CHAPTER EVALUATING EARTHQUAKE RETROFITTING MEASURES FOR SCHOOLS: A COST-BENEFIT ANALYSIS

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1 CHAPTER 17 EVALUATING EARTHQUAKE RETROFITTING MEASURES FOR SCHOOLS: A COST-BENEFIT ANALYSIS A.W. Smyth, G. Deodats, G. Franco, Y. He and T. Gurvch Department of Cvl Engneerng and Engneerng Mechancs, Columba Unversty, Unted States

2 Evaluatng earthquake retrofttng measures for schools: A cost-beneft analyss Abstract: Based on a cost-beneft approach for evaluatng sesmc mtgaton optons for apartment buldngs n Istanbul, Turkey, ths paper presents a demonstraton study for a hypothetcal vulnerable school buldng. A probablstc cost-beneft analyss provdes a useful framework for assessng sesmc mtgaton measures, takng nto consderaton lmted resources and socal costs. The hypothetcal school s analysed over a varety of tme-horzons to determne the break-even pont for nvestments for several sesmc retrofttng optons. Introducton In Smyth et al. (2004), a smple cost-beneft analyss was performed to evaluate sesmc retrofttng measures of an apartment buldng n Istanbul, Turkey. The study combned probablstc sesmc hazard estmates, 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, n addton to the drect dollar losses due to a potental collapse, were consdered. In addton, to translate 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. Whle the approach s promsng for apartment structures, ts potental applcaton to school buldngs s even greater. Ths s smply because n many regons schools are desgned usng smlar buldng methods, wth smlar geometres. Therefore, t would not be necessary to perform a detaled analyss for each ndvdual structure. 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. The results of ths analyss should not be used to draw major conclusons for practce; the presentaton of the methodology n the context of schools s the purpose of ths paper. The structure to be consdered A prototype school model was developed based on rough descrptons, photographs and other qualtatve nformaton (Fgure 17.1). Fgure Typcal school structures n Mexco (a) School n Guerrero (b) School n Mexcal (Photos courtesy of Bran Tucker, GeoHazards Internatonal) (a) (b) OECD

3 Keepng schools safe n earthquakes Ths structural model conssts of a two-storey buldng wth a footprnt of 10 m 40 m and a storey heght of 3 m. The structure, the frame of whch s shown n Fgure 17.2(a), s dvded nto eght bays wth a wdth of 5 m n the long drecton and one bay wth a wdth of 10 m n the short drecton. A 2 m 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 2.50 kn/m 2. A lve load of about 1.91 kn/m 2 was also consdered. These loads are appled on both storeys to allow for the typcal practce of constructng addtonal floors. The materal s assumed to be renforced concrete of average qualty wth a concrete compressve strength of kn/m 2 and a yeld strength of kn/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 Eurocode 1999 s used for dmensonng the steel renforcement wth the approprate safety factors for loads and materals. As desgned, the structure s vulnerable; t s capable of approprate standard servce loads but unft to sustan any strong loads other than gravty. Fgure Model of the structural frame for the orgnal and retroftted structures (a) Orgnal structure (b) Frst steel bracng opton (c) Second steel bracng opton (d) Renforced-concrete bracng retroft (a) (b) (c) (d) 210 OECD 2004

4 Evaluatng earthquake retrofttng measures for schools: A cost-beneft analyss 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 completed for actual school buldngs, 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 Fgures 17.2(b) to 17.2(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 that also braces the end walls. Fnally, a more substantal renforced-concrete bracng alternatve s consdered. Ths renforced concrete opton whle somewhat more labour 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. Note that n developng countres, t s not uncommon to fnd that a substandard structural analyss was undertaken pror to a buldng s constructon, and that lttle f any qualty control was carred out n the manufacturng of materals. It s also typcal to fnd evdence of poor constructon practces e.g. nsuffcent cover for the rebar or nsuffcent spacng between the steel renforcement bars n collapsed buldngs after earthquakes (EERI, 2000). From ths perspectve, the desgn carred out n ths paper s sound; the cover for the rebar s no less than 5 cm and the spacng s consstent wth the Eurocode 1999 norm. Ths model s desgned wth the help of the software package SAP2000 v.7.40, whch s a standard tool for structural calculatons. The dynamc analyss was also undertaken usng ths software. Fraglty analyss The fraglty of a gven structure s defned as the probablty that for a gven ground moton shakng level (peak ground acceleraton), 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 (PGA) because the structural response deformatons wll, n general, be dfferent for dfferent ground moton tme hstores wth the same PGA. For each of the structural confguratons, the fraglty curves are shown n Fgure Four damage levels E are consdered: slght, moderate, major and total collapse. These damage levels are defned by nter-storey drft ratos n accordance wth the HAZUS99-SR2 Techncal Manual. Note that retroft strengthenng has the 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. OECD

5 Keepng schools safe n earthquakes Fgure Derved fraglty curves for the four structural confguratons (a) Orgnal structure (b) Frst steel bracng opton (c) Second steel bracng opton (d) Renforced-concrete bracng retroft Probablty of exceedng damage (a) (b) (c) (d) Slght Moderate Major Collapse Peak Ground Acceleraton (g) 212 OECD 2004

6 Evaluatng earthquake retrofttng measures for schools: A cost-beneft analyss Loss estmaton procedure In order to perform a basc cost-beneft analyss, the expected losses for arbtrary tme horzons must be computed. The basc equaton to calculate the present value of losses usng a real (socal) dscount rate d s: Total loss n present value for a gven tme horzon T* (n years) = * T 4 amax [ Rˆ a + da, T Rˆ a, T ] P ( E only a) D ( ) ( ) a T 1 mn T = 1 = 1 1+ C ( d) where R ˆ ( a, T ) = the probablty of exceedng the PGA value a, gven that no earthquake has occurred n the prevous years = (the probablty of exceedng the PGA value a n year T) x (the probablty that no earthquake has occurred n the prevous (T-1) years) R = ( amn )( T 1) R( a) e R( amn )( T 1) ( a) e R s the probablty that no earthquake has occurred n the prevous (T-1) years, assumng 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, the lower lmt a mn s set equal to 1% of g. The annual hazard curve R(a) was the same as that used n Smyth et al. (2004). Ths nformaton s regon-specfc and requres the nput of sesmologcal experts. The addtonal probablty n the above expresson s: P ( E only a) = the probablty of only event E occurrng for a gven PGA value a. Ths probablty s needed so that damage levels whch are lower than (or fall wthn the set of) more severe damage levels wll not be counted twce. Ths expresson s easly related to fraglty curves. D C = The losses assocated wth damage state are summarsed n Table Table Losses assocated wth damage state Damage level Cost ( C D 1 = ( s1 S) + ( 0 V ) E 1 Slght damage C D % s = ( s S) + ( 0 V ) 1 E 2 Moderate damage C D = ( s S) + ( 0 V ) 2 E 3 Major damage C D = ( s3 S) + ( 0 V ) E 4 Total collapse C D = ( s S) + ( N V ) 1 2 ) Comments 0 1 s2 0% s s2 1 da 100% (s 1 = 1%) 100% (s 2 = 10%) 3 s 3 = 100% s 4 4 L 4 = 100% OECD

7 Keepng schools safe n earthquakes Results of the economc cost-beneft analyss In order to perform a cost-beneft analyss, realstc estmates of the costs of the retrofttng D measures as well as the losses C for each damage state must be establshed. As 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 = USD , and the costs of each retroft C are: M M Retroft 1: Steel bracng n 1 bay C = USD M Retroft 2: Steel bracng n 3 bays C = USD M Retroft 3: Renforced-concrete bracng C 3 = USD The socal dscount rate s assumed to be 3% (Wensten et al., 1996). The fact that chldren would typcally only occupy a school for one-thrd of the day (eght hours) was also factored nto the calculaton. Therefore n the loss calculatons above, the assumed number of lves lost N L s actually one-thrd of the number of 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. Table 17.2 llustrates the cost-beneft analyss results for an assumed value of human lfe V = USD , and an assumpton that 15 lves would be lost f collapse occurred. The table lsts net present values for dfferent retrofttng decsons. Negatve values ndcate Table Expected net present value wth 15 fataltes and V = USD (NPV(5)) * Alternatve (A ) Tme horzon =1 Steel bracng 1 (USD) =2 Steel bracng 2 (USD) =3 Renforced-concrete bracng (USD) * Negatve values (unshaded) ndcate economcally undesrable choces for the gven tme-horzon, whle postve values (shaded) ndcate economcally desrable choces. 214 OECD 2004

8 Evaluatng earthquake retrofttng measures for schools: A cost-beneft analyss economcally undesrable choces for the gven tme-horzon, whle postve values ndcate an economcally desrable choce. Note that the second steel bracng retrofttng opton only breaks even after three years of hazard exposure. The renforced-concrete bracng opton, whch s about as effectve as the more expensve three-bay steel bracng opton, naturally hts ts break-even pont sooner. In all cases, 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 further work As mentoned at the outset, n order for ths approach to be appled to a partcular stock of school buldngs, more careful modellng of the partcular constructon type s requred. To apply ths approach 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 authors are 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 are consdered. In 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 estmaton of ndrect losses. References Earthquake Engneerng Research Insttute (EERI) (2000), 1999 Kocael, Turkey Earthquake Reconnassance Report, Earthquake Spectra, Supplement to Volume 16. SAP2000 (2000), Integrated Fnte Element and Desgn of Structures, Analyss Reference Manual, Computers and Structures, Inc., Berkeley. Smyth, A.W., et. al. (2004), Probablstc Beneft-Cost Analyss for Earthquake Damage Mtgaton: Evaluatng Measures for Apartment Houses n Turkey, Earthquake Spectra, Vol. 20, No. 1, pp Wensten, M., et al. (1996), Recommendatons of the Panel on Cost-Effectveness n Health and Medcne: Consensus Statement, Journal of the Amercan Medcal Assocaton, Vol. 276, pp OECD

9 Keepng schools safe n earthquakes Acknowledgements Ths work was supported n part by a grant from the Columba Unversty Academc Qualty Fund. The Columba Earth Insttute also provded support for ths work. 216 OECD 2004

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