Fault Rupture Displacement Estimation: Caltrans’ Approach
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Fault Rupture Displacement Estimation:Caltrans’ Approach
Martha Merriam and Tom Shantz
2012 SSA Annual Meeting
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Caltrans bases the design fault rupture displacement on the larger of….
- mean Wells & Coppersmith (1994)- 5% in 50 year displacement hazard
Probabilistic assessment based on…
Abrahamson, N., 2006, Appendix C, Probabilistic Fault Rupture Hazard Analysis, San Francisco PUC, General Seismic Requirements for the Design on New Facilities and Upgrade of Existing Facilities…..
Petersen, M., Dawson, T., Rui, C., Cao, T., Wills, C., Schwartz, D., Frankel, A., Displacement Hazard for Strike-Slip Faults, BSSA, Vol 101, No. 2, pp. 805-825, April 2011
Design criteria and references
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Probabilistic Calculation (for 975 year displacement hazard)
Assume 95% of seismic moment is released by characteristic earthquake
Estimate MCHAR using fault dimensions and Hanks-Bakun (2002)
100 km
15 k
m MCHAR =7.3
Example
Mw
Mag
. Pro
b. D
ensit
y
7.3
M0= 101.5 MCHAR +16.05
Too small! Increase 15 to 20%.
Slip rate = 10 mm/yr
M0= (0.95) mAD
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mean recurrence interval M0
M0=
Probabilistic Calculation (con’t)
= 282 years
Annual rate of exceedence z > z0
( ) = Annual rate of EQCHAR( ) P[z > z0| EQCHAR]*
1/975 1/282Assume log-normal distribution of rupture displacement
Z0
What’s m and s?
No measurements:
m = W&C (AD)
With measurements:
m = measavg
epistemic aleatory
sT = 0.39 (log10 units)se = 0.35 sa = 0.17
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Example con’t: assume no past rupture displacement measurements are available
W&C (AD) = 1.8 m
e = 0.55
z = 1.8 * 100.55*0.39
Alt. 1:
= 2.95 m
Alt. 2:
Z% = m% * 100.55*sa
Z50% = 1.8 * 100.55*0.17 = 2.23 m
Uncertainty in fault location
Per Petersen et. al (2011) we characterize fault mapping as either (1) Accurate, (2) Approximate, (3) Concealed, or (4) Inferred
Probabilistic Calculation (con’t)
Z70% = 1.8 * 100.52*0.35 * 100.55*0.17 = 3.40 m
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Alder Creek Bridges, Mendocino County San Andreas Fault
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Old Alder Creek Bridge 1905
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Old Alder Creek Bridge 1906
Bancroft Library
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Alder Creek State Bridge, built in 1947
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San Andreas Fault parameters(North Coast section)
• MMax 8• Type strike-slip• Slip rate 24 mm/yr• Aseismic slip factor 0.0185• Site-specific* measurements 3 • Average displacement 5 m
*Within 1 km
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Displacement at fault
2.00 4.00 6.00 8.00 10.00 12.00 14.00
0.0001
0.001
0.01
D(m) SS
10% Fractile
30% Fractile
50% Fractile
70% Fractile
90% Fractile
Displacement (m)
Prob
abili
ty o
f Exc
eede
nce
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1974 Point Arena/Mallo Pass AP EFZ Maps
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Main Trace Secondary Trace Tertiary Trace
Map Rating (accurate, approximate, concealed, inferred)
Approximate Accurate Concealed
Trace (simple, complex)
Simple Simple Simple
Slip distribution 85% 10% 5%
Distance from bridge
0 -35 m 50 m
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Displacement at Alder Creek Bridge
-300 -200 -100 0 100 200 3000
1
2
3
4
5
6
Distance from trace (m)
Faul
t D
ispl
acem
ent
(m)
Main Trace
Secondary Trace
Tertiary Trace
Combined(for preliminary design)
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Recommendations to Engineer
• For preliminary design use 5.4 m of right lateral offset perpendicular to bridge and beneath any portion of the bridge
• Further investigation may refine location and reduce design offset
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East Warren Avenue Undercrossing Sunol Grade Hwy 680, Hayward Fault
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Hayward fault parameters(southern section)
• MMax 7.3• Type strike-slip• Slip rate 9.2 mm/yr• Aseismic slip factor 0.4
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0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
0.0001
0.001
0.01
D(m) HB
10% Fractile
30% Fractile
50% Fractile
70% Fractile
90% Fractile
Displacement (m)
Prob
abili
ty o
f Exc
eede
nce
Displacement at fault
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Main Trace Secondary Trace Tertiary Trace
Map Rating (accurate, approximate, concealed, inferred)
Accurate Accurate Concealed
Trace (simple, complex)
Simple Simple Simple
Slip distribution 85% 10% 5%
Distance from bridge
0 165 -40
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Displacement at East Warren Avenue Undercrossing
-300 -200 -100 0 100 200 3000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Distance from main trace (m)
Faul
t Dis
plac
emen
t (m
)
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Pasadena Freeway Bridges Raymond fault
1977 Los Angeles AP EFZ Map
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Raymond fault parameters
• MMax 6.7• Type strike-slip
dips north 79• Slip rate 1.5 mm/yr
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Displacement at fault
0.00 0.50 1.00 1.50 2.00 2.50 3.00
0.0001
0.001
0.01
D(m) HB
10% Fractile
30% Fractile
50% Fractile
70% Fractile
90% Fractile
Displacement (m)
Prob
abili
ty o
f Exc
eede
nce
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Main Trace Secondary Trace
Map Rating (accurate, approximate, concealed, inferred)
Approximate Approximate
Trace (simple, complex)Simple Simple
Slip distribution 50% 50%
Map Distance from bridge 40 m 100 m
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Displacement at Pasadena Freeway Prospect Ave Overcrossing
-150 -100 -50 0 50 100 150 200 2500
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Distance from trace (m)
Faul
t Dis
plac
emen
t (m
)
Trace 1
Trace 2
Combined (for preliminarydesign)
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Fault Trace
Map Rating (accurate, approximate, concealed, inferred)
Approximate
Trace (simple, complex) Simple
Slip distribution 100%
Map Distance from bridge 10 m
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Displacement on Pasadena Freeway Bridges 10 m from single trace
-150 -100 -50 0 50 100 150 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distance from main trace (m)
Faul
t Dis
plac
emen
t (m
) Use for
preliminary
design
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State Bridges With 1.8 m (6 feet) or more estimated offset
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Issues
• When is the assumption of characteristic magnitude-frequency behavior not justified?
• Need method for when MCHAR recurrence period is longer than 975 years
• What fractile (on epistemic uncertainty) should we use for displacement hazard?
• Use of time dependent hazard models• Consideration of aseismic creep