BUILDING TAGGING CRITERIA BASED ON AFTERSHOCK PSHA

Transcription

1 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 004 Paper No. 383 BUILDING TAGGING CRITERIA BASED ON AFTERSHOCK PSHA Gee Liek YEO 1, C. Allin CORNELL 1 SUMMARY The objective of yellow or red-tagging a building after an earthquake is to insure adequate life safety during a period of enhanced seisic activity. A ethodology for the life-safety evaluation of an earthquake-daaged building is proposed based on the explicit quantification of the tie-varying aftershock ground otion hazard at the site after a ajor earthquake. The ethodology takes into consideration the level of daage sustained by the building due to the ainshock and its residual capacity against lapse due to possible future aftershocks. The proposed ethodology enables us to classify buildings after an earthquake into three groups based on the probability of building lapse due to an aftershock. The fatality risk to an arbitrary occupant is presued to be proportional to this nuber. The classification criteria are based on the value of this lapse rate relative to the tolerable value iplied by current new building design. The first group of buildings is classified or tagged red iplying that iediate entry and re-occupancy are not peritted for any personnel. The second group of buildings is tagged yellow; entry by volunteer eergency personnel for repair or retrofit purposes or for continued operation of critical facilities is allowed as long as such personnel are infored of the increased risk they face and are appropriately copensated for it. The third group of buildings is tagged green peritting entry and re-occupancy for all personnel. The proposed ethodology also provides for the change of tag or as a function of elapsed tie fro the ainshock due to the decreasing aftershock hazard at the site. We also propose a ethodology to allow earlier entry into a red-tagged building by introducing the concept of a controlled work force where we liit the total probability of lapse faced by a selected infored and copensated volunteer worker. This can be achieved by liiting the duration these workers ay spend in daaged buildings, followed by a required, subsequent rotation to a safer working environent. INTRODUCTION After an earthquake buildings ight suffer significant daage without lapse. There is a need to tag such buildings to decide if it is necessary to evacuate their occupants based on the daage sustained by the buildings. If the occupants of a daaged building are evacuated, it is also necessary to decide if and 1 Departent of Civil and Environental Engineering, Stanford University, CA 94305

2 when eergency workers can enter the building for search-and-rescue or teporary shoring issions. Further, there are soe critical facilities where it is essential to counity recovery to ensure the continuation of their operations after the earthquake. Such facilities include water and power distribution networks etc. For such facilities, it ight be extreely iportant to allow a iniu nuber of workers to enter the daaged building after the earthquake to perfor critical functions. This case requires special consideration. Such tagging decisions are dependent on the daage state of the building iediately after the first earthquake which we shall refer to as the ainshock. The decision should be based on life-safety considerations in ters of the daaged building s ability to resist aftershocks. Unfortunately, such decisions are coplicated by the significantly increased likelihood of aftershocks in the post-ainshock environent. Aftershock rates are also dependent on the elapsed tie after the ainshock such that the ean rate of aftershocks is at its axiu iediately after the ainshock and subsequently decreases with tie. Also, the ainshock agnitude influences the ean rate of aftershocks in the post-earthquake environent. Aftershock-based conditions for perissible entry into earthquake-daaged buildings have been addressed in Gallagher [1]. If this reference is followed, for buildings that have been inspected and deterined to be unsafe but stable (a red-tagged building), depending on the ainshock agnitude, eergency workers can enter the building for a liited tie if they wait for a nuber of days to pass after the ainshock. For exaple, if the ainshock agnitude is equal to 6.5 or greater, eergency workers can enter the building for two hours if they wait for one day after the ainshock. These guidelines are iplicitly based on aftershock occurrence rates which are dependent on the ainshock agnitude and elapsed tie. The guidelines do not, however, take into consideration the possible aftershock ground otion intensities at the site which are necessary to deterine if the daaged building has sufficient residual capacity to resist aftershocks. The daage sustained by the building due to the ainshock also erits quantification. Here, we introduce a ethodology that takes into consideration the increased aftershock ground otion hazard at a site after a ainshock via a procedure referred to as Aftershock Probabilistic Seisic Hazard Analysis or APHSA for short. We also propose a ethodology to quantify the life-safety threat in a tievarying environent by representing the as Equivalent Constant Rates, or s. Lastly, we also need to consider the daage states of the building after the ainshock based on the residual capacity of the daaged building to resist aftershock ground otions. This capacity, denoted as Sa cap, is easured in ters of spectral acceleration of the first-ode period of the building. We describe next each of the three coponents. AFTERSHOCK PROBABILISTIC SEISMIC HAZARD ANALYSIS (APSHA) First, we need to be able to quantify the tie-varying post-ainshock hazard in ters of the possible ground otions that can occur at the site due to aftershocks. This process is referred to as Aftershock Probabilistic Seisic Hazard Analysis (APSHA), and interested readers are referred to the detailed anuscript in Yeo []. Here, we shall provide a brief suary of APSHA. Iediately following a ainshock of agnitude, aftershocks occur on a zone typically defined by the extent of the ainshock rupture zone. Aftershocks also occur with a tie-varying rate that is at its axiu iediately after the ainshock and decreases with increasing elapsed tie fro the ainshock. The rate of aftershocks is also dependent on the ainshock agnitude. The tie and

3 ainshock-agnitude dependence of aftershock rates is coonly referred to as Oori s Law: a typical California aftershock sequence studied by Reasenberg and Jones has paraeters a = -1.67, b = 0.91, p = 1.08 and c = See Reasenberg [3] for details. In Equation (1), λ(,; τ ) is defined as the ean instantaneous daily rate of aftershocks with agnitude or larger at tie τ following a ainshock of agnitude. a+ b( ) 10 λτ (,; ) = ( τ+ c) p (1) We truncate the lower and upper bounds of aftershock agnitudes at l and. We can then obtain the ean instantaneous daily rate of aftershocks with agnitudes between l and at tie τ (following a ainshock of agnitude ) by evaluating λ(,; τ l ) λ(, τ ; ). We denote this quantity as µτ (; ). We can also obtain the truncated exponential probability distribution function of aftershock agnitudes as f (; ) (See Yeo [] for details). The expressions for µ (; τ ) and f (; ) are shown in Equation () and Equation (3). µτ (; ) = a+ b( ) a l ( τ+ c) p () blog(10)( l ) blog(10)e f(; ) = for 1 e blog(10)( l l) (3) We can then perfor a ground otion analysis analogous to conventional PSHA for ainshocks (Kraer [4]) by integrating over all possible locations and agnitudes of the aftershocks. Here, we assue that aftershocks can only occur on the ainshock rupture zone to quantify the probability distribution function of the possible source-to-site distances given aftershock agnitude, f(r ). By considering a suitable attenuation law, we can then obtain the ean nuber of aftershocks in the tie interval of t and t+t after the ainshock which have first-ode spectral accelerations at the site (Sasite) greater than y. We denote this by µy as shown in Equation (4). t+ T (4) µ y = µ ( τ; )dτ P(Sasite > y,r)f (r )f (; )drd t l r The first integral in Equation (4) captures the teporal aspects and becoes: t+ T 1 p 1 p a+ b( l) a + c) + T + c) µτ (; )dτ=( 10 10) p 1 p 1 (5) t The second double integral in Equation (4) is solved by conventional PSHA coputer codes. It represents the probability of Sa site exceeding a level of y given the occurrence of an aftershock. Thus:

4 P(Sasite > y aftershock) = P(Sasite > y,r)f(r )f(; )drd (6) l r The process of quantifying the tie-varying aftershock hazard at a site in ters of a suitable ground otion intensity easure (Sa site in this case) is referred to as APSHA. QUANTIFICATION OF TIME-VARYING RATES AS EQUIVALENT CONSTANT RATES () The ability to quantify the tie-varying aftershock hazard is the first step towards developing a buildingtagging ethodology based on the post-ainshock ground otion hazard at a site. However, as discussed in the previous section, aftershock hazard is tie-varying in nature, and it depends on the nuber of elapsed days after the occurrence of the ainshock. Aftershock hazard is also dependent on the length of the tie interval taken into consideration. Such dependence on tie is inconsistent with conventional design criteria for buildings. For exaple, in the United States, design ground otion levels for new buildings are currently set at /year (or % in 50 years). This frequency is iplicitly assued to be constant and indefinite in tie. Life-safety is also norally stated in ters of annual frequency of fatality. For exaple, the Norwegian Petroleu Directorate (NPD) sets the axiu annual individual fatality risk per worker to 10-4 on new platfors for the offshore oil and gas industry (NPD [5]). Again, such criteria iplicitly assue tie-independent fatality risks that are constant and extend indefinitely into the future. In order to copare or calibrate safety criteria in a tie-varying environent (such as aftershocks) to the standard tie-invariant situation, soe eans ust be identified to transfor the forer into the latter. Such a ethodology has been developed in Yeo [6]. There, tie-varying rates are changed to equivalent constant rates with the desired characteristics by considering an iplied discounted investent in life-safety technologies for both the constant or hoogeneous ainshock case and the tievarying, nonhogeneous aftershock case on the basis of social equity. Such constant rates which represent the tie-varying aftershock rates are referred to as Equivalent Constant Rates, or s. Interested readers are referred to Yeo [6] for further details. In brief, after a ainshock of agnitude, we can assess the threat due to the tie-varying aftershock rates fro tie t d for an arbitrarily long duration into the future (i.e. fro t d to infinity when the aftershock rate is negligible) by evaluating d ; ) based on Equation (7). Here, t d refers to the date at which a decision is being ade about the building; t d includes day 1 of the ainshock but it also ay refer a later date when there ight be better inforation about the daage state of the building (for exaple, based on better inspection and/or ore sophisticated engineering analysis) to facilitate betterinfored building-tagging decisions (or revisions of previous building-tagging decisions). These decisions will be based on the assessent of the reaining threat to an occupant in the building. (This will be discussed in ore details in later sections.) Here, r refers to the inflation-adjusted discount rate appropriate for discounting societal investents in life-safety technologies in the future. τ r d ; ) = r e µτ ( ; )dτ (7) td

5 Equation (7) can be approxiated as Equation (8) because relative to e -rτ for increasing values of τ. µ (; τ ) decreases to zero ore rapidly ; ) r µ ( τ ; )d τ (8) d td Thus, fro Equation (8), the d ; ) can be easily estiated by coputing the integral in Equation (8). This is siply the expected nuber of aftershocks in the tie interval [t d, ] (which can be coputed by evaluating the area under the ean instantaneous daily aftershock rate curve fro t d to ) ultiplied by the inflation-adjusted discount rate r. A representative value of r is 3.5% per annu (Páte- Cornell [7]). Thus, as described above, we have transfored the tie-varying rate into an equivalent constant rate, d ; ), based on Equations (7) or (8). Note that d ; ) is dependent on t d, which is defined as the tie at which the tagging decision (or revision of a previous tagging decision) is ade. QUANTIFICATION OF RESIDUAL CAPACITY OF DAMAGED BUILDINGS TO RESIST AFTERSHOCKS The procedure briefly discussed below is based on Bazzurro [8]. Interested readers are referred to that anuscript for further details. The ethodology is based on perforing a nonlinear static procedure (NSP) on the daaged building to estiate the building s residual capacity to resist aftershocks. The dynaic response is then inferred fro the static response by using the SPOIDA spreadsheet tool (Vavatsikos [9]) and the edian residual dynaic capacity of the building is found in ters of spectral acceleration, Sa cap. This capacity provides an indication of the life-safety threat that the occupants are exposed to. The peritted occupancy status of the building will be deterined below based on the edian residual capacity to resist aftershocks and the likelihood of an aftershock ground otion exceeding that capacity. For a daaged building in daage state with a rando capacity (defined by its edian Sa cap (denoted as Ŝa cap ) and dispersion β cap (standard deviation of the logarith of Sa cap )), one can define ) as the equivalent constant lapse rate corresponding to the expected nuber of aftershocks (due to a ainshock of agnitude ) resulting in lapse of the daaged building fro tie t d for an infinite duration. Under certain assuptions, this rate can be found to be nuerically equal to Equation (9). ; ) ; ) P(Sa Sa aftershock)e 1 k β cap d = [ d ] ˆ site > cap (9) d ; ) has been defined previously. P(Sa ˆ site > Sa cap aftershock) can be evaluated based on 1 k β cap Equation (6). The ter e is a factor to account for the dispersion of the Sa cap value, where k is the slope of the linearly-approxiated log-log hazard curve. See Cornell [10] for details.

6 The equivalent constant lapse rate, ), is assued to be proportional to the fatality risk to an arbitrary occupant in the daaged building. On the basis of life-safety, given and for a building in daage state, we will next copare ) to existing safety criteria to deterine if the safety criteria have been satisfied. This will for the basis of our proposed building-tagging ethodology. PROPOSED BUILDING-TAGGING METHODOLOGY Using the three coponents described above, we now propose a building-tagging ethodology based on ). Given the ainshock agnitude,, the location of the building, the ainshock rupture zone and the degree of daage of the building in ters of Ŝa cap and β cap, we have above quantified the ) of the daaged building as a function of t d. An occupant in a daaged building will be exposed to a tie-varying lapse rate, and thus, a tie-varying fatality risk. On the basis of life-safety, we propose to copare ) to a specified acceptable lapse rate to deterine the appropriate tag for the daaged building. Depending on when the tagging decision is to be ade, the appropriate tag for the building ay iprove with an increase in the elapsed tie fro the ainshock. The possibility of considering changes of building tags arises because of the reduction of the aftershock hazard with increasing elapsed tie fro the ainshock. As discussed earlier, the degree of daage of the building will be evaluated to different degrees of accuracy at different ties. For exaple, shortly after the ainshock, quick visual inspection provides us with inforation about the daage state with high degrees of uncertainty as indicated by large β cap values. Better inspection (for exaple, inspection of the connections in a SMRF building) and engineering analysis (for exaple, nonlinear tie history analysis) provides us with ore inforation about the daage state of the building with different Ŝa cap and saller β cap values. This would provide us with an opportunity to re-assess the reaining threat to an occupant in the daaged building and to reake our building-tagging decision based on ore accurate inforation about the daage sustained by the building. We propose three possible tags for buildings after the earthquake, siilar to Gallagher [1]. When a building is green-tagged, all occupants ay enter the building. When a building is yellow-tagged, only eergency workers ay enter the building for search-and-rescue issions, or to restore operations in critical facilities such power production and distribution facilities. Such eergency workers need to be infored of the increased risk that they face when they volunteer to perfor their tasks in daaged buildings, and they also need to be appropriately copensated for the increased risk that they face. When a building is red-tagged, neither noral occupants nor eergency workers ay be in the daaged building for extended periods of tie. These tagging designations are analogous but not equivalent to FEMA [11]. Acceptable Collapse Rate for each Building Tag First, we need to establish the range of acceptable lapse rates for each of the three building tags. It is proposed to specify the acceptable (or tolerable) lapse rates for the various tagging states in ters of P 0, the acceptable lapse rate for new, intact buildings designed for ainshocks. This nuber is

7 iportant for operations to continue uninterrupted. We propose a coparatively high level of α 1 for such facilities. For non-safety-critical coercial and office buildings, the level of α 1 is set to be lower than that of critical facilities. For residential buildings, the level of α 1 is set to be between that of critical facilities and coercial buildings. We also need to set a axiu acceptable lapse rate of α P0 beyond which entry by all personnel (including noral occupants and eergency workers) is not allowed on the basis of life-safety. For lapse rates between α 1 P 0 and α P 0, the building will be yellow-tagged. Entry is peritted for infored, copensated and voluntary eergency workers for the ranges of ) above. Again, the relative level of α should be set according to the function of the building.. The building tags and their corresponding ranges of lapse rates are shown in Figure 1. Green: Entry for all purposes acceptable. Yellow: Entry acceptable for volunteer workers who are infored of increased risk and who are appropriately copensated. Red: Entry unacceptable P 0 Design Level of New Buildings α1p0 αp0 ) All occupants Infored, copensated volunteer workers only Figure 1: Buildings tags and their corresponding allowable lapse rates Representative values of α 1 and α ight be 5 and 10 for critical counity recovery facilities, 3 and 6 for coercial and office buildings and 4 and 8 for residential buildings. Priary Building-Tagging Basis We now propose a tagging ethodology based on quantifying ) of the daaged building, first ignoring possible repair or upgrade to the building. We will consider a revised tagging ethodology for buildings that ight have been repaired or upgraded after the ainshock in a later section. In order to tag the building, we first evaluate ) of the building as a function of t d. Specifically, we represent (1; ) (one day after the ainshock) as γ P0. We copare the value of γ to the values of α 1 and α for the building. If γ is less than α 1, then the building is green-tagged one day after the ainshock and the occupants of the building do not need to be evacuated. If γ is less than α but ore than α 1, then the building is yellow-tagged and only entry by infored, copensated and voluntary eergency workers is allowed. If γ is greater than α, then the building will be red-tagged after the ainshock and coplete evacuation of the building is necessary on the basis of life-safety. If γ is greater than α such that the building is red-tagged after the ainshock (see Figure ), the tag will d reain red until the ; ) decreases to a level equal to α P0 on the k th day. This is when the building tag changes to yellow corresponding to an ) which will be less than α P0 fro

8 α but ore than α 1, then the building is yellow-tagged and only entry by infored, copensated and voluntary eergency workers is allowed. If γ is greater than α, then the building will be red-tagged after the ainshock and coplete evacuation of the building is necessary on the basis of life-safety. If γ is greater than α such that the building is red-tagged after the ainshock (see Figure ), the tag will d reain red until the ; ) decreases to a level equal to α P0 on the k th day. This is when the building tag changes to yellow corresponding to an ) which will be less than α P0 fro that day on. Siilarly, when the ) decreases to a level equal to α 1P0 on the k th day, the building tag changes to green. The decreasing nature of ) ensures that the building tag will change fro red to green to yellow with increasing elapsed days fro the ainshock. d ; ) per annu γp 0 αp0 Infored and copensated workers only α1p0 Ordinary workers and occupants Figure : 1 k k t d ) of a daaged building. The building should be tagged red fro day 1 to day k, yellow between days k and k and green fro day k on. Special Tagging Cases: Eergency Workers There ight also be special situations where it is necessary to allow eergency workers to enter a daaged building to perfor critical tasks even when the building is red-tagged. For exaple, it is iportant to ensure continued operations at power distribution networks in the post-earthquake environent, and hence it ight be necessary to allow eergency workers to enter such facilities to perfor short-ter critical repairs or periodic onitoring or switching. In soe other facilities, it ight also be necessary to allow eergency workers to enter red-tagged buildings for search-and-rescue issions or lapse-prevention shoring activities. We propose a revised tagging ethodology to allow entry into buildings that have been red-tagged by providing a controlled working environent for eergency workers based on the total life-safety threat that they face by entering such daaged buildings with a high ). Again, this ethodology ignores as yet possible repair or upgrade to the building after the ainshock. Consider the ) for a critical facility in daage state as shown in Figure 3. The building has been red-tagged iediately after the ainshock because γ is greater than α. It is necessary to allow the entry of eergency workers shortly after the ainshock to perfor soe critical repairs which cannot wait till the k th day when the building tag will change to yellow. To allow such operations, these

9 eergency workers can enter the building earlier at tie j if their work schedule and location are properly controlled. This requires both a liited duration, d, in the daaged building and a subsequent rotation after departure to a safer environent (SE). The duration d can be deterined for an arbitrary start tie j by ensuring that: SE + α 0 (j; ) (j d'; )+ (j'; ) P (10) d ; ) per annu γp 0 α P 0 α 1 P 0 j k j d t d Figure 3: Tie-varying ) of a daaged building. Eergency workers can enter the daaged building on day j for a total duration of d days if their working environent is properly controlled. The first two ters reflect the risk associated with the interval in the red-tagged building and the third ter reflects the tie in the safer environent. The safer environent can be achieved by housing and/or eploying the workers in a building with deonstrated higher capacity or by oving the workers to a location which is further away fro the aftershock zone where the aftershock hazard is lower, or a cobination of both. The ) of the safer environent needs to be evaluated based on the edian assessed Sa cap of the new building that they are relocated to, and/or on a revised Aftershock Probabilistic Seisic Hazard Analysis (APSHA) which takes into consideration the location of the new building with respect to the ainshock rupture zone. If further occupancy is needed in the ainshockdaaged building, a new group of controlled workers can be engaged to begin on day j. This new group of workers should have been controlled in a safer environent since day j. This tagging proposal is, in effect, a liited cuulative risk concept where we evaluate the cuulative threat to a person due to occupancy in a daaged building and in a safer environent. See Cornell [1] for ore details. Tagging Basis with Repair We next propose a building tagging criterion where we allow possible upgrade or repair to the building after the ainshock. We show in Figure 4 the ) curves for the daaged building (daage state ), a new intact building, and the repaired building (repaired state is denoted as R). Note that the R ) curve for the repaired building could be either above or below that of the curve for the new intact building.

10 d ; ) per annu γp 0 α P 0 Daaged Building α 1 P 0 j j j k d d t d Repaired Building (could be above or below intact case) Intact Building Figure 4: Tagging of a daaged building with possible repair or upgrade to the building Again, based on the concept of the controlled working environent, eergency repair workers can enter the building fro tie j for d days when the building is red-tagged, where the duration d can be deterined based on Equation (10). If building is not copletely repaired to code-standard in d days and assuing that it has been repaired to an interediate level R, a second group of workers can work for d days by ensuring that: R' R' SE + α 0 (j'; ) (j' d''; )+ (j''; ) P (11) If repair is copleted on day k (after which one should consider the repaired building), noral occupants can enter the building only if R d ; ) curve for the R α1 0 (k; ) P (1) If not, noral occupants can enter the repaired building only after the building has decreased to α 1P0. R d ; ) for the repaired The proposed ethodology allows us to take advantage of our knowledge of the tie-varying aftershock hazard at the site and the daage state of the building to provide an appropriate tag for the ainshockdaaged building based on life-safety considerations. WORKED EXAMPLE To illustrate our proposed-ethodology, we consider a three-story steel oent-resisting frae (SMRF) building located at the Stanford, California site. The building has a structural period equal to 0.73s. We assue that a ainshock of agnitude 7.0 has occurred on the San Andreas Fault which has ruptured the neighboring Mid Peninsula Segent. Details can be found in Yeo []. We assue that aftershocks can occur anywhere on the ainshock rupture zone with equal likelihood. A scheatic layout of the site with respect to the ainshock rupture zone is shown in Figure 5.

11 Stanford Site 10k Length = 85k Peninsula Segent of San Andreas Fault Figure 5 : Location of site with respect to ainshock rupture zone The instantaneous daily aftershock rates are shown in Figure 6 as a function of elapsed tie fro the ainshock. Here, we consider aftershocks with agnitudes between 5.0 and 7.0, the ainshock agnitude. Note that, for exaple, the expected total nuber of aftershocks starting 10 days after the ainshock over a tie interval of infinite length is equal to seven, i.e. the shaded area shown below in Figure 6. Instantaneous Aftershock Rate /day t Figure 6: Instantaneous tie-varying daily aftershock rate as a function of elapsed tie fro the ainshock of agnitude 7.0 Next, we convert the instantaneous daily aftershock rates to d ; ) on an annual basis by using Equation (8). In this case, we assue an inflation-adjusted discount rate of 5% per year. We plot the d ; ) as a function of t d in Figure 7. In particular, the d ; ) 10 days after the ainshock over a tie interval of infinite length is equal to 0.35 events/year, approxiately equal to the product of five percent and seven.

12 d ; ) per annu t d Figure 7: d ; ) as a function of t d for a ainshock of agnitude 7.0, assuing an inflation-adjusted discount rate of 5% per year We then perfor an APSHA. We are interested in evaluating the probability of exceeding any particular site Sa given an aftershock, i.e. Equation (6). The APSHA is perfored for Sa with T = 0.75s, close to the structural period of our three-story SMRF building of 0.73s. The results are shown in Figure 8. Note that this function ties the aftershock rate in Figure 6 gives Equation (4). 1.0E+00 Probability of exceeding Sa at site 1.0E E-0 1.0E E E Sa/g Figure 8: Probability of exceeding site Sa (with T = 0.75s) given an aftershock of rando agnitude at a rando location relative to the site. We next evaluate the ) of the building given different initial post-ainshock daage states. Again, we note here that ) for a building in a particular daage state corresponds to characterizing the equivalent lapse rate of a building as a function of t d. We consider three daage states for the building. Daage state 1, or 1, corresponds to onset of nonlinear behavior in the building, and the edian assessed Sa cap to bring a building in 1 to lapse in an aftershock is 1.4g. The edian Sa cap for a building in 1 is the sae as that for an intact building. Daage state, or, corresponds to fracture of exterior bea-un connections of the first floor in the building, and the edian assessed Sa cap to bring a building in to lapse in an aftershock is 1.g. Daage state 3, or 3, corresponds to fracture of interior connections of the frae (in addition to exterior connections), and

13 the edian assessed Sa cap to bring a building in 3 to lapse in an aftershock is 1.1g. Details of the characteristics of the building can found in Bazzurro [8]. The edian Sa cap values are obtained by Dr. Joe Maffei of Rutherford and Chekene (Maffei [13]). The resulting annual ) for the three daage states are shown in Figure 9. d ; ) per annu Intact/ t d Figure 9: d ; ) for three-story SMRF progressing to lapse given different post-ainshock daage states We assue that the three-story SMRF building is a residential building with α 1 = 3 and α = 5. Consider the case when the building is in 3 after the ainshock. We apply our proposed building-tagging ethodology to this daaged building. For P 0 = /year (corresponding to % in 50 years) and assuing no repair or upgrade to the building, we can copute γ ( (1; ) noralized by P 0 ) to be equal to This is greater than the α value of 5. Thus, the building is red-tagged iediately after the ainshock. We need to wait for three days before the value of ) reduces to α P0 and the building becoes yellow-tagged. The building only becoes green-tagged 40 days after the ainshock. See Figure )per annu ; ) 0.00 α P α 1P days 40 days t d Figure 10: Tagging of daaged building in 3 assuing no repair or upgrade

14 We next consider a case where we provide a controlled working environent for volunteer eergency workers so that they can enter the daaged building when it is red-tagged. We assue that the eergency Intact workers will be relocated to a new intact building at the sae site with ) as shown in Figure 9 after copletion of repair. We also assue for illustration that the building repair will be 3 3 Intact copleted in two days. In this case, we copute (1; ) (3; ) and (3; ). The su of the two values above is equal to /year, less than α P0 which has a value equal to 0.00/year. Hence, the eergency workers can enter the daaged building on day one when the building is red-tagged to coplete the repair. The longest allowable duration d * for repair can be evaluated by trial and error by ensuring that 3 3 * Intact * (1; ) (1 + d ; ) + (1 + d ; ) is less than α P0. Intact Also, when we evaluate (3; ), we notice that the value of (3; ) is less than α 1P0. This eans that the building will be green-tagged three days after the ainshock if the eergency workers are able to repair the building to its intact capacity in two days. Intact d ; ) per annu α P α 1P Repair copleted on third day Intact/1 0 3 days t d Figure 11: Tagging of daaged building in 3 with repair CONCLUSION We propose a tagging ethodology for daaged buildings after the ainshock based on life-safety considerations. We consider the aftershock hazard at the site in ters of possible future aftershock ground otions. The daage state of the building after the ainshock is also taken into account. The proposed ethodology allows for entry into a red-tagged building after the ainshock by introducing the concept of a controlled working environent for eergency workers. Possible repair or upgrade to the daaged building can also be introduced in the proposed ethodology. It is our hope that such a ethodology will allow better tagging decisions to be ade after the ainshock. The proposed procedure for given ainshock agnitude and daage state of the building is also used in Bazzurro [8] to assess preainshock likelihoods of each of the potential future tagging states of the building.

15 ACKNOWLEDGEMENTS This work was supported in part by the Pacific Earthquake Engineering Research Center (PEER Contract SA41) through the Earthquake Engineering Research Centers Progra of the National Science Foundation under Award nuber EEC The authors would like to thank Dr. Paolo Bazzurro and Dr. Nicholas Luco for their helpful coents and suggestions. REFERENCES 1. Gallagher RP, Reasenberg PA, Poland CD. Earthquake aftershocks entering daaged buildings. ATC TechBrief, Applied Technology Council, Yeo GL, Cornell CA. Aftershock probabilistic seisic hazard analysis. In preparation. 3. Reasenberg PA, Jones LM. Earthquake hazard after a ainshock in California. Science 1989, 43: Kraer SL. Geotechnical earthquake engineering. John Wiley & Sons, Inc, Norwegian Petroleu Directorate (NPD). Guidelines for safety evaluation of platfor conceptual design. Oslo, Norway, Yeo GL, Cornell CA. Representation of tie-dependent ean failure frequencies by an equivalent constant rate. In preparation. 7. Páte-Cornell ME. Personal counication, Bazzurro P, Cornell CA, Menun C, Motahari M. Guidelines for seisic assessent of daaged buildings. Proceedings of the 13 th World Conference on Earthquake Engineering, Vancouver, Canada. Paper no Vavatsikos D, Cornell CA. Increental dynaic analysis. Earthquake Engineering and Structural Dynaics (3): Cornell CA, Jalayer F, Haburger RO, Foutch DA. The probabilistic basis for the 000 SAC/FEMA steel oent frae guidelines. ASCE Journal of Structural Engineering (4): Federal Eergency Manageent Agency (FEMA). Steel oent frae buildings: postearthquake evaluation and repair criteria FEMA-35. Prepared by the SAC Joint Venture for the Federal Eergency Manageent Agency, Washington, DC, Cornell CA, Bandyopadhyay KK. Should we relax seisic criteria for shorter syste exposure ties? Proceedings of Pressure Vessels and Piping Conference. New York: ASME; Maffei JR, Mohr, Holes WT. Test application of advanced seisic assessent guidelines 3-story steel oent-frae building: Draft. Rutherford and Chekene; Oakland, CA, 00.