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)
EDP
Capacity
Pile shear
V at Mmax
Seible pile tests
Unseating
Longit. displ.
Seat length
D
Abutment slumping
Lap splice
Mmax, esteel
(Caltrans
inspectors?)
Mspall
P/T pile T
T
Tult
DM and DV aspects of
Caltrans I-880 Meeting
1.
2.
3.
4.
Post-earthquake decision-making process
Inspectors assess safety of bridges
At EOC, compile database of bridge open/closed
status, recs and cost of repair
Prioritize repairs with traffic engineers. If
important routes are closed, can they be shored
& opened?
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
PLs
DVs
DMs
PL1: Open
DV1: p[PL|T]
DM1: residual vertical
capacity
PL2: Briefly closed to
repair minor damage
DV2: p[PL|event]
DM2: residual lateral
capacity
PL3: Closed, shored,
opened
DV3: p[Trepair|PL4c]
DM3: abutment D
PL4,critical: Closed. Faster
of repair/replace
DV4: p[Treplace|PL4c]
DM4: expansion jt D
PL4,non-critical: Closed.
DV5: p[Crepair|PL4nc]
Cheaper of repair/replace
DV6: p[Creplace|PL4nc]
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 Xi
• Assess sensitivity of DF to uncertainty in Xi
• Illustrate with the Van Nuys testbed
Methodology, 1/3
• Identify basic variables XT = [X1, X2,…XN] in
repair cost C = f(X)
• Assess E[Xi], Var[Xi] for i = 1, 2, … N
• Assess Xi,50 = 50th percentile of Xi
• Assess Xi,10 = 10th percentile of Xi
• Assess Xi,90 = 90th percentile of Xi
Methodology, 2/3
1.
2.
3.
4.
5.
Describe facility B as a collection of
standard assembly types j = 1, 2, … Nj with possible
damage states d = 1, 2, … Nj,d, each with
uncertain capacity Fj,d, and
uncertain repair costs Cj,d
Structural analysis : EDP = g(GM, B)
Damage analysis: for each assembly k,
if EDPk > Fi,d, then DMk ≥ d
Loss analysis: C = (1 + COP)SjSdNj,dCj,d
Damage factor DF = C/RCN
(RCN: replacement cost, new)
Methodology, 3/3
•
•
•
•
•
Calculate baseline C0 = f(X1,50, X2,50, … XN,50)
Ci,10= f(X1,50, X2,50,…Xi,10,… XN,50): i = 1…N
Ci,90= f(X1,50, X2,50,…Xi,90,… XN,50): i = 1…N
Swingi = |Ci,90 – Ci,10|
Sort Xi by swingi & plot in a “tornado diagram”
Results: Xi
Xi
Xi,10
X i,50
X i,90
0.11
(LA50, 0.52)
0.27
(LA50, 1.28)
0.58
(LA50, 2.74)
LA45, 1.10
LA50, 1.28
LA49, 1.26
0.87Mn
Mn
1.13Mn
Damping
2.4%
5.0%
7.6%
Force-def. multiplier
0.90
1.00
1.10
Assembly capacity
e lnxm 1.28
xm
e lnxm 1.28
xm and  from Table 4
Costs: unit cost
e lnxm 1.28
xm
e lnxm 1.28
xm and  from Table 5
0.15
0.175
0.20
Sa (g)
Ground motion
Mass
O&P
Comment
Spectral acceleration
(Record, scaling factor)
Record, scaling factor
Mn: nominal mass
Constant stiffness
CO&P of Equation 11
Results: Tornado Diagram
Assembly capacity
Sa
Ground motion record
Unit cost
Damping
F-d multiplier
Mass
O&P
0.00
0.25
0.50
Damage factor
0.75
1.00
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: www.peertestbeds.net/Crosscutting.htm