Fault Rupture Displacement Estimation:Caltrans’ Approach

Martha Merriam and Tom Shantz

2012 SSA Annual Meeting

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

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

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

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

Alder Creek Bridges, Mendocino County San Andreas Fault

Old Alder Creek Bridge 1905

Old Alder Creek Bridge 1906

Bancroft Library

Alder Creek State Bridge, built in 1947

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

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

1974 Point Arena/Mallo Pass AP EFZ Maps

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

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)

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

East Warren Avenue Undercrossing Sunol Grade Hwy 680, Hayward Fault

Hayward fault parameters(southern section)

• MMax 7.3• Type strike-slip• Slip rate 9.2 mm/yr• Aseismic slip factor 0.4

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

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

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

)

Pasadena Freeway Bridges Raymond fault

1977 Los Angeles AP EFZ Map

Raymond fault parameters

• MMax 6.7• Type strike-slip

dips north 79• Slip rate 1.5 mm/yr

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

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

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)

Fault Trace

Map Rating (accurate, approximate, concealed, inferred)

Approximate

Trace (simple, complex) Simple

Slip distribution 100%

Map Distance from bridge 10 m

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

State Bridges With 1.8 m (6 feet) or more estimated offset

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