Crosscutting Topic 2 Bridge Impacts and DVs Keith Porter PEER Bridge Testbed Progress Meeting Richmond Field Station May 22, 2002

Objectives for 10:00-10:50 Impacts, DVs Inform modelers about DMs and DVs from other studies & from Caltrans Draft & formalize DMs and DVs? Identify implications for methodology Development needs

EDP, DM aspects of Caltrans Humboldt meeting Failure mode (DM)EDPCapacity Pile shearV at M max Seible pile tests UnseatingLongit. displ.Seat length Abutment slumping  (Caltrans inspectors?) Lap spliceM max, e steel M spall P/T pile TTT ult

DM and DV aspects of Caltrans I-880 Meeting Post-earthquake decision-making process 1.Inspectors assess safety of bridges 2.At EOC, compile database of bridge open/closed status, recs and cost of repair 3.Prioritize repairs with traffic engineers. If important routes are closed, can they be shored & opened? 4.Construction or design engineers design repairs

Straw Man: Suggested Means of Defining DVs and DMs Define performance DVs to model Caltrans’ implicit or explicit post-earthquake performance levels, i.e., p[PL|T] or p[PL|event] Define helper DVs: parameters that drive Caltrans’ repair & replacement decisions Define DMs as physical damages that drive determination of PL and post-earthquake decisions

Straw Man: PLs, DMs and DVs PLsDVsDMs PL 1 : OpenDV 1 : p[PL|T]DM 1 : residual vertical capacity PL 2 : Briefly closed to repair minor damage DV 2 : p[PL|event]DM 2 : residual lateral capacity PL 3 : Closed, shored, opened DV 3 : p[T repair |PL 4c ] DM 3 : abutment  PL 4,critical : Closed. Faster of repair/replace DV 4 : p[T replace |PL 4c ] DM 4 : expansion jt  PL 4,non-critical : Closed. Cheaper of repair/replace DV 5 : p[C repair |PL 4nc ] DV 6 : p[C replace |PL 4nc ]

Van Nuys Sensitivity Study Keith Porter PEER Bridge Testbed Progress Meeting Richmond Field Station 22 May 2002

Objectives Assess gross sensitivity of damage factor (DF) to uncertainty in basic random variables (X) Assess variability in each X i Assess sensitivity of DF to uncertainty in X i Illustrate with the Van Nuys testbed

Methodology, 1/3 Identify basic variables X T = [X 1, X 2,…X N ] in repair cost C = f(X) Assess E[X i ], Var[X i ] for i = 1, 2, … N Assess X i,50 = 50 th percentile of X i Assess X i,10 = 10 th percentile of X i Assess X i,90 = 90 th percentile of X i

Methodology, 2/3 1.Describe facility B as a collection of standard assembly types j = 1, 2, … N j with possible damage states d = 1, 2, … N j,d, each with uncertain capacity F j,d, and uncertain repair costs C j,d 2.Structural analysis : EDP = g(GM, B) 3.Damage analysis: for each assembly k, if EDP k > F i,d, then DM k ≥ d 4.Loss analysis: C = (1 + C OP )  j  d N j,d C j,d 5.Damage factor DF = C/RCN (RCN: replacement cost, new)

Methodology, 3/3 Calculate baseline C 0 = f(X 1,50, X 2,50, … X N,50 ) C i,10 = f(X 1,50, X 2,50,…X i,10,… X N,50 ): i = 1…N C i,90 = f(X 1,50, X 2,50,…X i,90,… X N,50 ): i = 1…N Swing i = |C i,90 – C i,10 | Sort X i by swing i & plot in a “tornado diagram”

Results: X i

Results: Tornado Diagram

Conclusions For this model & this building, assembly capacity and shaking intensity swamp other uncertainties Important uncertainties omitted, need study: –F-d model selection, R/C joint capacity, difference between field & lab fragility, repair method | damage state, nonunion vs. union, demand surge, … Tornado diagram depicts important RVs Model for UC Science Building? Bridges? Report: