Evaluating Earthquake Retrofitting Measures for Schools: A Demonstration Cost-Benefit Analysis

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1 Evaluatng Earthquake Retrofttng easures for Schools: A emonstraton Cost-Beneft Analyss A.W. Smyth, G. eodats 2, G. Franco 3, Y. He 4, and T. Gurvch 4 ept. of Cvl Engneerng & Engneerng echancs Columba Unversty, New York, NY 27, USA Abstract Based on a recent cost-beneft approach developed by several of the authors for evaluatng sesmc mtgaton optons for apartment buldngs, a demonstraton study s presented for a hypothetcal vulnerable school buldng n the developng world. Probablstc cost-beneft analyss provdes a useful framework wthn whch socety can evaluate sesmc mtgaton measures under the backdrop of lmted resources and numerous demands. In the case of schools, competng demands mght be books or other learnng materals, teachers, or nutrton and healthcare programs. The hypothetcal school s analyzed over a varety of tme-horzons to determne the break-even pont for nvestments n several sesmc retrofttng optons. The hazard n ths study s assumed to be probablstc, however, due to the prelmnary nature of the study, the structure s assumed to be determnstc. Introducton In Smyth et al. (24) a straghtforward cost-beneft analyss was performed to evaluate sesmc retrofttng measures for an actual apartment buldng n Istanbul, Turkey. That study combned the probablstc sesmc hazard estmate, sophstcated structural analyss technques and economc cost-beneft prncples to select the best of three retrofttng optons proposed by local contractors. Actual cost estmates for the retrofttng measures as well as the drect dollar losses due to a potental collapse were consdered. In addton, to force all of the losses nto one common metrc, the dollar cost of human lves lost n the event of a structural collapse was also consdered. Although the approach s promsng for apartment structures, the potental of extrapolatng broader conclusons for school buldngs s even greater. Ths s smply because n many regons schools are desgned usng smlar buldng methods and havng smlar geometres. Therefore a detaled analyss may not have to be performed for each ndvdual structure, but rather a probablstc structure could be consdered to represent a class of school structure type. Gven the demonstraton nature of ths study, a determnstc and hypothetcal school structure wll be consdered, and n no way should the results of ths analyss be used to draw major conclusons for practce. Rather, the presentaton of the methodology n the context of schools s the objectve here. The Structure to be Consdered Based on qualtatve nformaton, rough descrptons and photographs (see Fgure ) a prototype school model was developed. Assocate Professor 2 Professor 3 Columba Earth Insttute Post-octoral Research Fellow 4 Graduate Student

2 Fgure Typcal school structures n exco, one n Guerrero (left) and one n excal (rght). Photographs courtesy of Bran Tucker of GeoHazards Internatonal Inc. Ths structural model conssts of a two-story buldng wth a footprnt of m 4m and a story heght of 3m. The structure, whose frame s shown n Fgure 2(a), s dvded nto 8 bays wth a wdth of 5m n the long drecton and one bay wth a wdth of m n the short drecton. A 2m cantlevered slab on each floor acts as an access corrdor for the dfferent classrooms. To mmc possble poor desgn practce n developng countres, no lateral loads such as sesmc loadng were consdered n the desgn. The structure was desgned for gravty loads, whch nclude the weght of the structural elements (beams and columns), the weght of the slab and permanent elements estmated at about 2.5kN/m 2. Also a lve load of about.9kn/m 2 was consdered. These loads are appled on both stores to account for the typcal practce of leavng the possblty of constructng further addtonal floors open. The materal s assumed to be renforced concrete of average qualty wth a concrete compressve strength of 2,684 kn/m 2 and a yeld strength of 43,686kN/m 2 for the steel. The mass of each of the elements s consdered and addtonal masses are added on each floor to smulate the slabs. The Euro-Code of 999 s used for dmensonng the steel renforcement wth the approprate safety factors for loads and materals. As desgned the structure s vulnerable, capable of approprate standard servce loads but unft to sustan any strong loads other than gravty. Whle ths desgn s approprate for hghlghtng n general terms the effectveness of retrofttng and the economc analyss methodology, should a study of ths type be done for real applcaton purposes, a survey of desgns and materals used n exstng structures must be carred out to model these buldngs more accurately. The three retrofttng measures consdered are shown n Fgure 2(b)-2(d). The frst nvolves the addton of lght steel bracng at the central bay to stffen the weak axs of the structure. The second s a more aggressve steel bracng retroft whch now also braces the end walls. Lastly a more substantal renforced concrete bracng alternatve s consdered. Ths renforced concrete opton (whle somewhat more labor ntensve) s assumed to be cheaper than the second opton smply because steel shapes are not always readly avalable n rural regons n developng countres. 2

3 a b c d Fgure 2 odel of the structural frame for the orgnal and retroftted structures. (a) orgnal structure, (b) st steel bracng opton, (c) 2 nd steel bracng opton, and (d) renforced concrete bracng retroft. Note that n developng countres, t s not nfrequent to fnd that there was substandard structural analyss carred out pror to the constructon of the buldng, and lttle f any qualty control process n the manufacturng of the materals. It s also typcal to fnd evdence of poor constructon practces n collapsed buldngs after earthquakes (eg., EERI Spectra, 2) showng nsuffcent cover for the rebar or nsuffcent spacng between the steel renforcement bars. Therefore, from ths perspectve, the desgn carred out n ths paper s on the safe sde, snce the cover for the rebar s forced to be not less than 5cm and the spacng s approprate accordng to the Euro-Code 999 norm. Ths model s desgned wth the help of the software package SAP2 v.7.4, whch s a standard and well establshed tool for structural calculatons. The dynamc analyss s also carred out usng ths software. Fraglty Analyss The fraglty of a gven structure s defned as the probablty that for a gven ground moton shakng level (PGA) the structural response wll exceed a gven threshold level correspondng to a partcular damage level. The structural response s probablstc n terms of peak ground acceleraton because the structural response deformatons wll, n general, be dfferent for dfferent ground moton tme hstores wth the same peak ground acceleraton. For each of the structural confguratons, the fraglty curves are shown n Fgure 3. Four damage levels E are consdered; slght, moderate, major and total collapse. These damage levels are defned by nterstory drft ratos n accordance wth the HAZUS99-SR2 Techncal anual. Notce that retroft strengthenng has the 3

4 Orgnal School Steel Bracng n Center Bay Retroft Probablty of Exceedng amage Probablty of Exceedng amage.2.2. Slght. Slght Peak Ground Acceleraton (g) Peak Ground Acceleraton (g) (a) (b) Steel Bracng n Center and Extreme Bays Retroft Concrete Bracng n Center Bay Retroft Probablty of Exceedng amage Probablty of Exceedng amage.2.2. Slght..2 Peak Ground Acceleraton (g). Slght..2 Peak Ground Acceleraton (g) (c) (d) Fgure 3 erved fraglty curves for the 4 structural confguratons: (a) orgnal structure, (b) st steel bracng opton, (c) 2 nd steel bracng opton, and (d) renforced concrete bracng retroft. effect of pushng the fraglty curves to the rght,.e., for the same PGA value the probablty of exceedng a gven damage state s lower. 4

5 Loss Estmaton Procedure In order to perform a basc cost-beneft analyss one must be able to compute the expected losses for arbtrary tme horzons. The basc equaton to calculate the present value of losses usng a real (socal) dscount rate d s gven by the followng equaton: * Total loss n present value for a gven tme horzon T (n years) = * T 4 amax C Rˆ ( a da T ) Rˆ [ +, ( a, T )] P( E only a) da () a T mn d where ( a T ) ( ) T= = + R, = the probablty of exceedng the PGA value a gven that no earthquake has occurred n the prevous ( T ) years. = (the probablty of exceedng the PGA value a n year T) x (the probablty that no earthquake has happened n the prevous T- years) R amn R a e T = ( ) ( )( ) ( )( ) R amn T Ths last term e represents the probablty that no earthquake has occurred n the prevous (T-) years based on the assumpton of a Posson dstrbuton of earthquake occurrence. The term a mn denotes the lower lmt of PGAs consdered, so f ths value s not exceeded, then a (sgnfcant) earthquake wll not have occurred. In ths study ths lower lmt a mn s set equal to % of g. For ths study, the annual hazard curve R( a ) was the same as that used n Smyth et al., 24. Ths nformaton s regon-specfc and requres the nput of sesmologcal experts. The addtonal probablty n the expresson above s gven by: P( E only a) = the probablty of only event E occurrng for a gven PGA value a. Ths s needed so as not to count damage levels twce whch are lower than (or fall wthn the set of) more severe damage levels. Ths expresson s easly related to the fraglty curves. = The losses assocated wth damage state, as summarzed below. C amage Level Cost ( C ) Comments E : slght damage C = ( s S ) + ( V ) % s s ( % E 2 : moderate damage C = ( s2 S ) + ( V ) % s s ( 2 % E 3 : major damage C = ( s S ) + ( V ) s 3 = % 2 % 2 2 % = s 4 S + N L V s = 4 % E 4 : total collapse C ( ) ( ) 5

6 Results of the Economc Cost-Beneft Analyss In order to perform the cost beneft analyss one must frst establsh realstc estmates of the costs of the retrofttng measures as well as the losses C for each damage state. Because ths s not a real buldng, assumed values were selected wthout the usual consultaton wth local experts. The replacement cost of the entre structure s assumed to be S=$6,, and the costs of each retroft are: Retroft - Steel Bracng n bay C = $8, Retroft 2 - Steel Bracng n 3-bays C 2 = $2, Retroft 3 Renf. Concrete Bracng C 3 = $3, The socal dscount rate s assumed to be 3% (Wensten et al. 996). The fact that chldren would typcally only occupy a school for /3 of the day (8 hours) was also factored nto the calculaton. Therefore n the loss calculatons above, the assumed number of lves lost N L s actually /3 of the actual lves lost n the event of collapse. The net present value s the beneft mnus the certan cost of retroft. The beneft s smply the dfference n expected losses wth and wthout mtgaton. C TABLE. Expected net present value wth 5 fataltes and V =$4, (NPV(5)) Alternatve (A ) = =2 =3 Steel Steel Tme Horzon Braced Bracng 2 RC Bracng -$3 -$899 -$ $366 -$448 $279 3 $5466 $233 $96 4 $922 $8535 $593 5 $266 $4234 $ $58 $9452 $ $8694 $2423 $ $2335 $2867 $ $23754 $3265 $429 $25969 $36285 $ $4362 $6553 $ $49344 $756 $83238 Table llustrates the cost-beneft analyss results for an assumed value of human lfe V =$4,, and an assumpton that 5 lves would be lost f collapse occurred. The table lsts net present values for dfferent retrofttng decsons. Negatve values ndcate economcally undesrable choces for the gven tme-horzon, whle postve values ndcate an economcally desrable choce. The shaded values are postve. Notce that the second steel bracng retrofttng opton only breaks even after 3 years of hazard exposure. The RC bracng opton, whch s about as effectve as the more expensve 3- bay steel bracng opton, naturally hts ts break-even pont sooner. In all cases for ths 6

7 example, the break-even pont occurs rather quckly smply because the retrofttng optons are nexpensve relatve to the potental loss of lfe due to collapse. From ths hypothetcal and smplstc example one can begn to apprecate the types of decson-makng nformaton that the cost-beneft approach yelds. For other combnatons of parameters, costs etc., the conclusons would change. Ths also permts analysts to perform senstvty analyses to test the robustness of decsons. Conclusons and Future Work As mentoned at the outset, n order for ths approach to be appled to a partcular stock of school buldngs, more careful modelng of the partcular constructon type needs to be done. To allow applcaton to an ensemble of dfferent structures of the same type, some randomness also needs to be ntroduced n the structural model. Ths wll have the effect of makng the fraglty curves ascend more gradually, because of the ncreased uncertanty. The team s currently workng on a framework to ntroduce randomness to capture materal, geometrc and workmanshp uncertantes. Another lmtaton of ths demonstraton study s that only drect losses were consdered. For the case of a school buldng the obvous dsrupton caused by a buldng collapse and tme requred to rebuld should be consdered. The modular framework presented here can easly accommodate ndrect losses as long as they can be estmated. Acknowledgements Ths work was supported n part by a grant from the Columba Unversty Academc Qualty Fund as well as support from the Columba Earth Insttute. References EERI Earthquake Spectra (2), 999 Kocael, Turkey Earthquake Reconnassance Report, ecember. SAP2, Integrated Fnte Element and esgn of Structures, Analyss Reference anual, (2), Computers and Structures, Inc. Berkeley, CA, USA. Smyth, A.W., Altay, G., eodats, G., Erdk,., Franco, G., Gülkan, P., Kunreuther, H., Luş,H., ete, E., Seeber, N and Yüzügüllü, Ö., (24), Probablstc Beneft-Cost Analyss for Earthquake amage tgaton: Evaluatng easures for Apartment Houses n Turkey, EERI Earthquake Spectra, February. Wensten,., Segel, J.E., Gold,.R., Kamlet,.S., and Russell, L.B., 996. Recommendatons of the Panel on Cost-Effectveness n Health and edcne: Consensus Statement, Journal of the Amercan edcal Assocaton 276: