wthn the MAE Center for Memphs, Tennessee was coordnated by USGS as part of ther Memphs Hazards Mappng Project. As a result of the research conducted durng the Memphs Hazards Mappng Project, the MAE Center has been able to develop a generalzed approach for estmatng lquefacton potental at Memphs, TN (see Appendx B for a descrpton of the algorthm and the background that nfluenced ts development). Probabltes of lquefacton nduced damage are estmated as a functon of duraton adjusted PGA and regresson coeffcents correlated to sol types. The ground falure hazard metrc used by the MAE Center s lquefacton potental ndex (LPI). Coeffcents are provded to estmate probabltes of LPI 5 and LPI 15, whch correspond to the formaton of sand bols and lateral spreadng, respectvely. See Appendx secton B for further detals. Uncertanty s ntroduced nto LPI (and therefore ground falure hazard estmaton) by the lmted standard penetraton test (SPT) and cone penetraton test (CPT) data avalable, both n terms of the lmted number of samplng ponts and also the lack of a complete set of data for partcular samples (many samples do not extend the full depth preferred for LPI determnaton), the way n whch SPT and CPT data are mplemented (usng all, none, or some weghted porton of each data set), groundwater table elevaton, assumed homogenety of geologc unts, and the selecton of sesmc sources and attenuaton functons. However, uncertanty n the lquefacton hazard s not currently characterzed quanttatvely for the lquefacton hazard algorthm suppled by the MAE Center. 74

75 4. ENGINEERING ENGINES (FRAGILITY CURVES) 4.1 MAEVz Implementaton MAEVz can currently estmate structural damage to buldngs and brdges based on ground shakng hazard. Brdge fragltes are functons of PGA, but buldng fragltes are typcally functons of spectral acceleraton, and are therefore dependent on perod of the structure. The followng modfcatons are recommended for MAEVz hazard estmaton: Implement Parametrc Fragltes. Propagate hazard uncertanty effects through evaluaton of vulnerablty. Implement generalzed () nonstructural buldng fragltes. Combne ground shakng and ground falure probabltes of damage. Implement transportaton lfelne fragltes. Implement utlty lfelne fragltes. 75

76 4.1.1 Implement Parametrc Fragltes. Algorthm Inputs: Hazard n terms of PGA, 0.2 sec Sa, or 1.0 sec Sa, dependng on whch fraglty sets are beng used (hazard s gven n master buldng fraglty database). Three medan and lognormal standard devaton pars for each fraglty set (e.g., 3 pars of λ and β for a low-rse concrete shear wall structure, one par for each lmt state). Process: Prompt user to choose whether or not to use MAE Center parametrc fragltes. If user chooses to use parametrc fragltes, use mapped fragltes (see Appendx C). Evaluate probablty of exceedng each lmt state usng Equaton ( ). Outputs: probabltes of exceedng lmt states at lower bounds of Moderate, Heavy, and Complete damage. Example Parametrc fragltes offer an alternatve method of estmatng structural damage. Data for mappng of parametrc fragltes s provded n Appendx C. These fragltes may be used nstead of fragltes when the MAE Center has not performed research for a specfc buldng type. Durng the preparaton of ths document, only data for the Lowlands sol profle and 84 th percentle ground motons were avalable. In the future, data wll be provded for both Uplands and Lowlands at 50 th and 84 th percentle ground motons. The choce of ncluded ground moton uncertanty wll be a user opton, but MAEvz should determne whether Uplands or Lowlands sol underles a partcular buldng. For the mappng shown below, t s assumed that the user selected to use parametrc fragltes keyed to 0.2 second Sa hazard. Table Example Buldng Mappng for Parametrc Fragltes (Lowlands sol profle, 84 th percentle ground motons) Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Default Mapped Parametrc Fraglty Parametrc Pre- Low Rse Concrete Frame Parametrc Pre- Low Rse Unrenforced Masonry Parametrc Pre- Low Rse Unrenforced Masonry Default Fraglty ID SF_C1_42 SF_URM_9 SF_URM_9 76

77 Damage can be estmated usng a lognormal standard devaton, λs λ a P( LS = Φ λ S ) a ( ) β If parametrc fragltes were selected for use, then hazard would be calculated based on the hazard parameter approprate for a specfc parametrc fraglty database, whch would be 0.2 second Sa n ths case. In Table , the Perod column entres are all N/A (0.2) because a 0.2 second perod s used to estmate hazard, regardless of what the actual perod of the structure s. Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3) Table Example Ground Shakng Hazard Data Lattude Longtude Perod Mean, λ S a ln S a Standard devaton, N W N/A (0.2) N W N/A (0.2) N W N/A (0.2) β S a 77

78 Structural damage can be estmated by usng the hazard data n Table wth approprate fraglty parameters n Equaton ( ), resultng n the probablty of exceedence data shown n Table Table Sample Structural Fraglty Calculatons wth Parametrc Fragltes Inventory tems Lmt states, LS PL1 PL2 PL3 I1 Concrete Bracc (3-story) ) λ β P λ ( LS Sa I2 URM Wen (2-story) ) λ β P λ ( LS Sa I3 URM Wen (2-story) ) λ β P λ ( LS Sa 78

79 4.1.2 Propagate hazard uncertanty effects through evaluaton of vulnerablty. Algorthm Inputs: Medan and lognormal standard devaton of hazard n terms of PGA or Sa. Three medan and lognormal standard devaton pars for each fraglty set. Process: Compute equvalent lognormal uncertanty usng Equaton ( ). Use equvalent lognormal uncertanty from Equaton ( ) n Equaton ( ). NOTE: If structure type uncertanty s consdered, calculate damage for each structure type n the nventory. Outputs: probabltes of exceedng lmt states at lower bounds of Moderate, Heavy, and Complete damage, adjusted for hazard uncertanty. Example When hazard uncertanty s quantfed (see Table ), that effect can be reflected n the estmaton of vulnerablty. A closed form approach has been developed by J. Song wthn the MAE Center to reflect hazard uncertanty n damage estmaton (see Appendx D for more nformaton). The frst step s to evaluate an equvalent lognormal standard devaton, as shown n Equaton ( ). ( β ) 2 ( β ) 2 β = + ( ), equv Sa Where β S s the standard devaton of hazard (obtaned drectly from attenuaton functons), and a β s the lognormal standard devaton used n defnng a fraglty. The calculaton generally has the effect of flattenng the fraglty curve, reflectng a greater degree of uncertanty n damage estmaton. MAEVz calculatons to date have assumed that hazard estmaton s perfect,.e., has no uncertanty. Table shows the λ and β terms used to evaluate damage for the sample buldngs, as well as the estmatons of probablty of exceedence when consderng the effects of hazard uncertanty. 79

80 Table Sample Structural Fraglty Calculatons Inventory tems Lmt states, LS PL1 PL2 PL3 I1 Concrete Bracc λ β (3-story) P(LS ) I2 URM Wen λ β (2-story) P(LS ) I3 URM Wen λ β (2-story) P(LS ) If uncertanty s consdered for the nventory, then these same fraglty calculatons would need to be performed for each buldng type for each buldng. In ths small example, consderng only the three gven buldngs to be the entrety of the nventory, calculatons would have to be performed for a URM structure subjected to the I1 hazard and for a concrete structure subjected to the I2 and I3 hazards. 80

81 4.1.3 Implement generalzed () nonstructural buldng fragltes. Algorthm Inputs: Hazard n terms of Sa. Buldng perod obtaned from nventory database. Three medan and lognormal standard devaton pars for each fraglty set, for each type of nonstructural assets (acceleraton-senstve (AS NS) and drft-senstve (DS NS)). Process: Calculate equvalent lognormal spectral dsplacement usng lognormal spectral acceleraton and buldng perod, as shown n Equaton ( ). Compute equvalent lognormal uncertanty usng Equaton ( ). Evaluate AS NS and DS NS fragltes smlarly to buldng structural fragltes, usng equvalent lognormal uncertanty from Equaton ( ) n Equaton ( ) for each lmt state. NOTE: If structure type uncertanty s consdered, calculate damage for each structure type n the nventory. Outputs: probabltes of exceedng lmt states at lower bounds of Moderate, Heavy, and Complete damage, adjusted for hazard uncertanty, for AS NS and DS AS components. Example Most buldngs wll not have data to defne specfc nonstructural entty attrbutes, so a generalzed approach wll be mplemented n the nterm, pendng more refned data and algorthms. λ and β parameters to defne two generalzed types of nonstructural assets, drftsenstve and acceleraton-senstve, have been provded n the master fraglty database. The analyss approach s smlar to that used for structural vulnerablty. The only sgnfcant dfference beng that drft-senstve fragltes use spectral dsplacement rather than spectral acceleraton as a hazard parameter. To evaluate drft-senstve damage, the typcal fraglty expresson n terms of spectral acceleraton (see Equaton ) wll need to be adjusted to use spectral dsplacements, as shown n Equaton ( ). λs λ d P( LS = Φ ) ( ) β where λ and β are medan and lognormal standard devaton of capacty n terms of spectral dsplacement, and the mean demand n terms of lognormal spectral dsplacement may be related to the mean demand n terms of spectral acceleraton (that s, the typcal drect output of attenuaton functons) usng 81

82 2 ( 9.78 T ) λ = λ + ln ( ) Sd S a The natural perod, T, s obtaned for each structure from the nventory database (see Secton 2.1.2). In accordance wth the mappng shown n Appendx C, nonstructural fragltes used for I1 correlate to pre-code, low-rse concrete frame buldngs n, and nonstructural fragltes used for I2 and I3 correlate to pre-code, low-rse unrenforced masonry. Sample fraglty calculatons for nonstructural nventory are provded n Tables and Table Sample Acceleraton-Senstve Nonstructural Fraglty Calculatons Inventory tems Lmt states, LS PL1 PL2 PL3 I1 Concrete Bracc λ β (3-story) P(LS ) I2 URM Wen λ β (2-story) P(LS ) I3 URM Wen λ β (2-story) P(LS )

83 Table Sample Drft-Senstve Nonstructural Fraglty Calculatons Inventory tems Lmt states, LS PL1 PL2 PL3 I1 Concrete Bracc λ β (3-story) P(LS ) I2 URM Wen λ β (2-story) P(LS ) I3 URM Wen λ β (2-story) P(LS )

84 4.1.4 Combne ground shakng and ground falure probabltes of damage. Algorthm Inputs: Probablty of exceedng each lmt state for structural, AS NS, and DS NS components, as descrbed n Sectons and (ground shakng hazard). Probablty of major lquefacton, from Secton (ground falure hazard). Process: Compute probabltes of exceedng lmt states based solely on lquefacton, as shown n Equatons ( ) through ( ). Compute combned probabltes of exceedng lmt states based on both ground shakng and lquefacton, as shown n Equatons ( ) through ( ). Repeat ths process three tmes, once each for structural, AS NS, and DS NS damage. Compute dscrete combned probabltes of damage states, as shown n Equatons ( ) through ( ). Repeat ths process three tmes, once each for structural, AS NS, and DS NS damage. NOTE: If structure type uncertanty s consdered, calculate dscrete damage state probabltes for each component of each structure type n the nventory. Outputs: dscrete probabltes of damage states resultng from both ground shakng and ground falure hazard, for structural, AS NS, and DS AS components. Example Ground falure (lquefacton) s consdered to cause complete damage when LPI > 15, and to not cause apprecable damage otherwse. The calculaton to estmate the probablty of LPI > 15 was shown n Secton Table shows the nterpretaton of ground falure hazard calculatons relatve to damage states. Table Probabltes of Exceedng Damage State Thresholds caused by Ground Falure P(LPI>15) Lmt states, LS PL1 PL2 PL3 Inventory 1 (I1) Inventory 2 (I2) Inventory 3 (I3)

85 The data shown n Table can be wrtten n equaton form as follows ( PL1) = P ( LPI 15) ( PL2) = P ( LPI 15) ( PL3) = P ( LPI 15) P GF ( ) P GF ( ) P GF ( ) Where the GF subscrpt ndcates that the probablty s based on ground falure. Next, the probabltes of damage states resultng from combnatons of ground shakng (GS) and ground falure (GF) hazard types are calculated by: P P P ( DS C) = PGS ( PL3) + PGF ( PL3) PGS ( PL3) PGF ( PL3) ( DS H ) = PGS ( PL2) + PGF ( PL2) PGS ( PL2) PGF ( PL2) ( DS M ) = PGS ( PL1) + PGF ( PL1) PGS ( PL1) PGF ( PL1) ( DS I ) = 1 ( ) COMB ( ) COMB ( ) COMB P GF n all cases by defnton ( ) Where the probabltes of exceedence based on ground shakng were calculated as shown n Sectons and The damage states n Equatons ( ) through ( ) correspond to Complete (C), Heavy (H), Moderate (M), and Insgnfcant (I). Ths process s carred out for structural, acceleraton-senstve nonstructural, and drft-senstve nonstructural probabltes of exceedng damage states. For ths example, the combned probabltes of exceedng damage states are gven n Table , where AS NS ndcates acceleraton-senstve nonstructural, and DS NS ndcates drft-senstve nonstructural. As an example, to calculate the combned probablty of exceedence of Moderate damage (probablty that damage wll be at least Moderate ) for structural damage to tem I1, the probablty of ground shakng damage causng at least Moderate damage s (from Table ) and the probablty of ground falure damage causng at least Moderate damage s (from Table ). Equaton ( ) can then be used to obtan P COMB P COMB ( DS M ) = ( DS M ) = For another example calculaton, combned probablty of exceedence of Heavy acceleratonsenstve nonstructural damage for tem I2 can be calculated usng the probablty of ground shakng damage causng at least Heavy damage, from Table , and the probablty of 85

86 ground falure damage causng at least Heavy damage, from Table , n Equaton ( ) to obtan P COMB P COMB ( DS H ) = ( DS H ) = Table Sample Combned Probabltes of Exceedence Inventory tems Damage states, DS Moderate (M) Heavy (H) Complete (C) I1 Concrete Bracc (3-story) I2 URM Wen (2-story) I3 URM Wen (2-story) Structural AS NS DS NS Structural AS NS DS NS Structural AS NS DS NS Fnally, the dscrete probabltes of occurrence for each damage state are: P P P P COMB COMB COMB COMB ( DS C) = PCOMB ( DS C) ( DS H ) = PCOMB ( DS H ) PCOMB ( DS C) ( DS M ) = PCOMB ( DS M ) PCOMB ( DS H ) ( DS I ) = P ( DS M ) = ( ) = ( ) = ( ) = 1 ( ) COMB For example, the probablty of the Insgnfcant damage state, based on combned ground shakng and ground falure hazards, for acceleraton-senstve nonstructural assets n tem I2 s determned usng the probablty of at least Moderate damage, n Table , and Equaton ( ). 86

87 P COMB P COMB [ DS = I ] = [ DS = I ] = Table Sample Dscrete Probabltes of Damage States for Combned Hazard Inventory tems Damage states, Insgnfcant (I) Moderate (M) Heavy (H) Complete (C) DS I1 Concrete Bracc (3-story) I2 URM Wen (2-story) I3 URM Wen (2-story) Structural AS NS DS NS Structural AS NS DS NS Structural AS NS DS NS

88 4.1.5 Implement transportaton lfelne fragltes. Algorthm Inputs: Hazard n terms of PGA. Four medan and lognormal standard devaton pars for each fraglty set. Process: Evaluate probablty of exceedng each lmt state usng Equaton ( ). Compute dscrete probabltes of damage states, as shown n Equatons ( ) through ( ). Outputs: dscrete probabltes of None, Slght, Moderate, Extreme, and Complete damage states. Example Brdge damage may be estmated by applyng Equaton ( ) to obtan the results shown n Table Note that λ = LN(Medan PGA) for each fraglty curve. λpga λ P( LS λ = Φ PGA ) ( ) β Table Sample Brdge Fraglty Calculatons Parameters Damage States, DS Slght Moderate Extensve Complete λ Brdge 1 β P(LS λ PGA ) λ Brdge 2 β P(LS λ PGA ) λ Brdge 3 β P(LS λ PGA )

89 To obtan dscrete probabltes of damage states, use equatons ( ) through ( ), where N corresponds to a None damage state. P P P P P ( DS C) = P( DS C) = ( ) ( DS E) = P( DS E) P( DS C) = ( ) ( DS M ) = P( DS M ) P( DS E) = ( ) ( DS S ) = P( DS S ) P( DS M ) = ( ) ( DS N ) = P( DS S ) = 1 ( ) The dscrete probabltes of damage states for the sample brdges are shown n Table Table Sample Brdge Probabltes of Damage Probabltes of Damage States, DS None Slght Moderate Extensve Complete Brdge Brdge Brdge

90 4.1.6 Implement utlty lfelne fragltes. Electrc Power Plants Algorthm Inputs: Hazard n terms of PGA and Sa. One medan and lognormal standard devaton par for each fraglty set, one set for each component, as shown n Tables through Process: Evaluate probablty of exceedng the lmt state for each component usng Equaton ( ) for Sa or Equaton ( ) for PGA, dependng on partcular component (see Tables through ). Outputs: probabltes of damaged component for each component. Example Tables through present the fraglty curve nformaton for electrc power plant components. Note that λ = LN(Medan PGA) for each fraglty curve. The fragltes are calbrated to use ether PGA or Sa, as noted n the Tables through , n a logstandard CDF (smlar to buldngs wth Sa and brdges wth PGA). Table Electrc Power Plant Equpment - Electrcal Components - Well Anchored Component ID Component Medan A (g) β EPP_EC_1 Desel Generators EPP_EC_2 Battery Racks EPP_EC_3 Swtchgear EPP_EC_4 Instrument Racks and Panels EPP_EC_5 Control Panels EPP_EC_6 Aux. Relay Cabnets / MCCs / Crcut Breakers EPP_EC_7 Turbne

91 Table Electrc Power Plant Equpment - Mechancal Equpment - Well Anchored Component ID Component Medan A (g) β EPP_MC_1 Large vertcal vessels wth formed heads EPP_MC_2 Bolers and Pressure Vessels EPP_MC_3 Large horzontal vessels EPP_MC_4 Small to medum horzontal vessels EPP_MC_5 Large vertcal pumps EPP_MC_6 Motor Drven pumps EPP_MC_7 Large Motor Operated Valves EPP_MC_8 Large Hydraulc and Ar Actuated Valves EPP_MC_9 Large Relef, Manual and Check Valves EPP_MC_10 Small Motor Operated Valves Table Electrc Power Plant Equpment - Other Equpment Component ID Component Medan A (g) β EPP_OTH_1 Cable Trays EPP_OTH_2 HVAC Ductng EPP_OTH_3 HVAC Equpment Fans

92 Applyng the fraglty parameters gven above to the sample power plant nventory, probablty of damage may be estmated as shown n Table Note the power plant component fragltes estmate the probablty of damage occurrng to a partcular component, not the probablty of fallng nto one of several damage states, as was the case wth buldngs and brdges. Table Sample Electrc Power Plant Fraglty Calculatons Component Component ID λ β P(damage μ) EPP 1 Bolers + Steam Generators EPP_MC_ EPP 2 Bolers + Steam Generators EPP_MC_ EPP 3 Bolers + Steam Generators EPP_MC_

93 Electrc Substatons Algorthm Inputs: Hazard n terms of PGA. One medan and lognormal standard devaton par for each fraglty set, one set for each component, as shown n Tables through Process: Evaluate probablty of exceedng the lmt state for each component usng Equaton ( ) for Sa or Equaton ( ) for PGA, dependng on partcular component (see Tables through ). Outputs: probabltes of damaged component for each component. Example Tables through present the fraglty curve nformaton for electrc substaton components. The fragltes are calbrated to use PGA n a logstandard CDF (smlar to brdges). Note that λ = LN(Medan PGA) for each fraglty curve. 93

94 Table VHV Substaton Components (500 kv and Hgher) Component ID Component Medan A (g) β ESS_VHV_1 Transformer - Anchored ESS_VHV_2 Transformer - Unanchored ESS_VHV_3 Lve Tank Crcut Breaker - Standard ESS_VHV_4 Lve Tank Crcut Breaker - Sesmc ESS_VHV_5 Dead Tank Crcut Breaker - Standard ESS_VHV_6 Dsconnect Swtch - Rgd Bus ESS_VHV_7 Dsconnect Swtch - Flexble Bus ESS_VHV_8 Lghtnng Arrestor ESS_VHV_9 CCVT - Cantlevered ESS_VHV_10 CCVT - Suspended ESS_VHV_11 Current Transformer (gasketed) ESS_VHV_12 Current Transformer (flanged) ESS_VHV_13 Wave Trap - Cantlevered ESS_VHV_14 Wave Trap - Suspended ESS_VHV_15 Bus Structure - Rgd ESS_VHV_16 Bus Structure - Flexble ESS_VHV_17 Other Yard Equpment

95 Table HV Substaton Components (165kV kv) Component ID Component Medan A (g) β ESS_HV_1 Transformer - Anchored ESS_HV_2 Transformer - Unanchored ESS_HV_3 Lve Tank Crcut Breaker - Standard ESS_HV_4 Lve Tank Crcut Breaker - Sesmc ESS_HV_5 Dead Tank Crcut Breaker - Standard ESS_HV_6 Dsconnect Swtch - Rgd Bus ESS_HV_7 Dsconnect Swtch - Flexble Bus ESS_HV_8 Lghtnng Arrestor ESS_HV_9 CCVT ESS_HV_10 Current Transformer (gasketed) ESS_HV_11 Wave Trap - Cantlevered ESS_HV_12 Wave Trap - Suspended ESS_HV_13 Bus Structure - Rgd ESS_HV_14 Bus Structure - Flexble ESS_HV_15 Other Yard Equpment

96 Table MHV Substaton Components (100 kv - 165kV) Component ID Component Medan A (g) β ESS_MHV_1 Transformer - Anchored ESS_MHV_2 Transformer - Unanchored ESS_MHV_3 Lve Tank Crcut Breaker - Standard ESS_MHV_4 Lve Tank Crcut Breaker - Sesmc ESS_MHV_5 Dead Tank Crcut Breaker - Standard ESS_MHV_6 Dsconnect Swtch - Rgd Bus ESS_MHV_7 Dsconnect Swtch - Flexble Bus ESS_MHV_8 Lghtnng Arrestor ESS_MHV_9 CCVT ESS_MHV_10 Current Transformer (gasketed) ESS_MHV_11 Wave Trap - Cantlevered ESS_MHV_12 Wave Trap - Suspended ESS_MHV_13 Bus Structure - Rgd ESS_MHV_14 Bus Structure - Flexble ESS_MHV_15 Other Yard Equpment

97 Applyng the fraglty parameters gven above to the sample substaton nventory, probablty of damage may be estmated as shown n Table Note the substaton component fragltes estmate the probablty of damage occurrng to a partcular component, not the probablty of fallng nto one of several damage states, as was the case wth buldngs and brdges. Table Sample Electrc Substaton Fraglty Calculatons Component Component ID λ β P(damage λ Sa or λ PGA ) ESS 1 Transformer - Anchored ESS_MHV_ ESS 2 Transformer - Unanchored ESS_MHV_ ESS 3 Lve Tank Crcut Breaker - Standard ESS_VHV_

98 Water Tanks Algorthm Inputs: Hazard n terms of PGA. Four medan and lognormal standard devaton pars for each fraglty set, as shown n Tables through Partcular λ, β pars used for any gven water tank depend on the mappng scheme chosen n (Tables through ). Process: Evaluate probablty of exceedng each lmt state usng Equaton ( ). Compute dscrete probabltes of damage states, as shown n Equatons ( ) through ( ). Outputs: dscrete probabltes of None, Slght, Moderate, Extreme, and Complete damage states. Example The followng Tables provde data for water tank fragltes. All water tank fragltes are calbrated to use PGA as the hazard parameter n a logstandard CDF (smlar to brdges). If no data s suppled to allow mappng, use the frst fraglty gven n Table (Fll >= 50%, N=251) as a default. Table shows fragltes dependant upon the amount of flud n the tank, and Table presents fraglty nformaton dependant upon the anchorage of the tank. These parameters can be used to map approprate fragltes to nventory, assumng the user has the requred data. Note that λ = LN(Medan PGA) for each fraglty curve. Table Water Tank Fraglty Curves from Ednger (2001) by % Fll All Tanks, N=531 Fll < 50%, N=95 Fll >= 50%, N=251 Fll >= 60%, N=209 Fll >= 90%, N=120 Damage State Medan β Medan β Medan β Medan β Medan β Slght Damage Moderate Damage > Extensve Damage Complete Damage Table Water Tank Fraglty Curves from Ednger (2001) by Anchorage Fll >= 50%, N=251 Fll >= 50%, Anchored N=46 Fll >= 50%, Unanchored N=205 Damage State Medan β Medan β Medan β Slght Damage Moderate Damage Extensve Damage Complete Damage

99 Table presents water tank fraglty curves separated by the heght to dameter rato (H/D) and by the percentage of flud n the tank. Medan values gven n the tables are values of PGA wth unts of g. Note that λ = LN(Medan PGA) for each fraglty curve. Table Water Tank Fraglty Curves from O Rourke and So (1999) All Tanks H/D < 0.70 H/D >= 0.70 % Full > 50% Damage State Medan β Medan β Medan β Medan β Slght Moderate Extensve Complete Damage States (O'Rourke, M and So 1999) None No Damage Slght Damage to roof, mnor loss of content, mnor shell damage, no elephant foot falure Moderate Elephant foot buckng wth no leak or mnor loss of contents Extensve Elephant foot bucklng wth major loss of content, severe damage Complete Total falure, tank collapse 99

100 The fraglty curves appled to nventory and resultng probabltes of damage wll vary dependng on how the user chooses to map nventory to fragltes. If the user chooses to map to fragltes based on fll, the data shown n Table s obtaned, assumng the user has provded fll data for all tanks. The All Tanks fraglty s not used unless the user specfcally maps to t. Note that the probabltes shown are probabltes of exceedence. Table Sample Water Tank Fraglty Calculatons when Mappng by Fll (assumes user provdes fll data) Fll Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete Water Tank 1 40 Fll < 50% λ β P(LS λ PGA ) Water Tank % <= Fll < 60% λ β P(LS λ PGA ) Water Tank % <= Fll < 90% λ β P(LS λ PGA )

101 Alternatvely, f the user chooses to map based on fll, but does not provde fll data for some or all of the tanks, use the fraglty for fll greater than or equal to 50% and less than 60%. Usng that mappng, the data shown n Fgure s obtaned. Table Sample Water Tank Fraglty Calculatons when Mappng by Fll (assumes user does NOT provde fll data) Fll Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete Water Tank 1 Water Tank 2 Water Tank 3 50% <= Fll < 60% 50% <= Fll < 60% 50% <= Fll < 60% λ β P(LS λ PGA ) λ β P(LS λ PGA ) λ β P(LS λ PGA )

102 If the user chooses to map to fragltes based on anchorage, the data shown n Table s obtaned, assumng the user has provded fll data for all tanks. Note that the probabltes shown are probabltes of exceedence. Table Sample Water Tank Fraglty Calculatons when Mappng by Anchorage (assumes user provdes anchorage data) Anchored Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete λ Water Tank 1 N Unanchored β P(LS λ PGA ) λ Water Tank 2 Y Anchored β P(LS λ PGA ) λ Water Tank 3 Y Anchored β P(LS λ PGA )

103 Alternatvely, f the user chooses to map based on anchorage, but does not provde anchorage data for some or all of the tanks, use the fraglty whch represents an average of the anchored and unanchored water tank fragltes. Usng that mappng, the data shown n Fgure s obtaned. Table Sample Water Tank Fraglty Calculatons when Mappng by Anchorage (assumes user does NOT provde anchorage data) Anchored Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete Water Tank 1 Water Tank 2 Water Tank 3 Anchorage Unknown Anchorage Unknown Anchorage Unknown λ β P(LS λ PGA ) λ β P(LS λ PGA ) λ β P(LS λ PGA )

104 If the user chooses to map to fragltes based on H/D rato, the data shown n Table s obtaned, assumng the user has provded H/D data and fll level for all tanks. The H/D rato only enters the mappng f the fll level of the water tank s less than or equal to 50%. The All Tanks fraglty based on H/D s not used unless the user specfcally maps to t. Note that the probabltes shown are probabltes of exceedence. Table Sample Water Tank Fraglty Calculatons when Mappng by H/D and Fll (assumes user provdes H, D, and fll data) H/D % Fll > 50? Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete Water Tank False H/D < 0.7 λ β P(LS λ PGA ) λ Water Tank True Fll > 50%, H/D s N/A β P(LS λ PGA ) λ Water Tank True Fll > 50%, H/D s N/A β P(LS λ PGA )

105 Alternatvely, f the user chooses to map based on H/D rato, but does not provde ether H/D data, fll data, or both, for some or all of the tanks, use the fraglty whch represents an average of the water tank fragltes based on H/D ratos. Usng that mappng, the data shown n Fgure s obtaned. Table Sample Water Tank Fraglty Calculatons when Mappng by H/D and Fll (assumes user does NOT provde H, D, and fll data) H/D Fll Fraglty Parameters Damage States, DS Slght Moderate Extensve Complete Water Tank 1 Water Tank 2 Water Tank 3 All H/D and fll All H/D and fll All H/D and fll λ β P(LS λ PGA ) λ β P(LS λ PGA ) λ β P(LS λ PGA )

106 Fnally, to obtan dscrete probabltes of damage states, use equatons ( ) through ( ), where N corresponds to a None damage state, as for brdges. The dscrete probabltes for the water tanks are shown n Table resultng from varous mappng schemes. Table Sample Water Tank Probabltes of Damage for all Mappng schemes Fraglty Probabltes of Damage States, DS None Slght Moderate Extensve Complete Fll < 50% % <= Fll < 60% Water Tank 1 Unanchored Anchorage Unknown H/D < All H/D and fll % <= Fll < 60% % <= Fll < 60% Water Tank 2 Anchored Anchorage Unknown Fll > 50%, H/D s N/A All H/D and fll % <= Fll < 90% % <= Fll < 60% Water Tank 3 Anchored Anchorage Unknown Fll > 50%, H/D s N/A All H/D and fll

107 Bured Ppelnes Algorthm Inputs: Mapped fraglty set to use for ppes. Hazard n terms of PGV. Ppe materal requred for any ppe fraglty. Ppe dameter, jont type, and sol data may be requred, dependng on whch fragltes were selected by the user. Ppe segment lengths. Process: Evaluate repar rate usng nputs and backbone fraglty curves correspondng to the Researcher and fraglty mappng. Multply repar rate by the lengths of ppes to obtan expected number of repars. Outputs: expected number of repars for each ppe. Example Fraglty curves for bured ppelnes use PGV and ppe dameter nputs, and output repars per length of ppe. Table dsplays fraglty curves from three separate analyses for varyng types of bured ppelnes. The fragltes are lsted n order of preference n Table Requred mappng data s also lsted n Table Table shows the K coeffcents to be used wth the algorthm developed by Ednger (2001) presented n Table to determne ppe damage. 107

108 Table Fraglty curves for Bured Ppelnes Req d Non-dmensonal Source Mappng Materal Researcher Backbone Fraglty Curve Coeffcent (K) Earthquakes Data NOTES: Cast-Iron Ppe RR=0.050*(PGV/D ) Ppe materal, dameter RR: Repars / Km Ductle Iron Ppe O'Rourke,T and Jeon (1999) RR=0.004*(PGV/D ) N/A Northrdge Earthquake Ppe materal, dameter PGV: cm / sec Asbestos Cement Ppe Log (RR) = *Log(D)+8.96 (1994) Ppe materal, dameter D: cm Asbestos Cement Ppe Log(RR) = 2.26*Log(PGV) Ppe materal PGV: cm / sec Bured Ppelne O'Rourke, M and Ayala (1993) RR=K x (PGV) Cast-Iron, Asbestos, Cement, Concrete 11 data ponts from 4 US and 2 Mexcan Earthquakes Ppe materal RR: Repars / Km PGV: cm / sec Steel, Ductle Ppe materal Iron, PVC Bured Ppelne Ednger (2001) RR=K* *PGV Depends on Composton, Jont Type, Sol Condton, and Dameter 81 data ponts from 18 Earthquakes (Β: 1.15) Ppe materal, dameter, jont type, sols (see Table 2) PGV: n / sec RR: Repars / 1000 ft Table K Coeffcents from Ednger (2001) Ppe Materal Jont Type Sols Dameter K Cast Iron Cement All Small 1.0 Cast Iron Cement Corrosve Small 1.4 Cast Iron Cement Non-Corrosve Small 0.7 Cast Iron Rubber Gasket All Small 0.8 Welded Steel Lap - Arc Welded All Small 0.6 Welded Steel Lap - Arc Welded Corrosve Small 0.9 Welded Steel Lap - Arc Welded Non-Corrosve Small 0.3 Welded Steel Lap - Arc Welded All Large 0.2 Welded Steel Rubber Gasket All Small 0.7 Welded Steel Screwed All Small

109 Ppe Materal Jont Type Sols Dameter K Welded Steel Rveted All Small 1.3 Asbestos Cement Rubber Gasket All Small 0.5 Asbestos Cement Cement All Small 1.0 Concrete w/ Steel Cylnder Lap - Arc Welded All Large 0.7 Concrete w/ Steel Cylnder Rubber Gasket All Large 1.0 Concrete w/ Steel Cylnder Rubber Gasket All Large 0.8 PVC Rubber Gasket All Small 0.5 Ductle Iron Rubber Gasket All Small 0.5 For the sample ppelne, the length may be extracted from the shapefle data or calculated by MAEvz. A calculaton usng the Great Crcle method results n an approxmate dstance between the end nodes of km. Also, from Table , the lognormal mean PGV for the segment s Ths value s the natural log of PGV wth unts of cm/sec, so the expected mean of PGV s exp(3.4434) = cm/sec = n/sec. Usng the default mappngs descrbed n Secton wll provde the followng results. For Ednger (2001), the K term wll be taken as 1.0 to match the fraglty (Cast Iron, Cement, All, Small). Then repars 1000 ft repars RR = K PGV = = = ft km km And the total number of expected repars s repars E repars = km = km [ ] repars For O Rourke, M. and Ayala (1993), the K term wll be taken as 1.0 to match the fraglty (Cast Iron). Then repars RR = K PGV = ( 31.29cm / sec) = km And the total number of expected repars s repars E repars = km = 2. 8 km [ ] repars For O Rourke, T. and Jeon (1999), the dameter must be converted from 18 nches to cm. Then, for Cast Iron materal, 109

110 0.865 PGV 31.29cm / sec repars RR = = = D ( 45.72cm) km And the total number of expected repars s repars E 23 km [ repars] = km = 0. repars 110

111 4.1.7 Implement lquefacton damage estmaton for buldngs. Algorthm Inputs: Probablty of lquefacton for each buldng. Expected lateral spreadng for each buldng. Expected ground settlement for each buldng. Foundaton type for each structure (shallow or deep foundaton, assume shallow by default f no data s provded). Process: Calculate probabltes of exceedence for damage states as shown n Equatons ( ) through ( ) and adjust for deep foundatons, f applcable. Use the maxmum probabltes of exceedence between lateral spreadng and settlement. Outputs: Probabltes of exceedence for damage states resultng from ground falure. Example To calculate probablty of exceedng the Moderate and Heavy damage states for both lateral spreadng and ground settlement, use the typcal lognormal cumulatve dstrbuton functon (the same as for buldng fragltes) multpled by probablty of lquefacton, Equaton ( ). For shallow foundatons, the λ value s ln(60) for lateral spreadng and ln(10) for settlement when estmatng probablty of exceedng Moderate damage. The β value s 1.2 n both cases. The probablty of exceedng Heavy damage s taken as 20% of the probablty of exceedng Moderate damage. That s, for lateral spreadng, P GF P GF P GF ( PL ) ( PL ) ( PL ) ( E[ lateral _ spreadng] ) ln( 60) ln 1 = Φ P[ lquefacton] ( ) 1.2 ( E[ lateral _ spreadng] ) ln( 60) ln 2 = Φ P[ lquefacton] ( ) 1.2 ( E[ lateral _ spreadng] ) ln( 60) ln 3 = 0.2 Φ P[ lquefacton] ( ) 1.2 and for settlement, P GF P GF ( PL ) ( PL ) ( E[ settlement] ) ln( 10) ln 1 = Φ P[ lquefacton] ( ) 1.2 ( E[ settlement] ) ln( 10) ln 2 = Φ P[ lquefacton] ( )

112 P GF ( PL ) ( E[ settlement] ) ln( 10) ln 3 = 0.2 Φ P[ lquefacton] ( ) 1.2 For buldngs wth deep foundatons, the probabltes evaluated n Equatons ( ) through ( ) are dvded by 10, and the probabltes evaluated n Equatons ( ) through ( ) are dvded by 2. Probabltes of ground falure damage are then combned wth probabltes ground shakng falure as ndcated n Secton From Secton 3.1.6, P [ lquefacton] = 0.25 [ lateral _ spreadng] = n [ settlement] = n E 67 E 3 Then for lateral spreadng of shallow foundatons P GF P GF P GF ( PL ) ( PL ) ( PL ) ( 67) ln( 60) ln 1 = Φ 0.25 = ( 67) ln( 60) ln 2 = Φ 0.25 = ( 67) ln( 60) ln 3 = 0.2 Φ 0.25 = and for ground settlement of shallow foundatons P GF P GF P GF ( PL ) ( PL ) ( PL ) () 3 ln( 10) ln 1 = Φ 0.25 = () 3 ln( 10) ln 2 = Φ 0.25 = () 3 ln( 10) ln 3 = 0.2 Φ 0.25 = The maxmum exceedence probabltes are used, so the quanttes used for combnaton wth ground shakng hazard are P GF P GF P GF ( PL1 ) = MAX (0.539, 0.158) = ( PL2 ) = MAX (0.539, 0.158) = ( PL3 ) = MAX (0.108, 0.032) = Calculatons for lateral spreadng wth deep foundatons are smlar to those performed for shallow foundatons, except wth smple multplers. 112

113 P GF P GF P GF ( PL ) ( PL ) ( PL ) ( 67) ln( 60) ln 1 1 = Φ 0.25 = ( 67) ln( 60) ln 1 2 = Φ 0.25 = ( 67) ln( 60) ln 1 3 = 0.2 Φ 0.25 = and for ground settlement of deep foundatons P GF P GF P GF ( PL ) ( PL ) ( PL ) () 3 ln( 10) ln 1 1 = Φ 0.25 = () 3 ln( 10) ln 1 2 = Φ 0.25 = () 3 ln( 10) ln 1 3 = 0.2 Φ 0.25 = Agan, the maxmum exceedence probabltes are used, so the quanttes used for combnaton wth ground shakng hazard are P GF P GF P GF ( PL1 ) = MAX (0.269, ) = ( PL2 ) = MAX (0.269, ) = ( PL3 ) = MAX (0.054, ) =

114 4.1.8 Implement Capacty Spectrum Method (CSM) for fragltes. Algorthm Inputs: Spectral acceleraton at 0.3 and 1 second perods, ncludng sol effects. (If 0.2 second Sa s avalable nstead of 0.3 second for USGS CEUS attenuatons, dvde by 1.4 to obtan approxmate 0.3 second hazard for CEUS.) Spectral acceleraton and dsplacement at yeld, and spectral acceleraton at ultmate for buldng type and code level (from NIBS (2006)). Lognormal medan and standard devaton for buldng type and code level (from NIBS (2006)). Process: Determne demand for a gven structure usng the CSM. Evaluate structural, drft- and acceleraton-senstve damage usng cumulatve lognormal dstrbuton and demand from CSM. Calculate dscrete probabltes of damage states (adjust for lquefacton f approprate). User opton: adjust probabltes of damage states so that nonstructural damage s at least as lkely to experence complete damage as structural damage. Outputs: Dscrete probabltes of damage states usng CSM. Example Consder the I1 example buldng (3-story, Pre- C1 structure) subjected to CEUS ground motons from an M w = 7.9 event at Blythevlle, AR. Usng Ste Class D for NEHRP factors, S a at 0.2 seconds s 0.703g and Sa at 1 second s 0.374g. The frst step n ths case s to calculate an approxmate S a at 0.3 seconds usng the 0.2 seconds value, / 1.4 = 0.502g. The S a value at 0.3 seconds wll be referred to as S s, and the S a value at 1 second wll be referred to as S 1. Compute spectral dsplacement at the end of the constant spectral acceleraton range usng Equaton ( ) S dlh 2 S 1 = 9.8 ( ) S s For the sample buldng, S dlh = 2.73 nches. The capacty spectrum wll be a blnear functon, lnearly ncreasng from S a and S d = 0, and havng constant S a wth ncreasng S d at the ultmate spectral acceleraton capacty of the structure, A u. The slope of the lnear porton s defned by the spectral acceleraton and dsplacement at yeld, A y and D y. These three parameters are avalable n the Techncal 114

115 Manual (NIBS, 2006). For the sample buldng, NIBS (2006) lsts D y = 0.1 nches, A y = 0.062g, and A u = 0.187g. There are three possble scenaros for the CSM: the nclned porton of the capacty curve ntersects the constant porton of the demand curve, the nclned porton of the capacty curve ntersects the decreasng porton of the demand curve, or the nclned porton of the capacty curve ends before reachng the demand curve. To determne whch of these cases controls, and calculate CSM demand parameters, use the followng method: Ay S s If AND S s Au D S y dlh Then S a = S s ( ) Dy S d = S s ( ) Ay If A u = 0.55g rather than 0.187g, ths case would apply. The CSM would provde results as shown n Fgure , wth S a = 0.502g and S d = nches. Spectral Acceleraton, Sa (g) Spectral Dsplacement, Sd (n) Demand Capacty Intersecton Fgure Example CSM result for Case 1 Else If 9.8 A A y S s y < AND S1 Au Dy S dlh Dy Then 115

116 S S a d 9.8 Ay = S1 ( ) D y 9.8 Dy = S1 ( ) A y If A u = 0.55g rather than 0.187g and D y = 0.5 nches rather than 0.1 nches, ths case would apply. The CSM would provde results as shown n Fgure , wth S a = 0.412g and S d = nches. Spectral Acceleraton, Sa (g) Spectral Dsplacement, Sd (n) Demand Capacty Intersecton Fgure Example CSM result for Case 2 Else S a = A u ( ) S d 2 S1 = 9.8 ( ) A u Ths s the case that apples to the sample structure wth the parameters gven n NIBS (2006). The CSM provdes results as shown n Fgure , wth S a = 0.187g and S d = nches. 116

117 Spectral Acceleraton, Sa (g) Spectral Dsplacement, Sd (n) Demand Capacty Intersecton Fgure Example CSM result for Case 3 Wth the S a and S d hazard parameters obtaned from the CSM, evaluaton of buldng structural and nonstructural damage may be carred out usng cumulatve lognormal dstrbuton functons, as currently mplemented. Usng the λ and β parameters for Pre- C1L structures n NIBS (2006), probabltes of exceedence for performance lmts may be determned, and dscrete probabltes of ndvdual damage states may then be computed, as shown n Table (these calculatons assume lquefacton s neglgble). Table Sample Base Calculatons for fragltes wth CSM Damage States, DS I M H C I1 C1L (3-story) Structural Drft-Senstve Nonstructural Acceleraton-Senstve Nonstructural These damage state probabltes may be used as they are to compute expected losses, or f the user elects, they may be adjusted to ensure that nonstructural components have at least the same probablty of Complete damage as the structure tself. To make ths adjustment, use Equatons ( ) and ( ) for both drft- and acceleraton-senstve nonstructural damage state probabltes. NS ( 1 P( DS C ) NS NS str P ( DS C) adj = P( DS = C) base + P( DS = C) = ) base = ( ) 117

118 NS Where P ( DS = C) adj s the adjusted probablty of complete damage for nonstructural NS components, P ( DS = C) base s the base probablty of complete damage for nonstructural str components as shown n Table , and P ( DS = C) s the probablty of complete damage for the structural components. Ths equaton should be appled once for each of drft- and acceleraton-senstve nonstructural components. Then, use NS adj NS base str ( 1 P( DS C ) P ( DS ) = P( DS ) = ) ( ) NS to adjust other nonstructural damage state probabltes, where P ( DS ) adj are the adjusted NS probabltes of damage states for nonstructural components, and P ( DS ) base are the base probabltes of damage states for nonstructural components as shown n Table DS ranges from Insgnfcant to Heavy, for a total of sx applcatons of Equaton ( ) per buldng (2 types of nonstructural components tmes 3 damage states). Sample calculatons for adjusted damage state probabltes are gven n Table Table Sample Adjusted Calculatons for fragltes wth CSM Damage States, DS I M H C I1 C1L (3-story) Structural Drft-Senstve Nonstructural Acceleraton-Senstve Nonstructural

119 4.2 Background Buldng structures Buldng Structural Damage Buldng fragltes have been developed by the MAE Center for constructon typcal of the Md-Amerca regon (e.g., Erberk and Elnasha, 2006; Kwon and Elnasha, 2006; Ba and Hueste, 2006; Ba and Hueste, 2007; Celk and Ellngwood, 2006; Ellngwood, 2005; Hueste and Ba, 2007; Hueste and Ba, 2007; Ramamoorthy et al., 2006; Ramamoorthy et al., 2006). These vulnerablty functons were derved by conductng structural analyses that accounted for aleatory uncertanty related to both structural characterstcs and exctaton uncertanty. Structural uncertantes are ntroduced by varatons n materal and geometrc propertes. Exctaton uncertanty s ntroduced by ncludng varous synthetc ground motons wth dfferent frequency contents and duratons. Uncertanty n sesmc ntensty s obtaned from the hazard model. Table lsts the fraglty curves that have been derved for buldngs wthn the MAE Center. See Appendx C for a proposed mappng scheme relatng nventory to fragltes, as well as supplementary fraglty metadata. Table MAE Center Buldng Fraglty Curves PI Hueste (TAMU) Structure 5 Story flat-slab wth permeter RC moment frame (1980s central U.S. offce buldngs) Retrofts (1) Shear wall-permeter frames, (2) Column jacketng, (3) Confnng wth steel plates at column ends. (Sesmc/Nonsesmc) Sesmcty Sa at fundamental buldng perods (from gven number of stores). (Ground motons by (1) Wen & Wu and (2) Rx & Fernandez-Leon.) Lmt states FEMA356 (Based on nterstory drft ratos) (1) IO (mmedate occupancy: global/member), (2) LS (lfe safety: global/member), (3) CP (collapse preventon: global/member), (4) FY (frst yeld), (5) PMI (plastc mechansm ntaton), (6) SD (strength degradaton). Parameters λ and β of lognormal CDF. See Equaton ( ). Fundamental As-bult T 1 = 0.32 *, 1.62 seconds for model buldng Perod Retroft (1) T 1 = 0.13 *, 0.66 seconds for model buldng Retroft (2) T 1 = 0.28 *, 1.38 seconds for model buldng Retroft (3) T 1 = 0.32 *, 1.62 seconds for model buldng PI Structure Retrofts Sesmcty Bracc & Gardon (TAMU) RC moment frame systems (desgned prmarly for gravty loads) story heghts 1-10 (fraglty surfaces) Low-rse RC frames retroftted by column strengthenng (ACI 318 requrements). Sa at fundamental buldng perods (from gven number of stores). 119

120 Lmt states From FEMA 356: Immedate Occupancy (0.5% IDR), Lfe Safety (1% IDR), Collapse Preventon (2% IDR) Parameters lognormal CDF usng α 11 α 12 α 13 α 14 α 21 α 22. See Equatons ( ) and ( ). η Fundamental T 1 = η ( ) 2 1 h, whereη 1 = 0.097, η 2 = 0.624, and h = heght of buldng frame from base Perod (ft). Typcally assume 13 ft story heght. PI Ellngwood (GT) & Rosowsky (TAMU) Structure Low-rse steel frames, wood shear walls Selected story heghts Retrofts N/A Sesmcty Sa at selected fundamental buldng perods. Lmt states Steel: Elastc Lmt (vares), 2%, Collapse Preventon based on IDA Wood: 0.5%, 1%, 2% Interstory Drft Parameters Medan Sa (= S a ) and β of lognormal CDF. See Equaton ( ). Fundamental Perod 2-story PR steel frame, T 1 = 1.07 seconds for model buldng 3-story FR steel frame, T 1 = 2.01 seconds for model buldng 4-story PR steel frame, T 1 = 1.34 seconds for model buldng 6-story X-braced steel frame, T 1 = 1.04 seconds for model buldng 1-story wood frame on slab-on-grade, T 1 = 0.24 seconds for model buldng 1-story wood frame on crpple wall/crawl space, T 1 = 0.22 seconds for model buldng 2-story wood frame on slab-on-grade, T 1 = 0.38 seconds for model buldng PI Wen (UIUC) Structure Unrenforced masonry buldngs Selected story heghts Retrofts N/A Sesmcty Sa at selected fundamental buldng perods. Lmt states Un-renforced masonry: IO (0.3% FEMA), LS (0.6% FEMA), IC (1.5% IDA) Parameters Medan Sa (= S a ) and β of lognormal CDF. See Equaton ( ). Fundamental T 1 = 0.3 *, 0.55 seconds for model buldng Perod PI Structure Retrofts Sesmcty Lmt states Elnasha (UIUC) 5-story 3-bay flat slab moment frame wth masonry nfll walls N/A Sa at selected fundamental buldng perods. Lmt States, based on Interstory Drft Rato (IDR) Slght (0.1% IDR), Moderate (1% IDR), Extensve (2% IDR), Complete (3.5% IDR) 120

121 Parameters λ and β of lognormal CDF. See Equaton ( ). Fundamental T 1 = 0.2 *, 0.98 seconds for model buldng Perod PI Elnasha (UIUC) & Kuchma (UIUC) Structure Frame Core wall coupled system (hgh-rse) Retrofts N/A Sesmcty Sa at selected fundamental buldng perods. Lmt states Servceablty (0.2% IDR), Damage Control (0.2% IDR), Collapse Preventon (0.2% IDR) Parameters λ and β of lognormal CDF. See Equaton ( ). Fundamental T 1 = 0.08 *, 3.05 seconds for model buldng Perod Most fragltes developed wthn the MAE Center to estmate structural damage use lognormal medan and standard devaton parameters λ and β. The equaton descrbng the probablty of exceedng a certan lmt state, gven a spectral acceleraton s P ( LS S ) ( S ) ln a λ a = Φ ( ) β Where S a s the demand spectral acceleraton, obtaned from attenuaton functons for a scenaro event or from a map for a probablstc hazard analyss. Φ represents the standard normal cumulatve dstrbuton functon. In some cases, MAE Center PIs report medan spectral acceleraton values for lmt states. Equaton ( ) may stll be used n those cases, except that λ must be taken as λ = ln( medan S a ) = ln( S ). An alternatve form s also ncluded n the MAE Center fragltes for fraglty surfaces whch apply to several story heghts (Ramamoorthy et al., 2006). The MAE Center fraglty surface equatons have the form P when and when ( LS S ) a ln = Φ 0.87 T (sec) ( S a ) ( α + T ) ( ) 11 α12 α13 + α14t ( S a ) ( α + α ) ( α + α 0.87) a ( S ) ( ) ln 11 ln a α 21 P ( LS S ) = Φ + ( 0.87 ) a T ( ) α 22 0 < T < 0.87(sec) 121

122 where S a and Φ are the same as n Equaton ( ), and the α terms are specfed for each lmt state by the MAE Center PI provdng the fragltes. For MAE Center buldng fragltes, there are consstently four damage states (DS): Insgnfcant (I), Moderate (M), Heavy (H), and Complete (C). uses fve damage states: None, Slght, Moderate, Extensve, and Complete. MAE Center damage states Complete, Heavy, and Moderate map approxmately to Complete, Extensve, and Moderate. The MAE Center Insgnfcant damage state s approxmately equvalent to the combnaton of None and Slght damage states. Therefore, when comparng results between MAE Center fragltes and fragltes, or when adaptng fragltes for use n MAEVz, the three heavest damage states wll be consdered to map drectly to each other, whle the combnaton of the two lghtest damage states wll be consdered to map to the Insgnfcant MAE Center damage state. MAE Center fraglty curves set the thresholds for probabltes of exceedng these lmt states, therefore ( DS I ) = P( PL1 S a ) ( DS M ) = P( PL2 S a ) ( DS H ) = P( PL3 ) P > ( ) P > ( ) P > ( ) S a Where the numbers followng PL correlate to the use of fraglty parameters for approprate lmt states (gven by MAE Center PIs). For the fragltes, the lmt state numbers would ncrease by 1 n each case. For example, PL4 for corresponds to the probablty of havng damage heaver than Extensve, and the Extensve damage state s approxmately equvalent to the Heavy damage state n the MAE Center. Ths can also be stated as the probablty of havng damage greater than or equal to Complete damage. For clarty, expressons have been provded n ( ) through ( ) to defne equvalent MAE Center damage states from damage states. ( DS I ) = P( DS M ) = P( PL2 S d ) ( DS M ) = P( DS E ) = P( PL3 S d ) ( DS H ) = P( DS C ) = P( PL3 S ) P > ( ) P > ( ) P > ( ) Dscrete probabltes of damage states may then be computed by ( DS C) = P( DS H ) ( DS H ) = P( DS > M ) P( DS H ) ( DS M ) = P( DS > I ) P( DS M ) ( DS I ) = P( DS I ) P = > ( ) P = > ( ) P = > ( ) P = 1 > ( ) d 122

123 Buldng Nonstructural and Contents Damage The MAE Center has provded nonstructural fragltes to descrbe specfc nonstructural components for the MLGW project. When avalable, specfc nonstructural nventory data wll be used for loss assessments and pared wth approprate fragltes for specfc components. In most cases, specfc nonstructural nventory data are not avalable, and nonstructural damage algorthms wll need to be adapted from -MH as an nterm measure pendng the mplementaton of MAE Center algorthms for estmatng damage to general nonstructural and contents. -MH does not consder specfc nonstructural nventory tems, but rather breaks nonstructural nventory nto two subsets: drft-senstve and acceleraton-senstve. Values of each subset of nonstructural nventory can be parttoned from the total buldng value usng the percentages shown n Table The drft senstve non-structural fragltes are based on global buldng dsplacement, whch may be estmated as the spectral dsplacement, S d, related to spectral acceleraton, S a, as shown n Equaton ( ). Accordng to the Techncal Manual (NIBS, 2006), uncertanty for each non-structural drft senstve damage state s assumed to orgnate from one of three contrbutors: uncertanty n the damage state threshold of nonstructural components, varablty n capacty of the model buldng type that contans the nonstructural components (.e., dsplacements determned by Capacty Spectrum Method), and varablty n response of the model buldng type due to the spatal varablty of ground moton demand. These uncertantes are combned to arrve at a sngle β term, whch s coupled wth a medan spectral dsplacement, S d, to defne a lognormal fraglty formulaton. Values of S d and β from the Techncal Manual are provded n Appendx C. Note that damage states Complete, Extensve, and Moderate correlate approxmately to MAE Center damage states Complete, Heavy, and Moderate, respectvely. The MAE Center damage state Insgnfcant s approxmately equvalent to the combnaton of Slght and None damage states. Fragltes for acceleraton-senstve nonstructural assets are based on spectral acceleraton. Accordng to the Techncal Manual, nonstructural acceleraton-senstve components are dvded nto two subpopulatons: (1) components at or near ground level and (2) components at upper floors or on the roof. Also, accordng to the Techncal Manual, PGA, rather than spectral acceleraton, s a more approprate hazard nput for components at or near ground level. Fraglty curves used by for nonstructural acceleraton-senstve components assume 50% (low-rse), 33% (md-rse) or 20% (hgh-rse) of nonstructural components are located at, or near, the ground floor, and represent a weghted combnaton of the probablty of damage to components located at, or near, ground level and components located at upper-floor levels of the buldng. Varablty of each non-structural acceleraton senstve damage state s consdered to orgnate from the same three contrbutors mentoned prevously wth regard to 123

124 drft-senstve fragltes. The general form of the fraglty equaton for acceleraton-senstve nonstructural components s smlar to Equaton ( ), except that the Techncal Manual provdes medan Sa values nstead of λ values. Equaton ( ) can be used to descrbe acceleraton-senstve nonstructural damage f ln(medan Sa) s substtuted for λ. Nonstructural acceleraton senstve medan S a and lognormal β fraglty parameters from the Techncal Manual are provded n Appendx C. Note that uses acceleratonsenstve nonstructural fragltes to estmate damage to contents, as well Parametrc fraglty curves A methodology has been developed wthn the MAE Center whereby fragltes can be generated n a relatvely short amount of tme based on fve key structural parameters: perod, strength, ductlty, dampng and post-to-preyeld stffness rato. Addtonal nformaton s provded n Table Fndng the parameters that correspond to the structure types n the nventory data wll be essental for ths methodology s use n a CBE framework. Databases have currently been developed based on usng parameters obtaned from the Techncal Manual whch descrbe partcular structure types, and modelng the parameterzed structures under tme hstory analyss wth synthetc ground motons. Table MAE Center Parameterzed Buldng Fraglty Curves PI Amr Elnasha Structure Generc buldngs characterzed by (1) perod, (2) strength (as rato to weght), (3) ductlty (4) dampng and (5) post-to-pre-yeld stffness rato // For nventory tems, these parameters can be determned by push-over analyses or more smply determned n the followng way: (1) perod estmated from the heght or equatons avalable n the lterature, (2) rato of strength to weght; 1-1.5% for no lateral force desgn, 2-3% for wnd-desgn, 3-5% low sesmc desgn, 5-9% medum, 10-12% full (3) dampng: 2-8% dependng on the level of ductlty, (4) post-yeld stffness rato: 10% full sesmc, 5% for medum, 2% for low, 0% for wnd, -2~-4% for no lateral load desgn, etc. Retrofts Flexble, reflected n parameters used for modelng Sesmcty Currently PGA, 0.2 second Sa, 1.0 second Sa (g) future versons may also use PGV, PGD, Sv, and Sd Lmt states Drft of an SDOF system; e.g., 0.8% servceablty, 1.5% damage control, 3% collapse. Parameters medan Sa and β of lognormal CDF Transportaton systems The MAE Center has developed fragltes for common brdge types found n the Central and Eastern U.S., as well as fragltes descrbng the performance of brdges after nstallaton of retrofts (Cho et al., 2004; DesRoches, 2003). The fragltes consder uncertantes from materal (e.g., steel grade, concrete strength), geometry (e.g., heght of columns, length of deck), 124

125 and ground moton (duraton, frequency content). Smlar to the buldng fraglty curves, uncertanty n sesmc ntensty s obtaned from the hazard model. Table lsts the fraglty curves that have been derved for buldngs wthn the MAE Center. Table MAE Center Brdge Fraglty Curves PI Structure Retrofts Sesmcty Lmt states Parameters Regnald DesRoches Nne brdge classes (# of Spans): Contnuous Concrete (3), Contnuous Slab (3), Contnuous Steel Grder (3), Smply Supported Concrete Grder (3), Smply Supported Concrete Box Grder (3), Smply Supported Slab (3), Smply Supported Steel Grder (3) Concrete Grder (1), Steel Grder (1) Steel restraner cables, elastomerc bearngs, seat extenders, steel jackets PGA (g) Slght, Moderate, Extensve, Complete * Percent functonal after 0, 1, 3, 7 and 30 days Slght: Moderate: Extensve: Complete: λ and β of lognormal CDF, see Equaton ( ). Substtute PGA for Sa n Eq ( ) The fraglty equaton for brdges s dentcal to Equaton ( ), except that brdge fragltes are based on PGA nstead of spectral acceleraton. Evaluaton of brdge drect damage or loss of functonalty follows the same general procedure as n Equatons (4-4) through (4-10), except that there s an addtonal damage state. The MAE Center currently does not have fraglty data to represent brdges constructed to resst earthquakes n hgh sesmc zones, although, n the future, modfers are expected to be developed to adjust the non-sesmc fraglty curves to represent the nfluence of sesmc desgn Utlty Lfelne Fragltes Bured Ppelnes The development of fraglty curves for bured ppelnes has been largely based upon emprcal evdence and engneerng judgment. Typcally, fraglty curves are expressed n terms of ppe damage versus demand ntensty, such as peak ground acceleraton (PGA) or peak ground velocty (PGV). However, ppe fraglty curves are expressed as a repar rate per length of ppe versus the demand parameter. Due to the susceptblty of bured ppelnes to wave propagaton, peak ground velocty wll be used as the demand parameter for the ppelne 125

126 fragltes. A ppe repar can ether be due to a complete fracture of the ppe, a leak n the ppe, or damage to an appurtenance of the ppe. A break takes longer to repar; however, the type of repar s the same for both states. Therefore, to estmate the cost of repars, one must make an engneerng judgment concernng the average tme t takes a crew to repar a break or leak. Barenberg (1988) conducted a study to compute the relatonshp between bured cast ron ppe damage n breaks/km, observed n four past earthquakes, and PGV experenced at the assocated stes. Ths study was the frst to adopt PGV rather than the Modfed Mercall Intensty levels to determne damage. Ths swtch was mportant because there are mathematcal models whch relate the PGV to the strans nduced n the ppes, whch has been deemed the actual cause of damage. Then, O Rourke, M. and Ayala (1993) provded addtonal emprcal data for ppe damage versus peak ground velocty. Ths study plotted damage rate versus PGV for cast ron, concrete, prestressed, and asbestos cement ppes. Ths was based on sngle data ponts from the 1965 Puget Sound, 1969 Santa Rosa, and 1989 Mexco events; two data ponts from the 1971 San Fernando and 1983 Coalnga events; and four data ponts from the 1985 Mchoacán event n Mexco. Ths database s sgnfcant because t was the frst to nclude large dameter asbestos cement ppes (20 and 48 dameters), wth mostly cemented jonts. Ednger (1998) then conducted a study of the East Bay Muncpal Utlty Dstrct after the 1989 Loma Preta earthquake. Upon analyss of the database, the queston arose concernng whch of the followng two formats to use to represent the ppe fraglty: RR=K * a (PGV) b, where a and b are constants developed by the entre emprcal ppe database and k s some set of ppe-specfc constants, or RR=a (PGV) b, where a and b are ppe-specfc constants whch depend on all factors such as jonery, materal, age, etc. A GIS-based analyss of the ppelne damage from 1994 Northrdge to the Los Angeles Department of Water and Power was conducted by O Rourke, T. and Jeon (1999). The data used cast ron, ductle ron, asbestos cement, and steel ppes up to 24 n dameter. To ensure that each data pont had an equal nfluence for the length of ppe t represents, O Rourke, T. and Jeon (1999) weghted each data pont to normalze the results. The results of ths study show that the smaller samples of ppes at hgher PGV levels have a small nfluence on the regresson coeffcents, and the regresson curve wth weghtng s almost lnear (power coeffcent = 0.99). The results suggested that cast ron ppes were 30% more vulnerable than average, asbestos cement ppes were 30% less vulnerable than average, and ductle ron ppes were 10% less vulnerable than average. Ednger (2001) organzed the avalable damage to bured ppelnes from 18 prevous earthquake events nto a set of fraglty curves. Most of the emprcal evdence pror to 1989 shows only the performance of small dameter ppes (< 12 nches) because ths was the most 126

127 prevalent ppe sze n use n water systems at that tme. The ncluson of more modern earthquakes has expanded the database to nclude ppes composed of asbestos cement, ductle ron, and welded steel ppe; however, a complete emprcal database for all ppe materals under all levels of shakng stll does not exst. Analyses show that ppe materal, ppe dameter, and earthquake magntude all affect ppelne performance. Thus, usng the exstng database and the O Rourke and Jeon (1999) results, whch ndcate a lnear regresson curve to be adequate, Ednger (2001) selected the followng form for the ppelne fraglty: RR = K * a (PGV), where a s a constant developed from the entre emprcal ppelne database. The K values were developed to account for specfc ppe materals, ppe dameters, sol condtons, and ppe jont type. Ednger (2001) found ductle ron and steel ppe to be less vulnerable than cast ron by less than a factor of two, and asbestos cement has exhbted the best performance. Ths trend s nconsstent wth the conventonal thnkng that brttle materals, such as cast ron or asbestos cement, are more vulnerable than ductle materals, such as steel or ductle ron, by more than a factor of three, as assumed n. Further, the emprcal data from Loma Preta, 1989, and Northrdge, 1994, dffers sgnfcantly from the prevously reported data for asbestos cement ppe n Hacheng or Mexco Cty as observed by O Rourke and Ayala (1993). A possble explanaton for ths s that the asbestos cement ppe damage n Mexco Cty and Hacheng were often the result of nflexble cemented jonts rather than the more flexble rubber gasketed jonts. Thus, the K factor for rubber gasketed jonts s ½ the value for cemented jonts, and cemented jonts more closely resemble cast ron ppes. Also, evdence has shown that large dameter ppes have lower damage rates than small dameter ppes. Ths assumpton s reasonable because large dameter ppes typcally have fewer servce connectons, fewer bends, and thcker walls to contan an equal amount of pressure. For Ednger (2001), the most common materal n the database was cast ron (38 ponts) followed by steel (13), asbestos cement (10), ductle ron (9), and concrete (2). Another 9 ponts have both cast and ductle ron ppe combned. The database mostly contans ppes szes assocated wth dstrbuton man systems; n fact, only 8 ponts were dentfed as beng specfcally for large dameter ppes (> 12 nches). Addtonal analyses were conducted, and t has been determned that the sample sze of 8 data ponts was not enough to show a marked dfference n the relatve vulnerablty between a dstrbuton ppe and a small dameter ppe. Therefore, Ednger (2001) has K factors whch reflect the sze of the ppe dameter, but they are mostly the result of engneerng judgment Water Tanks To predct the damage to water tanks, one must know the PGA or response spectrum at a partcular dampng level, or f lquefacton s possble, PGD. One also needs the fraglty curves for each damage state, the replacement value of the tank, and the correlaton between the damage 127

128 state and economc losses. The most common form of damage s the outward bucklng of the bottom shell courses, or elephant foot bucklng. Other mportant falure mechansms nclude damage due to sloshng of the contents, anchorage falure, tank support system falure, and foundaton falure. Ednger (2001) dentfed several trends from the emprcal data for 531 tanks over 22 earthquakes. It was observed that tanks wth fll levels below 50% have a much hgher medan acceleraton; therefore, they typcally experence less damage. Also, the lognormal standard devatons are typcally around 0.80, whch ndcates a large uncertanty nvolved n the tank database. When compared to the fraglty curves, t was noted that the unanchored tanks were n the same range as the emprcal curves. Also, the curves ndcate an ncrease n capacty for anchored tanks compared to unanchored tanks, and the emprcal database shows an even larger ncrease. O Rourke and So (1999) also constructed fraglty curves from a database of 422 tanks over 9 earthquakes. Most of the fraglty curves algn well wth Ednger (2001), and the dscrepances observed can be attrbuted to the fact that O Rourke and So excluded all damage from an Alaskan earthquake, durng whch 32 of 39 tanks were damaged. Thus, the O Rourke and So analyss has a hgher medan PGA for the slght damage state Tunnels Dowdng and Rozen (1978) created fraglty curves from 68 post earthquake tunnels. The three damage states dentfed were none, slght mnor crackng of the tunnel lner, and moderate damage moderate crackng of the tunnel lner and rock falls. However, ths database made no delneaton among the types of tunnel lner and the materal through whch the tunnel was constructed. Power et al. (1998) constructed a database of 217 bored tunnels that had experenced strong ground motons due to pror earthquakes. Snce most damage occurs to the tunnel lner, the fraglty curves provded by Power were presented as a functon of the lner system. Ths database was also used by ; however, also consders the qualty of constructon Electrc System Ednger (1994) developed the damage algorthms for substaton equpment based upon emprcal evdence strongly tempered wth engneerng judgment. There are currently no known publcly avalable databases of damage algorthms for major substaton equpment. Gven ths lmtaton, the damage algorthms were developed from the lmted results of 10 earthquakes and engneerng judgment. Informaton used to develop the fraglty curves for mechancal and electrcal equpment was obtaned from the US Army Corps of Engneers SAFEGUARD program, whle the dstrbuton crcut damage algorthms were developed from the 1994 Northrdge earthquake. 128

129 4.2.4 Combned Damage from Ground Shakng and Ground Falure Damage s expected to be strongly correlated to lateral spreadng, so the probablty of LPI 15 s taken equal to the probablty of Complete damage caused by ground falure. When ground falure nfluences damage, the actual damage must be estmated as a combnaton of ground falure and ground shakng. The conceptual process of assgnng damage states to structures based on a combnaton of the two hazard types assumes the damage from each type to be statstcally ndependent. Currently, ground falure damage s defned as causng ether no damage or Complete damage. 129

130 5. SOCIAL AND ECONOMIC LOSSES 5.1 MAEVz Implementaton The followng upgrades are recommended for MAEVz hazard estmaton: Implement Buldng Structural Damage Factors. Implement Buldng Nonstructural and Contents Damage Factors. Implement Brdge Repar Factors. Implement utlty lfelne damage factors. Adjust Loss Calculatons to Consder Inventory Uncertanty. Aggregate Losses of Inventory wthn Study Regon. 130

131 5.1.1 Implement Buldng Structural Damage Factors and Compute Loss of Structural Value. Algorthm Inputs: Dscrete probabltes of damage states for structural components from Secton Mean and standard devaton of damage factors from Table Value of structural components from buldng stock nventory database (see Secton ). Process: Compute expected loss rato for each buldng s structural loss from dscrete probabltes of damage states and mean damage factors, as shown n Equaton ( ). Compute varance of expected loss of buldng s structural components usng standard devaton and mean damage factor for each damage state, dscrete probabltes of damage states, and the expected loss rato, as shown n Equaton ( ). Compute mean expected loss for each buldng by multplyng expected loss rato for structural components and value of structural components. Outputs: Mean and varance of expected loss rato for structural components of each buldng. Mean of expected loss of structural value for each buldng. Example The MAE Center has provded damage factors representng the fracton of value lost as a result of damage to structural elements, as shown n Table Table MAE Center Structural Damage Factors MAE Center Damage State Range of Beta Dstrbuton (%) Mean of Damage Factor, μ D DS (%) Standard Devaton of Damage Factor, σ D DS (%) Insgnfcant (I) [0, 1] Moderate (M) [1, 30] Heavy (H) [30, 80] Complete (C) [80, 100] For both the MAEC and buldng fraglty sets, for each fraglty set, three fraglty curves are gven. These demarcate between the four damage states lsted n the frst column above. Each damage state has an expected proporton of loss, as well as some measure of 131

132 uncertanty about that proporton. An overall expected loss rato and loss rato varance can be computed usng Equatons ( ) and ( ), respectvely. 4 [ P( DS ) μd DS ] μ = ( ) D = 1 σ 2 D 4 = [ P DS ) ( σ + μ )] μ = ( ) ( D DS D DS D Equatons ( ) and ( ) may be appled to I2 to obtan μ D 2 ( σ I 2 ( σ 2 ( σ = % % % % = 33.80% 2 μ ) = + I μ ) = 2 M + M H 2 ( σ σ 2 μ ) = + H 2 μ ) = C + C 2 D 2 2 ( ) = ( ) = ( ) = ( ) = ( 33.80% ) 1274% = = The mean expected structural loss ratos and varance of expected structural loss ratos for all three sample structures s shown n Table Table MAE Center Sample Structural Damage Rato Mean and Varance μ D (%) 2 σ D (% 2 ) I1 Concrete Bracc (3-story) I2 URM Wen (2-story) I3 URM Wen (2-story) The mean of expected structural loss for each buldng may then be computed by multplyng structural value by expected structural loss rato (note the expected loss rato s shown as a percentage), resultng n the data shown n Table Table MAE Center Sample Mean Structural Loss μ D (%) Structural Value ($) Expected Loss of Structural Value ($) I1 Concrete Bracc (3-story) ,415 8,012 I2 URM Wen (2-story) ,126 41,276 I3 URM Wen (2-story) ,381 41,

133 5.1.2 Implement Damage Factors and Compute Losses of Buldng Nonstructural and Contents. Algorthm Inputs: Dscrete probabltes of damage states for nonstructural components from Secton Mean and standard devaton of damage factors from Tables through Value of nonstructural components and contents from buldng stock nventory database (see Secton ). Process: Compute expected loss rato for each buldng s nonstructural and contents loss from dscrete probabltes of damage states and mean damage factors, as shown n Equaton ( ). Use acceleraton senstve probabltes of damage states when evaluatng contents losses. Compute varance of expected loss of buldng s nonstructural and contents losses usng standard devaton and mean damage factor for each damage state, dscrete probabltes of damage states, and the expected loss rato, as shown n Equaton ( ). Compute mean expected nonstructural and contents losses for each buldng by multplyng respectve expected loss ratos and values of components. Outputs: Mean and varance of expected loss rato for AS NS, DS NS, and contents for each buldng. Mean of expected loss of value for AS NS, DS NS, and contents for each buldng. Example Damage factors smlar to structural damage are also avalable for nonstructural and contents loss estmaton, as shown n Tables through Table Acceleraton-Senstve Nonstructural Damage Factors MAE Center Damage State Range of Beta Dstrbuton (%) Mean of Damage Factor, μ D DS (%) Standard Devaton of Damage Factor, σ D DS (%) Insgnfcant (I) [0, 6] 3 2 Moderate (M) [6, 20] Heavy (H) [20, 65] Complete (C) [65, 100]

134 Table Drft-Senstve Nonstructural Damage Factors MAE Center Damage State Range of Beta Dstrbuton (%) Mean of Damage Factor, μ D DS (%) Standard Devaton of Damage Factor, σ D DS (%) Insgnfcant (I) [0, 6] 3 2 Moderate (M) [6, 30] 18 8 Heavy (H) [30, 75] Complete (C) [75, 100] Table Contents Damage Factors MAE Center Damage State Range of Beta Dstrbuton (%) Mean of Damage Factor, μ D DS (%) Standard Devaton of Damage Factor, σ D DS (%) Insgnfcant (I) [0, 3] Moderate (M) [3, 15] 9 4 Heavy (H) [15, 37.5] Complete (C) [37.5, 50] Equatons ( ) and ( ) are also applcable to nonstructural and contents losses. Note that the probabltes of acceleraton-senstve nonstructural damage are used to determne contents losses. Mean and varance of expected damage factors for the sample buldngs are shown n Table Table MAE Center Sample Nonstructural and Contents Damage Mean and Varance Acceleraton-Senstve Nonstructural Drft-Senstve Nonstructural Contents μ D (%) 2 σ D (% 2 ) μ D (%) 2 σ D (% 2 ) μ D (%) 2 σ D (% 2 ) I1 Concrete Bracc (3-story) I2 URM Wen (2-story) I3 URM Wen (2-story)

135 The mean of expected AS NS, DS NS, and contents loss for each buldng may then be computed by multplyng the value of the each component by ts respectve expected loss rato (note the expected loss rato s shown as a percentage), resultng n the data shown n Tables through Table MAE Center Sample Mean Acceleraton-Senstve Nonstructural Loss μ D (%) AS NS Value ($) Expected Loss of AS NS Value ($) I1 Concrete Bracc (3-story) ,890 10,084 I2 URM Wen (2-story) ,034 21,970 I3 URM Wen (2-story) ,226 69,502 Table MAE Center Sample Mean Drft-Senstve Nonstructural Loss μ D (%) DS NS Value ($) Expected Loss of DS NS Value ($) I1 Concrete Bracc (3-story) ,095 3,665 I2 URM Wen (2-story) ,233 21,125 I3 URM Wen (2-story) ,739 17,186 Table MAE Center Sample Mean Contents Loss μ D (%) Contents Value ($) Expected Loss of Contents Value ($) I1 Concrete Bracc (3-story) ,600 12,043 I2 URM Wen (2-story) ,393 29,641 I3 URM Wen (2-story) ,217,019 83,

136 5.1.3 Implement Brdge Repar Factors and Calculate Expected Economc Loss for Brdges. Algorthm Inputs: Dscrete probabltes of damage states for brdges from Secton Mean and standard devaton of damage factors from Tables Number of spans from brdge nventory data (requred to estmate damage from Complete damage state). Brdge structure type and total length and wdth from nventory. Replacement cost data from Table Process: Compute expected loss rato for each brdge from dscrete probabltes of damage states and mean damage factors, as shown n Equaton ( ). Compute varance of expected loss of each brdge usng standard devaton and mean damage factor for each damage state, dscrete probabltes of damage states, and the expected loss rato, as shown n Equaton ( ). Compute expected loss for each brdge from the expected loss rato, the mean replacement cost n Table , and the total surface are of the brdge, as shown n Equaton ( ). Outputs: mean and varance of expected loss rato and mean of expected loss for each brdge. Example Damage factors are avalable for brdges, as shown n Table The damage factors are generally applcable to brges throughout the US and are very smlar to values used by - MH (NIBS, 2006). The brdge damage factors represent the fracton of value whch must be repared as a result of earthquake damage. The n shown n the Complete damage row refers to the number of spans. 136

137 Table Brdge Damage Factors MAE Center Damage State Mean of Damage Factor, μ SL (%) Standard Devaton of Damage Factor, σ SL (%) Range of Beta Dstrbuton (%) None (N) [0, 1] Slght (S) [1, 3] Moderate (M) [2, 15] Extensve (E) [10, 40] Complete (C) 65 (n <= 2) /n (n > 2) (200/3n)-10 [30, 100] Equatons ( ) and ( ) are agan applcable to evaluatng brdge damage, smlarly to buldng damage. Applyng the equatons to the sample brdges damage state probabltes n Table yelds the results shown n Table Table Sample Brdge Damage Mean and Varance μ BrD 2 σ BrD Brdge Brdge Brdge

138 Approxmate replacement values are gven n Table The values were specfcally developed for South Carolna, but provde a reasonable estmaton of damage n Memphs n leu of factors developed specfcally for Tennessee. Table Brdge Mean and Standard Devaton of Replacement Cost μ replace σ replace MSC_Concrete MSSS_Concrete SS_Concrete MSC_Steel MSSS_Steel SS_Steel MSC_Conc Box MSSS_Conc Box MSC_Slab MSSS_Slab The table values carry unts of dollars per square foot, so mean expected damage to a partcular brdge can be determned by Equaton ( ). μ Loss = μ L W μ ( ) BrD brdge brdge replace Mean damage for each of the sample brdges s shown n Table Table Sample Brdge Mean Damage μ Loss ($) Brdge Brdge Brdge

139 5.1.4 Implement utlty lfelne damage factors. Electrc Power Plants Algorthm Inputs: Probabltes of damage for each component from Secton Mean damage factors from Table through Process: Compute expected loss rato for each component from probabltes of damage and mean damage factors, as shown n Equaton ( ). Compute expected loss for each component by multplyng expected loss rato and value for each component. Outputs: mean of expected loss rato and dollar value of expected loss for each component of each power plant. Example Tables through present the damage factors for electrc system power plant components. The damage factors shown n the tables are the rato of the repar cost to the replacement value of the component. Note that the probablty of damage obtaned from the fragltes s also the probablty of loss of functon. Table Electrc Power Plant Equpment - Electrcal Components - Well Anchored Component ID Component Damage Descrpton Damage Factor EPP_EC_1 Desel Generators 0.00 EPP_EC_2 Battery Racks falure of batteres 0.05 EPP_EC_3 Swtchgear spurous actuaton of relays 0.00 EPP_EC_4 Instrument Racks and Panels relay chatter 0.00 EPP_EC_5 Control Panels malfunctonng equp EPP_EC_6 Aux. Relay Cabnets / MCCs / Crcut Breakers 0.00 EPP_EC_7 Turbne Turbne Trp 0.00 *Damage Factor s the rato of the repar cost of the component / replacement value of component NOTE: The probablty of exceedence computed from the fraglty for each component s also the probablty of loss of functon. 139

140 Table Electrc Power Plant Equpment - Mechancal Equpment - Well Anchored Component ID Component Damage Factor EPP_MC_1 Large vertcal vessels wth formed heads 0.25 EPP_MC_2 Bolers and Pressure Vessels 0.40 EPP_MC_3 Large horzontal vessels 0.25 EPP_MC_4 Small to medum horzontal vessels 0.25 EPP_MC_5 Large vertcal pumps 0.50 EPP_MC_6 Motor Drven pumps 0.50 EPP_MC_7 Large Motor Operated Valves 0.25 EPP_MC_8 Large Hydraulc and Ar Actuated Valves 0.25 EPP_MC_9 Large Relef, Manual and Check Valves 0.25 EPP_MC_10 Small Motor Operated Valves 0.25 Table Electrc Power Plant Equpment - Other Equpment Component ID Component Damage Descrpton Damage Factor EPP_OTH_1 Cable Trays 0.25 EPP_OTH_2 HVAC Ductng Support System Falure 0.12 EPP_OTH_3 HVAC Equpment Fans

141 Losses for the sample components are shown n Table Table Sample Electrc Power Plant Component Losses Component Component ID Mean Expected Loss ($) EPP 1 Bolers + Steam Generators EPP_MC_2 399 EPP 2 Bolers + Steam Generators EPP_MC_ EPP 3 Bolers + Steam Generators EPP_MC_

142 Electrc Substatons Algorthm Inputs: Probabltes of damage for each component from Secton Mean damage factors from Table through Process: Compute expected loss rato for each component from probabltes of damage and mean damage factors, as shown n Equaton ( ). Compute expected loss for each component by multplyng expected loss rato and value for each component. Outputs: mean of expected loss rato and dollar value of expected loss for each component of each power plant. Example Tables through present the damage factors for electrc system substaton components. The damage factors shown n the tables are the rato of the repar cost to the replacement value of the component. Note that the probablty of damage obtaned from the fragltes s also the probablty of loss of functon. Table VHV Substaton Components (500 kv and Hgher) Component ID Component Damage Factor ESS_VHV_1 Transformer - Anchored 0.40 ESS_VHV_2 Transformer - Unanchored 0.60 ESS_VHV_3 Lve Tank Crcut Breaker - Standard 0.60 ESS_VHV_4 Lve Tank Crcut Breaker - Sesmc 0.10 ESS_VHV_5 Dead Tank Crcut Breaker - Standard 0.40 ESS_VHV_6 Dsconnect Swtch - Rgd Bus 0.50 ESS_VHV_7 Dsconnect Swtch - Flexble Bus 0.10 ESS_VHV_8 Lghtnng Arrestor 1.00 ESS_VHV_9 CCVT - Cantlevered 1.00 ESS_VHV_10 CCVT - Suspended

143 ESS_VHV_11 Current Transformer (gasketed) 0.60 ESS_VHV_12 Current Transformer (flanged) 0.40 ESS_VHV_13 Wave Trap - Cantlevered 1.00 ESS_VHV_14 Wave Trap - Suspended 0.50 ESS_VHV_15 Bus Structure - Rgd 0.15 ESS_VHV_16 Bus Structure - Flexble 0.05 ESS_VHV_17 Other Yard Equpment

144 Table HV Substaton Components (165kV kv) Component ID Component Damage Factor ESS_HV_1 Transformer - Anchored 0.40 ESS_HV_2 Transformer - Unanchored 0.60 ESS_HV_3 Lve Tank Crcut Breaker - Standard 0.60 ESS_HV_4 Lve Tank Crcut Breaker - Sesmc 0.10 ESS_HV_5 Dead Tank Crcut Breaker - Standard 0.40 ESS_HV_6 Dsconnect Swtch - Rgd Bus 0.50 ESS_HV_7 Dsconnect Swtch - Flexble Bus 0.10 ESS_HV_8 Lghtnng Arrestor 1.00 ESS_HV_9 CCVT 1.00 ESS_HV_10 Current Transformer (gasketed) 0.50 ESS_HV_11 Wave Trap - Cantlevered 1.00 ESS_HV_12 Wave Trap - Suspended 0.50 ESS_HV_13 Bus Structure - Rgd 0.15 ESS_HV_14 Bus Structure - Flexble 0.05 ESS_HV_15 Other Yard Equpment

145 Table MHV Substaton Components (100 kv - 165kV) Component ID Component Damage Factor ESS_MHV_1 Transformer - Anchored 0.40 ESS_MHV_2 Transformer - Unanchored 0.60 ESS_MHV_3 Lve Tank Crcut Breaker - Standard 0.60 ESS_MHV_4 Lve Tank Crcut Breaker - Sesmc 0.10 ESS_MHV_5 Dead Tank Crcut Breaker - Standard 0.40 ESS_MHV_6 Dsconnect Swtch - Rgd Bus 0.50 ESS_MHV_7 Dsconnect Swtch - Flexble Bus 0.10 ESS_MHV_8 Lghtnng Arrestor 1.00 ESS_MHV_9 CCVT 1.00 ESS_MHV_10 Current Transformer (gasketed) 0.50 ESS_MHV_11 Wave Trap - Cantlevered 1.00 ESS_MHV_12 Wave Trap - Suspended 0.50 ESS_MHV_13 Bus Structure - Rgd 0.15 ESS_MHV_14 Bus Structure - Flexble 0.05 ESS_MHV_15 Other Yard Equpment

146 Losses for the sample components are shown n Table Table Sample Electrc Substaton Component Losses Component Component ID Mean Expected Loss ($) ESS 1 Transformer - Anchored ESS_MHV_ ESS 2 Transformer - Unanchored ESS_MHV_ ESS 3 Lve Tank Crcut Breaker - Standard ESS_VHV_

147 5.1.5 Adjust Loss Calculatons to Consder Inventory Uncertanty. Algorthm Inputs: Mean and varance of expected loss rato for each possble structure type for each nventory tem. If there are 10 structure types avalable for a gven set of nventory, then there would be 9 addtonal sets of analyses for each buldng smlar to those performed n the prevous sectons. The followng steps wll be requred for each buldng: Iterate through possble buldng types other than the expected type (e.g., for I1 n the full Memphs nventory, RM, URM, Wood frame, and all other buldng types except concrete moment frame would be consdered). Assgn structural and nonstructural fragltes approprate to each possble buldng type. Allow users to decde f they want to calculate hazard at an approprate perod for each buldng type. Set the default settng to NO. If the user adjusts ths opton to YES, calculate approprate hazard for each buldng type based on approxmate perod as descrbed prevously. Calculate probabltes of damage states for structural and nonstructural components, as descrbed prevously, for each possble buldng type. Calculate mean and varance of loss rato, as prevously dscussed, for each possble buldng type. User specfed level of nventory uncertanty. Process: Defne probablty of accurate dentfcaton. Compute a weghted average of expected loss, wth weghts based on the user specfed nventory uncertanty and the relatve number of each structure type beleved to exst n the nventory. Outputs: Mean and varance of expected loss rato adjusted for nventory uncertanty. Example For a general case, the probablty of accurate dentfcaton, denoted by p d, wll be defned by the user. Ths means there s ( 1 pd ) probablty that the structure belongs to any of the other structural types n the nventory. Then, the mean of the damage rato s calculated as μ = μ p ) μ ( ) ~ p D d D + (1 d D r 147

148 where μ D ~ s the mean damage rato wth the nventory uncertanty consdered, μ D s the mean damage rato based on the dentfed structure type, as calculated n prevous sectons, and μ r s D the representatve mean damage rato assumng an naccurate predcton of structure type. The representatve mean damage rato s estmated as the weghted average of the mean damage ratos based on all the dentfed structural types except for the orgnally predcted type, that s, N 1 j μ = μ ( ) d D n r j N j = 1 D where N d s the number of the structure types dentfed n the nventory mnus one (for the orgnally predcted type); n j s the number of the nventory tems dentfed as the j-th structural N type, j = 1,..., N d ; N = d n j j s the total number of nventory tems excludng those dentfed j as the orgnally predcted type; and μ D s the mean damage rato estmated based on the j-th structural type at the gven ste. Note that for ths example, the hazard wll be assumed constant wth respect to structure type. In fact, each structure type can have ts own perod, and a calculaton should be performed for each perod to estmate an approprate spectral acceleraton to maxmze the accuracy of the predctons. When the hazard s transformed from spectral acceleraton to spectral dsplacement for drft-senstve damage estmaton, the perod correspondng to the partcular structure type s used, regardless of whether the spectral acceleraton hazard has been recalculated for the approprate perod. Varance can be adjusted to account for nventory uncertanty by calculatng 2 ~ σ 2 ~ = E[ D ] μ ~ = p μ + σ + (1 p ) μ + σ μ ( ) D and D 2 [ ( ) ( ) ] ~ d D D d D D r D Nd ( ) n 2 2 μ σ = ( μ + σ ) j D + D r N j= 1 j D D ( ) where terms are defned smlarly to those used n Equatons ( ) and ( ). Note that n Equatons through , the j superscrpts are counters for structural types, not exponents. Consder that the user specfes a level of nventory uncertanty of 15%. For computatonal smplcty, assume that the buldngs could only be assgned concrete moment frame or URM buldng types (for purposes of ths example, t s mpossble that the buldngs could have been classfed as wood or steel frame or any other buldng type). As a result, the buldng that was dentfed as a concrete frame has a 15% probablty of beng somethng else, whch for ths example could only be URM. Lkewse, the URM buldngs each have a 15% probablty of actually beng a concrete frame buldng nstead of URM. Usng Equaton ( ) wth an nventory uncertanty of 15%, the mean of the damage factors can be calculated wth the formula gven below: 148

149 μ = μ 0. 15μ ( ) ~ 0.85 D D + D r The μ D term wll vary n general, dependng on what the expected type of buldng was. In ths r URM concrete example, μ D r = μ D for the concrete frame buldng, and μ D r = μ D for the URMs. For a general case, the representatve would be based on a weghted average of how many of each buldng are expected n the total nventory excludng the predcted type (see Table ). The updated mean of damage factors can be wrtten as concrete ~ 0.85μ D D + URM D μ = 0. 15μ ( ) for nventory tem I1, and concrete ~ 0.15μ D D + URM D μ = 0. 85μ ( ) for nventory tems I2 amd I3. Also, the varance for the concrete buldng can be calculated as σ 2 2 concrete 2 2 [.85( ) 0. ( ) ] 2 URM μ D + σ D + μ D + σ D μ ~ 2 ~ 0 15 D D = ( ) 2 where the μ ~ term s calculated n Equaton ( ) for the concrete frame buldng. D Lkewse, the varance for each of the URM buldngs can be calculated as σ 2 2 concrete 2 2 [.15( ) 0. ( ) ] 2 URM μ D + σ D + μ D + σ D μ ~ 2 ~ 0 85 D D = ( ) 2 where the μ ~ term s calculated n Equaton ( ) for each URM buldng. D Wth Eqs. ( ) through ( ), the mean and varance for the example nventory can be updated wth 15% nventory uncertanty as shown n Table Table Updatng wth Inventory Uncertanty Inventory Buldngs Wthout Inventory Uncertanty Wth 15% Inventory Uncertanty I1 Concrete Buldng Structural damage μ var Non-structural damage μ

150 Inventory Buldngs (acceleraton-senstve) Contents loss Non-structural damage Wthout Inventory Uncertanty Wth 15% Inventory Uncertanty var μ var μ (drft-senstve) var Structural damage Non-structural damage μ var μ I2 URM 1 (acceleraton-senstve) var μ Contents loss var Non-structural damage μ (drft-senstve) var Structural damage Non-structurald damage μ var μ I3 URM 2 (acceleraton-senstve) var μ Contents loss var Non-structural damage μ (drft-senstve) var

151 The small sample of buldngs used n the example s not fully descrptve of the process. If the buldngs were consdered to be part of the full Memphs buldng nventory (verson 4), expected mean and varance of loss ratos would need to be evaluated consderng several other buldng types, and weghtng factors would need to be appled to those calculated values to obtan a representatve value for naccurate structure type predcton, as shown n Table Weghtng factors are calculated as the number of buldngs n the entre nventory wth a certan predcted structure type dvded by the total number of buldngs excludng the predcted structure type of the nventory tem under consderaton. For example, tem I1 was classfed as a concrete moment frame, so the cell for concrete moment frame buldng count under I1 s left blank. The total number of buldngs n the nventory, excludng those predcted to be concrete moment frames, s 291,910. The weghtng factor for Lght Wood Frame s ( 269,725 / 291,910 ) = When computng the representatve damage rato for an naccurate predcton of I1 structure type, the damage rato calculated assumng a Lght Wood Frame structure type would be multpled by to obtan ts contrbuton to the total representatve damage rato. Table Inventory Uncertanty Weghtng Factors for Full v4 MTB Inventory Structure Types Concrete Moment Resstng Frame Concrete Frame wth Concrete Shear Wall I1 Inventory Uncertanty I2 and I3 Inventory Uncertanty Buldng Count Weghtng Factor Buldng Count Weghtng Factor Concrete Tlt-up 1, , Precast Concrete Frame Renforced Masonry 2, , Steel Frame Lght Metal Frame 6, , Unrenforced Masonry 6, Lght Wood Frame 269, , Commercal Wood Frame 4, , TOTALS 291, ,

152 5.1.6 Scale losses to account for nflaton. Algorthm Inputs: Table of nflaton factors. Estmated drect economc losses for nventory tems. Data for each nventory tem dentfyng year of apprasal. Process: Lookup approprate nflaton factor from suppled table based on year of apprasal for each nventory tem. Multply estmated losses by approprate nflaton factors for each nventory tem. Outputs: Adjusted drect economc loss accountng for nflaton. Example [Example data not currently avalable] 152

153 5.1.7 Aggregate Losses of Inventory wthn Study Regon. Algorthm Inputs: Mean and varance of expected loss rato for tems to be aggregated (e.g., buldng structural, brdges). Value of tems (and components, as approprate) for whch losses are beng aggregated. User specfed confdence level for loss rato. Process: Calculate mean of loss for each tem and sum per Equaton Calculate varance of aggregated loss per Equaton Calculate mean and standard devaton of the loss rato per Equatons and Calculate λ and β for a lognormal dstrbuton of loss rato per Equatons and Outputs: Plot of probablty densty functon wth respect to loss rato usng Equaton Plot of probablty of exceedence as a functon of loss rato usng Equaton Confdence bounds for loss rato usng Equaton Example Loss The general form of the equaton for total drect economc loss for a buldng s gven by SD NA ND CL = ( α μ + α μ ~ + α μ ~ + α μ ~ ) ( ) M ~ SD NA ND CL D D D D where M s the total assessed value of the -th nventory tem; α SD NA ND α and α are the fractons of the values of structural and non-structural (acceleraton- and drft-senstve) CL components; α s the rato of the contents value to the total assessed value; μ SD D ~, μ NA D ~ and μ are the damage ratos of the -th nventory tem adjusted by the nventory uncertanty; and ND D ~ μ CL D ~ s the adjusted content loss rato. Values of M α were calculated for structural, acceleraton-senstve nonstructural, and drft-senstve nonstructural assets n Secton CL Currently, the MAEC nventory data ncludes a pre-calculaton of M α n ther own data CL feld pror to ngeston nto MAEvz, so the α coeffcents are not vsble. The value of the varous components may be represented n equaton form as M SD = M α s the structural component value ( a) SD 153

154 M M M NA ND CL = M α s the acceleraton-senstve nonstructural component value ( b) NA = M α s the drft-senstve nonstructural component value ( c) ND = M α s the contents value ( d) CL The total loss of the nventory s obtaned by aggregatng the losses of the nventory tems, that s, Loss = N = 1 Loss ( ) Then mean of the total loss s estmated as N SD NA ND CL ( M μ ) ~ SD M μ D ~ NA M μ D ~ ND M μ D ~ CL D μ = ( ) Loss = 1 Assumng the damage ratos of dfferent nventory tems are condtonally ndependent gven a sesmc ntensty, the varance of the total loss s computed as N SD 2 2 NA 2 2 ND 2 2 CL 2 2 ( M ) σ ) ~ SD ( M ) σ D ~ NA ( M ) σ D ~ ND ( M ) σ D ~ CL D 2 σ = ( ) Loss = 1 The coeffcent of varaton (c.o.v.) of the total loss s σ Loss δ Loss = ( ) μ Loss The mean, standard devaton and c.o.v. of the total loss of the example nventory are estmated as (mllon US$), (mllon US$) and 56.92%, respectvely. Loss Rato ( L r ) may be defned as the total loss normalzed by the sum of structural, nonstructural and content values n a regon, that s, Loss Loss Loss L r = = = ( ) N N SD NA ND CL CL M total M ( α + α + α + α ) M + M = 1 = 1 Then, mean and standard devaton of the loss rato are, respectvely, μ Loss μ L = ( ) r M total and σ Loss σ L = ( ) r M total The c.o.v. of the loss rato s the same as that of the total loss. For the example nventory, the mean and standard devaton of the loss rato are estmated as 11.4 % and 6.51 %, respectvely. 154

155 The probablty dstrbuton of the loss rato can be determned, gven the estmated mean and standard devaton, and an assumed dstrbuton type. It s assumed that the loss rato follows the lognormal dstrbuton. The lognormal dstrbuton requres two parameters λ and β, whch are the mean and standard devaton of the natural logarthm of the quantty. These parameters are obtaned from the estmated mean and standard devaton of the loss rato as follows. 2 σ L r β = ln 1 + ( ) μ Lr λ = ln μ 2 L 0.5β ( ) r The lognormal parameters of the loss rato n the example are λ = and β = The probablty densty functon (PDF) of the loss rato s defned as ln l r λ f L r ( lr ) = exp ( ) 2πβl 2 β r The plot of ths functon for the sample data s shown n Fgure Probablty Densty Functon Loss Rato, L r Fgure Probablty Densty Functon for Loss Rato. The complementary cumulatve densty functon (CCDF) can also be plotted to show probabltes of exceedence for varous levels of loss rato. The CCDF s defned by 155

156 ln( lr ) λ C Lr ( lr ) = 1 Φ ( ) β whch can be plotted as shown n Fgure Table lsts the exceedance probabltes at selected thresholds of loss rato Probablty of Exceedence Loss Rato, L r Fgure Probablty of Exceedence n terms of Loss Rato. Table Selected Probabltes of Exceedance Loss rato (%) Probablty of exceedence, % (lognormal dstrbuton)

157 Loss rato (%) Probablty of exceedence, % (lognormal dstrbuton) Based on the estmated uncertanty n the loss rato, we can predct the loss rato by an nterval wth a certan level of confdence. An nterval that encloses the true loss rato wth probablty 1 α (or an nterval wth confdence level 1 α ) s [ λ k α β), exp( λ + k )] exp( 2 / 2 / α β ( ) where k 1 α / 2 = Φ (1 α / 2). Table shows the coeffcent values for selected confdence levels and the correspondng confdence ntervals. Table Confdence ntervals for loss rato Confdence level, 1 α (%) k α / 2 Confdence nterval (%) [6.37, 15.53] [5.74, 17.22] [5.04, 19.61] [4.16, 23.77] [3.52, 28.09] [2.54, 38.92] 157

158 5.1.8 Calculate Fscal Losses (Property Tax Revenue). Algorthm Inputs: Mean damage factors for structural, acceleraton-senstve nonstructural, and drft-senstve nonstructural buldng components for each buldng. Value for each set of buldng components for each buldng. Property Tax rate applcable to each buldng (based on jursdcton). Ths wll lkely be determned nternally by MAEvz by comparng buldng locatons to polygons n a shapefle wth an assocated attrbute of Property Tax. Process: Calculate Drect Economc Damage for buldng components only (do NOT nclude contents losses) by multplyng buldng component values by mean loss factors, as shown n Equaton μ = + ( ) DED SD NA ND M μ ~ + M D μ ~ M D μ ~ D SD NA ND Calculate Loss Rato for Drect Economc Damage as shown n Equaton , where s the assessed buldng value orgnally suppled n the nventory database. μ μ = DED Lr DED ( ) M If the Loss Rato for Drect Economc Damage s greater than 0.1 (10%), then calculate Property Tax loss as shown n Equaton , TR j s the property tax rate for jursdcton j, determned by comparng a buldng s locaton to a map of property tax rates for varous jursdctons. f μ DED > 0. 1 then PTL = μ DED TR j ( ) L r Repeat these steps for each buldng n the nventory. Allow the user to select a group of tems for aggregaton (offer summaton by jursdcton as a default) and sum PTL to obtan fscal losses. Outputs: Fscal losses for ndvdual buldngs and groups of buldngs as selected by the user. Example [Example data not currently avalable] M 158

159 5.2 Background Economc Loss for Buldng structures Buldng Structural Damage A framework has been advanced wthn the MAE Center to establsh correlatons between structural damage states and drect economc losses (.e., repar and replacement), as shown n Table (Ba et al., 2006). The damage factors, μ L, form a brdge between the engneerng engne outputs (.e., probabltes of exceedng lmt states defned by analytcal thresholds, such as nterstory drft rato) and economc losses n terms of monetary values Buldng Nonstructural and Contents losses There s not currently any MAE Center research addressng drect economc losses from nonstructural and contents. In the absence of MAE Center research, nonstructural and contents damage factors may be adapted from. provdes determnstc damage factors for dscrete damage states, wth no stated ranges or uncertantes. The determnstc damage factors may be converted to approxmate ranges by assumng that ranges extend to the mdponts between adjacent damage factors. Damage factors and uncertantes presented smlarly to the values n Table are provded n Tables through Socal Impacts The MAEC s actvely developng socal mpact algorthms (Peacock and Zhang, 2005; Prater et al., 2005; French, 2005; French, 2005; French et al., 2005), but the algorthms are not yet ready for ncluson n the MAEC CRM framework and MAEvz. 159

160 6. NETWORK MODELING The MAE Center s presently engaged n developng network models for transportaton and utlty lfelne functonalty. The transportaton models are currently more advanced than utlty network models, and are beng mplemented for a transportaton testbed at Charleston, SC (DesRoches et al., 2006; Duthe et al., 2006; Karoonsoontawong and Waller, 2005; Km et al., 2006). Transportaton network models nclude two phases. The frst phase consders the orgnal traffc flow pattern and how that pattern can be expected to be perturbed by a major earthquake. The second phase examnes how the modfed flow pattern wll be affected by damage to transportaton network components (.e., brdges) and what economc consequences can be expected as an end result of perturbed traffc flow n terms of costs to commuters resultng from tme lost n transt. Models for loss effects of utlty networks are stll n development, and are not yet ready for mplementaton. 7. SYSTEM INTERDEPENDENCIES The MAE Center s currently developng a methodology for predctng losses n utlty networks resultng from falures n other networks (e.g., water network functonalty mpacted by loss of electrc power to pump statons). A general framework has been developed wthn the MAE Center (Duenas-Osoro et al., 2004; Duenas-Osoro, 2005) but s not currently ready for mplementaton. 8. DECISION SUPPORT The overarchng vew of decson support seeks to provde tools for decson makers to maxmze the beneft of captal nvestments. Ths effort s generally facltated usng one of three approaches: (1) Equvalent cost analyss (ECA): convert all losses to monetary values (2) Mult-attrbute utlty theory (MAUT): value-measurng theory ncorporatng rsk-atttude of decson makers. (3) Jont probablty decson makng (JPDM): probablty that crtera wll be satsfed. Another capablty of decson support s senstvty analyss, whch allows the user to nvestgate the senstvty of the above results wth respect to changes n varous parameters. Decson support currently reles on a methodology developed by Park (2004). Park (2004) focuses prmarly on retroft of general buldng stock, and draws an approxmate correlaton between code level n and retroft performance objectves. There s a basc presumpton that the buldng under consderaton s approprately modeled wth Pre- 160

161 fragltes n, and that fraglty data for hgher code levels can be mapped to performance objectves as follows: Low Lfe Safety (LS) Moderate Immedate Occupancy (IO) Hgh New Constructon The Park (2004) methodology s rgd, requrng the use of fragltes to approxmately represent the nstallaton of retrofts. The methodology has been adjusted to now consder MAEC parametrc fragltes based on physcal parameters stated n the techncal manual. A promsng opton whch wll be explored n the near future wll seek to make retroft objectves more flexble by targetng code levels as objectves, and allowng the user to have greater freedom to nfluence the exact level of performance desred. The MAEC parametrc fraglty curves have far greater flexblty n representng varous retroft schemes relatve to the publshed code-level parameters for, and specfc behavors could be modeled, such as ncreasng stffness ndependently wth respect to force capacty and ductlty to represent the nstallaton of shear walls. Decson support wll also buld on ncreasngly sophstcated loss models and consder a broader scope of analyss ncludng traffc flow, lfelne network models, and system nterdependences. 9. CONCLUSIONS Ths document presents an overvew of the current knowledge base avalable wthn the MAE Center for use n the Consequence-based Rsk Management framework, as well as an overvew of the currently mplemented and proposed features for MAEvz. Whle the knowledge base s qute extensve and detaled for nventory collecton, hazard defnton, and vulnerablty estmaton, several ssues are stll outstandng whch should be addressed to make the MAE Center CRM framework truly comprehensve and as accurate as possble. Socal and economc mpact algorthms are currently n development by many researchers wthn the MAE Center, and the results of ther efforts wll play a key role n brdgng the gap between engneerng damage estmaton and socal and economc losses affectng socety. Further nvestgaton s also warranted for buldng stock nonstructural loss estmaton. Nonstructural and contents losses can often far exceed losses n structural value, but the MAE Center s currently forced to adapt the approxmate methodologes used by for valuaton, damage estmaton, and losses caused by nonstructural damage due to a lack of research n ths key area. Network modelng, system nterdependences, and decson support capabltes are all developng rapdly and wll soon be able to be fully ntegrated nto the MAE Center CRM framework and MAEvz. 161

162 REFERENCES Atknson, G. M., and Boore, D. M. (1995). "Ground Moton Relatons for Eastern North Amerca." Bulletn of the Sesmologcal Socety of Amerca, 85(1), Ba, J.-W. and Hueste, M. D. (2006). Sesmc Fraglty of a Tlt-Up Concrete Buldng n the Central Unted States, Proceedngs of the 8th U.S. Natonal Conference on Earthquake Engneerng, San Francsco, Calforna, Aprl 18-22, 2006, Earthquake Engneerng Research Insttute, Oakland, Calforna. Ba, J.-W. and Hueste, M. D. (2007). Determnstc and Probablstc Evaluaton of Retroft Alternatves for a Fve-Story Flat-Slab RC Buldng, Md-Amerca Earthquake (MAE) Center Techncal Report, Ba, J.-W., Hueste, M. D., and Gardon, P. (2006). A Probablstc Framework for the Assessment of Structural Losses due to Sesmc Events, Lmted dstrbuton n preparaton for publcaton, June 30, Borcherdt, R. D. (1994). Estmates of Ste-Dependent Response Spectra for Desgn (Methodology and Justfcaton), Earthquake Spectra, Vol. 10, pp Celk, O. C. and Ellngwood, B. R. (2006). Fraglty Assessment of Renforced Concrete Frames Desgned for Regons of Moderate Sesmcty, Proceedngs of the 1st European Conference on Earthquake Engneerng and Sesmology, Geneva, Swtzerland, September 3-8, 2006, Symporg SA, Geneva, Swtzerland (ISBN 10: ). Cho, E., DesRoches, R., and Nelson, B., (2004), Sesmc Fraglty of Typcal Brdges n Moderate Sesmc Zones, Engneerng Structures, Vol. 26, No. 2, pp , January. DesRoches, R. (2006). Memphs Testbed Brdge Inventory from Natonal Brdge Inventory, personal communcaton. DesRoches, R., Leon, R. T., and Dyke, S., (2003), Response Modfcaton of Brdges, Internal Report, CD Release 03-08,, Urbana, Illnos, December. DesRoches, R., Padgett, J. E., Elnasha, A. S., Kn, Y. S., and Reed, D. (2006) MAE Center Transportaton Test Bed, Proceedngs of the 8 th U. S. Natonal Conference on Earthquake Engneerng, San Francsco, Calforna, 2006, Earthquake Engneerng Research Insttute, Oakland, Calforna. Dobry, R., Borcherdt, R. D., Crouse, C. B., Idrss, I. M., Joyner, W. B., Martn, G. R., Power, M. S., Rnne, E. E., and Seed, R. B. (2000). New Ste Coeffcents and Ste Classfcaton System Used n Recent Buldng Sesmc Provsons, Earthquake Spectra, Vol. 16, pp

163 Dowdng, C. H. and Rozen, A. (1978). Damage to Rock Tunnels from Earthquake Shakng, Journal of the Geotechncal Engneerng Dvson, Amercan Socety of Cvl Engneers, New York, New York, February. Duenas-Osoro, L., (2005), Interdependent Response of Networked Systems to Natural Hazards and Intentonal Dsruptons, Ph.D. Dssertaton, Georga Insttute of Technology, Atlanta, Georga. Duenas-Osoro, L., Crag, J. I., and Goodno, B. J., (2004), Probablstc Response of Interdependent Infrastructure Networks, 2004 ANCER Annual Meetng, Honolulu, HI, July 28-30, Duthe, J., Unnkrshnan, A., and Waller, S. T. (2006). Network Evaluaton wth Uncertan and Correlated Long-Term Demand, Proceedngs of the 85th Annual Meetng of the Transportaton Research Board, Washngton, DC. Ednger, J. (2001). Sesmc Fraglty Formulatons for Water Systems, sponsored by the Amercan Lfelnes Allance, G&E Engneerng Systems Inc., web ste. < Ellngwood, B. R. (2005). Sesmc Fraglty Assessment of Lght-Frame Wood Resdental Constructon, Proceedngs of the Lus Esteva Symposum Earthquake Engneerng, Challenges and Tendences, Mexco Cty, Mexco, September 7-11, 2005, Unversdad Naconal Autonoma de Mexco, Mexco, DF. Erberk, M. A., and Elnasha, A. S. (2006). Loss Estmaton Analyss of Flat-Slab Structures, Natural Hazards Revew, Vol. 7, No. 1, pp , February. Federal Hghway Admnstraton (FHWA) (1995). Recordng and Codng Gude for the Structure Inventory and Apprasal of the Naton s Brdges, U.S. Department of Transportaton, Offce of Engneerng, Brdge Dvson, Report No. FHWA-PD , December, Fernandez, J. A. (2006). Hard Rock Attenuaton Correcton Factors. Personal communcaton. Fernandez, J. A., and Rx, G. J. (2006). Sol Attenuaton Relatonshps and Sesmc Hazard Analyses n the Upper Msssspp Embayment. Proceedngs of the 8 th U.S. Natonal Conference on Earthquake Engneerng San Francsco, Calforna, Aprl 18-22, 2006, Earthquake Engneerng Research Insttute, Oakland, Calforna. Frankel, A., Mueller, C., Barnhard, T., Perkns, D., Leyendecker, E. V., Dckman, N., Hanson, S., and Hopper, M. (1996). "Natonal Sesmc Hazard Maps: Documentaton." OFR , U.S. Geologcal Survey. French, S. P. (2005). Conceptualzng the Socal and Economc Consequences of Natural Hazards, Presentaton at the 46th Annual Conference of the Assocaton of Collegate Schools of Plannng, Kansas Cty, Mssour, October 27-30,

164 French, S. P. (2006). Memphs Water Ppelne and Water Tank Databases, Personal communcaton. French, S. P. (2006). Valuaton of Buldng Stock, Personal communcaton. French, S. P. (2005). Socal Scence Research n the, Internal Report,, Urbana, Illnos French, S. P., Lee, D., and Rees, J. (2005). Estmatng the Socal and Economc Consequences of Earthquakes and Other Natural Hazards, Presentaton at the 46th Annual Conference of the Assocaton of Collegate Schools of Plannng, Kansas Cty, Mssour, October 27-30, French, S.P., and Muthukumar, S. (2006). MTB Inventory Summary, verson 3. Personal communcaton. French, S. P., and Muthukumar, S. (2006). Memphs Buldng Stock Inventory Shapefles and Databases, Verson 4. Personal communcaton. French, S. P., and Muthukumar, S. (2006). Advanced Technologes for Earthquake Rsk Inventores, Journal of Earthquake Engneerng, Vol. 10, No. 2, pp French, S. P., and Muthukumar, S. (2006). MTB roadway nventory. Personal communcaton. G & E Engneerng Systems, Inc. (1994). Earthquake Loss Estmaton Methods, Techncal Manual, Electrc Power Utltes, Natonal Insttute of Buldng Scences, Washngton, D.C. Hueste, M. D. and Ba, J.-W. (2007). Sesmc Retroft of a Renforced Concrete Flat-Slab Structure: Part I Sesmc Performance Evaluaton. Engneerng Structures, n press. Hueste, M. D. and Ba, J.-W. (2007). Sesmc Retroft of a Renforced Concrete Flat-Slab Structure: Part II Sesmc Fraglty Analyss. Engneerng Structures, n press.. Karoonsoontawong, A., and Waller, S. T. (2005). Comparson of System and User-Optmal Stochastc Dynamc Network Desgn Models Usng Monte Carlo Boundng Technques, Journal of the Transportaton Research Board, No. 1923, Transportaton Research Board, Washngton, D.C. Km, Y. S., Elnasha, A. S., Spencer, B. F., Ukkusur, S., and Waller, S. T. (2006) Sesmc Performance Assessment of Hghway Networks, Proceedngs of the 8 th U. S. Natonal Conference on Earthquake Engneerng, San Francsco, CA, Aprl 18-22, 2006, Earthquake Engneerng Research Insttute, Oakland, Calforna. Kwon, O.-S., and Elnasha, A. (2006). The Effect of Materal and Ground Moton Uncertanty on the Sesmc Vulnerablty Curves of RC Structure, Engneerng Structures, Vol. 28, No. 2, pp , February. Memphs Lght, Gas & Water (MLGW) (2005). Memphs Cast-Iron Ppelne Database, Personal communcaton. 164

165 Natonal Insttute of Buldng Scences (NIBS) (2006). -MH MR2 Users Manual, Federal Emergency Management Agency, Washngton, D.C. O Rouke, M. J., and Ayala, G. (1993). Ppelne Damage due to Wave Propagaton, Journal of Geotechncal Engneerng, ASCE, Vol. 119, No. 9, pp , September. O Rourke, T. D., and Jeon, S-S. (1999). Factors Affectng the Earthquake Damage of Water Dstrbuton Systems, TCLEE Monograph No. 16, ASCE. O Rourke, M. J., and So, P. (1999). Sesmc Behavor of On-Grade Steel Tanks; Fraglty Curves, TCLEE Monograph No. 16, ASCE. Park, D., and Hashash, Y. M. A. (2005). Evaluaton of Sesmc Factors n the Msssspp Embayment: I. Estmaton of Dynamc Propertes, Sol Dynamcs and Earthquake Engneerng, Vol. 25, pp , February. Park, J. (2004). Development and Applcaton of Probablstc Decson Support Framework for Sesmc Rehabltaton of Structural Systems, Ph.D. Thess, Georga Insttute of Technology, Atlanta, Georga. Patterson, G. (2006). Memphs School, Fre Staton, and Brdge Databases, personal communcaton. Peacock, W. G., and Zhang, Y. (2005). Sngle Famly Housng Recovery after Hurrcane Andrew, Proceedngs of the CASA/NCAR Decson Scences Workshop, Boulder, Colorado, December 12, 2005, Proceedngs of the Southern Socologcal Socety Meetngs, Charlotte, North Carolna, Aprl 14-17, 2005, Natonal Center for Atmospherc Research, Boulder, Colorado. (PMH) Offce of Amercas/North Amerca & Homeland Securty Dvson (2006). Homeland Securty Infrastructure Program (HSIP) GOLD Dataset, Washngton, D.C., (2) DVD set. Prater, C., Peacock, W. G., Lndell, M. K., Lu, J. C., and Zhang, Y. (2005). DS-8: A Socal Vulnerablty Approach to Estmatng Potental Socoeconomc Impacts of Earthquakes, Internal Report,, Unversty of Illnos, Urbana, Illnos. Ramamoorthy, S.K., Gardon, P., and Bracc, J.M. (2006) Probablstc Demand Models and Fraglty Curves for Renforced Concrete Frames, Journal of Structural Engneerng, October Ramamoorthy, S.K., Gardon, P., and Bracc, J.M. (2006) Sesmc Fraglty and Confdence Bounds for Gravty Load Desgned Renforced Concrete Frame of Varyng Heght, Submtted to Journal of Structural Engneerng, May Romero, S. and Rx, G. J. (2005). Ground Moton Amplfcaton of Sols n the Upper Msssspp Embayment, Internal Report, CD Release 05-01, Md-Amerca Earthquake Center, Urbana, Illnos, March. 165

166 Slva, W., Gregor, N., and Darragh, R. (2003). "Development of Regonal Hard Rock Attenuaton Relatons for Central and Eastern North Amerca, Md-Contnent and Gulf Coast Areas." Pacfc Engneerng and Analyss, El Cerrto, CA. Toro, G. and Slva W. (2001). Scenaro Earthquakes for St. Lous, MO, and Memphs, TN, and Sesmc Hazard Maps for the Central Unted States Regon Includng the Effect of Ste Condtons, Internal Report, U. S. Geologcal Survey, Department of the Interor, Washngton, D.C. 166

167 APPENDIX A SUPPLEMENTARY INVENTORY INFORMATION A Utlty Component Mappng Data Default component value mappng data for electrc substatons may be obtaned from Tables A through A Table A Electrc Substaton General Subcomponent Value Parttonng Factors General Component Parttonng Factor (%) Transformers 40 Crcut Breakers 15 Dsconnect Swtches 2 Lghtnng (Surge) Arrestors 1 CCVTs 1 Current Transformers 2 Wave Traps 1 Bus Structures 7 Control Buldng 10 Batteres 1 Electrcal Control Equpment 9 Other Yard Equpment

168 Table A Electrc Substaton Subcomponent Value Parttonng For VHV Substatons, Sesmc Zones 0/1/2 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_VHV_1 Transformer - Unanchored ESS_VHV_2 Lve Tank Crcut Breaker - Standard ESS_VHV_3 Lve Tank Crcut Breaker - Sesmc ESS_VHV_4 Dead Tank Crcut Breaker - Standard ESS_VHV_5 Dsconnect Swtch - Rgd Bus ESS_VHV_6 Dsconnect Swtch - Flexble Bus ESS_VHV_7 Lghtnng Arrestor ESS_VHV_8 CCVT - Cantlevered ESS_VHV_9 CCVT - Suspended ESS_VHV_10 Current Transformer (gasketed) ESS_VHV_11 Current Transformer (flanged) ESS_VHV_12 Wave Trap - Cantlevered ESS_VHV_13 Wave Trap - Suspended ESS_VHV_14 Bus Structure - Rgd ESS_VHV_15 Bus Structure - Flexble ESS_VHV_16 Other Yard Equpment ESS_VHV_17 168

169 Table A Electrc Substaton Subcomponent Value Parttonng For VHV Substatons, Sesmc Zones 3/4 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_VHV_1 Transformer - Unanchored ESS_VHV_2 Lve Tank Crcut Breaker - Standard ESS_VHV_3 Lve Tank Crcut Breaker - Sesmc ESS_VHV_4 Dead Tank Crcut Breaker - Standard ESS_VHV_5 Dsconnect Swtch - Rgd Bus ESS_VHV_6 Dsconnect Swtch - Flexble Bus ESS_VHV_7 Lghtnng Arrestor ESS_VHV_8 CCVT - Cantlevered ESS_VHV_9 CCVT - Suspended ESS_VHV_10 Current Transformer (gasketed) ESS_VHV_11 Current Transformer (flanged) ESS_VHV_12 Wave Trap - Cantlevered ESS_VHV_13 Wave Trap - Suspended ESS_VHV_14 Bus Structure - Rgd ESS_VHV_15 Bus Structure - Flexble ESS_VHV_16 Other Yard Equpment ESS_VHV_17 169

170 Table A Electrc Substaton Subcomponent Value Parttonng For HV Substatons, Sesmc Zones 0/1/2 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_HV_1 Transformer - Unanchored ESS_HV_2 Lve Tank Crcut Breaker - Standard ESS_HV_3 Lve Tank Crcut Breaker - Sesmc ESS_HV_4 Dead Tank Crcut Breaker - Standard ESS_HV_5 Dsconnect Swtch - Rgd Bus ESS_HV_6 Dsconnect Swtch - Flexble Bus ESS_HV_7 Lghtnng Arrestor ESS_HV_8 CCVT ESS_HV_9 Current Transformer (gasketed) ESS_HV_10 Wave Trap - Cantlevered ESS_HV_11 Wave Trap - Suspended ESS_HV_12 Bus Structure - Rgd ESS_HV_13 Bus Structure - Flexble ESS_HV_14 Other Yard Equpment ESS_HV_15 170

171 Table A Electrc Substaton Subcomponent Value Parttonng For HV Substatons, Sesmc Zones 3/4 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_HV_1 Transformer - Unanchored ESS_HV_2 Lve Tank Crcut Breaker - Standard ESS_HV_3 Lve Tank Crcut Breaker - Sesmc ESS_HV_4 Dead Tank Crcut Breaker - Standard ESS_HV_5 Dsconnect Swtch - Rgd Bus ESS_HV_6 Dsconnect Swtch - Flexble Bus ESS_HV_7 Lghtnng Arrestor ESS_HV_8 CCVT ESS_HV_9 Current Transformer (gasketed) ESS_HV_10 Wave Trap - Cantlevered ESS_HV_11 Wave Trap - Suspended ESS_HV_12 Bus Structure - Rgd ESS_HV_13 Bus Structure - Flexble ESS_HV_14 Other Yard Equpment ESS_HV_15 171

172 Table A Electrc Substaton Subcomponent Value Parttonng For MHV Substatons, Sesmc Zones 0/1/2 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_MHV_1 Transformer - Unanchored ESS_MHV_2 Lve Tank Crcut Breaker - Standard ESS_MHV_3 Lve Tank Crcut Breaker - Sesmc ESS_MHV_4 Dead Tank Crcut Breaker - Standard ESS_MHV_5 Dsconnect Swtch - Rgd Bus ESS_MHV_6 Dsconnect Swtch - Flexble Bus ESS_MHV_7 Lghtnng Arrestor ESS_MHV_8 CCVT ESS_MHV_9 Current Transformer (gasketed) ESS_MHV_10 Wave Trap - Cantlevered ESS_MHV_11 Wave Trap - Suspended ESS_MHV_12 Bus Structure - Rgd ESS_MHV_13 Bus Structure - Flexble ESS_MHV_14 Other Yard Equpment ESS_MHV_15 172

173 Table A Electrc Substaton Subcomponent Value Parttonng For MHV Substatons, Sesmc Zones 3/4 Specfc Component Parttonng Factors (%) General Specfc Overall Multpler Component ID Transformer - Anchored ESS_MHV_1 Transformer - Unanchored ESS_MHV_2 Lve Tank Crcut Breaker - Standard ESS_MHV_3 Lve Tank Crcut Breaker - Sesmc ESS_MHV_4 Dead Tank Crcut Breaker - Standard ESS_MHV_5 Dsconnect Swtch - Rgd Bus ESS_MHV_6 Dsconnect Swtch - Flexble Bus ESS_MHV_7 Lghtnng Arrestor ESS_MHV_8 CCVT ESS_MHV_9 Current Transformer (gasketed) ESS_MHV_10 Wave Trap - Cantlevered ESS_MHV_11 Wave Trap - Suspended ESS_MHV_12 Bus Structure - Rgd ESS_MHV_13 Bus Structure - Flexble ESS_MHV_14 Other Yard Equpment ESS_MHV_15 173

174 APPENDIX B SUPPLEMENTARY HAZARD INFORMATION B Attenuaton to Locatons Insde the Msssspp Embayment The seven attenuaton functons and default weghts, as proposed by Fernandez and Rx (2006), are shown n Table B Table B Default Attenuaton Functons and Weghts for the Msssspp Embayment Applcable Regon / Attenuaton Functon Weght Event Atknson and Boore (1995) Frankel et al (1996) Hgh Medan Stress Drop New Madrd Sesmc Frankel et al (1996) Med Medan Stress Drop Zone wthn Msssspp Frankel et al (1996) Low Medan Stress Drop Embayment Slva et al (2003) Hgh Medan Stress Drop Slva et al (2003) Med Medan Stress Drop Slva et al (2003) Low Medan Stress Drop The attenuaton functons of Fernandez and Rx (2006) take the followng general form, 2 R ln ( y) = c1 + c2 M + c3 ( M 6) + c4 ln( RM ) + c5 max ln, 0 + c6 RM (B ) 70 where R M s defned as R M ( c M ) R + c7 exp (B ) = 8 In Equatons (B ) and (B ), y can be peak ground dsplacement n centmeters, peak ground velocty n centmeters/second, or 5% damped spectral acceleraton n unts of g. R s the epcentral dstance n klometers, whch s taken as the shortest dstance travelng along the curved surface of the Earth assumng the average radus of the Earth to be approxmately 6373 km. M s the moment magntude of the source event, and c 1 through c 8 are regresson coeffcents whch may be obtaned from Regresson coeffcents are selected based on whether ground motons are beng calculated at a locaton wth Upland or Lowland sol (see Fgure ), and also what the depth of sol s expected to be. The general form of the equaton used to compute the aleatory standard devaton of the natural logarthm of hazard parameters s (Fernandez and Rx, 2006), σ c M c (B ) ln y = + ( )

175 where M s moment magntude and c 9 and c 10 are regresson coeffcents, smlar to Equatons (B ) and (B ). B Estmatng Probablty of Lquefacton-Induced Ground Falure [ The followng text n Secton B was suppled by Dr. Glenn Rx, unless noted otherwse. Fgures, Tables, and Equatons have been renumbered to be consstent wth the numberng scheme of the overall document.] The purpose of ths algorthm s to estmate the probablty of moderate or major lquefacton-nduced ground falures gven an earthquake magntude M w and a resultng peak ground acceleraton a max defned at the ground surface at locaton P(x,y). The algorthm descrbed heren s based on the lquefacton potental ndex (LPI) proposed by Iwasak et al. (1978; 1982). Iwasak et al. (1982) dentfed LPI values of 5 and 15 as the lower bounds of moderate and major lquefacton, respectvely, from SPT measurements at 85 Japanese stes subjected to sx earthquakes. Toprak and Holzer (2003) correlated LPI wth surface manfestatons of lquefacton usng 50 CPT soundngs at 20 stes affected by the 1989 Loma Preta (M w = 6.9) earthquake. They found that medan values of LPI equal to 5 and 12 corresponded to the occurrence of sand bols and lateral spreadng, respectvely. Analyses of lquefacton features from the 2003 M w = 6.5 San Smeon earthquake also support the use of LPI=5 as the threshold for surface manfestatons of lquefacton (Holzer et al., 2005). LPI s potentally of great use for spatal analyss of lquefacton hazards because t allows one to develop a two-dmensonal representaton of a three-dmensonal phenomenon (.e., FS vs. depth), whch s deal for mappng (Luna and Frost, 1998), and t correlates well wth lquefacton effects (Toprak and Holzer, 2003). Rx and Romero-Hudock (2006) developed the methodology descrbed heren to map lquefacton hazards n the Memphs/Shelby County, Tennessee area. The method s smlar to that used by Holzer et al. (2002; 2006a) to develop lquefacton potental maps for the Oakland, CA area for scenaro earthquakes on the Hayward Fault and by Holzer et al. (2006b) to predct the extent of lquefacton n East Bay flls due to a repeat of the 1906 San Francsco earthquake. Applcaton of the method to areas other than Memphs/Shelby County should be done wth cauton because sol condtons (and thus susceptblty to lquefacton) may vary sgnfcantly. Furthermore, the method s ntended as a screenng method; ste-specfc studes are needed to better estmate the magntude of resultng permanent ground deformatons and other lquefacton-related ground falures. Step 1. Determne the sol unt n whch P(x,y) les The lquefacton susceptblty of the sol unts lsted n Table B and shown n Fgure B was evaluated by Rx and Romero-Hudock (2006). Step 1 conssts of determnng whch sol unt the locaton P(x,y) les n. 175

176 Table B Surfcal geology of the Memphs/Shelby County, Tennessee area (Van Arsdale and Cox, 2003). Surfcal Geology Qal Qa Ql Qtl Artfcal Fll (af) Descrpton Holocene alluvum; sand, clayey slt, and mnor gravel; sand s very fne to coarse graned quartz wth chert; thck-bedded basal pont bar sands are overlan by alternatng thn beds of sand and slt and capped by overbank clayey slt. Holocene alluvum; slt wth mnor mxed sand and clay; dspersed sand s very fne to very coarse graned quartz and mnor chert; floodplan of Nonconnah Creek and trbutares to Wolf Rver and Nonconnah Creek consst of reworked loess; channel bars are covered wth sand and gravel. Late Plestocene loess; slt wth < 10 percent sand and < 10 percent clay; loess s domnantly quartz; thckness ranges from 2 to 20 m. Plestocene loess-covered terrace; dense, cross-bedded, medumgraned sand capped by loess slt. Holocene, man-made; mostly slt, sand, and chert gravel locally derved from loess, alluvum, and the Lafayette gravel. 176

177 Fgure B Surface Geology of Memphs/Shelby County, Tennessee (Broughton and Van Arsdale, 2004; Cox, 2004, Moore and Dehl, 2004a; 2004b; Van Arsdale, 2004a; 2004b) Step 2. Determne the Magntude Scalng Factor For the scenaro earthquake beng analyzed, determne the Magntude Scalng Factor (MSF) by nterpolatng lnearly between values gven n Table B Table B Magntude Scalng Factors Moment Magntude Magntude Scalng Factor Step 3. Calculate the Duraton-Adjusted Peak Ground Acceleraton 177

178 For the peak ground acceleraton a max calculated (ndependently) for the locaton P(x,y), calculate the duraton-adjusted peak ground acceleraton: a max.adjusted = a max MSF < 0.55g Note that the duraton-adjusted peak ground acceleraton may not exceed 0.55 g. (B ) Step 4. Estmate the probablty of moderate or major lquefacton-nduced ground falures Usng the sol unt dentfed n Step 1 and the desred severty of lquefacton-nduced ground falures ( moderate corresponds to LPI = 5; major corresponds to LPI = 15), estmate the probablty of lquefacton-nduced ground falures of that severty by calculatng a weghted average of results determned by Cone Penetraton Test (CPT) and Standard Penetraton Test (SPT) technques: a P[LPI > x] = w b 1 exp c 1 a max.adjusted [ ( )] + w 2 a 2 [ 1+ b 2 exp( c 2 a max.adjusted )] (B ) where a 1, b 1, and c 1 are coeffcents selected from Table B for the CPT results for a gven sol unt and severty; a 2, b 2, and c 2 are coeffcents selected from Table B for the SPT results for the same sol unt and severty; w 1 and w 2 are factors to weght the relatve contrbutons from CPT and SPT tests, respectvely. The factors w 1 and w 2 must sum to 1.0. Rx and Romero-Hudock (2006) used w 1 = and w 2 =

179 Table B Coeffcents for Each Sol Unt, Test Type, and LPI Value. Sol Unt Type of Test LPI Value a b c CPT Qa SPT CPT SPT CPT 5 NA [0] NA [0] NA [0] Qal SPT CPT 15 NA [0] NA [0] NA [0] SPT CPT Ql SPT CPT SPT CPT x Qtl SPT CPT SPT CPT x af SPT CPT SPT

180 APPENDIX C SUPPLEMENTARY FRAGILITY INFORMATION C4.2.1 Supplementary Fraglty Data Table provdes a proposed mappng scheme between nventory and fragltes for Shelby County, TN, usng Fraglty ID s to condense the table. Descrptve data for the mapped fragltes has been excerpted from the master buldng fraglty database and provded n Table In cases where MAE Center research does not provde fraglty data, fraglty curves may be adapted from. For structural damage, fragltes for Moderate, Extensve, and Complete damage states map approxmately to the typcal PL1, PL2, and PL3 lmts used by the MAE Center. Fraglty ID s correspond to rows n the master buldng fraglty database. Mappngs are also provded to parametrc fragltes developed by Jeong and Elnasha, whch may be used as alternates to the typcal MAE Center and fragltes. Note that parametrc fragltes, unlke fragltes from the MAE Center and, must be evaluated wth specfc hazards (.e., PGA, 0.2 sec Sa, 1.0 sec Sa) whch may not correspond to expected sesmc loads for the structure (based on structure perod). The λ, β pars for parametrc fragltes provded n the attached spreadsheet must be evaluated wth the approprate hazard parameter, as noted n the spreadsheet. In the followng table, Fraglty ID s for parametrc fragltes correspond to curves whch must be evaluated wth 0.2 sec Sa. General mappng checks are broken down nto two categores: heght and age. Buldng heghts are generally broken down nto three categores: 1. Low-Rse (1-3 stores) 2. Md-Rse (4-7 stores) 3. Hgh-Rse (8+ stores) Buldng age s generally broken down nto two categores, wth the followng code level mplcatons: 1. Pre- (before 1992, when Memphs frst adopted a sesmc buldng code) 2. Low- ( present, after Memphs adopted the SBC)

181 Table C Default Inventory-to-Fraglty Mappng Scheme MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete T 1 = 0.32 * Hueste 5- SF_C1_1 T 1 = 0.13 * Hueste SF_C1_2 SF_C1_43 SF_C1_52 NSF_DS_C1_2 NSF_AS_C1_2 Moment >= 4 & >= 4 & story flat shear Frame (C1) plate w/ walls <= 7 & <= 7 & permeter OCC_TYPE = OCC_TYPE = moment Offce & COM4 & frame YEAR_BLT YEAR_BLT >= 1977 & >= 1977 & YEAR_BLT YEAR_BLT <= 1992 <= 1992 Concrete T 1 = 0.32 * Hueste 5- SF_C1_1 T 1 = 0.28 * Hueste SF_C1_3 SF_C1_43 SF_C1_52 NSF_DS_C1_2 NSF_AS_C1_2 Moment >= 4 & >= 4 & story flat column Frame (C1) plate w/ jackets <= 7 & <= 7 & permeter OCC_TYPE = OCC_TYPE = moment Offce & COM4 & frame YEAR_BLT YEAR_BLT >= 1977 & >= 1977 & YEAR_BLT YEAR_BLT <= 1992 <=

182 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete T 1 = 0.32 * Hueste 5- SF_C1_1 T 1 = 0.32 * Hueste SF_C1_4 SF_C1_43 SF_C1_52 NSF_DS_C1_2 NSF_AS_C1_2 Moment >= 4 & >= 4 & story flat confnng Frame (C1) plate w/ plates at <= 7 & <= 7 & permeter column OCC_TYPE = OCC_TYPE = moment ends Offce & COM4 & frame YEAR_BLT YEAR_BLT >= 1977 & >= 1977 & YEAR_BLT YEAR_BLT <= 1992 <= 1992 Concrete T 1 = 0.2 * Erberk SF_C1_9 T 1 = 0.75 SF_C1_28 SF_C1_46 SF_C1_55 NSF_DS_C1_5 NSF_AS_C1_5 Moment >= 4 & >= 4 & and C1M Frame (C1) Elnasha 5- Hgh <= 7 & <= 7 & story flat OCC_TYPE = Resdental_MF (Mult Famly) & YEAR_BLT >= 1992 OCC_TYPE = RES3 & YEAR_BLT >= 1992 plate w/ masonry nfll walls 182

183 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete Moment >= 1 & >= 1 & T 1 = η η ( ) 2 1 h, Bracc Gravty SF_C1_10 T 1 = 0.40 C1L Hgh SF_C1_27 SF_C1_42 SF_C1_51 NSF_DS_C1_1 NSF_AS_C1_1 Frame (C1) where η 1 = Load <= 3 & <= 3 & 0.097, η 2 = Desgned YEAR_BLT YEAR_BLT 0.624, and h = (GLD) <= 1976 <= 1976 heght of buldngs buldng frame from base (ft). Typcally assume 13 ft story heght. Concrete Moment >= 4 & >= 4 & T 1 = η η ( ) 2 1 h, Bracc Gravty SF_C1_10 T 1 = 0.75 C1M SF_C1_28 SF_C1_43 SF_C1_52 NSF_DS_C1_2 NSF_AS_C1_2 Frame (C1) where η 1 = Load Hgh <= 7 & <= 7 & 0.097, η 2 = Desgned YEAR_BLT YEAR_BLT 0.624, and h = (GLD) <= 1976 <= 1976 heght of buldngs buldng frame from base (ft). Typcally assume 13 ft story heght. 183

184 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete Moment >= 8 & >= 8 & T 1 = η η ( ) 2 1 h, Bracc Gravty SF_C1_10 T 1 = 1.45 C1H Hgh SF_C1_29 SF_C1_44 SF_C1_53 NSF_DS_C1_3 NSF_AS_C1_3 Frame (C1) YEAR_BLT YEAR_BLT where η 1 = Load <= 1976 <= , η 2 = Desgned 0.624, and h = (GLD) heght of buldngs buldng frame from base (ft). Typcally assume 13 ft story heght. Concrete T 1 = 0.08 * Concrete SF_C1_15 T 1 = 1.45 SF_C1_29 SF_C1_47 SF_C1_53 NSF_DS_C1_6 NSF_AS_C1_6 Moment >= 20 >= 20 frame wth C1H Hgh Frame (C1) shear wall core Concrete T 1 = 0.4 Adapted SF_C1_21 T 1 = 0.4 SF_C1_27 SF_C1_45 SF_C1_51 NSF_DS_C1_4 NSF_AS_C1_4 Moment >= 1 & >= 1 & C1L Hgh Frame (C1) Low <= 3 & <= 3 & C1L YEAR_BLT YEAR_BLT >= 1992 >=

185 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete T 1 = 0.4 Adapted SF_C1_18 T 1 = 0.4 SF_C1_27 SF_C1_42 SF_C1_51 NSF_DS_C1_1 NSF_AS_C1_1 Moment >= 1 & >= 1 & C1L Hgh Frame (C1) Pre- <= 3 & <= 3 & C1L YEAR_BLT < YEAR_BLT < Concrete T 1 = 0.75 Adapted SF_C1_22 T 1 = 0.75 SF_C1_28 SF_C1_46 SF_C1_52 NSF_DS_C1_5 NSF_AS_C1_5 Moment >= 4 & >= 4 & C1M Frame (C1) Low Hgh <= 7 & <= 7 & C1M YEAR_BLT YEAR_BLT >= 1992 >= 1992 Concrete T 1 = 0.75 Adapted SF_C1_19 T 1 = 0.75 SF_C1_28 SF_C1_43 SF_C1_52 NSF_DS_C1_2 NSF_AS_C1_2 Moment >= 4 & >= 4 & C1M Frame (C1) Pre- Hgh <= 7 & <= 7 & C1M YEAR_BLT < YEAR_BLT < Concrete T 1 = 1.45 Adapted SF_C1_23 T 1 = 1.45 SF_C1_29 SF_C1_47 SF_C1_53 NSF_DS_C1_6 NSF_AS_C1_6 Moment >= 8 & >= 8 & C1H Hgh Frame (C1) YEAR_BLT YEAR_BLT Low- >= 1992 >= 1992 C1H 185

186 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete T 1 = 1.45 Adapted SF_C1_20 T 1 = 1.45 SF_C1_29 SF_C1_44 SF_C1_53 NSF_DS_C1_3 NSF_AS_C1_3 Moment >= 8 & >= 8 & C1H Hgh Frame (C1) YEAR_BLT < YEAR_BLT < Pre C1H Concrete T 1 = 0.08 * Concrete SF_C1_15 T 1 = 1.09 SF_C1_29 SF_C1_47 SF_C1_53 NSF_DS_C2_6 NSF_AS_C2_6 Frame wth >= 20 >= 20 frame wth C2H Hgh Concrete shear wall Shear Walls core (C2) Concrete T 1 = 0.35 Adapted SF_C2_4 T 1 = 0.35 SF_C2_10 SF_C2_28 SF_C2_34 NSF_DS_C2_4 NSF_AS_C2_4 Frame wth >= 1 & >= 1 & C2L Hgh Concrete Low Shear Walls <= 3 & <= 3 & C2L (C2) YEAR_BLT YEAR_BLT >= 1992 >= 1992 Concrete T 1 = 0.35 Adapted SF_C2_1 T 1 = 0.35 SF_C2_10 SF_C2_25 SF_C2_34 NSF_DS_C2_1 NSF_AS_C2_1 Frame wth >= 1 & >= 1 & C2L Hgh Concrete Pre- Shear Walls <= 3 & <= 3 & C2L (C2) YEAR_BLT < YEAR_BLT <

187 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete T 1 = Adapted SF_C2_5 T 1 = SF_C2_11 SF_C2_29 SF_C2_35 NSF_DS_C2_5 NSF_AS_C2_5 Frame wth >= 4 & >= 4 & C2M Concrete Low Hgh Shear Walls <= 7 & <= 7 & C2M (C2) YEAR_BLT YEAR_BLT >= 1992 >= 1992 Concrete T 1 = Adapted SF_C2_2 T 1 = SF_C2_11 SF_C2_26 SF_C2_35 NSF_DS_C2_2 NSF_AS_C2_2 Frame wth >= 4 & >= 4 & C2M Concrete Pre- Hgh Shear Walls <= 7 & <= 7 & C2M (C2) YEAR_BLT < YEAR_BLT < Concrete T 1 = 1.09 Adapted SF_C2_6 T 1 = 1.09 SF_C2_12 SF_C2_30 SF_C2_36 NSF_DS_C2_6 NSF_AS_C2_6 Frame wth >= 8 & >= 8 & C2H Hgh Concrete YEAR_BLT YEAR_BLT Low Shear Walls >= 1992 >= 1992 C2H (C2) Concrete T 1 = 1.09 Adapted SF_C2_3 T 1 = 1.09 SF_C2_12 SF_C2_27 SF_C2_36 NSF_DS_C2_3 NSF_AS_C2_3 Frame wth >= 8 & >= 8 & C2H Hgh Concrete YEAR_BLT < YEAR_BLT < Pre- Shear Walls C2H (C2) 187

188 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Concrete YEAR_BLT YEAR_BLT T 1 = 0.35 Adapted SF_PC1_2 T 1 = 0.35 Adapted SF_PC1_4 SF_PC1_10 SF_PC1_12 NSF_DS_PC1_2 NSF_AS_PC1_2 Tlt-Up >= 1992 >= 1992 (PC1) Low Hgh PC1 PC1 Concrete YEAR_BLT < YEAR_BLT < T 1 = 0.35 Adapted SF_PC1_1 T 1 = 0.35 Adapted SF_PC1_4 SF_PC1_9 SF_PC1_12 NSF_DS_PC1_1 NSF_AS_PC1_1 Tlt-Up (PC1) Pre- Hgh PC1 PC1 Precast T 1 = 0.35 Adapted SF_PC2_4 T 1 = 0.35 Adapted SF_PC2_10 SF_PC2_28 SF_PC2_34 NSF_DS_PC2_4 NSF_AS_PC2_4 Concrete >= 1 & >= 1 & Frame (PC2) Low Hgh <= 3 & <= 3 & PC2L YEAR_BLT YEAR_BLT PC2L >= 1992 >= 1992 Precast T 1 = 0.35 Adapted SF_PC2_1 T 1 = 0.35 Adapted SF_PC2_10 SF_PC2_25 SF_PC2_34 NSF_DS_PC2_1 NSF_AS_PC2_1 Concrete >= 1 & >= 1 & Frame (PC2) Pre- Hgh <= 3 & <= 3 & PC2L YEAR_BLT < YEAR_BLT < PC2L

189 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Precast T 1 = 0.56 Adapted SF_PC2_5 T 1 = 0.56 Adapted SF_PC2_11 SF_PC2_29 SF_PC2_35 NSF_DS_PC2_5 NSF_AS_PC2_5 Concrete >= 4 & >= 4 & Frame (PC2) Low Hgh <= 7 & <= 7 & PC2M YEAR_BLT YEAR_BLT PC2M >= 1992 >= 1992 Precast T 1 = 0.56 Adapted SF_PC2_2 T 1 = 0.56 Adapted SF_PC2_11 SF_PC2_26 SF_PC2_35 NSF_DS_PC2_2 NSF_AS_PC2_2 Concrete >= 4 & >= 4 & Frame (PC2) Pre- Hgh <= 7 & <= 7 & PC2M YEAR_BLT < YEAR_BLT < PC2M Precast T 1 = 1.09 Adapted SF_PC2_6 T 1 = 1.09 Adapted SF_PC2_12 SF_PC2_30 SF_PC2_36 NSF_DS_PC2_6 NSF_AS_PC2_6 Concrete >= 8 & >= 8 & Frame (PC2) YEAR_BLT YEAR_BLT Low Hgh >= 1992 >= 1992 PC2H PC2H Precast T 1 = 1.09 Adapted SF_PC2_3 T 1 = 1.09 Adapted SF_PC2_12 SF_PC2_27 SF_PC2_36 NSF_DS_PC2_3 NSF_AS_PC2_3 Concrete >= 8 & >= 8 & Frame (PC2) YEAR_BLT < YEAR_BLT < Pre- Hgh PC2H PC2H 189

190 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Renforced T 1 = 0.35 Adapted SF_RM_8 T 1 = 0.35 Adapted SF_RM_18 SF_RM_48 SF_RM_58 NSF_DS_RM_8 NSF_AS_RM_8 Masonry >= 1 & >= 1 & (RM) Low Hgh <= 3 & <= 3 & RM2L YEAR_BLT YEAR_BLT RM2L >= 1992 & >= 1992 & EF = EFS1 EF = EFS1 Renforced T 1 = 0.35 Adapted SF_RM_3 T 1 = 0.35 Adapted SF_RM_18 SF_RM_43 SF_RM_58 NSF_DS_RM_3 NSF_AS_RM_3 Masonry >= 1 & >= 1 & (RM) Pre- Hgh <= 3 & <= 3 & RM2L YEAR_BLT < YEAR_BLT < RM2L 1992 & 1992 & EF = EFS1 EF = EFS1 Renforced T 1 = 0.35 Adapted SF_RM_6 T 1 = 0.35 Adapted SF_RM_16 SF_RM_46 SF_RM_56 NSF_DS_RM_6 NSF_AS_RM_6 Masonry >= 1 & >= 1 & (RM) Low Hgh <= 3 & <= 3 & RM1L YEAR_BLT YEAR_BLT RM1L >= 1992 >=

191 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Renforced T 1 = 0.35 Adapted SF_RM_1 T 1 = 0.35 Adapted SF_RM_16 SF_RM_41 SF_RM_56 NSF_DS_RM_1 NSF_AS_RM_1 Masonry >= 1 & >= 1 & (RM) Pre- Hgh <= 3 & <= 3 & RM1L YEAR_BLT < YEAR_BLT < RM1L Renforced T 1 = 0.56 Adapted SF_RM_9 T 1 = 0.56 Adapted SF_RM_19 SF_RM_49 SF_RM_59 NSF_DS_RM_9 NSF_AS_RM_9 Masonry >= 4 & >= 4 & (RM) Low Hgh <= 7 & <= 7 & RM2M YEAR_BLT YEAR_BLT RM2M >= 1992 & >= 1992 & EF = EFS1 EF = EFS1 Renforced T 1 = 0.56 Adapted SF_RM_4 T 1 = 0.56 Adapted SF_RM_19 SF_RM_44 SF_RM_59 NSF_DS_RM_4 NSF_AS_RM_4 Masonry >= 4 & >= 4 & (RM) Pre- Hgh <= 7 & <= 7 & RM2M YEAR_BLT < YEAR_BLT < RM2M 1992 & 1992 & EF = EFS1 EF = EFS1 191

192 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Renforced T 1 = 0.56 Adapted SF_RM_7 T 1 = 0.56 Adapted SF_RM_17 SF_RM_47 SF_RM_57 NSF_DS_RM_7 NSF_AS_RM_7 Masonry >= 4 & >= 4 & (RM) Low Hgh <= 7 & <= 7 & RM1M YEAR_BLT YEAR_BLT RM1M >= 1992 >= 1992 Renforced T 1 = 0.56 Adapted SF_RM_2 T 1 = 0.56 Adapted SF_RM_17 SF_RM_42 SF_RM_57 NSF_DS_RM_2 NSF_AS_RM_2 Masonry >= 4 & >= 4 & (RM) Pre- Hgh <= 7 & <= 7 & RM1M YEAR_BLT < YEAR_BLT < RM1M Renforced T 1 = 1.09 Adapted SF_RM_10 T 1 = 1.09 Adapted SF_RM_20 SF_RM_50 SF_RM_60 NSF_DS_RM_10 NSF_AS_RM_10 Masonry >= 8 & >= 8 & (RM) YEAR_BLT YEAR_BLT Low Hgh >= 1992 >= 1992 RM2H RM2H Renforced T 1 = 1.09 Adapted SF_RM_5 T 1 = 1.09 Adapted SF_RM_20 SF_RM_45 SF_RM_60 NSF_DS_RM_5 NSF_AS_RM_5 Masonry >= 8 & >= 8 & (RM) YEAR_BLT < YEAR_BLT < Pre- Hgh RM2H RM2H 192

193 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Unrenforced T 1 = 0.35 Adapted SF_URM_3 T 1 = 0.35 Adapted SF_RM_16 SF_URM_11 SF_RM_56 NSF_DS_URM_3 NSF_AS_URM_3 Masonry >= 1 & >= 1 & (URM) Low Hgh <= 2 & <= 2 & URML YEAR_BLT YEAR_BLT RM1L >= 1992 >= 1992 Unrenforced T 1 = 0.35 Adapted SF_URM_1 T 1 = 0.35 Adapted SF_RM_16 SF_URM_9 SF_RM_56 NSF_DS_URM_1 NSF_AS_URM_1 Masonry >= 1 & >= 1 & (URM) Pre- Hgh <= 2 & <= 2 & URML YEAR_BLT < YEAR_BLT < RM1L Unrenforced T 1 = 0.50 Adapted SF_URM_4 T 1 = 0.50 Adapted SF_RM_17 SF_URM_12 SF_RM_57 NSF_DS_URM_4 NSF_AS_URM_4 Masonry >= 3 & >= 3 & (URM) YEAR_BLT YEAR_BLT Low Hgh >= 1992 >= 1992 URMM RM1M Unrenforced T 1 = 0.50 Adapted SF_URM_2 T 1 = 0.50 Adapted SF_RM_17 SF_URM_10 SF_RM_57 NSF_DS_URM_2 NSF_AS_URM_2 Masonry >= 3 & >= 3 & (URM) YEAR_BLT < YEAR_BLT < Pre- Hgh URMM RM1M 193

194 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Steel T 1 = 1.07 Ellngwood SF_S1_1 T 1 = 0.50 Adapted SF_S1_13 SF_S1_16 SF_S1_25 NSF_DS_S1_1 NSF_AS_S1_1 Moment >= 1 & >= 1 & 2 story PR Resstng Hgh Frame (S1) <= 3 & <= 3 & S1L YEAR_BLT < YEAR_BLT < Steel T 1 = 1.04 Ellngwood SF_S2_1 T 1 = 0.86 Adapted SF_S2_12 SF_S2_30 SF_S2_36 NSF_DS_S2_5 NSF_AS_S2_5 Moment >= 4 & >= 4 & 6 story X- Resstng braced Hgh Frame (S1) <= 7 & <= 7 & YEAR_BLT YEAR_BLT S2M >= 1992 >= 1992 Steel T 1 = 0.50 Adapted SF_S1_7 T 1 = 0.50 Adapted SF_S1_13 SF_S1_19 SF_S1_25 NSF_DS_S1_4 NSF_AS_S1_4 Moment >= 1 & >= 1 & Resstng Low Hgh Frame (S1) <= 3 & <= 3 & S1L S1L YEAR_BLT YEAR_BLT >= 1992 >= 1992 Steel T 1 = 0.86 Adapted SF_S2_3 T 1 = 0.86 Adapted SF_S2_12 SF_S2_27 SF_S2_36 NSF_DS_S2_2 NSF_AS_S2_2 Moment >= 4 & >= 4 & Resstng Pre- Hgh Frame (S1) <= 7 & <= 7 & S2M YEAR_BLT < YEAR_BLT < S2M

195 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Steel T 1 = 1.77 Adapted SF_S2_7 T 1 = 1.77 Adapted SF_S2_13 SF_S2_31 SF_S2_37 NSF_DS_S2_6 NSF_AS_S2_6 Moment >= 8 & >= 8 & Resstng YEAR_BLT YEAR_BLT Low Hgh Frame (S1) >= 1992 >= 1992 S2H S2H Steel T 1 = 1.77 Adapted SF_S2_4 T 1 = 1.77 Adapted SF_S2_13 SF_S2_28 SF_S2_37 NSF_DS_S2_3 NSF_AS_S2_3 Moment >= 8 & >= 8 & Resstng YEAR_BLT < YEAR_BLT < Pre- Hgh Frame (S1) S2H S2H Lght Metal YEAR_BLT YEAR_BLT T 1 = 0.40 Adapted SF_S3_2 T 1 = 0.40 Adapted SF_S3_4 SF_S3_10 SF_S3_12 NSF_DS_S3_2 NSF_AS_S3_2 Frame (S3) >= 1992 >= 1992 Low Hgh S3 S3 Lght Metal YEAR_BLT < YEAR_BLT < T 1 = 0.40 Adapted SF_S3_1 T 1 = 0.40 Adapted SF_S3_4 SF_S3_9 SF_S3_12 NSF_DS_S3_1 NSF_AS_S3_1 Frame (S3) Pre- Hgh S3 S3 Wood Frame T 1 = 0.24 Ellngwood SF_W1_1 T 1 = 0.35 Adapted SF_W1_6 SF_W1_11 SF_W1_14 NSF_DS_W1_1 NSF_AS_W1_1 (W) = 1 & = 1 & 1 story YEAR_BLT < YEAR_BLT < Slab-on- Hgh grade W1 195

196 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Wood Frame T 1 = 0.35 Adapted SF_W1_4 T 1 = 0.35 Adapted SF_W1_6 SF_W1_12 SF_W1_14 NSF_DS_W1_2 NSF_AS_W1_2 (W) = 1 & = 1 & YEAR_BLT YEAR_BLT Low Hgh >= 1992 >= 1992 W1 W1 Wood Frame T 1 = 0.38 Ellngwood SF_W2_1 T 1 = 0.40 Adapted SF_W2_5 SF_W2_10 SF_W2_13 NSF_DS_W2_1 NSF_AS_W2_1 (W) = 2 & = 2 & 2 story YEAR_BLT < YEAR_BLT < Slab-on- Hgh grade W2 Wood Frame T 1 = 0.40 Adapted SF_W2_3 T 1 = 0.40 Adapted SF_W2_5 SF_W2_11 SF_W2_13 NSF_DS_W2_2 NSF_AS_W2_2 (W) = 2 & = 2 & YEAR_BLT YEAR_BLT Low Hgh >= 1992 >= 1992 W2 W2 Unknown EF = (EFFS EF = (EFFS T 1 = 0.35 Adapted SF_URM_3 T 1 = 0.35 Adapted SF_RM_16 SF_URM_11 SF_RM_56 NSF_DS_URM_3 NSF_AS_URM_3 OR EFPS OR OR EFPS OR EFS1) & EFS1) & Low Hgh URML <= 2 <= 2 RM1L & YEAR_BLT & >= 1992 YEAR_BLT >=

197 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Unknown EF = (EFFS EF = (EFFS T 1 = 0.35 Adapted SF_URM_1 T 1 = 0.35 Adapted SF_RM_16 SF_URM_9 SF_RM_56 NSF_DS_URM_1 NSF_AS_URM_1 OR EFPS OR OR EFPS OR EFS1) & EFS1) & Pre- Hgh URML <= 2 <= 2 RM1L & YEAR_BLT & < 1992 YEAR_BLT < 1992 Unknown EF = (EFFS EF = (EFFS T 1 = 0.50 Adapted SF_URM_4 T 1 = 0.50 Adapted SF_RM_17 SF_URM_12 SF_RM_57 NSF_DS_URM_4 NSF_AS_URM_4 OR EFPS OR OR EFPS OR EFS1) & EFS1) & Low Hgh URMM > 2 > 2 RM1M & YEAR_BLT & >= 1992 YEAR_BLT >= 1992 Unknown EF = (EFFS EF = (EFFS T 1 = 0.50 Adapted SF_URM_2 T 1 = 0.50 Adapted SF_RM_17 SF_URM_10 SF_RM_57 NSF_DS_URM_2 NSF_AS_URM_2 OR EFPS OR OR EFPS OR EFS1) & EFS1) & Pre- Hgh URMM > 2 > 2 RM1M & YEAR_BLT & < 1992 YEAR_BLT <

198 MAEC v3 Mappng v4 Mappng Non-Retroft Non- Non- Retroft Retroft Retroft Parametrc Parametrc Drft-Senstve Acceleraton- Structural Check(s) Check(s) Perod Retroft Retroft Perod Fraglty Fraglty Non- Retroft Fraglty ID Senstve Type (seconds) Fraglty Fraglty (seconds) ID Retroft Fraglty Fraglty ID ID Fraglty ID ID Unknown EF = EFHL EF = EFHL T 1 = 0.4 Adapted SF_C1_24 T 1 = 0.4 SF_C1_27 SF_C1_48 SF_C1_51 NSF_DS_C1_7 NSF_AS_C1_7 & YEAR_BLT & C1L Hgh >= 1992 YEAR_BLT Moderate >= 1992 C1L Unknown EF = EFHL & YEAR_BLT EF = EFHL & T 1 = η η ( ) 2 1 h, Bracc Gravty SF_C1_10 T 1 = 0.40 C1L Hgh SF_C1_27 SF_C1_42 SF_C1_51 NSF_DS_C1_1 NSF_AS_C1_1 < 1992 YEAR_BLT < where η 1 = Load , η 2 = Desgned 0.624, and h = (GLD) heght of buldngs buldng frame from base (ft). Typcally assume 13 ft story heght. 198

199 Table C Descrptve Data for Fragltes n Default Mappng Scheme Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Concrete Low- SF_C1_1 Hueste Moment Frame 5 Flat Slab wth Permeter Moment Frame Rx and Fernandez Sa g Concrete Hgh- SF_C1_2 Hueste Moment Frame 5 Flat Slab wth Permeter Moment Frame wth shear walls Rx and Fernandez Sa g Concrete Flat Slab wth Permeter Moment Frame wth column Moderate SF_C1_3 Hueste Moment Frame 5 jackets Rx and Fernandez - Sa g Concrete Flat Slab wth Permeter Moment Frame wth confnng Low- SF_C1_4 Hueste Moment Frame 5 plates at column ends Rx and Fernandez Sa g Elnasha and Concrete Low- SF_C1_9 Erberk Moment Frame 5 Flat Slab wth Masonry Infll Walls 10 actual records (worldwde) Sa g Concrete Pre- SF_C1_10 Bracc Moment Frame 0 Gravty Load Desgned Concrete Frames Rx and Fernandez, Wen Sa g Elnasha, Concrete Low- SF_C1_15 Kuchma, J Moment Frame 54 Hgh-rse wth dual-core wall system 30 actual records (worldwde) Sa g Concrete Pre- SF_C1_18 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sd n Concrete Pre- SF_C1_19 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sd n Concrete Pre- SF_C1_20 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sd n Concrete Low- SF_C1_21 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sd n Concrete Low- SF_C1_22 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sd n Concrete Low- SF_C1_23 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sd n 199

200 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Concrete Moderate SF_C1_24 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown - Sd n Concrete Hgh- SF_C1_27 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sd n Concrete Hgh- SF_C1_28 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sd n Concrete Hgh- SF_C1_29 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sd n Elnasha and Concrete 84th percentle, Memphs Pre- 0.2 sec SF_C1_42 Jeong Moment Frame 2 Low-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Pre- 0.2 sec SF_C1_43 Jeong Moment Frame 5 Md-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Pre- 0.2 sec SF_C1_44 Jeong Moment Frame 12 Hgh-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Low- 0.2 sec SF_C1_45 Jeong Moment Frame 2 Low-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Low- 0.2 sec SF_C1_46 Jeong Moment Frame 5 Md-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Low- 0.2 sec SF_C1_47 Jeong Moment Frame 12 Hgh-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Moderate 0.2 sec SF_C1_48 Jeong Moment Frame 2 Low-Rse Concrete Moment Frame Lowlands, Blythevlle, AR - Sa g Elnasha and Concrete 84th percentle, Memphs Hgh- 0.2 sec SF_C1_51 Jeong Moment Frame 2 Low-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Hgh- 0.2 sec SF_C1_52 Jeong Moment Frame 5 Md-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Elnasha and Concrete 84th percentle, Memphs Hgh- 0.2 sec SF_C1_53 Jeong Moment Frame 12 Hgh-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g 200

201 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Elnasha and Concrete 84th percentle, Memphs Pre- 1.0 sec SF_C1_55 Jeong Moment Frame 5 Md-Rse Concrete Moment Frame Lowlands, Blythevlle, AR Sa g Concrete Frame Pre- SF_C2_1 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Pre- SF_C2_2 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Pre- SF_C2_3 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Low- SF_C2_4 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Low- SF_C2_5 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Low- SF_C2_6 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Hgh- SF_C2_10 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Hgh- SF_C2_11 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sd n Concrete Frame Hgh- SF_C2_12 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sd n Elnasha and Concrete Frame 84th percentle, Memphs Pre- 0.2 sec SF_C2_25 Jeong w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Pre- 0.2 sec SF_C2_26 Jeong w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Pre- 0.2 sec SF_C2_27 Jeong w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Low- 0.2 sec SF_C2_28 Jeong w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g 201

202 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Elnasha and Concrete Frame 84th percentle, Memphs Low- 0.2 sec SF_C2_29 Jeong w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Low- 0.2 sec SF_C2_30 Jeong w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Hgh- 0.2 sec SF_C2_34 Jeong w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Hgh- 0.2 sec SF_C2_35 Jeong w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Elnasha and Concrete Frame 84th percentle, Memphs Hgh- 0.2 sec SF_C2_36 Jeong w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Lowlands, Blythevlle, AR Sa g Pre- SF_PC1_1 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown Sd n SF_PC1_2 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown Sd n Low- Hgh- SF_PC1_4 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown Sd n Elnasha and 84th percentle, Memphs Pre- 0.2 sec SF_PC1_9 Jeong Concrete Tlt-Up 1 Concrete Tlt-Up Lowlands, Blythevlle, AR Sa g SF_PC1_1 Elnasha and 84th percentle, Memphs Low- 0.2 sec 0 Jeong Concrete Tlt-Up 1 Concrete Tlt-Up Lowlands, Blythevlle, AR Sa g SF_PC1_1 Elnasha and 84th percentle, Memphs Hgh- 0.2 sec 2 Jeong Concrete Tlt-Up 1 Concrete Tlt-Up Lowlands, Blythevlle, AR Sa g Precast Concrete Pre- SF_PC2_1 Frame 2 Low-Rse Precast Concrete Frame Unknown Sd n Precast Concrete Pre- SF_PC2_2 Frame 5 Md-Rse Precast Concrete Frame Unknown Sd n Precast Concrete Pre- SF_PC2_3 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sd n 202

203 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Precast Concrete Low- SF_PC2_4 Frame 2 Low-Rse Precast Concrete Frame Unknown Sd n Precast Concrete Low- SF_PC2_5 Frame 5 Md-Rse Precast Concrete Frame Unknown Sd n Precast Concrete Low- SF_PC2_6 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sd n Precast Concrete Moderate SF_PC2_9 Frame 12 Hgh-Rse Precast Concrete Frame Unknown - Sd n SF_PC2_1 Precast Concrete Hgh- 0 SF_PC2_1 1 Frame 2 Low-Rse Precast Concrete Frame Unknown Precast Concrete Frame 5 Md-Rse Precast Concrete Frame Unknown Sd n Hgh- Sd n SF_PC2_2 Elnasha and Precast Concrete 84th percentle, Memphs Pre- 0.2 sec 5 Jeong Frame 2 Low-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_2 Elnasha and Precast Concrete 84th percentle, Memphs Pre- 0.2 sec 6 Jeong Frame 5 Md-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_2 Elnasha and Precast Concrete 84th percentle, Memphs Pre- 0.2 sec 7 Jeong Frame 12 Hgh-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_2 Elnasha and Precast Concrete 84th percentle, Memphs Low- 0.2 sec 8 Jeong Frame 2 Low-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_2 Elnasha and Precast Concrete 84th percentle, Memphs Low- 0.2 sec 9 Jeong Frame 5 Md-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_3 Elnasha and Precast Concrete 84th percentle, Memphs Low- 0.2 sec 0 Jeong Frame 12 Hgh-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_3 Elnasha and Precast Concrete 84th percentle, Memphs Hgh- 0.2 sec 4 Jeong Frame 2 Low-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g SF_PC2_3 Elnasha and Precast Concrete 84th percentle, Memphs Hgh- 0.2 sec 5 Jeong Frame 5 Md-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g 203

204 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts SF_PC2_3 Elnasha and Precast Concrete 84th percentle, Memphs Hgh- 0.2 sec 6 Jeong Frame 12 Hgh-Rse Precast Concrete Frame Lowlands, Blythevlle, AR Sa g Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Pre- SF_RM_1 Masonry 2 or Metal Deck Daphragms Unknown Sd n Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Pre- SF_RM_2 Masonry 5 or Metal Deck Daphragms Unknown Sd n Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Pre- SF_RM_3 Masonry 2 Concrete Daphragms Unknown Sd n Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Pre- SF_RM_4 Masonry 5 Concrete Daphragms Unknown Sd n Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Pre- SF_RM_5 Masonry 12 Precast Concrete Daphragms Unknown Sd n Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Low- SF_RM_6 Masonry 2 or Metal Deck Daphragms Unknown Sd n Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Low- SF_RM_7 Masonry 5 or Metal Deck Daphragms Unknown Sd n Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Low- SF_RM_8 Masonry 2 Concrete Daphragms Unknown Sd n Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Low- SF_RM_9 Masonry 5 Concrete Daphragms Unknown Sd n SF_RM_1 Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Low- 0 Masonry 12 Precast Concrete Daphragms Unknown Sd n SF_RM_1 Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Hgh- 6 Masonry 2 or Metal Deck Daphragms Unknown Sd n SF_RM_1 Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Hgh- 7 Masonry 5 or Metal Deck Daphragms Unknown Sd n SF_RM_1 Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Hgh- 8 Masonry 2 Concrete Daphragms Unknown Sd n 204

205 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts SF_RM_1 Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Hgh- 9 Masonry 5 Concrete Daphragms Unknown Sd n SF_RM_2 Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Hgh- 0 Masonry 12 Precast Concrete Daphragms Unknown Sd n SF_RM_4 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Pre- 0.2 sec 1 Jeong Masonry 2 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa g SF_RM_4 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Pre- 0.2 sec 2 Jeong Masonry 5 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa g SF_RM_4 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Pre- 0.2 sec 3 Jeong Masonry 2 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Pre- 0.2 sec 4 Jeong Masonry 5 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Hgh-Rse Renforced Masonry Bearng Walls wth 84th percentle, Memphs Pre- 0.2 sec 5 Jeong Masonry 12 Precast Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Low- 0.2 sec 6 Jeong Masonry 2 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Low- 0.2 sec 7 Jeong Masonry 5 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Low- 0.2 sec 8 Jeong Masonry 2 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_4 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Low- 0.2 sec 9 Jeong Masonry 5 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_5 Elnasha and Renforced Hgh-Rse Renforced Masonry Bearng Walls wth 84th percentle, Memphs Low- 0.2 sec 0 Jeong Masonry 12 Precast Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_5 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Hgh- 0.2 sec 6 Jeong Masonry 2 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_5 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood 84th percentle, Memphs Hgh- 0.2 sec 7 Jeong Masonry 5 or Metal Deck Daphragms Lowlands, Blythevlle, AR Sa n 205

206 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts SF_RM_5 Elnasha and Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Hgh- 0.2 sec 8 Jeong Masonry 2 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_5 Elnasha and Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast 84th percentle, Memphs Hgh- 0.2 sec 9 Jeong Masonry 5 Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_RM_6 Elnasha and Renforced Hgh-Rse Renforced Masonry Bearng Walls wth 84th percentle, Memphs Hgh- 0.2 sec 0 Jeong Masonry 12 Precast Concrete Daphragms Lowlands, Blythevlle, AR Sa n SF_URM_ Unrenforced Pre- 1 SF_URM_ 2 SF_URM_ 3 SF_URM_ 4 Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Unrenforced Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Unrenforced Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Unrenforced Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Sd n Pre- Sd n Low- Sd n Low- Sd n SF_URM_ Elnasha and Unrenforced 84th percentle, Memphs Pre- 0.2 sec 9 Jeong Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Lowlands, Blythevlle, AR Sa g SF_URM_ Elnasha and Unrenforced 84th percentle, Memphs Pre- 0.2 sec 10 Jeong Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Lowlands, Blythevlle, AR Sa g SF_URM_ Elnasha and Unrenforced 84th percentle, Memphs Low- 0.2 sec 11 Jeong Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Lowlands, Blythevlle, AR Sa g SF_URM_ Elnasha and Unrenforced 84th percentle, Memphs Low- 0.2 sec 12 Jeong Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Lowlands, Blythevlle, AR Sa g Steel Moment SF_S1_1 Ellngwood Resstng Frame 2 2-story Partally Restraned Steel Frame Unknown Sa g Steel Moment SF_S1_7 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sd n Steel Moment Pre- Low- Hgh- SF_S1_13 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sd n 206

207 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Elnasha and Steel Moment 84th percentle, Memphs Pre- SF_S1_16 Jeong Resstng Frame 2 Low-Rse Steel Moment Frame Lowlands, Blythevlle, AR PGA g Elnasha and Steel Moment 84th percentle, Memphs Low- SF_S1_19 Jeong Resstng Frame 2 Low-Rse Steel Moment Frame Lowlands, Blythevlle, AR PGA g Elnasha and Steel Moment 84th percentle, Memphs Hgh- SF_S1_25 Jeong Resstng Frame 2 Low-Rse Steel Moment Frame Lowlands, Blythevlle, AR PGA g Steel Braced SF_S2_1 Ellngwood Frame 6 6-story X-braced Steel Frame Unknown Sa g Steel Braced SF_S2_3 Frame 5 Md-Rse Steel Braced Frame Unknown Sd n Steel Braced SF_S2_4 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sd n Steel Braced SF_S2_7 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sd n Steel Braced SF_S2_12 Frame 5 Md-Rse Steel Braced Frame Unknown Sd n Steel Braced Low- Pre- Pre- Low- Hgh- Hgh- SF_S2_13 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sd n Elnasha and Steel Braced 84th percentle, Memphs Pre- 0.2 sec SF_S2_27 Jeong Frame 5 Md-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g Elnasha and Steel Braced 84th percentle, Memphs Pre- 0.2 sec SF_S2_28 Jeong Frame 13 Hgh-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g Elnasha and Steel Braced 84th percentle, Memphs Low- 0.2 sec SF_S2_30 Jeong Frame 5 Md-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g Elnasha and Steel Braced 84th percentle, Memphs Low- 0.2 sec SF_S2_31 Jeong Frame 13 Hgh-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g Elnasha and Steel Braced 84th percentle, Memphs Hgh- 0.2 sec SF_S2_36 Jeong Frame 5 Md-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g 207

208 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts Elnasha and Steel Braced 84th percentle, Memphs Hgh- 0.2 sec SF_S2_37 Jeong Frame 13 Hgh-Rse Steel Braced Frame Lowlands, Blythevlle, AR Sa g Lght Metal SF_S3_1 Frame 1 Steel Lght Frame Unknown Sd n Lght Metal SF_S3_2 Frame 1 Steel Lght Frame Unknown Sd n Lght Metal Pre- Low- Hgh- SF_S3_4 Frame 1 Steel Lght Frame Unknown Sd n Elnasha and Lght Metal 84th percentle, Memphs Pre- 0.2 sec SF_S3_9 Jeong Frame 1 Steel Lght Frame Lowlands, Blythevlle, AR Sa g Elnasha and Lght Metal 84th percentle, Memphs Low- 0.2 sec SF_S3_10 Jeong Frame 1 Steel Lght Frame Lowlands, Blythevlle, AR Sa g Elnasha and Lght Metal 84th percentle, Memphs Hgh- 0.2 sec SF_S3_12 Jeong Frame 1 Steel Lght Frame Lowlands, Blythevlle, AR Sa g Pre- SF_W1_1 Ellngwood Wood Frame 1 1-story Wood Frame on slab-on-grade Unknown Sa g SF_W1_4 Wood Frame 1 Lght Wood Frame Unknown Sd n Low- Hgh- SF_W1_6 Wood Frame 1 Lght Wood Frame Unknown Sd n SF_W1_1 Elnasha and 84th percentle, Memphs Pre- 0.2 sec 1 Jeong Wood Frame 1 Lght Wood Frame Lowlands, Blythevlle, AR Sa g SF_W1_1 Elnasha and 84th percentle, Memphs Low- 0.2 sec 2 Jeong Wood Frame 1 Lght Wood Frame Lowlands, Blythevlle, AR Sa g SF_W1_1 Elnasha and 84th percentle, Memphs Hgh- 0.2 sec 4 Jeong Wood Frame 1 Lght Wood Frame Lowlands, Blythevlle, AR Sa g Pre- SF_W2_1 Ellngwood Wood Frame 2 2-story Wood Frame on slab-on-grade Unknown Sa g 208

209 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts SF_W2_3 Wood Frame 2 Commercal and Industral Wood Frame Unknown Sd n Low- Hgh- SF_W2_5 Wood Frame 2 Commercal and Industral Wood Frame Unknown Sd n SF_W2_1 Elnasha and 84th percentle, Memphs Pre- 0.2 sec 0 Jeong Wood Frame 2 Commercal and Industral Wood Frame Lowlands, Blythevlle, AR Sa g SF_W2_1 Elnasha and 84th percentle, Memphs Low- 0.2 sec 1 Jeong Wood Frame 2 Commercal and Industral Wood Frame Lowlands, Blythevlle, AR Sa g SF_W2_1 Elnasha and 84th percentle, Memphs Hgh- 0.2 sec 3 Jeong Wood Frame 2 Commercal and Industral Wood Frame Lowlands, Blythevlle, AR Sa g NSF_DS_ Concrete Pre- C1_1 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Pre- C1_2 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Pre- C1_3 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Low- C1_4 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Low- C1_5 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Low- C1_6 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sd n NSF_DS_ Concrete Moderate C1_7 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown - Sd n NSF_DS_ Concrete Frame Pre- C2_1 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sd n NSF_DS_ Concrete Frame Pre- C2_2 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sd n 209

210 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_DS_ Concrete Frame Pre- C2_3 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sd n NSF_DS_ Concrete Frame Low- C2_4 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sd n NSF_DS_ Concrete Frame Low- C2_5 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sd n NSF_DS_ Concrete Frame Low- C2_6 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sd n NSF_DS_ Pre- PC1_1 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown NSF_DS_ PC1_2 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown Sd n Low- Sd n NSF_DS_ Precast Concrete Pre- PC2_1 Frame 2 Low-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Precast Concrete Pre- PC2_2 Frame 5 Md-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Precast Concrete Pre- PC2_3 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Precast Concrete Low- PC2_4 Frame 2 Low-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Precast Concrete Low- PC2_5 Frame 5 Md-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Precast Concrete Low- PC2_6 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sd n NSF_DS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Pre- RM_1 Masonry 2 or Metal Deck Daphragms Unknown Sd n NSF_DS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Pre- RM_2 Masonry 5 or Metal Deck Daphragms Unknown Sd n 210

211 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_DS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Pre- RM_3 Masonry 2 Concrete Daphragms Unknown Sd n NSF_DS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Pre- RM_4 Masonry 5 Concrete Daphragms Unknown Sd n NSF_DS_ Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Pre- RM_5 Masonry 12 Precast Concrete Daphragms Unknown Sd n NSF_DS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Low- RM_6 Masonry 2 or Metal Deck Daphragms Unknown Sd n NSF_DS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Low- RM_7 Masonry 5 or Metal Deck Daphragms Unknown Sd n NSF_DS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Low- RM_8 Masonry 2 Concrete Daphragms Unknown Sd n NSF_DS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Low- RM_9 Masonry 5 Concrete Daphragms Unknown Sd n NSF_DS_ Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Low- RM_10 Masonry 12 Precast Concrete Daphragms Unknown Sd n NSF_DS_ Unrenforced Pre- URM_1 Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Sd n NSF_DS_ Unrenforced Pre- URM_2 Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Sd n NSF_DS_ Unrenforced Low- URM_3 Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Sd n NSF_DS_ Unrenforced Low- URM_4 Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Sd n NSF_DS_ Steel Moment Pre- S1_1 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sd n NSF_DS_ Steel Moment Low- S1_4 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sd n 211

212 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_DS_ Steel Braced Pre- S2_2 Frame 5 Md-Rse Steel Braced Frame Unknown Sd n NSF_DS_ Steel Braced Pre- S2_3 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sd n NSF_DS_ Steel Braced Low- S2_5 Frame 5 Md-Rse Steel Braced Frame Unknown Sd n NSF_DS_ Steel Braced Low- S2_6 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sd n NSF_DS_ Lght Metal Pre- S3_1 Frame 1 Steel Lght Frame Unknown Sd n NSF_DS_ Lght Metal Low- S3_2 Frame 1 Steel Lght Frame Unknown Sd n NSF_DS_ Pre- W1_1 Wood Frame 1 Lght Wood Frame Unknown NSF_DS_ W1_2 Wood Frame 1 Lght Wood Frame Unknown NSF_DS_ W2_1 Wood Frame 2 Commercal and Industral Wood Frame Unknown NSF_DS_ W2_2 Wood Frame 2 Commercal and Industral Wood Frame Unknown Sd n Low- Sd n Pre- Sd n Low- Sd n NSF_AS_ Concrete Pre- C1_1 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sa g NSF_AS_ Concrete Pre- C1_2 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sa g NSF_AS_ Concrete Pre- C1_3 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sa g NSF_AS_ Concrete Low- C1_4 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown Sa g 212

213 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_AS_ Concrete Low- C1_5 Moment Frame 5 Md-Rse Concrete Moment Frame Unknown Sa g NSF_AS_ Concrete Low- C1_6 Moment Frame 12 Hgh-Rse Concrete Moment Frame Unknown Sa g NSF_AS_ Concrete Moderate C1_7 Moment Frame 2 Low-Rse Concrete Moment Frame Unknown - Sa g NSF_AS_ Concrete Frame Pre- C2_1 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Concrete Frame Pre- C2_2 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Concrete Frame Pre- C2_3 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Concrete Frame Low- C2_4 w/ Shear Walls 2 Low-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Concrete Frame Low- C2_5 w/ Shear Walls 5 Md-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Concrete Frame Low- C2_6 w/ Shear Walls 12 Hgh-Rse Concrete Frame w/ Shear Walls Unknown Sa g NSF_AS_ Pre- PC1_1 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown NSF_AS_ PC1_2 Concrete Tlt-Up 1 Concrete Tlt-Up Unknown Sa g Low- Sa g NSF_AS_ Precast Concrete Pre- PC2_1 Frame 2 Low-Rse Precast Concrete Frame Unknown Sa g NSF_AS_ Precast Concrete Pre- PC2_2 Frame 5 Md-Rse Precast Concrete Frame Unknown Sa g NSF_AS_ Precast Concrete Pre- PC2_3 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sa g 213

214 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_AS_ Precast Concrete Low- PC2_4 Frame 2 Low-Rse Precast Concrete Frame Unknown Sa g NSF_AS_ Precast Concrete Low- PC2_5 Frame 5 Md-Rse Precast Concrete Frame Unknown Sa g NSF_AS_ Precast Concrete Low- PC2_6 Frame 12 Hgh-Rse Precast Concrete Frame Unknown Sa g NSF_AS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Pre- RM_1 Masonry 2 or Metal Deck Daphragms Unknown Sa g NSF_AS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Pre- RM_2 Masonry 5 or Metal Deck Daphragms Unknown Sa g NSF_AS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Pre- RM_3 Masonry 2 Concrete Daphragms Unknown Sa g NSF_AS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Pre- RM_4 Masonry 5 Concrete Daphragms Unknown Sa g NSF_AS_ Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Pre- RM_5 Masonry 12 Precast Concrete Daphragms Unknown Sa g NSF_AS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Wood Low- RM_6 Masonry 2 or Metal Deck Daphragms Unknown Sa g NSF_AS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Wood Low- RM_7 Masonry 5 or Metal Deck Daphragms Unknown Sa g NSF_AS_ Renforced Low-Rse Renforced Masonry Bearng Walls wth Precast Low- RM_8 Masonry 2 Concrete Daphragms Unknown Sa g NSF_AS_ Renforced Md-Rse Renforced Masonry Bearng Walls wth Precast Low- RM_9 Masonry 5 Concrete Daphragms Unknown Sa g NSF_AS_ Renforced Hgh-Rse Renforced Masonry Bearng Walls wth Low- RM_10 Masonry 12 Precast Concrete Daphragms Unknown Sa g NSF_AS_ Unrenforced Pre- URM_1 Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Sa g 214

215 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_AS_ Unrenforced Pre- URM_2 Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Sa g NSF_AS_ Unrenforced Low- URM_3 Masonry 2 Low-Rse Unrenforced Masonry Bearng Walls Unknown Sa g NSF_AS_ Unrenforced Low- URM_4 Masonry 5 Md-Rse Unrenforced Masonry Bearng Walls Unknown Sa g NSF_AS_ Steel Moment Pre- S1_1 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sa g NSF_AS_ Steel Moment Low- S1_4 Resstng Frame 2 Low-Rse Steel Moment Frame Unknown Sa g NSF_AS_ Steel Braced Pre- S2_2 Frame 5 Md-Rse Steel Braced Frame Unknown Sa g NSF_AS_ Steel Braced Pre- S2_3 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sa g NSF_AS_ Steel Braced Low- S2_5 Frame 5 Md-Rse Steel Braced Frame Unknown Sa g NSF_AS_ Steel Braced Low- S2_6 Frame 13 Hgh-Rse Steel Braced Frame Unknown Sa g NSF_AS_ Lght Metal Pre- S3_1 Frame 1 Steel Lght Frame Unknown Sa g NSF_AS_ Lght Metal Low- S3_2 Frame 1 Steel Lght Frame Unknown Sa g NSF_AS_ Pre- W1_1 Wood Frame 1 Lght Wood Frame Unknown NSF_AS_ W1_2 Wood Frame 1 Lght Wood Frame Unknown NSF_AS_ W2_1 Wood Frame 2 Commercal and Industral Wood Frame Unknown Sa g Low- Sa g Pre- Sa g 215

216 Fraglty ID Author Structure Type Stores Descrpton Ground Motons Demand Type Demand Unts NSF_AS_ W2_2 Wood Frame 2 Commercal and Industral Wood Frame Unknown Low- Sa g 216

217 Fraglty Database Documentaton The fraglty database contans the followng felds: ID Numerc dentfer. Fraglty ID Unque ID code for each fraglty. Each ID code corresponds to data for a set of three fraglty curves. The general form for structural fraglty curves s SF_AA_BB, where AA corresponds to the structure type (e.g., AA = C1 for concrete moment frame, C2 for concrete frame wth shear walls), and BB s a numerc counter to unquely dentfy each fraglty set. The general form for nonstructural fraglty curves s NSF_CC_AA_BB, where AA and BB are the same as for structural fragltes, and CC s ether DS for drft-senstve or AS for acceleraton-senstve. Author Identfes the person(s) or entty(es) who provded each fraglty set. Structure Type Descrbes the structure type of the fraglty set. The structure type s always one of the followng: Concrete Moment Frame Concrete Frame w/ Shear Walls Concrete Frame w/ Unrenforced Masonry Infll Walls Concrete Tlt-Up Precast Concrete Frame Renforced Masonry Unrenforced Masonry Steel Moment Resstng Frame Steel Braced Frame Lght Metal Frame 217

218 Steel Frame w/ CIP Concrete Shear Walls Steel Frame w/ Unrenforced Masonry Infll Walls Wood Frame Other Stores Identfes the number of stores used for the model buldng when constructng fragltes. A value of 0 ndcates multple story levels were consdered (for fraglty surfaces). Descrpton A textual descrpton of the model buldng used when constructng fragltes. Ground Motons Ground moton records used for tme-hstory analyses when constructng fragltes. The level of sesmc demand requred by the buldng code when a model buldng s desgned. Damage Type Ether Structural or Nonstructural. Demand Type The type of sesmc demand assocated wth a partcular fraglty set. Demand s typcally spectral acceleraton (Sa) computed at the model buldng s natural perod or PGA for fragltes provded by the MAE Center. When fragltes are adapted from, the hazard parameter s spectral dsplacement (Sd), where spectral dsplacement and spectral acceleraton can be approxmately related by S d = S a 2 ( 9.78 T ) 218

219 Where Sd s n unts of nches, Sa s n unts of g, and the natural perod, T, s n unts of seconds. Parametrc fragltes are calbrated to use PGA, 0.2 second Sa, or 1.0 second Sa, regardless of the natural perod of the model buldng, as ndcated. Demand Unt The unts assocated wth each demand type. Unts are g s for all fraglty sets except those adapted drectly from, whch use nches. Lmt States The lmt states whch defne the transtons between damage states for each fraglty set. Perod Calculatons T Eqn Type, T Eqn Param0, T Eqn Param1, and T Eqn Param2 provde data requred to estmate the natural perod of a buldng to whch a fraglty set has been assgned. When T Eqn Type = 1 T = a 1 Where a = T Eqn Param0 when T Eqn Type = 2 T = a 1 NO _ STORIES Where a = T Eqn Param0 when T Eqn Type = 3 219

220 T = b 1 Where a = T Eqn Param0 b = T Eqn Param1 c = T Eqn Param2 ( a NO _ STORIES) c Frag Eqn Type Fraglty equaton type. The fraglty equaton type s ether 1 or 2, where 1 corresponds to P ( LS / Y ) ln = Φ ( Y ) β λ In whch Y s a hazard parameter (PGA, Sa, or Sd), and Φ ndcates the cumulatve normal dstrbuton functon. Fraglty equaton type 2 corresponds to P when and P when ( LS / S ) a ln = Φ 0.87 T (sec) ( LS / S ) a ln = Φ 0 < T < 0.87(sec) ( S a ) ( α11 + α12t ) ( ) α13 + α14t ( S a ) ( α + α ) ( α + α 0.87) ( 0.87 T ) 11 ln ( S ) n whch Sa s spectral acceleraton at the natural perod of a gven structure, and Φ ndcates the cumulatve normal dstrbuton functon as t dd for equaton type 1. a α α Parameters The number of parameters needed to defne the gven fraglty set. The number s typcally 6, whch s 3 pars of λ, β parameters. In the case of fraglty surfaces (fraglty equaton type 2, above), the number s 18, whch s 3 sets of 6 α terms. Medan and Beta Parameters 220

221 For fraglty equaton type 1, there are three pars of parameters whch are used to defne the three transtons between damage states. The medan parameters are substtuted for λ n the equaton for fraglty equaton type 1, and the beta parameters are lkewse substtuted for β. The number followng each parameter descrpton ndcates whch transton the parameter descrbes, where 0 s a transton between Insgnfcant and Moderate damage, 1 s a transton between Moderate and Heavy, and 2 s a transton between Heavy and Complete damage. FS Param (Fraglty Surface Parameters) The fraglty surface parameters functon smlarly to medan and beta parameters, except that there are 6 parameters per fraglty curve rather than 2. Consderng PL1, PL2, and PL3 to be the transton lmts between Insgnfcant and Moderate, Moderate and Heavy, and Heavy and Complete damage, the parameters should be substtuted nto the equatons gven above for fraglty equaton type 2 as follows: Table C Correlatons of database entres, α terms, and lmt states for fraglty surfaces PL1 PL2 PL3 α 11 FS Param0 FS Param6 FS Param12 α 12 FS Param1 FS Param7 FS Param13 α 13 FS Param2 FS Param8 FS Param14 α 14 FS Param3 FS Param9 FS Param15 α 21 FS Param4 FS Param10 FS Param16 α 22 FS Param5 FS Param11 FS Param17 221

222 APPENDIX D DIRECT ECONOMIC LOSS EXAMPLE FOR BUILDINGS SYSTEMATIC TREATMENT OF UNCERTAINTY IN CONSEQUENCE-BASED RISK MANAGEMENT OF SEISMIC REGIONAL LOSSES Lang Chang, Junho Song, Joshua Steelman and Jerome F. Hajjar 1241 Newmark Cvl Engneerng Laboratory 205 North Mathews Avenue Unversty of Illnos at Urbana-Champagn Urbana, Illnos

223 The Md-Amerca Earthquake (MAE) center ams to treat varous uncertantes nherent n ts Consequence-based Rsk Management (CRM) n a systematc manner. In order to acheve ths goal, a Task Group on Interdscplnary Coordnaton (TGIC) of the MAE center develops a probablstc framework to estmate the uncertanty n socal and economc losses n a regon caused by sesmc hazard. Ths document presents the probablstc framework under development wth a numercal example. The total drect loss of an nventory of three buldngs s estmated wth ts uncertanty quantfed. We ncorporate the uncertantes n the ntensty of a scenaro earthquake, nventory dentfcaton, performance of structural/non-structural components, content loss, lquefacton hazard, and damage states. Examples on the use of a probablstc hazard map n regonal loss estmaton and on the drect loss of a brdge nventory are currently under development. I. Inventory data and scenaro sesmc hazard For smplcty, ths example consders the total loss of three buldng nventory tems n the Memphs test bed regon. Table 1 lsts the structural and occupancy types of the nventory tems, the fundamental perods (T ) of the structures, the mean ( λ S ) and a standard devaton ( β S ) of the natural logarthm of the spectral acceleraton ( S ) a a at each nventory locaton, and ther assessed structural values (M ). URM denotes unrenforced masonry buldng. Table 1. Example data and scenaro hazard No. Structural Occupancy T ln S a type type (sec) λ S a β (US $) S a 1 Concrete Industral ,400 2 URM Commercal ,393 3 URM Industral ,346 M II. Structural damage II-1. Structural damage fraglty and lmt-state exceedance probablty The fraglty P ( LS Sa) s defned as the condtonal probablty that a certan type of structure wll exceed the prescrbed lmt state LS for a gven spectral acceleraton S a. The fragltes developed by the MAE center can be descrbed as ln S a λ P( LS = Φ Sa) (1) β 223

224 where Φ ( ) s the cumulatve densty functon (CDF) of the standard normal dstrbuton, and λ and β are the fraglty parameters for the -th lmt state of a gven structural type. Ths form of fraglty s beng nternally referred as Type I. There also exst MAE center fragltes descrbed n terms of drft (Wen et al. 2004). λc λd S a P ( LS Sa) = Φ (2) βc + βd S + β a M where λ C denotes the natural logarthm of the medan drft capacty for the -th lmt state, λ D S a s the natural logarthm of the medan drft demand determned from a ftted power law equaton (Cornell et al. 2002) for a gven spectral acceleraton, and β C, β D S a and β M are the standard devaton of the natural logarthm of the capacty, demand and a2 model error, respectvely. When the power law s defned as D = a1( S a ), the parameters of the Type I fragltes are ( λc ln a λ 1) = (3a) a βc + βd S + β a M β = (3b) a 2 The exceedance probablty for an unknown spectral acceleraton s derved as λs λ a P ( LS ) = Φ 2 2 (4a) β + βs a λc λd S a = ms P ( LS ) = Φ a (4b) βc + βd S + a2βs + β a a M where λ Sa m S = e s the medan of the spectral acceleraton. a MAE Center budng damage estmaton s based on the use of four damage states, wth three thresholds, or behavoral lmt states, to defne the boundares of the ndvdual damage states. The three lmt states may generally be referred to as PL1, PL2, and PL3, where the hgher numbers ndcate lmt states at the boundares of more severe damage states. Table 2 lsts the fraglty parameters for the three lmt states consdered; Immedate Occupancy (IO) for PL1, Lfe Safety (LS) for PL2, and Collapse Preventon (CP) for PL3. The exceedance probabltes P ( LS ) computed by Eq. (4a) are also lsted. Other behavoral lmt states may be used for varous levels of PL, such as Frst Yeld, or Plastc Mechansm Intaton, nstead of IO, LS, or CP, when some other behavor more closely represents a threshold of expected damage level. 224

225 Table 2. Fraglty parameters and lmt state exceedance probabltes (structural damage) Inventory tems Lmt states, LS PL1(IO) PL2(LS) PL3(CP) 1 λ Concrete β Bracc P ( LS ) (3-story) λ URM β Wen P ( LS ) (2-story) λ URM β Wen P ( LS ) (2-story) P(I) Exceedance Probablty IO LS CP P(M) P(H) P(C) Spectral Acceleraton, S a Fgure 1. Computng probabltes of damage states II-2. Probablty of structural damage states by ground shakng Ba et al. (2006) proposed four dstnct states for structural damages by ground shakng: Insgnfcant (I), Moderate (M), Heavy (H), and Complete (C). As llustrated n Fgure 1, we can compute the probabltes of the four damage states from the lmt-state exceedance probabltes as follows. 225

226 P( I) = 1 P( PL1) (5a) P( M ) = P( PL1) P( PL2) (5b) P( H ) = P( PL2) P( PL3) (5c) P ( C) = P( PL3) (5d) We compute the damage state probabltes from the lmt-state exceedance probabltes reported n Table 2 by usng Eq. (5) and report n Table 3. Table 3. Probabltes of structural damage states Inventory tems Probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) II-3. Consderaton of structural damages caused by ground falure A structure can be damaged not only by ground shakng, but also by ground falure such as sol lquefacton. If we use four states (I, M, H and C) for the damages by ground falure as well, and assume structural damage by ground shakng and that by ground falures are statstcally ndependent of each other, the probablty that a structure wll exceed a certan damage state ether by ground shakng or ground falure s obtaned as P COMB [ DS I] = 1 (6a) P P P COMB COMB COMB [ DS M ] = PGS [ PL1] + PGF [ PL1] PGS [ PL1] PGF [ PL1] [ DS H ] = PGS [ PL2] + PGF [ PL2] PGS [ PL2] PGF [ PL2] [ DS C] = P [ PL3] + P [ PL3] P [ PL3] P [ PL3] (6b) (6c) (6d) GS GF GS where P COMB [ DS X ] denotes the probablty that a structure wll exceed a damage state X ether by ground falure or ground shakng, and P GS and P GF denote the probabltes of exceedance by ground shakng and ground falure, respectvely. Then, the combned probabltes of damage states are computed as P P P P COMB COMB COMB COMB [ DS I ] = PCOMB [ DS M ] [ DS M ] = PCOMB [ DS M ] PCOMB [ DS H ] [ DS H ] = PCOMB [ DS H ] PCOMB [ DS C] [ DS C] = P [ DS C] = 1 (7a) = (7b) = (7c) = (7d) COMB GF 226

227 In ths example, the probablty of Complete ground falure, P GF [ DS C] = P GF [ DS = C] s defned as the probablty that the lquefacton potental ndex (LPI) s greater than 15. An algorthm has been developed and documented wthn the MAE Center to evaluate ths probablty, P ( LPI > 15). The proposed algorthm evaluates the complete ground falure probabltes of the three buldngs n the example as 1.51% (Concrete), 1.96% (URM1) and 1.93% (URM2), respectvely. In ths example, we also assume that a ground falure ether causes Complete (C) or Insgnfcant (I) damages only. Therefore, P GF [ DS M ] and P GF [ DS H ] are also the same as P ( LPI > 15). Combnng these ground falure probabltes wth the probabltes of structural damages caused by ground shakng (Table 3) by Eqs. (6) and (7), the combned probabltes of structural damages are obtaned and reported n Table 4. Table 4. Probabltes of structural damage after lquefacton hazard s consdered Inventory tems Combned probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) II-4. Mean and standard devaton of damage rato The damage ratos of nventory tems are crtcal nputs to socal and economc loss models. Ba et al. (2006) proposed a probablstc model for the structural damage ratos to account for the uncertanty n structural damages. They assume that a structure s subjected to one of the four damage states (I, M, H and C) wth the probabltes computed by Eq. (7). For a gven damage state, the damage rato follows the beta dstrbuton wth a prescrbed range. The mean of the Beta dstrbuton s assumed to be at the mdpont of the range whle the standard devaton s gven as one-thrd of the length of the range. Table 5 shows the proposed range, mean and standard devaton of Beta dstrbuton for each damage state. Table 5. Probablstc model for structural damage rato (Ba et al. 2006) Damage states, DS Range of Beta dstrbuton (%) Mean of damage rato, μ (%) D DS Standard devaton of damage rato, σ (%) 1: Insgnfcant [0, 1] : Moderate [1, 30] : Heavy [30, 80] : Complete [80, 100] D DS 227

228 by The mean and varance of the damage rato (D) of an nventory tem are computed 4 μ = [ P( DS ) μ (8a) D = 1 D DS ] σ 2 D = E[ D = = 4 2 { P( DS ) E[ D DS ]} = 1 4 = 1 2 ] μ 2 D [ P( DS ) ( σ + μ )] μ D DS D DS μ 2 D D (8b) where P ( DS ), = 1, K, 4 denotes the combned probabltes of the -th damage state such as those shown n Table 4, and μ D DS and σ D DS are the condtonal mean and standard devaton of Beta dstrbuton gven DS damage state, shown n Table 5. The means and varances of the damage ratos of the three nventory tems n ths example are computed by Eq. (8) and lsted n Table 6. Table 6. Mean and varance of structural damage ratos Inventory Mean, μ D Varance, 1: Concrete : URM : URM σ D III. Non-structural damage III-1. Probablstc models for non-structural damage states In order to estmate the probabltes of non-structural damage states, we adopt the non-structural fraglty curves developed for four lmt-states: Slght, Moderate, Extensve and Complete. As llustrated n Fgure 2, fve damage states, None (N), Slght (S), Moderate (M), Extensve (E) and Complete (C) are derved from the four lmt-states. To be consstent wth the probablstc model on the structural damage, we combne the damage states N and S and name t Insgnfcant (I). The other damage states M, E and C are renamed to Moderate (M), Heavy (H) and Complete (C), respectvely. For each damage state, assgns a determnstc damage rato. Consder the damage ratos gven n Fgure 3a. If a non-structural component s n Moderate state, for example, the damage rato s assumed to be b exactly. To be consstent wth the beta- 228

229 dstrbuton-based probablstc model proposed for structural damage, we ntroduce fourranges of non-structural damage states whose boundares are mdponts between the damage rato values (See Fgure 3b). Then, we assume that the mean of the damage rato n each nterval s at ts mdpont and the standard devaton s one thrd of the nterval length. There exst two types of non-structural damages: acceleratonsenstve and drft-senstve. Tables 7 and 8 show the probablstc models obtaned by the aforementoned procedure. 1 P(N) 0.8 P(S) Exceedance Probablty Slght Moderate P(M) 0.2 Extensve P(E) Complete P(C) Spectral Acceleraton, S a Fgure 2. Acceleraton-senstve non-structural fraglty curves () (a) damage ratos (0, a, b, c, 100) None Slght Moderate Extensve Complete 0 a b c 100 (b) Damage rato ntervals determned by mdponts Insgnfcant Moderate Heavy Complete 0 (a+b)/2 (b+c)/2 (c+100)/2 100 denotes mdpont. Fgure 3. Probablstc model for non-structural damage ratos 229

230 Table 7. Probablstc model for acceleraton-senstve non-structural damage rato Damage states, DS Range of Beta dstrbuton (%) Mean of damage rato, μ (%) D DS Standard devaton of damage rato, σ (%) 1: Insgnfcant [0, 6] : Moderate [6, 20] : Heavy [20, 65] : Complete [65, 100] D DS Table 8. Probablstc model for drft-senstve non-structural damage rato Damage states, DS Range of Beta dstrbuton (%) Mean of damage rato, μ (%) D DS Standard devaton of damage rato, σ (%) 1: Insgnfcant [0, 6] : Moderate [6, 30] : Heavy [30, 75] : Complete [75, 100] D DS III-2. Acceleraton-senstve non-structural damage acceleraton-senstve non-structural fragltes are gven n terms of spectral acceleratons. By combnng the uncertantes of spectral acceleraton by Eq. (4a), we can compute the exceedance probabltes P ( LS ) for acceleraton-senstve non-structural damage. Table 9 shows the fraglty parameters and the computed exceedance probabltes. Table 9. Fraglty parameters and lmt state exceedance probabltes (acceleratonsenstve non-structural damage) Lmt states, LS Inventory tems Moderate (M) Extensve (E) Complete (C) λ β Concrete P ( LS ) λ β URM P ( LS ) λ β URM P LS ) ( 230

231 The probabltes of the four damage states are then computed by P( I) = 1 P( Moderate) (9a) P( M ) = P( Moderate) P( Extensve) (9b) P( H ) = P( Extensve) P( Complete) (9c) P ( C) = P( Complete) (9d) Table 10 shows the computed probabltes of the damage states. Table 10. Probabltes of acceleraton-senstve non-structural damage states Inventory tems Probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) Non-structural damages caused by ground falure are taken nto account by the procedure n Eqs. (6) and (7). Table 11 shows the probabltes after lquefacton hazard s consdered. Table 11. Probabltes of acceleraton-senstve non-structural damage after combnng lquefacton hazard Inventory tems Combned probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) The means and varances of the damage ratos are computed by Eq. (8) and lsted n Table

232 Table 12. Mean and varance of acceleraton-senstve non-structural damage ratos Inventory Mean, μ D Varance, 1: Concrete : URM : URM σ D III-3. Drft-senstve non-structural damage The fraglty curves for drft-senstve non-structural damage are gven n terms of spectral dsplacement nstead of spectral acceleraton. As shown n Table 1, the uncertantes n the sesmc ntensty are quantfed n terms of spectral acceleraton. Hence, we derve the mean and varance of the logarthm of the spectral dsplacement from those of spectral acceleraton. When the unts of spectral acceleraton and dsplacement are the gravty acceleraton (g) and nches, respectvely, the spectral dsplacement S ) s descrbed n terms of the spectral acceleraton by d a e ( d S = S T (10) where T e s the fundamental perod of the structure shown n Table 1. Then, the mean and varance of the natural logarthms of the spectral dsplacement are computed as 2 λ = λ ln(9.8t ) (11a) S S + d a 2 2 Sd S a e β = β (11b) Table 13 shows the results of the converson. Table 13. Converson from spectral acceleraton to spectral dsplacement Inventory tems 2 λ λ = λ + ln(9.8t ) S a S d S a e β = β 2 2 Sd S a 1: Concrete : URM : URM Ths converson allows us to follow all the procedures developed for the acceleratonsenstve non-structural damages. Tables show the results of the computatons. 232

233 Table 14. Fraglty parameters and lmt state exceedance probabltes (drft-senstve non-structural damage) Lmt states, LS Inventory tems Moderate (M) Extensve (E) Complete (C) λ β Concrete P ( LS ) λ β URM P ( LS ) λ β URM P LS ) ( Table 15. Probabltes of drft-senstve non-structural damage states Inventory tems Probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) Table 16. Probabltes of drft-senstve non-structural damage consderng lquefacton Inventory tems Combned probablty of damage states I M H C 1 (Concrete) (URM1) (URM2) Table 17. Mean and varance of drft-senstve non-structural damage ratos Inventory Mean, μ D Varance, 1: Concrete : URM : URM σ D 233

234 IV. Contents Loss uses the acceleraton-senstve non-structural fragltes to determne the states of contents loss. For each content loss state, a determnstc loss rato s assgned. Table 18 shows a probablstc model proposed for the content loss ratos to be consstent wth the models for structural/non-structural damage ratos. Table 19 shows the means and varances of the content loss ratos of the buldngs n ths example. Table 18. Probablstc model for content loss rato Damage states, DS Range of Beta dstrbuton (%) Mean of damage rato, μ (%) D DS Standard devaton of damage rato, σ (%) 1: Insgnfcant [0, 3] : Moderate [3, 15] : Heavy [15, 37.5] : Complete [37.5, 50] D DS Table 19. Mean and varance of the contents loss ratos Inventory Mean, μ D Varance, 1: Concrete : URM : URM σ D V. Consderaton of nventory uncertanty There exst uncertan errors n dentfyng the structural types of nventory tems by remote sensng. For example, a concrete buldng could be mstakenly classfed nto the URM buldng category. We may assume a probablty of accurate dentfcaton, denoted by p d, to account for ths uncertanty. Ths means there s ( 1 pd ) probablty that the structure belongs to any of the other structural types n the nventory. Then, the mean of the damage rato s adjusted as μ ~ = p μ + (1 p ) μ (12) D d D d D r where μ D ~ s the mean damage rato wth the nventory uncertanty consdered, μ D s the mean damage rato based on the dentfed structure type such as those reported n Tables 6, 12, 17 and 19, and μ D r s the mean damage rato for unknown structural type. The latter, denoted as representatve mean damage rato, s estmated as the weghted average of the mean damage ratos based on the other dentfed structural types except for the orgnally predcted structure type, that s, 234

235 μ N 1 d j D = n r j μd N j= 1 (13) where N d s the number of representatve structure types dentfed,.e., the total number of structure types mnus 1; n j s the number of the nventory tems dentfed as the j-th N representatve structural type, j = 1,..., N d ; N = d n j j s the total number of j representatve nventory tems (excludng the orgnally predcted structures); and μ D s the mean damage rato estmated based on the j-th representatve structural type at the gven ste. Note that for ths example, the hazard wll be assumed constant wth respect to structure type. In fact, each structure type can have ts own perod, and a calculaton should be performed for each perod to estmate an approprate spectral acceleraton. When the hazard s transformed from spectral acceleraton to spectral dsplacement for drft-senstve damage estmaton, the perod s used. μ D r In ths example, the representatve damage rato s computed as = μ (14a) URM D for nventory tem I1, and μ D r = μ (14b) con D for nventory tem I2 and I3. con URM where μ D and μ D respectvely denote the mean damage rato estmated based on the dentfcatons as concrete and URM buldngs. Assumng p = 0.85, the mean damage rato s updated as d μ % = 0.85μ μ (15) D D D r For the frst nventory tem dentfed as a concrete buldng, the adjusted mean damage rato s μ % = μ + μ (16) D con 0.85 D 0.15 URM D The adjusted varance of the damage rato s σ = E[ D% ] μ D% D% con 2 con 2 URM 2 URM 2 2 = 0.85[( μd ) + ( σd ) ] [( μd ) + ( σd ) ] μd% For the second and thrd nventory tems dentfed as URM buldngs, the adjusted means and varances of the damage ratos are μ % = μ + μ (18a) D con 0.15 D 0.85 σ = E[ D% ] μ URM D D% D% con 2 con 2 URM 2 URM 2 2 = 0.15[( μd ) + ( σd ) ] [( μd ) + ( σd ) ] μd% (17) (18b) 235

236 Table 20 shows the structural/non-structural damage ratos and the content loss ratos adjusted by Eqs. (16) (18). Table 20. Means and varances of damage ratos and content loss ratos adjusted by nventory uncertanty μ 2 ~D Inventory buldngs D ~ σ SD : Concrete NA ND CL SD : URM NA ND CL SD : URM 2 NA ND CL Notaton: SD: structural damage, NA: acceleraton-senstve non-structural damage, ND: drft-senstve non-structural damage, CL: content loss VI. Loss estmaton As a smple example of socal and economc losses caused by sesmc hazard, we consder the loss of an nventory tem defned by SD ~ SD NA ~ NA ND ~ ND CL ~ CL Loss = M ( α D + α D + α D + α D ) (19) SD NA ND where M s the total assessed value of the -th nventory tem; α, α and α are the fractons of the values of structural and non-structural (acceleraton- and drftsenstve) components; α CL s the rato of the contents value to the structural assessed ~ value; SD NA D, D ~ ND and D ~ are the damage ratos of the -th nventory tem adjusted by CL the nventory uncertanty; and D ~ s the adjusted content loss rato. Table 21 shows the fractons of structural and non-structural values of commercal and ndustral occupances defned by. In ths example, we assume α CL to be 150, 100 and 150% for the CL nventory tems 1, 2 and 3, followng the assumpton by that α can be 50, 100 or 150% only. 236

237 Occupancy type Table 21. Fracton (%) of structural and non-structural values SD α NA α ND α Commercal Industral The total loss of the nventory s obtaned by aggregatng the losses of the nventory tems, that s, Loss = N = 1 Loss (20) Then mean of the total loss s estmated as μ Loss = N = 1 M SD NA ND CL ( α μ ~ + α μ ~ + α μ ~ + α μ ~ ) (21) D SD D NA D ND D CL Assumng the damage ratos of dfferent nventory tems are condtonally ndependent gven a sesmc ntensty, the varance of the total loss s computed as σ 2 Loss = N = 1 M 2 SD 2 2 NA 2 2 ND 2 2 CL 2 2 [ α ) σ ~ SD + ( α ) σ ~ NA + ( α ) σ ~ ND + ( α ) σ ~ CL ] ( (22) D The coeffcent of varaton (c.o.v.) of the total loss s σ D Loss δ Loss = (23) μ Loss The mean, standard devaton and c.o.v. of the total loss of the example nventory are estmated as (mllon US$), 0.208(mllon US$) and %, respectvely. Consder Loss Rato ( L r ), whch s the total loss normalzed by the sum of structural, non-structural and content values n a regon, that s, Loss Loss L r = = = M (1 + α ) N N SD NA ND CL M ( α + α + α + α ) = 1 = 1 D CL Loss M Then, mean and standard devaton of the loss rato are μ Loss / M total and σ Loss / M total, respectvely. The c.o.v. of the loss rato s the same as that of the total loss. For the example nventory, the mean and standard devaton of the loss rato are estmated as 11.42% and 6.48 %, respectvely. Gven the estmated mean and standard devaton, and an assumed dstrbuton type, we can fnd the probablty dstrbuton of the loss rato. We hereby assume the loss rato follows the lognormal dstrbuton. The lognormal dstrbuton requres two parameters λ and β, whch are the mean and standard devaton of the natural logarthm of the quantty. total D (24) 237

238 These parameters are obtaned from the estmated mean and standard devaton of the loss rato as follows. 2 β = ln[1 + ( σ / μ) ] (25a) 2 λ = ln μ 0.5β (25b) The lognormal parameters of the loss rato n the example are λ = 2.31 and β = The probablty densty functon (PDF) of the loss rato s defned as ln l r λ f L r ( lr ) = exp (26) 2πβl 2 β r Fgure 4 plots the PDF of the loss rato of the example nventory. Probablty Densty Functon Loss Rato, L r Fgure 4. Probablty densty functon of loss rato 238

239 Exceedance Probablty Loss Rato, L r Fgure 5. Exceedance probablty of loss rato We can also estmate the probablty that the loss rato wll exceed a certan threshold. Ths s often referred as complementary cumulatve dstrbuton functon (CCDF). The CCDF of the lognormal dstrbuton s ln( lr ) λ C Lr ( lr ) = 1 Φ (27) β The exceedance probablty of the loss rato s plotted n Fgure 5. Table 22 lsts the exceedance probabltes at selected thresholds of loss rato. Table 22. Probablty of exceedance Loss rato Probablty of exceedence, % (%) (lognormal dstrbuton)

240 Based on the estmated uncertanty n the loss rato, we can predct the loss rato by an nterval wth a certan level of confdence. An nterval that encloses the true loss rato wth probablty 1 α (or an nterval wth confdence level 1 α ) s [ λ β), exp( λ + k )] exp( k α / 2 α / 2β (28) where k 1 α / 2 = Φ (1 α / 2). Table 23 shows the coeffcent values for selected confdence levels and the correspondng confdence ntervals. Table 23. Confdence ntervals on loss rato Confdence level, 1 α k α / 2 (%) Confdence nterval (%) [6.36, 15.49] [5.73, 17.17] [5.04, 19.55] [4.16, 23.70] [3.52, 28.00] [2.54, 38.78] 240

241 APPENDIX: Data flow chart Fgure 6 llustrates the data flow of the proposed procedure wth equaton numbers shown. 241

242 Sesmc Intensty SD, NA and CL: ( λ S a, β S a ) ND: ( λ, β ) ~ Eq. (11) S d S d Compute lmt-state probablty P LS ) ~ Eq. (4) ( Fraglty: λ, β ) ( SD (MAE) NA, ND, CL () Compute damage-state probablty, P DS ) Eqs. (5) and (9) ( Consder lquefacton hazard P DS ) COMB ( ~ Eqs (6) and (7) Ground falure probabltes: P GF ( DS X ) Compute mean and varance of damage 2 rato, ( μ D, σ D ) ~ Eq (8) Damage rato models Ranges and μ, σ D DS D DS Consder nventory uncertanty ( μ ~, ~ ) D σ D ~ Eqs. (12) and (13) Probablty of accurate dentfcaton: p d Perform for each nventory tem Estmate total loss and loss rato Mean, std, c.o.v., PDF, CCDF and confdence nterval Eqs. (21), (22), (23), (26), (27) and (28) Fgure 6. Data flow chart of probablstc estmaton of sesmc regonal loss 242