Screening & Retrofit Prioritization of Truss Bridges

Transcription

1 Screening & Retrofit Prioritization of Truss Bridges Roupen Donikian, P.E. Sr. Associate, T.Y. Lin International Seismic Retrofit of Truss Bridges A Pilot Training Course December 12-14, 2005 St. Louis, Missouri Contents Screening of Truss Bridges Prioritization of SC Truss Bridges Seismic Rating Parameters for SC Truss Bridges Method of Indices Method of Expected Damage 1

2 Screening of Truss Bridges Identify Inventory of N Bridges SC Trusses Essential Bridges Compile group: G {B 1,, B N } Compilation of Basic Information (for each bridge) Structural characteristics Soil conditions & site hazard Performance level desired Importance of link in network Prioritization of SC Truss Bridges Pertinent Factors Function of bridge as a symbol to community Importance Physical condition Serviceability Service life category 2

3 Prioritization for Seismic Retrofit Prioritization Basis G {B 1,.., B N } Group of N bridges in a region $ M Resources allocated for rehabilitation of N bridges Prioritization Index: {P 1,., P N } Various Methods Subjective Computational Prioritization Algorithms Method of Indices: P (R, I, NSO) R Rank (function of seismic vulnerability) I Importance (function of ADT, cost, etc.) NSO Non-seismic & Other Factors Method of Expected Damage: P (R, H LOSS, NSO) R Rank (function of direct loss due to damage) H LOSS Indirect Loss NSO Non-seismic & Other Factors 3

4 Method of Indices P(R,I,NSO) α 1 R + α 2 I + α 3 NSO V E Non-Seismic & Other Factors a [r carried + r crossed + u + t ] + b [ $ retro / $ repl ] R, I, NSO [0,,100] α i relative weight; Σ α i 1.0 P [0-100] Rank α 1 R + α 2 I + α 3 NSO V E E 10 F v S 1 ; F v site coefficient S 1 Sa (T1sec) V max { V 1,V 2 } Vulnerability Index reflecting susceptibility to connection & bearing failure: 0 5 : low-to-moderate 6 10: moderate-to-high ~ Bridge Inspection ~ Vulnerability Assessment Observation Existing Data Base / Expert Input Analysis Vulnerability Index based on structural and foundation sub-systems susceptibility: 0 5 : low-to-moderate 6 10: moderate-to-high V 2 Σ w i V 2,i 4

5 Vulnerability Bridge over Trinity River, Near Livingston, Texas February 04 Importance Factor α 1 R + α 2 I + α 3 NSO r 1, r County Arterial County Hwy Local Access r 1 (d 1 /d ref ) r 2 (d 2 /d ref ) d 1, d 2 detour distances a [r carried + r crossed + u + t ] + b [ $ retro / $ repl ] scale factors costs ADT / ADT ref utility factor 1 - if utilities carried by bridge 0 - if no utilities on bridge 5

6 Non-Seismic & Other Factors α 1 R + α 2 I + α 3 NSO Non-Seismic & Other Factors does not lend itself to direct enumeration owner agency criteria assumed on relative basis Priority Index, Method of Indices P(R,I,NSO) α 1 R + α 2 I + α 3 NSO R, I, NSO [0,,100] α i relative weight; Σ α i 1.0 P [0-100] e.g. R I NSO α 1 1 α o α 2 1 α o α 3 1/4 α o Σα i 2.25 α o α o 1/2.25 6

7 Method of Expected Damage P(R,H LOSS,NSO) α 1 R + α 2 H LOSS + α 3 NSO R (B LOSS ) Direct Loss Parameter Indirect Loss Parameter Non-Seismic & Other Factors R, H LOSS, NSO [0,,100] α i relative weight; Σ α i 1.0 P [0-100] Rank α 1 R + α 2 H LOSS + α 3 NSO R (B LOSS ) 100 B LOSS / max {B LOSS of group} B LOSS U x RCR T Replacement cost Total repair cost ratio; function of 5 damage states: DS1 No Damage DS2 Slight Damage DS3 Moderate Damage DS4 Extensive Damage DS5 Collapse 7

8 Rank (cont d) RCR T Σ i RCR i P[DSi Sa(1)] Total repair cost ratio Sa(1) Sa at 1-sec period RCR i Repair cost of Damage State i, DSi P[DSi Sa(1)] Probability of DSi occurrence, for a give Sa(1) obtained from fragility curves {Sa(1) /Ai} -1.7 / βc Ai Median spectral acceleration to cause damage state i β c randomness & uncertainty parameter 0.6 recommended Rank (cont d) Damage State Damage Type Ai (g) None Slight Moderate Extensive Collapse Fragility Curves example P[D > DSi Sa(1)] DS1 (A g) DS2 (A g) DS3 (A g) DS4 (A g) DS5 (A5 1.0 g) Sa(1) (g) 8

9 Rank (cont d) Fragility Curves Load paths and potential damage mechanisms Limit states to characterize 5 damage states (DSi) R 100 B LOSS / max { B LOSS for group } Indirect Loss α 1 R + α 2 H LOSS + α 3 NSO Indirect Loss Factor does not lend itself to direct enumeration owner agency criteria assumed on relative basis 9

10 Non-Seismic and Other Factors α 1 R + α 2 H LOSS + α 3 NSO Non-Seismic & Other Factors does not lend itself to direct enumeration owner agency criteria assumed on relative basis Priority Index, Method of Expected Damage P(R,H LOSS,NSO) α 1 R + α 2 H LOSS + α 3 NSO R, H LOSS, NSO [0,,100] α i relative weight; Σ α i 1.0 P [0-100] e.g. R H LOSS NSO α 1 1 α o α 2 1/2 α o α 3 1/3 α o Σα i 1.83 α o α o 1/

11 Example 1: Method of Indices Group of 10 bridges: α o ; α 1 1 α o α 2 1 α o α 3 1/4 α o Bridge R I NSO P B B B B B B B B B B Example 2: Method of Expected Damage Group of 10 bridges: α o ; α 1 1 α o α 2 1/2 α o α 3 1/3 α o Bridge R H LOSS NSO P B B B B B B B B B B