PPEEEERR A Survey of Bridge

Practitioners to Relate Damage to Closure

Keith Porter

Bridge Testbed Meeting 21 Oct 2003

Bridge DVs

DVs measure performance in terms of collapse closure repair duration speed limitations load limitations other?

Small pilot study of current practice

Probabilistic relationship between what bridge inspectors see and what decision they make What they would do, not should do

Cases with inconclusive safety evidenceBridge category: “like Humboldt” AASHTO-Caltrans girder bridge Multi-span, single-column bent Modest traffic demand

If successful, I-880, other categories later

25 Feb 2002 Caltrans meeting

How do post-earthquake inspectors characterize performance?

(What are the DVs?)

What are the possible outcomes of a post-earthquake inspection?

(What values can DV take on?)

What evidence do inspectors consider when making their performance evaluation?

(What are the DMs?)

How is damage evidence assessed to result in a decision?

(How is DV related to DM?)

DVsPrimary concern: collapse potential DV1: collapsed, not collapsed

Post-earthquake, if not collapsed, inspectors have 2 alternatives: open or closed; if open, keep open? DV2: inspector closure decision: if not collapsed, open or

close?

Assessment protocol 1. Inspectors report inspections to Caltrans EOC2. EOC compiles database of observed damage; bridge open

or closed; recommended repair, repair cost estimate. DV2 = “closed” subdivided into closed briefly, closed longer DV3: cost3. Inspectors & traffic engineers decide which routes to open

first. Can important be opened after shoring? 4. Construction engineers or design engineers design repairs

DMs

SettlementMisalignmentLarge roadway gapsPhysical evidence of structural distress Permanent deformation Plastic hinging Fracture or buckling of flexural steel X-cracking and other evidence of shear

failure

Qualitative DM-DV2 relationship

Can bridge stand up to live load?Likely to collapse in an aftershock?If there is any question of the capacity of the bridge, it is closedRepair vs. replacement: time is the deciding factor, not cost Cost is a less-important DV

Expert system in development If widely adopted, present results may

become outdated

Mean time, how to encode DM-DV practice

Surveying practitioners on DM-DV2

Decision Damage ↓

No closure Close 1-3 days

Settlement of approach

<1 in 1-3 in 3-6 in >6 in

<1 in 1-3 in 3-6 in >6 in

Vertical offset at abutment

<1 in 1-3 in 3-6 in >6 in

<1 in 1-3 in 3-6 in >6 in

(Thanks, Eberhard, Conte,Kunnath, Mahin, DesRoches)

DV2: inspector’s closure decision meaningful only for no collapse; doesn’t address cost

Survey form

Instructions Provide summary info Review the damage measures (2

blanks) Consider the decision values (2

blanks) Judge the max DM consistent with DV2

Comment

Survey form (ver. 1) summary info

NameAgency or affiliationArea of expertise Geotech, design, inpect/maint, traffic

Bridge category (Humboldt)Level of familiarity (1-5)

DMs (rows; 2-4 ranges)Settlement of approach Vertical offset at abutment Horizontal offset at abutment Vertical offset at expansion jt Horizontal offset at expansion jt Max. beam or column flexural crack width

Max. beam or column shear crack width Concrete beam or column spalling (y/n)Beam or column rebar buckling, fracture, pullout (y/n)Shear key or backwall shear cracking or spalling (y/n)

DV2 values (ver.-1 columns)

No closureClose 1-3 daysClose > 3 daysReduced speed

Not examining closure duration as continuum—not an issue for the

judgment of the inspector

Administering survey1st Tri-center Workshop on Earthquake Loss Estimation Methodologies for Transportation Systems; June 200315-20 DOT engineers from around USAdministered the survey in 2 of 3 breakouts12 responses6 self-rate as 4 or 5 on 1-5 scale

Is 6 adequate?

Analyzing survey

DM No closure Close 1-3 days Close > 3 days Reduced speed<1 in 1 0 0 01-3 in 3 1 0 33-6 in 2 3 1 2>6 in 0 1 3 0no response 0 1 2 1

DM1: Settlement of approach

4 of 6 say, “If DM1 > 3 in, then close ≥ 1 day”

1 of 6 say, “If DM1 > 1 in, then close ≥ 1 day”

6 of 6 say, “If DM1 > 6 in, then we would close at ≥ 1 day”

Let X = capacity to resist ≥ 1 day closure in terms of DM1

X = 3.67 in. lnX = 1.17X = 1.97 in. lnX = 0.50

Creating a fragility function

0.00

0.25

0.50

0.75

1.00

0 2 4 6 8 10

Approach settlement, in.

P[≥

1 d

ay c

losu

re |

set

tlem

ent]

LN(X=3.7 in; lnX=0.5)

Results

Parameters of 13 functions values 0.3 ~ 0.7

Table 1. Parameters of DM-DV relationships

DM1: Settlement of approach, in. Close at least briefly Close at least 3 days X 3.67 5.50 X 1.97 3.14 X 0.54 0.57 x̂ 3.23 4.78 X 0.50 0.53

DM2: Vertical offset at abutment, in. Close at least briefly Close at least 3 days X 3.75 5.50 X 1.50 3.14 X 0.40 0.57 x̂ 3.48 4.78 X 0.39 0.53

2

ˆln| i

X

x xP DV dv DM x

Combining results for different DMs

Problem: Survey did not test vector DMs How to combine P[DV | DMi]?

Possibilities1. Independent decisions?

P[DV ≥ dvj|DM] = 1 – Πi(1 – P[DV ≥ dvj|DMi])

2. Worst DM controls? P[DV ≥ dvj|DM] = maxi(P[DV ≥ dvj|DMi])

Must still account for correlation in DMCheck w/survey using sample vectors DM?

Problems & next stepsLarger survey: 2nd round in ~Nov; web survey ~DecRevise DVs closed >0, >3, >30 days to regular

traffic ditto, emergency vehicles

Rephrase questions: “What is the minimum DM causing this decision?”Include picturesExplore I-880 DM-DV as wellTest clarity of questions

Discussion

DMs & their rangesDitto, DVsCombination of p[DV2] values

Combination with other DVs

DM2: Vertical offset at abutment, in. Close at least briefly Close at least 3 days X 3.75 5.50 X 1.50 3.14 X 0.40 0.57 x̂ 3.48 4.78 X 0.39 0.53

DM3: Horizontal offset at abutment, in. Close at least briefly Close at least 3 days X 6.00 7.00 X 3.29 3.90 X 0.55 0.56 x̂ 5.26 6.12 X 0.51 0.52

DM4: Vertical offset at expansion joint, in. Close at least briefly Close at least 3 days X 0.83 1.17 X 0.26 0.65 X 0.31 0.56 x̂ 0.80 1.02 X 0.30 0.52

DM5: Horizontal offset at expansion joint, in. Close at least briefly Close at least 3 days X 1.20 1.33 X 0.45 0.60 X 0.37 0.45 x̂ 1.12 1.22 X 0.36 0.43

DM6: Maximum beam or column flexural crack width, in. Close at least briefly Close at least 3 days X 0.078 0.156 X 0.051 0.063 X 0.66 0.40 x̂ 0.065 0.145 X 0.60 0.39 DM7: Maximum beam or column shear crack width, in.

Close at least briefly Close at least 3 days X 0.063 0.104 X 0.048 0.067 X 0.77 0.64 x̂ 0.049 0.088 X 0.69 0.59

Simulation of DVP[DV = dvj|DM] = 1 – P[DV ≥ dv1|DM] j=0

= P[DV ≥ dvj|DM] – P[DV ≥ dvj+1|DM] 1 ≤ j < n

= P[DV ≥ dvn|DM] j = n

FDV|DM(DV = dvn|dm) = j=1..n P[DV = dvj|DM]

u ~ U(0,1)DV* = F-1

DV|DM(u)