Earthquake countermeasures for wood houses to mitigate seismic loss and total cost

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1 Safety, Reliability and Risk of Strctres, Infrastrctres and Engineering Systes Frta, Frangopol & Sinozka (eds) 2 Taylor & Francis Grop, London, ISBN Eartqake contereasres for wood oses to itigate seisic loss and total cost Y. Hasebe Gradate Scool of Engineering, Kyoto University, Kyoto, Japan A. Saratani Daiwa Hose Indstry, Nara, Japan T.Morii, Y. Hayasi Gradate Scool of Engineering, Kyoto University, Kyoto, Japan ABSTRACT: It is said tat plate sbdction-zone eartqakes and inland sallow eartqakes ay occr in several decades in Japan. However, any residents do not try to perfor seisic retrofit, even if teir wooden oses ave poor seisic perforance and will sffer extensive daage if a severe eartqake occrs. In order to otivate residents to ipleent an effective eartqake contereasre for teir oses, tis paper proposes evalation indexes to select te ost cost effective eartqake contereasre for teir own oses. Ten, we ave perfored soe case stdies canging location and eartqake contereasre tecniqes and tiing to deonstrate te validity of te proposed indexes and to discss ow to prepare for te big eartqakes. INTRODUCTION After te 995 Hyogo-ken Nanb Eartqake, te seisic activity in Japan is activated, and large eartqakes, sc as te Noto Hanto Eartqake and te Niigata Cets-Oki Eartqake in 27, tat case wooden oses te extensive daage appen freqently in varios places freqently. In addition, it is believed certain tat te ge ocean-trenc eartqake sc as Nankai and Tonankai eartqakes will occr witin several decades in te ftre. Terfore, to itigate te eartqake daage of te wooden oses dring tose large eartqakes is togt to be a ig-priority isse for te eartqake disaster prevention easres fro te viewpoint of te life and property protection. Especially, it is necessary for te wooden oses were te extensive daage is assed wen a large eartqake occrs to perfor seisic retrofit. However, seisic retrofit to prepare in a approacing eartqake are not advanced enog in te assption eartqake-stricken region. Altog te sbsidy syste of seisic retrofit by te contry and nicipality as increased, it is a crrent state tat tere are a lot of wooden oses wic do not perfored seisic retrofit even if teir seisic perforance is low now. Tis is attribted to te fact tat residents are sspicios of te effects of te seisic retrofit, or tey can not afford te cost. Te factor wic can evalate a seisic loss corresponding to dwelling perforance and stdy it tat can itigate te seisic loss as been proposed so far (Isida. H,24 & Takaasi. Y,25 & Fksia. S, 25). Tog an aseisic perforance of te wooden ose is pointed ot te possibility of decreasing as tie ticks away by te inflence of te biodeterioration sc as te wood destroying fngs and terite and so on (Hayasi. Y, 24), tis effect is not considered in teir seisic risk evalation. On te oter and, in te seisic azard, te probability of te eartqake occrrence is different according to te scenario eartqake, and as for te sae scenario eartqake it canges at tie goes by. Bt te tie cange of te seisic azard is not considered in teir seisic risk evalation. Since te in-service period of te wooden ose is c sorter tan te interval of te eartqake occrrence, it is iportant for tinking abot te seisic daage decrease plan in te wooden ose to consider wat type of te seisic retrofit work so well and wen it st ipleent. Fro te above-entioned tis researc ais to constrct te etodology wic considers seisic environent and seisic occrrence tie in eac regions, and te tie cange of an aseisic perforance of te wooden ose, akes te residents teselves be able to recognize te existing seisic risk of teir wooden oses and te effect of te daage itigation of teir wooden oses by te seisic retrofit and te aintenance, and becoes possible for te residents to ake a coice of te seisic retrofit. Terefore, tis paper focses te decrease of a expected loss and life cycle cost (total cost) of te 99

2 wooden ose by te seisic retrofit, and considers its etod, tiing, and cost wic can ipleent te seisic retrofit effectively and econoically. At first, in te second capter, tis paper describes a seisic daage evalation etod and a seisic risk evalation etod considering te seisic azard and an aged deterioration of te wooden ose, ten draws on an Expected Seisic Loss. Next, in te tird capter, it proposes two evalation indexes, a Loss Redction Index and a Total Cost Redction Index, based on te preceding capter. Te two indexes can evalate te cost-effective seisic retrofit and its tiing of ipleentation. Finally, in te fort capter, sensitivity analysis is perfored in five cities (Osaka, Kyoto, Nagoya, Ts, and Koci in Japan), by sing te proposed etods and two evalation indexes. Seisic azard is different in eac five cities. In te sensitivity analysis, te focs is appropriated to seisic perforance (to strengtening or iproving deforation perforance) witin eartqake contereasres, and ow region, tiing, and etod of te eartqake contereasre inflences te proposal index is verified at te tie of te seisic retrofit. In addition, seisic contereasres needed by te region were te seisic risk is different are considered by sing te reslt of te sensitivity analysis. 2 OUTLINE OF EARTHQUAKE RISK EVALUATION TECHNIQUE 2. Introdction In tis capter, tis paper explains te seisic risk evalation etod sown in Figre considering te aged deterioration of te wooden ose and an age softening of te seisic azard based on retrospective researces (Hayasi. Y, 27). Since te recrrence interval of eac seisic activity is c longer tan te in-service period of te wooden ose, it is iportant for tinking abot eac probability of te eartqake occrrence. Ten, it is togt tat te eartqake size and te probability of occrrence in eac eartqake sorce cange every year and te seisic azard is calclated every elapsed year in consideration of te tie cange. 2.2 Eartqake daage level evalation tecniqe for considering aged deterioration First, fragility fnction, probability distribtion fnction (PDF) of daage, considering aged deterioration is explained. Te fragility fnction P fr wit te axi orizontal deforation angle R and age τ of a wood ose can be given by P R, τ = Φ ln R ln τ ζ () ( ) [{ ( ) ( ( ))} ] fr R Were Φ is te clative distribtion fnction (CDF) of te standard noral distribtion, and ln(r(τ)) and ζ R (=.4) are te average and standard deviation of ln(r). Te R(τ) decreases wit age τ sc as R(τ)=d(τ)R() as sown in Figres 2-3. Te redction factor d(τ) is written as 2 (2) d( τ ) = ax{ exp(.7( τ βτ ) ),.5} were te β τ is te drable years deterined by constrction etod of wooden ose, regional cliate, and aintenance condition based on te Drability Design Gideline (DDG) (Ministry of Land, 986). At tis tie, in te aged deterioration crve inverted redction factor fro te statistical daage data of wooden oses, te drable years are, for exaple, estiated as βτ =33 for oses in Kobe and βτ =8 for tose in Tottori based on te DGG. Te βτ is assed as β= for te sake of siplicity below. To calclate te axi deforation angle R, a ose is odeled by te SDOF syste. If te restoring force-displaceent relation is assed to be bilinear, eqivalent natral period T and daping factor for te axi deforation angle R can be expressed as follows sing te eqivalent ass µ and eqivalent eigt H e, yield base sear coefficient C y and yield deforation angle R y (=/). T ( R) = 2π H R ( C g) e µ ( R).2( R R ) +. 5 = y y R (3) Aged deterioration crve R (τ) Seisic risk crve P(v,t) Daage probability P fr R R R ( τ ) = d( τ ) ( ) R Fragility fnction P fr (R,τ) P fv (v,τ) Loss fnction L f (v,τ) Probability density fnction f(v,t).5 Aged deterioration.5. R Expected seisic loss ESL(t) Figre. Flow cart of te seisic risk Evalation etod of wooden ose. Max deforation angle R (τ) R () Figre 2. Fragility fnction wit deterioration Age τ Drable years βτ Figre 3. Redction in deforation perforance 9

3 Te yield base sear coefficient Cy is calclated fro te seisic capacity evalation of an existing ose. As for a scenario eartqake, te axi deforation angle R in Eq.() can be evalate by aking te acceleration response spectr S a (T,) of te estiated grond otions eqal to C y g/µf (R), were F (R)=.5/(+(R)). On te oter and, te probability density fnctions wit te axi deforation angle R in Eq.() are written as tat wit te peak grond velocity (PGV) v for te siplicity of azard analyses. In tat process, acceleration response spectra are related to v as (4) S T, R = 2v 2π T F R a ( ( )) ( ) ( ) Based on te above assptions, te fragility fnction wit te PGV v can be approxiated by te following eqations (Saratani. A, et al, 26). (5) Pfv ( v, τ ) = Φ[ { ln( v) ln( v ( τ ))} ζ v ( τ )] were 2 [{ ( )} R ( )] 2 { ( ) F ( R ( τ ))} ( τ ) = gh ec y µ F R ( τ ) ζ R ( τ ) = ζ 2 + ln F R ( τ ) e v 25 τ ζ v R 2.3 Eartqake risk evalation tecniqe based on eartqake azard Next, a seisic risk evalation etod considering te aged deterioration of a wooden ose is proposed. Te seisic daage loss expectation of a wooden ose is evalated as sown in te followings. At first, te seisic loss of te wooden ose wen an eartqake occrred τ years after by sing a seisic loss fnction L f (v,τ) calclated as te prodct-s of daage probability P fvi (v,τ) given by Eq.(5) and loss L i for eac daage level i (Fig. 4). L v,τ = (6) P v,τ L τ f ( ) ( ) ( ) i fvi i Here, ratio of te loss to an asset vale (Sown in Capter 4) corresponding to eac daage level is constant witot relying on age τ, bt te asset vale decreases by age τ. Terefore, loss L i decreases by age τ. In te seisic azard analyses, on te oter and, te expected vale of seisic loss by any eartqakes over te in-service period of te wood ose is estiated considering local seisic azard and interannal cange in occrrence probability of eartqakes, wic are evalated by te Sbcoittee for Long-ter Evalations of te Eartqake Researc Coittee of te Headqarters for Eartqake Researc Prootion in Japan (J-SHIS, 26). In te calclation of te seisic loss fnction in Eq. (6), τ=τ is sbstitted into Eq.(5) were τ satisfies t d ( τ ) dτ t = d( τ ). Naely, te seisic perforance of te wooden ose is assed to be eqal to te average vale dring te t years of in-service period for siplicity (Fig. 5). Tis assption can sow te difference of te expected seisic loss wic is discssed below by te difference at te drable years even if te inservice period becoes long. Te exceedance probability P(v,t) of te PGVs of eartqakes occrred arond a site being ore tan v once at least dring t years is given as follows, if probability density fnction and probability distribtion fnction of te PGV v dring in-service period t years are denoted by f(v, t) and F(v, t), respectively. ( v, t) = v f ( v, t) dv, P( v, t) = F( v t) F, (7) In addition, as well as docent, te probability of occrrence of a pecliar eac eartqake is calclated based on stationary Poisson process for stationary seisic activity odel, and based on pdating process or BPT distribtion on te basis of teporal prediction odel for nonstationary seisic activity odel. First, f(v,t) is calclated fro a seisic azard crve P(v,t). Ten, te seisic risk density dring t years is denoted by L f (v,t). f(v,t). Finally, te expected seisic loss ESL(t) is given by ESL ( t) = L ( v t) f ( v, t) f, dv Loss fnction L f d(τ) : Redction factor Expected seisic loss ESL(t) L f =ΣP fvi L i d(t) d(τ)dτ/ t Te average vale d(t) dring te t years of in-service period ESL ( t) L( v, t) f ( v, t) = v dv Peak grond velocity v In-service period t Age τ In-service period t Figre 4. Seisic loss fnction Figre 5. Aged deterioration of seisic perforance dring in-service period Figre 6. Expected seisic loss 9

4 3 EVALUATION INDEX OF COST- EFFECTIVENESS 3. Introdction Next, it proposes two evalation indexes, Loss Redction Index and Total Cost Redction index, wic can evalate cost-effectiveness based on te expected seisic loss obtained by te preceding capter. Tese indexes can evalate te aged deterioration of te wooden ose, and te tie cange and regional difference of te seisic azard. In addition, te period wen te seisic contereasres are done is conted based on elapsed years fro present. Here, a relation of tie series aong elapsed years, in-service period t, age τ, and drable years τ is sown in Figre Loss Redction Index (LRI) Te Loss Redction Index (LRI) is an index tat evalates ow seisic loss decreased by te seisic contereasre, so it is te expected vale fnction of seisic loss saved on by te seisic contereasre. Te Loss Redction Index LRI() is defined as (8) LRI = ESL ESL ( ) ( ) ( ) b a were ESL b () is te expected seisic loss witot any seisic contereasres, and ESL a () is te expected seisic loss wit soe sort of seisic contereasres. Te fragility fnction P fv to v decreases by doing seisic contereasres, and as a reslt te vale of ESL decreases. It is sown tat te bigger te LRI is, te bigger te seisic loss decreased wit seisic contereasres is, in oter words, te safer te wooden ose becoes. 3.3 Total Cost Redction Index (TCRI) Te Total Cost Redction Index (TCRI) is an index tat evalates ow te total of te cost spent on te ose by ipleenting seisic contereasres is eld down, so it is te expected vale fnction of a Total Cost TC() canged by ipleenting seisic contereasres. Here, te Total Cost incldes initial cost of constrction, aintenance cost, and Redction factor d(τ) casal loss of oses, and it is a s of tese costs over elapsed years fro specified tie. In addition, te lower te Total Cost is, te bigger te costeffectiveness is (Fig. 8).Frterore, if elapsed years correspond to in-service period t in te Total Cost, te Total Cost is seen as a Life Cycle Cost. Te Total Cost TC () is written as TC = c + ESL + c (9) ( ) ( ) = were c is te initial cost, and c is te cost of eartqake contereasres in te -t year. Ten, te TCRI ( ) = TCb ( ) TCa ( ) = ( c + ESL ( ) ) c + ESL ( ) = ( ESL ( ) ESL ( ) ) = LRI b b Total Cost Redction Index TCRI() is defined as were TC b () is te Total Cost witot any seisic contereasres, and TC a () is te Total Cost wit soe sort of seisic contereasres. As te Eq.() sows, te TCRI can be indicated a difference between te cost of eartqake contereasres and te LRI. Te bigger te TCRI, te ore cost-effective te contereasres are. Especially, if te TCRI is a positive vale, it can be said tat te Total Cost is decreased after te contereasres, and ipleenting te is econoical rater tan noting (Fig. 9). ( a + c ) ( ) c () = Total Cost TC() LRI Σc a = Initial cost c Elapsed years Figre 8. Total Cost. c Cost of eartqake contereasres Σc Expected seisic loss ESL() LRI = Drable years τ In-service period t ESL b ESL a ESL b Σc ESL a c c c c τ Age τ New constrction present Elapsed years TCRI< TCRI> Figre 7. A relation of tie series. Figre 9. Total Cost Redction Index. TC b TC a TC b TC a 92

5 4 SENSITIVITY ANALYSIS 4. Standard case setting In tis capter, to easre ow tie and te etod of eartqake contereasres and difference between regions inflence te evalation indexes, tese sensitivities are analyzed. First of all, te necessary conditions for sensitivity analysis are set as follows. (a)sensitivity analysis is applied to five cities, Osaka, Kyoto, Nagoya, Ts, and Koci sown in Figre, and tose seisic azard crves over in-service period of t years for tose cities are sown in Figre. (b)a wooden ose is assed to be newly bilt in26 (τ=). Initial constrction cost of te ose c is 5 illion yen. Yield base sear coefficient C y is.. Drable years βτ are 25. (c)eartqake contereasre tecniqes ay inclde seisic retrofitting to strengtening or iproving deforation perforance, drability enanceent to increase drable years, and rebilding. Here, te tecniqes are liited to te seisic retrofitting. Te seisic retrofitting to strengtening (Contereasre A) raises yield base sear coefficient C y fro. to.3 wit paying.4 illion yen (Sato. K, 26). Te seisic retrofitting to iproving deforation perforance (Contereasre B) brings aged deterioration crve R (τ) back to initial vale wit paying.4 illion yen, siilarly (Table ). (d)tere are tree daage levels, coplete, alf and no destrction. Te daage probability P fi and te loss L i of eac daage level i are sown in Table 2. Te R () of coplete and alf destrction are. and.5, respectively. In addition, if te ose is copletely destroyed, it asses tat te ose is rebilt. Te loss of coplete and alf destrction are te asset vale pls reconstrction cost L (all) and L (all) /3, respectively. Te asset vale is written off for depreciation by te vale of 5% every 25 years, and te new-bilt asset vale A is eqal to initial constrction cost. Te reconstrction cost is eqal to initial constrction cost. Te asset vale n years n fro now A n is written as An = ( r) A () were r is depreciable rate. Table. Eartqake contereasre tecniqes. Eartqake contereasre Contereasre A seisic retrofitting to strengtening Contereasre B seisic retrofitting to iproving deforation perforance Effect raises yield base sear coefficient C y fro. to.3 brings aged deterioration crve R (t) back to initial vale Cost c.4 illion yen.4 illion yen Table 2. Daage probability and loss of eac daage level. Figre. Seisic azard in 3 years in Japan. Daage level i Coplete destrc- Half destrc- No destrc- Daage probability P fi Loss L i P f (all) P fv(all) L (all) A +A n P f (alf) P fv(alf) -P fv(all) L (alf ) P f (no) -P fv(alf) L (no) A /3+A n /3 Exceedance probability over years.. t =. 5 5 PGVv Exceedance probability over 25 years.. t = PGVv Exceedance probability over years.. t =. 5 5 PGVv Figre. Seisic azard crves over t years. Osaka city Kyoto city Nagoya city Ts city Koci city 93

6 4.2 Cange in indexes according to tiing of eartqake contereasre First of all, sensitivity analysis is applied to Koci city in te case of canging tiing of ipleentation of Contereasre A. Te sensitivity analysis reslt is sown in Figre 2. As sown on te Figre 2, te vales of bot indexes cange significantly st after seisic contereasres. It is becase te aseisic perforance of te wooden ose iproves at te tie of ipleentation of seisic contereasres, and te ESL is decreased sbseqently. Based on te presption tat strengt of oses is not decreased every year for siplicity, yield base sear coefficient C y of te ose is invariable regardless of tiing of ipleentation. Hence, te LRI is also invariable regardless of te tiing. In addition, since cost of eartqake contereasres is sae, te TCRI after contereasres is invariable regardless of te tiing likewise. In te case of ipleenting at tis tie ( =), altog te LRI rises early, te TCRI goes negative vale dring present tie to abot 5 years later ( =~5). On te oter and, in te case of ipleenting at 5 years later ( =5), altog te TCRI reains positive vale, te LRI keeps zero to 5 years later ( =~5).At te case of =25 or 5 years, te TCRI is positive vale st after ipleentation, becase decreasing of seisic loss by te contereasre is bigger tan te cost for te contereasre. In order to acieve ore loss redction effect and be ore cost-effective, te Contereasre A sold be ipleented arond te tie of excanging te TCRI negative to positive. In tis way, te indexes can consider a ore costeffective tiing of ipleenting an eartqake contereasre by coparing different tiing of te contereasres. 4.3 Cange in index according to eartqake contereasre tecniqes Next, sensitivity analysis is applied to Osaka city in te case of canging eartqake contereasre tecniqes ipleented 25 years later ( =25). Te reslt of sensitivity analysis wic ipleents Contereasre A and B respectively is sown in Figre 3. Te LRI of Contereasre A is iger tan te LRI of Contereasre B. Ts, Contereasre A as a iger loss redction effect tan Contereasre B. In addition, te TCRI of Contereasre A is positive vale. Tat eans Contereasre A is cost-effective. On te oter and, te TCRI of Contereasre B is negative vale alost in elapsed years. Tat eans Contereasre B is not cost-effective. Terefore, in tis case, it can be said tat Contereasre A sold be ipleented rater tan Contereasre B. In tis way, te indexes can consider a ore effective eartqake contereasre tecniqe by coparing different contereasre tecniqes according to te indexes. 4.4 Cange in index by location of eartqake contereasre Finally, sensitivity analysis is applied to five cities, Osaka city, Kyoto city, Nagoya city, Ts city, and Koci city, in te case of ipleenting Contereasre A 25 years later ( =25). Te reslt of sensitivity analysis at 5 years later (=5) is sown in Figre 4. An especially big effect for LRI and TCRI is acieved in Nagoya, Ts, and Koci wic are profondly affected by Nankai and Tonankai eartqakes. On te oter and, a low effect for LRI and TCRI is acieved in Osaka, and Kyoto. In tis way, te effect of te loss redction and cost-effectiveness are different according to locations even if it is te sae contereasres. Terefore, it leads to local eartqake contereasre according to te indexes. Loss Redction Index (,JPY) Tiing of contereasre 25 5 Total Cost Redction Index (,JPY) Figre 2. Cange in indexes according to tiing of eartqake contereasre. Tiing of contereasre

7 Loss Redction Index (,JPY) Contereasre A Contereasre B Total Cost Redction Index (,JPY) daage dring Hyoto-ken Nanb Eartqake and Western Tottori Prefectre Eartqake -, New frontiers in arcitectre for daage itigation and Contereasre recovery fro disasters, A All Figre 3. Cange in indexes according to eartqake contereasre tecniqes. Contereasre B Loss Redction I ndex (JPY) Elapsed years : 5YRS Osaka Kyoto Nagoya Koci Ts Figre 4. Cange in indexes by location of eartqake contereasre. Total Cost Redction Index (JPY) Elapsed years : 5YRS 5 CONCLUSION Tis paper presents a seisic risk evalation etod considering aged deterioration of wooden ose and age softening of seisic azard, and proposes indexes (Loss Redction Index and Total Cost Redction Index) based on te etod. Tese indexes easre cost-effectiveness of eartqake contereasre. Ten, in order to assess te validity of te indexes, it ipleents sensitive analysis wit te indexes. Conseqently, it confirs tat tese proposal indexes can dge cost-effective tiing and tecniqe of eartqake contereasre depending on location. REFERENCES Isida, H. 24. Seisic risk evalation etod for bilding strctres based on nifor azard response spectra considering aplification of sbsrface strctre, Motosaka, M (ed), J. Strct. Constr. Eng., AIJ, No.583, 23-3 (in Japanese). Takaasi, Y. 25. Seisic risk anageent of a bilding in seisically active region, Masaki, N. Anaara, K. and Isoda, H (eds). J. Strct. Constr. Eng., AIJ, No.59, (in Japanese). Fksia, S. 25, Seisic perforance level of bildings based on te eartqake risk of portfolio, Yasiro, H (ed), J. Strct. Constr. Eng., AIJ, No.593, (in Japanese) Hayasi Y. 24. Analysis of relationsip between daage ratio of wooden oses and constrction years - Based on conications and discssions, AIJ, No.2, 7-75 (in Japanese). Hayasi, Y. 27. Seisic risk evalation of wood ose considering aged deterioration and long-ter occrrence probability of eartqakes. Saratani, A & Morii, T (eds), 2 nd international conference on rban disaster redction: Engineering Affairs Division of Constrction Minister s Secretariat / Japan Institte of Constrction Engineering986. Drability enanceent tecnology of wood ose, Giodo sppan, Japan (in Japanese). Saratani, A. 26. Fragility fnction wit peak grond velocity of wood oses considering aged deterioration. Morii, T & Hayasi, Y (eds), Proc. Japan Eartqake Engineering Syposi, Japan, No.. (in Japanese). National Researc Institte for Eart Science and Disaster Prevention. 26. Seisic Hazard Map. ttp:// (in Japanese). Sato, K. 26. A stdy on resident consciosness for retrofitting of existing oses by contingent valation etod: a case stdy at Icikawa city, Ciba Pref., Taara, M (ed), Jornal of social safety science, No.8, 8-87 (in Japanese). 95