Effect of construction quality variability on seismic fragility of reinforced concrete building

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1 Proeedings o the Ninth Paii Conerene on Earthquake Engineering Building an Earthquake-Resilient Soiety -6 April,, Aukland, New Zealand Eet o onstrution quality variability on seismi ragility o reinored onrete building P. Rajeev Monash University, Melbourne, VIC, Australia. S. Tesamariam The University o British Columbia, Kelowna, BC, Canada. ABSTRACT: This paper disusses eet o onstrution deets on probabilisti seismi demand model (PSDM o reinored onrete (RC rames. A six-storey three-bay moment resisting RC rame is designed to a 98 Canadian Conrete Design Code. The RC rame is urther modiied to investigate variability o onstrution quality (CQ on the PSDM. Three levels o CQ are onsidered, poor, average, and good. Forty ive ground motion reords were used to study the ground motion variability. The numerial model o the rame was developed in OpenSees and nonlinear dynami analyses were perormed, and the maximum interstorey drit is obtained as a response parameter or all simulations. The PSDM parameters are alulated using "loud analysis" or all ombinations o onstrution quality. The variation in the PSDM parameters is studied. Finally, the eets o CQ on the seismi ragilities are disussed. INTRODUCTION Design and onstrution praties have signiiantly improved over the years, yet earthquakes ontinue to ause severe damage and losses (Tesamariam and Saatioglu, 8. Reent earthquakes, Haiti and Chile in, Italy in 9, El Salvador and India in, and Turkey and Taiwan in 999, or example, highlight the seismi vulnerability o existing buildings and resulting damage. The reported auses o building damage entail poor quality materials, inadequate reinorement detailing and absene o apaity design priniples (e.g., Pampanin et al., ; Elnashai, ; Sezen et al., 999. However, no lear trend an be observed towards the orretion o the inadequate onstrution praties that have been time and again observed rom various earthquakes (Meli and Aloer,. Though quality o material and onstrution are reported ause o damage, there are very ew studies undertaken on this subjet. Pampanin et al. ( tested /-saled beam-olumn sub-assemblages, with strutural deiienies prevalent in 95 s and 97 s Italian onstrution pratie. Lu et al. ( experimentally estimated the seismi apaity o a two-storey reinored onrete (RC rame with insuiient oninement in the ritial zones o the olumns. Dimova and Negro (5, 6 have experimentally and analytially quantiied the eet o onstrution quality deets, resulted rom deiienies in arrangement o the reinorement, on the seismi perormane o a ast-in-situ one-storey industrial reinored onrete rame designed aording to Euroodes. In this study, the eets o onstrution quality (CQ on probabilisti seismi demand model (PSDM and seismi ragility o RC rames is analytially investigated. The variation in material and strutural detailing are onsidered as the ause o CQ unertainty. Interation o dierent material and strutural detailing on the response o the rame is also presented. Sine the damage to buildings an be related to the interstorey drit (e.g., FEMA 56 (FEMA, the seismi demand model and ragility are derived in terms o interstorey drit. BUILDING DESIGN CONSIDERATION A six-storey three-bay moment resisting RC rame is designed to a 98 Canadian Conrete Design Code. The building is or oie use and is loated in Vanouver, Canada, whih is onsidered to be high seismi hazard zone (NBCC 5. The plan o the building is m x m, and the storey Paper 7

2 heights are.65 m. The distane between the longitudinal rames is 6 m. The lateral load resisting system onsists o moment-resisting RC rames both in longitudinal and the transverse diretions. Seondary beams between the longitudinal rames are used at the loor levels in order to redue the depth o the loor slabs. The loor system onsists o a one-way slab spanning in the transverse diretion. In this study, only the interior transverse rame o the building is onsidered (Figure. Figure. Elevation o the six-storey struture loated in Vanouver FINITE ELEMENT MODELLING OF RC FRAME Finite element analysis o the rame was perormed using OpenSees inite element analysis pakage (MKenna et al. 7. Columns are modelled with distributed plastiity nonlinear beam-olumn elements while the beams are modelled with beam with hinge elements. P-Δ eet is onsidered and tangent-stiness proportional damping has been used, alibrated to yield a 5% equivalent visous damping ratio on the irst elasti mode. Conrete behaviour is modelled by a uniaxial Kent-Sott-Park model (Conrete with degrading, linear, unloading/reloading stiness, without onsideration o tensile strength. For the onined onrete, the strength and strain values have been inreased aording to the ormulae developed by Mander et al. (988. Steel behaviour is represented by a uniaxial Giure-Menegotto-Pinto model (Steel. VARIABILITY IN MATERIAL PROPERTIES AND STRUCTURAL DETAILING The CQ is quantiied by varying the material and strutural detailing. The orresponding variabilities are ategorized into three CQ levels {poor, average, good} as summarized in Table. The material unertainty parameters onsidered are ompressive strength o onrete (, yield strength o reinoring steel ( y, and hardening ratio o steel (b h. The strutural detailing unertainties onsidered are tie spaing at the olumn (s and reinorement ratio at the olumn (. The material unertainty is due to the dierent onstrution phases, while the strutural detailing unertainty is due to the dierent design methods and ator o saety onsidered in the design and onstrution phase. Table. Material and strutural detailing unertainty Material unertainty Unit Poor Average Good Compressive strength o onrete ( MPa Yield strength o reinoring steel ( y MPa 9 5 Hardening ratio o steel (b h % Strutural detailing unertainty Unit Poor Average Good Tie spaing at the olumn (s mm Reinorement ratio at the olumn ( %.8..6

3 5 EARTHQUAKE GROUND MOTIONS In order to perorm time-history analyses, an ensemble o 5 ground motion reords (three groups o 5 reords are seleted (Naumoski et al. 6. Eah group mathes dierent aeleration to veloity (A/V ratios, i.e. aelerograms with high A/V ratios (A/V >., intermediate A/V ratios (.8 < A/V <., and low A/V ratios (A/V <.8, where A is in g, and V is in m/s. The seleted aelerograms are reorded on rok or sti soil sites, inluding large and distant, large and lose, moderate and lose as well as intermediate earthquake reords. The magnitude (M w range rom 5.5 to 7.8 and soure-tosite distanes (r range is < r < 79 km. These reords are representative distanes and expeted magnitude ranges o Canadian earthquakes. Figure shows the target uniorm hazard spetrum o %, 5%, and % in 5 years return period or Vanouver, and the elasti 5% damped response spetrum o eah 5 reords saled to math the average elasti spetrum T. The undamental irst mode period (T o the base struture is.8 s, where the material and strutural detailing have values o average (Table. Figure. Target and average demand spetra or Vanouver, Canada 6 PROBABILISTIC SEISMIC DEMAND MODEL AND FRAGILITY A probability distribution or the demand onditioned on the intensity measure (IM is known as a probabilisti seismi demand model (PSDM. The demand on the struture is quantiied using some hosen metri(s (e.g. inter storey drit, dutility. Cornell et al. ( suggested that the estimate or the median demand ( Dˆ an be represented by the ollowing power model: b D ˆ a IM ( where IM is the seismi intensity measure o hoie; both a and b are regression oeiients. In this study, spetral aeleration at the irst mode period o the struture S a (T is seleted as the IM and the interstorey drit ( max is seleted as the demand parameter. The nonlinear dynami analyses an be used to quantiy the PSDM parameters. One proedure, known as Cloud Analysis (Jalayer et al., 7, is a onvenient hoie (though not the most aurate. An advantage o this method is that it is based on the ground motions as they are reorded and does not require saling. The proedure onsists o applying a suite o ground motion reords (in the order o - reords to the struture and alulates the demand D. Then, by perorming a simple linear regression o the logarithm o D against the logarithm o IM, one an obtain the PSDM parameters a and b. Furthermore, the distribution o the demand about its median is oten assumed to ollow a two parameter lognormal probability distribution. Thus, the dispersion ( D IM o the demand about its median an be omputed and is onditioned upon the IM. The dispersion is assumed be onstant or the range o IM values interested. The ragility is simply the probability that the seismi demand (D plaed on the struture is greater than the apaity (C o the struture. This probability statement is onditioned on a hosen IM, whih Soure:

4 represents the level o seismi loading. The generi representation o this onditional probability is: Fragility P( D C IM ( The ragility untion (Equation an be evaluated by onvolving PSDM with a distribution o the apaity. As explained above, due to the lognormal distribution assumption o the demand at eah level o IM and apaity, the onditional probability an be expressed as: P( D C IM ln( Cˆ ln( a IM b D IM ( where Ĉ is the median strutural apaity, assoiated with the limit state. 6. Impat o Constrution Quality in PSDM To study impat o CQ on the PSDM parameters, the RC rame s material properties and detailing are varied onsidering the variability summarized in Table. Sine the number o unertain parameter is ive, where eah has three levels, the number o sample RC models is ( 5. The maximum interstorey drit max is omputed or eah sample struture by perorming the nonlinear time history analysis with the 5 ground motion reords. Thus, the total number o time history analysis arried out is 95 (5*. The seismi demand model is developed or eah sample struture (Equation. The probabilisti seismi demand model and model parameters (a, b and β θ max Sa(T are shown in Figure or the base struture. The histogram o the distribution o PSDM parameters is shown in Figure. Table summarizes the statistial property o PSDM parameters. It an be observed that the a and β S (T show more than % oeiient o variation (CoV. θ max a Figure. Probabilisti seismi demand model o base struture Figure. Histogram o PSDM parameter

5 Table. Statistial property o PSDM parameters Parameter Median CoV (% Range a.66. [.,.7] b [.65,.9] β. 6. [.9,.] θmax Sa(T Figure 5 illustrates sensitivity o PSDM parameters on the variability o CQ. The sensitivity analysis is arried out by hanging one parameter at a time, where or eah level o the parameter (Table, orresponding the minimum, average and maximum values o PSDM parameters are omputed. Parameter a shows (Figure 5a:. dereasing trend with inrease in and,. inreasing rom poor (9 MPa to average (5 MPa then dereasing with inrease in y, and. inreasing trend with inrease in b h and s. Parameter b shows (Figure 5b:. inreasing trend with inreasing, y, and b h,. dereasing trend with inrease in s, and. inreasing rom poor to average and keep the same value rom average to good with. Parameter β θ max Sa(T shows (Figure 5:. dereasing trend with inreasing,. inreasing trend with inrease in s. y, b h and, and 5

6 PSDM parameter, Strength o onrete (MPa Strength o onrete (MPa Strength o onrete (MPa PSDM parameter, Yield strength o steel (MPa Yield strength o steel (MPa Yield strength o steel (MPa PSDM parameter, Hardening ratio o steel (% Hardening ratio o steel (% Hardening ratio o steel (% PSDM parameter,.... Tie spaing (mm Tie spaing (mm Tie spaing (mm PSDM parameter, Reinorement ratio (% Reinorement ratio (% Reinorement ratio (% (a (b ( Figure 5. Sensitivity o PSDM parameter to variablity in CQ: (a a, (b b, and ( β S (T θmax a 6

7 6. Impat o Constrution Quality in Seismi ragilities To generate the ragilities, the apaities are deined by the maximum interstorey drit that orrespond to three perormane levels, immediate oupany (IO, lie saety (LS, and ollapse prevention (CP. Table presents the medians o max assoiated with these limit states aording to FEMA 56 (FEMA. Table. Parameters used or estimating apaity Parameter Limit state Interstorey drit limit (% IO Ĉ (% LS CP Results o the ragility urves are depited in Figure 6. Figure 6 shows the 95% onidene bounds on all sampled rame model ragilities, median ragility and average CQ model rame ragilities. Table gives the median and orresponding ratile lognormal distribution parameters ( Sˆ C ( g and logarithmi standard deviation. Figure 6. The 95% onidene bounds on all sampled rame model ragilities, median ragility and average CQ model rame ragility Table. Fragility parameters Perentile Sˆ C (g ξ IO LS CP IO LS CP Average CQ model Figure 6 and Table show that median ragility o sampled rame and the average CQ model ragility are bounded between the 95% onidene bound or all limit states. The median spetral apaity omputed using the sampled strutures ragility urve is very lose to the average CQ strutural model apaity. It an also be noted that unertainty in the ragility untion inreases aross the limit states, rom IO to CP. The unertainty in the ragility o CP is signiiantly less in the lower probabilities that at the higher probabilities. The median ragility and average CQ model ragility do not show muh variation, however the median ragility is below the average CQ model ragility at low umulative probabilities and above at high umulative probabilities. 7

8 7 DISCUSSION AND CONCLUSIONS A six storey reinored onrete rame designed or Vanouver, Canada was used in this study. Three group o 5 ground motion reords representative o three levels o A/V range is used. Eah group is saled to math the target spetrum o %, 5% and % exeedane in 5 years in the Vanouver region. The material and strutural detailing unertainty is onsidered and eah unertain parameter has three levels, suh as {poor, average and good}. The dierent ombinations o the unertain parameters are used to generate dierent strutures. The maximum interstorey drit max obtained rom nonlinear time history analysis o the rames was onsidered as a response parameter, and the spetral aeleration at the undamental strutural period S a (T was onsidered as an intensity measure to develop the PSDM. The PSDM is onvoluted with apaity o the struture to generate the ragility urves. The results showed that the PSDM parameters a, b and β θ max Sa(T has onsiderable dependene in CQ and the CoV is nearly or above % or all three parameters. The ragility urves obtained or the rame show larger variability, whih depends on the limit state. The median spetral apaity omputed using the sampled strutures ragility urve is very lose to the average CQ strutural model apaity. Preliminary analysis showed that the PSDM and ragility are quite sensitive to CQ. This subjet, however, is still under investigation by this authors. REFERENCES: Cornell, A.C., Jalayer, F. & Hamburger, R.O.. Probabilisti basis or SAC ederal emergeny management ageny steel moment rame guidelines. Journal o Strutural Engineering, 8( Dimova, S.L. & Negro, P. 5. Inluene o onstrution deiienies on the seismi response o strutures, Earthquake Engineering and Strutural Dynamis, Dimova, S.L. & Negro, P. 6. Assessment o seismi ragility o strutures with onsideration o the quality o onstrution, Earthquake Spetra, ( Elnashai, A.S.. Analysis o the damage potential o the Koaeli (Turkey earthquake o 7 August 999. Engineering Strutures, FEMA (Federal Emergeny Management Ageny.. Prestandard and Commentary or the Seismi Rehabilitation o Buildings, FEMA Report 56, Washington, D.C. Lu, Y., Hong, H., Carydis, P.G. & Mouzakis, H.. Seismi perormane o RC rames designed or three dierent dutility levels, Engineering Strutures, Mander, J.B., Priestley, J.N. & Park, R Theoretial stress strain model or onined onrete. ASCE Journal o Strutural Engineering, ( MKenna, F., Fenves, G.L., Jeremi, B. & Sott, M.H. 7. Open System or Earthquake Engineering Simulation, Meli, R. & Aloer, S.M.. Implementation o strutural earthquake-disaster mitigation programs in developing ountries. ASCE Natural Hazards Review, 5( 9-9. Naumoski, N., Saatioglu, M., Lin, L., & Amiri-Hormozaki, K. 6. Evaluation o the eets o spetrumompatible seismi exitations on the response o medium-height reinored onrete rame buildings. Canadian Journal o Civil Engineering, ( -9. NRCC. 5. National building ode o Canada 5. Institute or Researh in Constrution, National Researh Counil o Canada, Ottawa, Ont., Canada. Pampanin, S., Calvi, G.M. & Morrati, M.. Seismi behaviour o RC beam olumn joints designed or gravity loads, In Proeedings o the th European Conerene on Earthquake Engineering, Elsevier, paper 76. Sezen, H., Whittaker, A.S., Elwood, K.J. & Mosalam, K.M.. Perormane o reinored onrete buildings during the August 7, 999 Koaeli, Turkey earthquake, and seismi design and onstrution pratie in Turkey, Engineering Strutures, 5. Tesamariam, S. & Saatioglu, M. 8. Risk-based seismi evaluation o reinored onrete buildings. Earthquake Spetra, (