Damage, Death and Downtime Risk Attenuation in the 2011 Christchurch Earthquake

Transcription

1 Damage, Death and Downtime Risk Attenuation in the 2011 Christhurh Earthquake J.B. Mander & Y. Huang Zahry Department of Civil Engineering, Texas A&M University, College Station, TX USA NZSEE Conferene ABSTRACT: Following a atastrophi earthquake, 3d (damage, death and downtime) rapid estimates of the extent and severity of losses are desperately needed in order to better aid in post-event response and reovery. A quantitative risk analysis approah is advaned to investigate the 3d loss types for typial New Zealand onstrution as exemplified by the Redbook building for the 2011 Christhurh earthquake. The results are presented in terms of attenuation urves whih show that within the entral business distrit: the expeted loss ratio (related to insurane laims) is about 50% of the asset value; the expeted hane that someone is killed is 5%; and the expeted downtime is 1- year. However, onsiderable unertainties also exist, thus one an only be 90% onfident that these results will not be higher than: 100% damage, implying ollapse is a distint possibility; 10% hane of fatalities, implying there may also be some deaths and possibly signifiant injuries; and 2-year downtime due to reonstrution demand surge. These salutary results demonstrate that in spite of strutures being well-engineered, downtime in partiular is unaeptably large. Two methods an be used to solve this problem: to make the struture slightly stronger and more robust through damage avoidane design. 1 INTRODUCTION Historially, engineers have prinipally aimed at ensuring life-safety through ollapse-prevention due to earthquakes. However, over many years of researh and more reently in pratie, partial damage, death and downtime losses are gradually being taken into onsideration as they turn out to ontribute a signifiant portion of the overall earthquake-indued losses, espeially when one onsiders equivalent monetary value. In this researh, the general four-step quantitative risk analysis approah of Mander and Sirar (2011) is extended from the general all-hazard based loss model to an earthquake-speifi or senario-based 3d loss model. The well-known Redbook Building is onsidered to be an exemplar of the state-of-the-pratie for good strutural design in New Zealand (CCANZ, 1998). This building, whih is based on using redued design strength along with dutile detailing, is adopted as the basis for onduting a 3d seismi risk analysis. It will be shown that signifiant damage an be expeted when subjeted to the Christhurh earthquakes. Some deaths may also be expeted. But it is the downtime that is most worrying aspet, as this is proving to be most undesirable from a building owner s standpoint. Therefore, three alternative design senarios are explored and disussed. The first of these is to merely make the building stronger to defray the onset of damage. The seond maintains the existing strength, but employs Damage Avoidane Design (DAD) details. While both of these aforementioned strategies are shown to make some improvements in performane along with the redution in damage, it is finally demonstrated that what is really needed are buildings that are both stronger and have better (damage avoidane) performane attributes. 2 SCENARIO-BASED 3d OSS MODE Reently, Mander and Sirar (2011) developed a quantitative risk analysis approah for the loss Paper Number 016

2 estimation of strutures. The approah develops an equation-based inter-relationship using a four-step proedure between (a) seismi hazard; (b) strutural response; () damage; and (d) loss. In this researh, the all-hazard based analysis of Mander and Sirar (2011) is extended to a senariobased risk analysis method. It is well known that for any given speifi earthquake there exists an attenuation relationship that relates the shaking intensity with respet to the distane to the earthquake s epientre. Suh an attenuation relationship an be substituted into the Mander and Sirar (2011) theory. As shown in Figure 1, the senario-based four-step risk analysis onsists of: (a) hazard-intensity attenuation modelling; (b) strutural analysis; () damage analysis; and (d) lossattenuation estimation. Figure 1 shows that eah of the four steps are essentially linear when plotted in log-log spae. Therefore, a single ompound equation may be written to express the interonnetion between eah of the four graphs. b ab Sa R (1) r r ar r S R in whih r = a referene (senario) earthquake event; = a loss ratio; struture drift, an engineering demand parameter (EDP); S a = spetral aeleration, an intensity measure (IM); R = radial distane from the epientre of the earthquake; and a, b, and d are the slopes shown in the four graphs in Figure 1, these are interrelated suh that d = -ab. Drift R(km) IM (b) 1 Toppling/Failure b IM oss () 1 1 (d) d d oss Damage Onset Drift R(km) Figure 1: Senario-based 3d oss Model: (a) seismi hazard intensity-attenuation model; (b) strutural analysis; () damage analysis; and (d) loss-attenuation estimation In the first step, instead of assoiating the intensity measures with annual frequeny as Mander and Sirar (2011) proposed, a simple attenuation relationship is proposed that relates the intensity measure with the radial distane from the earthquake epientre. In the seond step, the response of the struture whih is exposed to different levels of ground shaking is predited. In the third step, the strutural drift is related to the damage losses. In the fourth step, damage or other losses (suh as death and downtime) at a ertain radial distane from the earthquake epientre are modelled. 2

3 It should be noted that earthquakes in the near-field (approximately < 8 km) may impose seismi demands that are either greater than the apaity of the struture, or less than the strutural toppling/failure apaity, as depited in Figure 1. This input (in Figure 1a) affets the outome, as shown in Figure 1d. 2.1 Senario-based Physial oss Model The model for alulating the physial damage loss ratio is: ; on u 1.3 (2) where = unit loss, whih taken as the monetary value of the struture under steady-state (nondisaster) priing, or as = 1.0 for omparative (unit-prie) studies; = struture drift at the onset of omplete ollapse; on = physial loss ratio at the onset of damage state 2; on = struture drift at the onset of damage 2; and u = physial loss ratio at the omplete ollapse of struture, u > 1 with a suggested median value u =1.3 presumes a 30% post-event prie surge. 2.2 Senario-based Death oss Model Fault and Event trees are used to analyse the probability of death loss arising from building damage due to the earthquake. The value of the slope in the damage analysis was alibrated using the fault and event trees, and is taken as = 2.6 as proposed in Ghorawat (2011). The model for alulating the probability of death loss is: D D ; Don D Du 0.75 (3) where D = probability of death loss at the onset of omplete damage, whih is generally taken as D = 0.1 (Mander and Elms 1994); D on = probability of death loss at the onset of damage; D u = probability of death loss of omplete damage, whih is normally taken as D u = 0.75, assuming the imum oupany of a building is 75%. 2.3 Senario-based Downtime oss Model Guided by earlier studies (Mander and Basoz, 1999; and Ghorawat, 2011) a downtime loss model is proposed as DT DT ; DTon DT DTu 150 (4) where DT = the downtime at the onset of omplete damage; DT on = the downtime at the onset of damage; and DT u = the downtime at omplete damage, whih is taken as DT u = 150 (weeks). 2.4 Unertainty and Randomness Consider the unertainty and randomness in the seismi demand and in the establishment of the model, is used to represent the dispersions through whih the median values ould be transformed to other fratiles. The dispersion of all ombined unertainty and randomness is given (Kennedy et al. 1980) using the following expression: (5) T D U C where D aounts for the variabilities in demand; U aounts for the unertainty in modelling, whih is taken as U = 0.25; and C aounts for the variabilities in struture apaity, whih is taken herein 3

4 as C = 0.2. Further, to aount for the overall dispersion in loss with respet to the radial distane from the epientre, it an be shown that: U (6) T R where U = 0.35 is assumed to aount for the unertainty in loss (Mander and Sirar, 2011). 3 3d OSS MODE CONSIDERING SPATIA DISTRIBUTION OF OSSES A ommonly adopted onservative assumption is that the damage of a building is uniformly distributed over the entire height. Thus a Maximum oss Model is defined as: i (7) 1/ (8) where = imum 3d loss ratio; = imum struture drift in the struture; and i = struture drift of the i th storey. As buildings beome taller, the onservative assumption that the imum loss is spread equally over all storeys an lead to a substantial overestimation of total loss. This is beause the most severe damage tends to be onentrated within a few floors, typially the lower storeys. Deshmukh (2011) developed a method to address this issue and proposed an Average oss Model. This requires the alulation and summation of the loss at eah storey of the building and then averaged over the entire height of the building, as follows: avg n i i1 n 1/ n i ; (10) i1 n avg where avg = average 3d loss ratio (for physial damage loss, avg 1.0; for death loss, D avg 0.1; and for downtime loss, DT avg 75); n = total number of storeys of the building; and avg = average struture drift in the struture. In reality, neither the imum loss model, nor the average loss model will hold universally true for all potential earthquake shaking intensities. For example, under stronger shaking if only one storey is near ollapse, then insurers will ondemn the entire struture in spite of most other storeys being in pristine ondition. This is a ase where building replaement is neessary and thus the imum loss model is appliable. Therefore, a proposed new loss model is developed by ombining the imum and the average loss models to give a omposite onditional loss model. For physial damage loss, the proposed model is expressed in terms of whether the building is repaired or replaed as follows: The building is repaired when: eff ( 1.0) (11) avg on (9) The building is replaed when: 4

5 eff (1.0 u ) (12) where eff = the effetive physial damage loss ratio for the proposed physial damage loss model. Similarly, for the death loss, the proposed model is expressed as: D eff ( D D 0.1) (13) Davg on Deff (0.1 D D u ) (14) D where D eff = the effetive probability of death loss for the proposed death loss model. And for the downtime loss, the proposed model is expressed as: DT eff ( DT DT 75) (15) DTavg on DTeff (75 DT DT u ) (16) DT where DT eff = the effetive downtime loss for the proposed downtime loss model. Other variables to represent the key oordinates in the proposed loss model are alulated by 1/d rr rr r (17) r R R R R d rr rl r (18) r where R rr = radial distane from the epientre of the earthquake orresponding to the 3d loss ratio rr (for physial damage loss, rr = 1.0; for death loss, D rr = 0.1; for downtime loss, DT rr = 75), note that this distane separates repair and replaement outomes; rl = 3d loss ratio of the average loss model orresponding to the radial distane from the epientre of the earthquake R rr. 4 RESUTS AND IMPICATIONS From the senario-based 3d loss models, the losses at a ertain radial distane from the earthquake epientre an be easily determined. The well-known 10-storey reinfored onrete Redbook Building (CCANZ 1998) was seleted as the exemplar struture in this researh. The senariobased 3d loss models were implemented for the Redbook Building based on the 22 February 2011 Christhurh earthquake. Compared to the imum loss model, the estimated 3d losses based on the senario-based 3d loss models, onsidering spatial distribution of damage losses over the height of the buildings, are onsiderably smaller. The 3d loss model results show that for the standard Redbook Building, within the entral business distrit taken as some 17 km radial distane away from the earthquake epientre: (i) the expeted physial damage loss ratio is about 50% of the asset value; (ii) the expeted probability of killing someone is about 3%; and (iii) the expeted downtime is 6 months. Considering the randomness and unertainties, one an have 90% onfidene that the losses will not be higher than: (i) 100% physial damage loss ratio; (ii) 5% of probability of death loss; and (iii) 1-year of downtime loss. When onsidering the spatial distribution of losses, the analysis results show that for the standard Redbook Building, at a 17 km radial distane from the earthquake epientre: (i) the physial damage loss is about 20%; (ii) the probability of death loss is only 0.7%; and (iii) the downtime loss is about 2 months. Compared to the imum loss model, it is observed that the estimated losses are signifiantly redue when onsidering spatial distribution of damage over the height of the struture. 5

6 IM Replae Repair Downtime oss Death oss Damage oss Drift R (km) Figure 2: Proposed 3d loss model for standard Redbook Building 5 DISCUSSION: WHAT CAN BE DONE TO AMEIORATE OSSES? In monetary terms it has been shown that the downtime loss is the most signifiant loss ompared to the physial damage loss and death loss (Ghorawat, 2011). It is therefore neessary to take downtime loss more seriously into onsideration in the pre-event analysis and design. To investigate how one might ameliorate losses, and in partiular minimize downtime by design, a sensitivity (swing) analysis has been performed. The Cases onsidered onsist of: 6

7 (a) Making the building 30% stronger (this degree of strengthening is in keeping with the proposed inrease in the seismi hazard for Christhurh); (b) Making the building more deformable and as damage-free as pratiable, without making the building stronger. Using the Damage Avoidane Design (DAD) armouring details along with reentering attributes as proposed in various reent studies by Rodgers et al. (2008, 2012) and Solberg et al (2008). () A ombination of Cases (a) and (b) above. Downtime oss Death oss Damage oss R (km) Figure 3: Proposed 3d loss model results for different buildings Results of this swing analysis are presented in Figure 3. When ompared with the Redbook Building as the benhmark, one an observe that for Case (a) the stronger building: (i) the physial damage loss ratio delined to about 20%; (ii) the probability of death loss redues to 0.4%; and (iii) the downtime loss is about 1 month. The values indiate that the building with a stiffer onstrution an learly derease the damage losses, espeially the downtime loss. For Case (b), the more dutile building, the 17 km radial distane from the earthquake epientre is just at the onset of the damage loss area, whih 7

8 means that no damage is done to the building is possible. However, at distanes loser than 17 km omplete damage requiring replaement is not really improved. For Case (), where the building is both strengthened and detailed to avoid damage, both replaement and repairs are redued. The swing analysis indiates that a stronger building will help inhibit ollapse and thus redue replaement losses, but repairs are still required at moderate distanes from the epientre (R > 9 km). A more deformable (DAD) onstrution is evidently more effetive in reduing the repair losses, but under severe shaking replaements may still be neessary; there is no substitution for strength when omplete toppling/ollapse/replaement is onerned. However, the more dutile building is notieably more effetive in dereasing the earthquake inflited damage and almost eliminates the need for building repairs. Therefore, to redue the need for both replaements and repairs, strutures need to be respetively made both stronger and more deformable (with DAD details). The stronger and more dutile building an ahieve the best performane and have the minimum 3d losses ompared to the other three types of buildings. For the ase of modifying the Redbook Building by inreasing the strength by 30 perent, plus altering the onnetions to armoured DAD details, all damage beyond 10 km from the epientre an theoretially be eliminated. To redue this entirely the building would need to be made stronger again. 6 CONCUSION By making a building stronger by design, the need for omplete replaement is redued, but damage and thus repairs along with the inevitable downtime an still be expeted. Conversely, by making a building more deformable, the need for repairs will be redued, but toppling or omplete failure will only be eliminated if the building is also made stronger. REFERENCES: Cement and Conrete Assoiation of New Zealand (CCANZ) Examples of onrete strutural design to NZS 3101:1995 Redbook. Cement and Conrete Assoiation of New Zealand, Wellington, New Zealand. Deshmukh, P.B Rapid spatial distribution seismi loss analysis for multistory buildings. M.S. thesis, Texas A&M University, Texas, United States. Ghorawat, S Rapid loss modeling of death and downtime aused by earthquake indued damage to strutures. M.S. thesis, Texas A&M University, Texas, United States. Kennedy, R. P., Cornell, C.A., Campbell, R. D., Kaplan, S., & Perla, H.F Probabilisti seismi safety study of an existing nulear power plant. Nulear Engineering and Design, 59(2), Mander, J.B., & Basoz, N Seismi fragility theory for highway bridges: Optimizing post-earthquake lifeline system reliability. Pro., Fifth US Conferene on ifeline Earthquake Engineering, Seattle, WA Mander, J. B., & Elms, D.G Quantitative risk assessment of large strutural systems. Strutural Safety & Reliability, 3(1), Mander, J.B., Sirar, J., & Damnjanovi I Diret loss model for seismially damaged strutures. Earthquake Engineering & Strutural Dynamis. (on-line) Rodgers, G.W., Solberg, K.M., Mander, J.B., Chase, J.G., Bradley, B.A., & Dhakal R.P High-fore-tovolume seismi dissipater embedded in a jointed preast onrete frame. Journal of Strutural Engineering. (on-line) Rodgers, G.W., Solberg, K.M., Chase, J.G., Mander, J.B., Bradley, B.A., Dhakal, R.P., et al Performane of a damage-proteted beam-olumn subassembly utilizing external HF2V energy dissipation devies. Earthquake Engineering & Strutural Dynamis, 37(13), Solberg, K., Dhakal, R.P., Bradley, B., Mander, J.B., & i, Seismi performane of damage-proteted beam-olumn joints. ACI Strutural Journal, 105(2),