Lecture 13 Building Populations
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Dan Abrams + Magenes Course on Masonry

Dan Abrams + Magenes Course on Masonry

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  • 1. Seismic Design and Assessment of Seismic Design and Assessment of Masonry Structures Masonry Structures Lesson 13: Assessing Seismic Risk across Populations of Unreinforced Masonry Buildings Notes Prepared by: Daniel P. Abrams Willett Professor of Civil Engineering University of Illinois at Urbana-Champaign October 28, 2004 Masonry Structures, lesson 13 slide 1 A Methodology to Assess Seismic Risk for Populations of Unreinforced Masonry Buildings Ömer O. Erbay Ph.D. Advisor: Daniel P. Abrams University of Illinois at Urbana-Champaign, 2003 Masonry Structures, lesson 13 slide 2
  • 2. Research motivation August 17, 1999, Kocaeli EQ, Turkey, M=7.4 ~ 50,000 injuries • Awareness ~ 250,000 homeless • Preparedness 3-6.5 billion $ • Mitigation • Consequences Picture taken from Hurriyet Press, 1999 Decision makers: City officials, building owners, insurance companies Need: Simple and rapid assessments of seismic damage, economic loss and risk across their regions Masonry Structures, lesson 13 slide 3 Inventory Sample from NOVA Digital Systems, Inc. Masonry Structures, lesson 13 slide 4
  • 3. Building specific damage estimates Typical steps P • Identify building configuration f’m and structural frame P • Estimate variation in material L-shaped 2-story qf properties and load levels • Represent hazard char. at the building site • Calculate building response variation Exceedence, % Probability of Response variation • Estimate building damage state 0.3g 0.8g Sa 0.3g 0.8g Sa Masonry Structures, lesson 13 slide 5 Loss from damage curves Rep. Cost Ratio Loss, Exceedence, % Probability of + Hazard level, Sa NO-IO IO-LS LS-CP CP-TC Damage (Rep. Cost Ratio) Loss, Hazard level, Sa For a defined Sa level Masonry Structures, lesson 13 slide 6
  • 4. Regional versus building specific loss Building Specific = Lossi | Hazard Level = Sai Loss Lossi = RCRi x κA fns Σ Expected Building Regional = Specific Loss for all buildings Loss i in the region Masonry Structures, lesson 13 slide 7 Regional risk assessment Scenario Based Expected Seismic Risk = Regional X Prob Defined Hazard Loss Total Seismic Risk = Σ for all possible Scenario Based Seismic Risk scenarios Masonry Structures, lesson 13 slide 8
  • 5. The total loss/risk concept Building Loss Individual 49% 14% 57% 55% 33% 60% 57% 75% 14% Cumulative building Loss (Total Loss) 8% Actual 3% Estimate 21% Relative 9% 80% Error 19% 12% 33% Masonry Structures, lesson 13 slide 9 The total loss/risk concept: Mathematical Probability Let, 2σL Seismic loss in a building represented by a random variable, L µL ∑ Li Total Regional Loss, L = Loss, TRL all bldgs Correlated, ρij = 1.0 µ TRL = ∑ µL i δ TRL = δ L σ TRL = ∑ σ L + ∑ ∑ ρijσ L σ L 2 2 i i j Uncorrelated, ρij = 0.0 σ TRL 1 δ TRL = δ TRL = δL µ TRL n Masonry Structures, lesson 13 slide 10
  • 6. The need: Sensitivity investigations • Investigate the sensitivity of regional risk/loss estimated on regional and building specific parameters that are observed to be important in past earthquakes. Hazard representation A rational approach to estimate building damage states Building population Masonry Structures, lesson 13 slide 11 Hazard representation: Ground motion selection A suite of 18 ground motions • Magnitude = 6.1 – 7.4 • Distance = 1 – 70 km • Soil type = A – D (USGS soil categorization) • PGA/PGV = 0.56 – 3.33 g.s/m • Scaled up and down to represent different levels of hazard Masonry Structures, lesson 13 slide 12
  • 7. Categorization of ground motions High Medium Low PGA PGA PGA = 1.4-3.3 g.s/m = 0.8-1.4 g.s/m < 0.8 g.s/m PGV PGV PGV vs = 360 m/s vs = 180-360 m/s vs < 180 m/s Near field, Rock Stiff – Medium Stiff Far field, Soft 0.5 0.5 0.5 Sa, g Sa, g Sa, g 0 0 0 0 1 2 0 1 2 0 1 2 Period, s Period, s Period, s Masonry Structures, lesson 13 slide 13 Analytical modeling Out-of-plane Wood walls diaphragm In-plane walls Lumped mass and lumped stiffness model Story Shear Story Shear Story Disp. Story Disp. Sliding Rocking Masonry Structures, lesson 13 slide 14
  • 8. Analytical modeling nxj piers side yi side yj twx side xj Shaded Area Shaded Area nyi piers nyj piers αx = αy = Floor Area Lpy Floor Area Lpx x y side xi nyi can be different than nyj twy nxi piers nxi = nxj = nx hs hpx hs hpy Masonry Structures, lesson 13 slide 15 Analytical modeling: Wall properties Em A f k xi, j = 0.1α x hpx Wall Stiffness = nyi, jEm A f k yi, j = 0.2α y nyi + nyj hpy Lpx ,y Rocking Hsrx, y = 0.9 Pfx , y hpx , y Wall Strength = ⎛ 3 Af ⎞ Sliding Hssx,y = ⎜ α x , yτ c + µ sld ⎟Pfx , y ⎜ 8 Pfx , y ⎟ ⎝ ⎠ Masonry Structures, lesson 13 slide 16
  • 9. Analytical modeling: Diaphragm stiffness Inertia force on the diaphragm Lx αd = Ly ∆d Assumed deformation Ly k dx = 4Gdα d shape 1 k dy = 4Gd R R αd Lx Masonry Structures, lesson 13 slide 17 From response to damage state: In-plane Interstory Drift ∆ x i + 1 − xi ∆ = hs hs xi+1 hs ⎛∆⎞ xi max⎜ ⎟ ⎜h ⎟ ⎝ s⎠ Masonry Structures, lesson 13 slide 18
  • 10. From response to damage state: Out-of-plane P P Excitations coming tw 4 from diaphragms tw 2 hs Ww Ww Ww O O R=P+Ww R=P+Ww tw R=P+Ww tw 6 0.9t w 1 ⎛ tw ⎞ ⎡5 P 1 ⎤⎛ t ⎞ acr ,nlb = ⎜ ⎟g acr ,lb = ⎢ + ⎥ ⎜ w ⎟g ⎜ ⎟ 3 ⎜ hs ⎟ ⎝ ⎠ ⎣ 6 Ww 3 ⎦ ⎝ hs ⎠ Masonry Structures, lesson 13 slide 19 From response to damage state: Out-of-plane Vt H ∆ tw ⎛ W ⎞ 0.9 ⎜P + w ⎟ H Vt − Vb hs ⎝ 2 ⎠ hs hs Pµk Vt + Vb t 2 0.45 w Ww hs Vb tw 2 tw ∆ ⎛ Pµ s ⎞ ⎡ P ⎛ 3 t2 ⎞ t2 ⎤ acon = ⎜ ⎜ W 2 ⎟g ⎟ PEf ,lb = Ww ⎜ 0.9 w + µk t w ⎟ + 0.45 w ⎥ ⎝ w ⎠ ⎢ ⎜ ⎟ 2 ⎢ Ww ⎣ ⎝ 4 hs ⎠ hs ⎥ ⎦ KEw = 1 Ww 2 12 g Vt + Vb 2 ( ) PEf ,nlb = Ww ⎡ ⎢ t2 ⎤ 0.45 w ⎥ 2 ⎣ hs ⎦ Masonry Structures, lesson 13 slide 20
  • 11. Damage state assignment In-plane, IP, damage state Out-of-plane, OP, damage state (based on interstory drift) (based on floor accelerations and velocities) IO LS CP TC IO CP TC 0.1% 0.6% 1.0% 2.0% Crk. Col. NLB Col. LB Wall Wall Final Damage = Higher of in-plane State and out-of-plane Masonry Structures, lesson 13 slide 21 From damage state to loss quantification 100 Probability, % Adopted from Abrams 75 and Shinozuka, 1997 50 25 0 0 0-1 1-10 10-30 30-60 60-100 Replacement cost ratio, % None Intermediate Medium Heavy Building replacement cost ratio for each damage state NO-IO IO-LS LS-CP CP-TC >TC 0% 2% 13% 66% 100% Masonry Structures, lesson 13 slide 22
  • 12. Investigated parameters Primary, building Primary, regional • Number of stories, ns • Ground motion category, High, Medium, Low • Floor area, Af • Size and type of building • Floor aspect ratio, αd population • Story height, hs Secondary, building • Wall density, αw • Average length of • Pier height ratio, αh openings, Lo • Distributed floor load, qf • Spacing between gravity • Elastic modulus, Em load carrying members, Ls • Shear modulus, Gd Masonry Structures, lesson 13 slide 23 Field surveys City Source # of bldgs. Parameters City of Urbana Urbana, IL and Wu, 2001 54 ns , A f , α d , (αh , Lo ) Personal invest. Wu, Crelling & ns , A f Carbondale, IL 72 Olshansky, 2001 Abrams & Memphis, TN Shinozuka, 1997 517 ns , A f , (αh , Lo , α d ) San Francisco, CA Holmes et. al., 2007 ns , A f , hs , α d 1990 Masonry Structures, lesson 13 slide 24
  • 13. Parameter distributions from field surveys 80 60 Percentage Percentage 40 30 0 0 1 2 3 4 5 6 <1.5 1.5-4 4-7 7-10 10-15 >15 Number of Stories, n s Floor Area, Af, (1000 ft2) 80 40 Percentage Percentage 40 20 0 0 <12 12-16 >16 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 4-4.5 >4.5 Story height, h s, (ft) Floor Aspect Ratio, α d Urbana, IL Memphis, IL This study Carbondale, IL San Francisco, CA Masonry Structures, lesson 13 slide 25 Assigned distributions 40 3 Probability, % Probability, % 2 20 1 0 0 1 2 3 4 5 6 0 5000 10000 15000 Number of Stories, ns Floor Area, Af, (ft2) 10 60 Probability, % Probability, % 40 5 20 0 0 8 12 16 20 0 1 2 3 4 Story height, hs, (ft) Floor Aspect Ratio, α d Masonry Structures, lesson 13 slide 26
  • 14. Sensitivity investigations Regional • Population size • Ground motion category Building specific • First order • Second order Masonry Structures, lesson 13 slide 27 Framework for sensitivity analyses Narrow Prob. Range {A}NR {A} , Ai {A} {A}NR c1 c2 c3 cn Prob. Full Range Randomize {A}FR Ai {A}FR L c1 H Diff. or STD Total Norm Reg. Loss L c2 H L c3 H L Hazard Level Hazard Level cn H Masonry Structures, lesson 13 slide 28
  • 15. Sensitivity investigations: Population size 15 Number of generated building populations 10 10 10 10 5 5 3 2 2 0 5 10 25 50 100 250 500 Number of buildings Masonry Structures, lesson 13 slide 29 Sensitivity investigations: Population size 1.0 1.0 TNRL TNRL 0.5 0.5 5 10 0.0 0.0 0 1 2 3 0 1 2 3 Sa, g Sa, g 1.0 1.0 TNRL TNRL 0.5 0.5 25 50 0.0 0.0 0 1 2 3 0 1 2 3 Sa, g Masonry Structures, g Sa, lesson 13 slide 30
  • 16. Sensitivity investigations: Population size 1.0 100A Total Normalized Regional Loss 100B 100C 0.5 250A 250B 500A 500B 0.0 0 1 2 3 Sa, g Masonry Structures, lesson 13 slide 31 Sensitivity investigations: Population size 0.3 0.3 0.3 Difference 5 10 25 0.0 0.0 0.0 -0.3 -0.3 -0.3 0 1 2 3 0 1 2 3 0 1 2 3 0.3 0.3 0.3 Difference 50 100 250 0.0 0.0 0.0 -0.3 -0.3 -0.3 0 1 2 3 0 1 2 3 0 1 2 3 Sa, g Sa, g Sa, g Masonry Structures, lesson 13 slide 32
  • 17. Sensitivity investigations: GM category 1.0 Total Normalized Regional Loss Mean High 0.5 Med Low Pop size = 250 0.0 0 1 2 3 Sa, g the mean curve 0.2 Difference with High 0.0 Med Low -0.2 0 1 2 3 Sa, g Masonry Structures, lesson 13 slide 33 Sensitivity investigations: First order TNRL or ERCR 1.0 1.0 1.0 0.5 0.5 0.5 ns αd αw 0.0 0.0 0.0 0 1 2 3 0 1 2 3 0 1 2 3 Sa, g Sa, g Sa, g TNRL or ERCR 1.0 1.0 1.0 0.5 0.5 0.5 hs Em Af 0.0 0.0 0.0 0 1 2 3 0 1 2 3 0 1 2 3 Sa, g Sa, g Sa, g Pop. Size = 50 Unbiased 10% 90% Masonry Structures, lesson 13 slide 34
  • 18. Sensitivity investigations: First order Par. Max Diff. 1.0 TNRL or ERCR 1.0 ns 22% 0.5 0.5 αd 18% αh qf αw 14% 0.0 0.0 0 1 2 3 0 1 2 3 hs 12% Sa, g Sa, g Em 11% 1.0 1.0 TNRL or ERCR Af 10% 0.5 0.5 αh 7% Lo Gd qf 6% 0.0 0.0 0 1 2 3 0 1 2 3 Lo 6% Sa, g Sa, g Masonry Structures, lesson 13 slide 35 Gd 4% Sensitivity investigations: Second order Probability Prob. A1 = A2 = A3 = 1.0 A1 Prob. A2 up 30 Prob. med 40 A3 Range Upper Lower Range Medium Range low 30 Original distribution and associated Distribution segments for cumulative distribution sub-intervals Masonry Structures, lesson 13 slide 36
  • 19. Sensitivity investigations: Second order Parameter Range 1 Range 2 Range 3 GM category High Medium Low ns 1 story 2-3 stories 4-5-6 stories αd 1.0-1.75 1.75-2.75 2.75-3.5 αw (%) 50-62 62-78 78-90 hs (ft) 9.0-12.5 12.5-14.8 14.8-20.0 Em (ksi) 500-710 710-990 990-1200 Af (ft2) 1000-2300 2300-4750 4750-30000 Total # of cases = 37 = 2187 Investigated cases = 432 Masonry Structures, lesson 13 slide 37 Sensitivity investigations: Second order 1.0 1.0 4 1 9 TNRL or ERCR TNRL or ERCR R 8 C 5 R 2 10 E 0.5 Scatter r 0.5 o 6 3 L R N 7 T 0.0 0.0 0 0 1 2 2 3 0 1 2 3 Sa, g Sa, g Sa, g Masonry Structures, lesson 13 slide 38
  • 20. Sensitivity investigations: Second order GM ns αd αw hs Em Af Group1 Group2 Group3 Group4 Group5 Group6 Group7 Group8 Group9 Group10 Uniform Range 1 Range 2 Range 3 Masonry Structures, lesson 13 slide 39 The methodology: Main steps Building Inventory Soil Variation Seismic Hazard Part I Data Collection A D Calculate Part II B C Total Regional Grouping Loss, TRL Part III Seismic Risk = TRL x Probability(Hazard) Risk estimation Masonry Structures, lesson 13 slide 40
  • 21. The methodology: Loss calculation Regional grouping Further sub-grouping of buildings for hazard variation A D B C Loss, (Rep. Cost Ratio) Hazard level, Sa Masonry Structures, lesson 13 slide 41 Test-bed application: S. G. D. Puglia, Molise Molise earthquakes Oct & Nov 2002 Mw = 5.7 PGA ~ 0.36g Epicenter ~ 5km Population ~ 1160 # of Bldgs ~ 100-150 %URM ~ 45-65% Masonry Structures, lesson 13 slide 42
  • 22. Test-bet application Part I Data collection Masonry Structures, lesson 13 slide 43 Part I: Hazard Historic seismicity Masonry Structures, lesson 13 slide 44 Picture taken from Mola et. al. 2002
  • 23. Part I: Hazard Figure taken from Mola et. al. 2002 Masonry Structures, lesson 13 slide 45 Part I: Soil variation Figure taken from SSN’s web site, 2002 Masonry Structures, lesson 13 slide 46
  • 24. Part I: Building inventory C.O ..M Picture taken from the site engineer Aerial photo of the region after the events Masonry Structures, lesson 13 slide 47 Part I: Building inventory Map taken from the site engineer Investigated buildings Red tagged buildings Green tagged buildings Collapsed buildings Masonry Structures, lesson 13 slide 48
  • 25. Part I: Parameter distributions Percentage 60 60 Percentage 30 30 0 0 5 0 5 0 5 .5 1. 2. 2. 3. 3. >3 0- 5- 0- 5- 0- 1 2 3 4 1. 1. 2. 2. 3. ns αd Percentage Percentage 50 90 25 45 0 0 0 60 70 80 90 0 <5 >9 <12 12-16 >16 - - - - 50 60 70 80 αw hs (ft) 40 Percentage 20 0 <5 5-10 10-15 15-20 20-25 25-30 30-35 >35 Af (100 ft2) Masonry Structures, lesson 13 slide 49 Test-bed application Part II Grouping Masonry Structures, lesson 13 slide 50
  • 26. Part II: Soil variation under building population Buildings are primarily located over artificially filled regions Masonry Structures, lesson 13 slide 51 Part II: Building parameters and GM category GM ns αd αw hs Em Af GM ns αd αw hs Em Af G3 G3 G7 G6 G1 continued G3 G3 G1 G3 Range 1 Range 2 Range 3 Masonry Structures, lesson 13 slide 52
  • 27. Part II: Total regional loss estimate 1.0 TNRL or ERCR 3 Sa = 0.36g x 2.0 = 0.72g 0.5 6 1 7 TNRL = 63.1% 0.0 0 1 2 3 Sa, g A B C D Group # 1 3 6 7 Value, % 6.5 79.7 10.2 3.6 ERCR 0.82 0.60 0.85 0.45 Loss, % 5.3 47.8 8.4 1.6 Masonry Structures, lesson 13 slide 53 Test-bed application Part III Risk estimation Masonry Structures, lesson 13 slide 54
  • 28. Part III: Risk estimate • Assuming earthquake occurrence follows a Poison’s distribution Tr = 500 years Seismic Risk = TRL x P(n = 1 | Sa = 0.72g) 1 ⎛ 1 ⎞ ⎜ ⋅ 1 year ⎟ ⎛ − 1 ⋅1 year ⎞ = 63.1 × ⎝ 500 ⎠ e⎜ 500 ⎝ ⎟ ⎠ = 12.5% / year 1! Masonry Structures, lesson 13 slide 55 Observed damage: Categorization EMS-98 Damage Scale FEMA-356 Damage Categories Grade 1: NO - IO Grade 2: IO - LS Grade 3: LS Grade 4: CP Grade 5: TC Masonry Structures, lesson 13 slide 56
  • 29. Observed damage: In-plane Masonry Structures, lesson 13 slide 57 Observed damage: Soft-story and sliding Masonry Structures, lesson 13 slide 58
  • 30. Observed damage: Out-of-plane Masonry Structures, lesson 13 slide 59 Observed damage: Load bearing wall failure Masonry Structures, lesson 13 slide 60
  • 31. Observed damage: Undamaged buildings Masonry Structures, lesson 13 slide 61 Damage Distribution 40 Masonry Buildings, % Percentage of 20 0 IO - LS LS - CP CP - TC > TC Damage Computed normalized loss ~ 43% Estimated loss = 63% Masonry Structures, lesson 13 slide 62
  • 32. Summary • To develop a regional risk/loss assessment methodology for unreinforced masonry buildings through rational and systematic investigation of building and region specific parameters. • Sensitivity investigations on building and region specific parameters are conducted around the concept of total loss/risk. Masonry Structures, lesson 13 slide 63 Conclusions • Hazard-loss relationships that are unacceptably scattered for individual building loss calculations can be utilized to estimate regional losses. • Number of stories, floor aspect ratio, wall density, and ground motion categories are the most significant parameters in regional loss estimates of unreinforced masonry buildings Masonry Structures, lesson 13 slide 64
  • 33. Conclusions • There exist an essential need for collection of complete damage data from real events. In data collection process, together with building damage states, building parameters that are found to be significant for loss estimates have to be collected. Masonry Structures, lesson 13 slide 65