Transcript Fragility Functions for Bridges in Liquefied and Laterally Spreading Ground Scott J. Brandenberg, Jian Zhang, Pirooz Kashighandi, Yili Huo, Minxing Zhao October 8th, 2010

Fragility Functions for Bridges in
Liquefied and Laterally Spreading
Ground
Scott J. Brandenberg, Jian Zhang, Pirooz Kashighandi, Yili Huo, Minxing Zhao
October 8th, 2010
2010 El Mayor Cucapah Earthquake
2/25
Landing Road Bridge: 1987 Edgecumbe Earthquake
3
Berrill et al. (2001)
Distribution of Caltrans Bridge Construction Year
Data from
National Bridge Inventory
P (Damage State > ds)
Existing Fragility Functions (HAZUS)
1
0.8
0.6
0.4
ds4
ds5
0.2
0
0
10
20
30
Free-field Ground Displacements (inches)
Transportation Network Analysis
Highway Demonstration Project (PEER report) A. Kiremidjian et al. (2006)
Global Equivalent Static Analysis
Global Equivalent Static Analysis
Input Parameter Selection
Input Parameter
Span Length, Pre-1971
Span Length, Post-1971
Deck Width
Dead Load Stress
Pier Column Height
Concrete Strength in Pier Columns, f'c, Pre-1971
Concrete Strength in Pier Columns, f'c, Post-1971
Reinforcing Steel Tensile Strength in Pier Columns, f' c, Pre-1971
Distribution
Median
Truncated Normal
22m
Truncated Normal
36m
Delta
12.2m
Normal
9.1kPa
Truncated Normal
6.5m
Truncated Normal 25000kPa
Truncated Normal 28000kPa
10000kPa
10000kPa , 55000kPa
60000kPa
10000kPa , 55000kPa
60000kPa
10000kPa , 55000kPa
0.06
0.04
0.03
9.1kPa
0.012
0.015
0.0019
0.0048
1.10
0.007
0.006
0.005
1.5kPa
0.004
0.004
0.0008
0.0020
0.05
none
none
none
5.5kPa , 16kPa
none
none
none
none
none
Truncated Normal 300000kPa
Truncated Normal 400000kPa
Reinforcing Steel Tensile Strength in Pier Columns, f' c, Post-1971
Ratio of Axial Load to Pier Column Axial Capacity, Single-column bents
Normal
Ratio of Axial Load to Pier Column Axial Capacity, 2-column bents
Normal
Ratio of Axial Load to Pier Column Axial Capacity, 3-column bents
Normal
Vertical Dead Load Stress Exerted by Superstructure
Truncated Normal
Pier Column Longitudinal Reinforcement Ratio, r, Pre-1971
Normal
Pier Column Longitudinal Reinforcement Ratio, r, Post-1971
Normal
Pier Column Transverse Reinforcement Ratio, r, Pre-1971
Normal
Pier Column Transverse Reinforcement Ratio, r, Post-1971
Normal
f'c,confined / f'c,unconfined, Pre-1971
Normal
Upper Bound, Lower
Bound
Standard Deviation
13m
10m , 60m
18m
10m , 60m
0
none
1.5kPa
none
1.7m
2m , 20m
10000kPa
10000kPa , 55000kPa
f'c,confined / f'c,unconfined, Post-1971
Vertical Bearing Stress, Pre-1971
Vertical Bearing Stress, Post-1971
0.38m Diameter Precast Concrete Pile Flexural Capacity, Pre-1971
0.38m Diameter Precast Concrete Pile Flexural Capacity, Post-1971
0.61m Diameter CIDH Pile Flexural Capacity
0.61m Diameter CISS Pile Flexural Capacity
Thickness of Non-Liquefiable Crust Layer
Undrained Shear Strength of Non-Liquefiable Crust Layer
Thickness of Liquefiable Sand Layer
p-multiplier, Liquefiable Sand
p-Multiplier, Dense Non-Liquefiable Sand
Embankment Height
y50 Between Nonliquefiable Crust Layer and Abutment Wall
Normal
Normal
Normal
Delta
Delta
Delta
Delta
Uniform
Log-Normal
Log-Normal
Log-Normal
Log-Normal
Uniform
Log-Normal
1.20
690kPa
1035kPa
80kN∙m
180kN∙m
400kN∙m
1980kN∙m
N/A
70kPa
3m
0.05
0.50
N/A
0.20m
0.05
103kPa
173kPa
0kN∙m
0kN∙m
0kN∙m
0kN∙m
N/A
81kPa
3m
0.06
0.58
N/A
0.11m
none
none
none
none
none
none
none
0m , 6m
none
none
none
none
3m, 9m
none
y50 Between Nonliquefiable Crust Layer and Pile
Log-Normal
0.05m
0.03m
none
Generation of Demand Fragility Surfaces
Generation of Demand Fragility Surfaces
 ln(im)   1   2 ln(edp)  
P( EDP  edp | IM  im)  0   
  5   6 ln(edp)   1



ln(
edp
)
 3 4
 

Sample Fragility Surfaces
Sample Fragility Surfaces
3-D Global Dynamic Analyses
3-D Analysis Examples
3-D Analysis Results
ACKNOWLEDGEMENTS
Co-PI Jian Zhang
PhD Students: Pirooz Kashighandi, Minxing Zhao, and Yili Huo.
Technical Coordinator: Tom Shantz
 Funding for this work was provided by the Pacific Earthquake
Engineering Research Center.
Site Response Analysis
50
50
Left Bent
Left Bent
40
Sanoliq (m/s2)
Saliq (m/s2)
40
30
20
30
20
10
10
0
0
0.01
0.1
1
Period (second)
10
0.01
4
10
2
Left Bent
Left Bent
3
1.5
Cliq
Cliq
0.1
1
Period (second)
2
1
1
0.5
0
0
0.01
0.1
1
Period (second)
10
0.01
0.1
1
Period (second)
10