Probabilistic Fault Displacement Hazard Analyses

Rui

ChenChris J. Wills

William A. BryantTim Dawson

Mark D. Petersen

Application to the Hayward Fault

Main Objective Develop a Probabilistic Fault

Displacement Hazard Map•

The idea of a fault displacement hazard map (PEER Lifelines, etc.)

•

PFDHA methodology and regressions (Mark Petersen et al.)

•

Fault displacement data (Tim Dawson, including some of Steve Wesnousky’s

2008 data)

•

Fortran code for PFDHA calculation (Tianqing

Cao

and Mark Petersen,

with modification)•

Detailed fault trace and fault branch activity (Bill Bryant)

•

Putting pieces together and developing the map

•

Calculating hazards at Highway 580 fault crossings

Methodology•

Mark Petersen et al. methodology (2004 –

2009). Regressions depend on: –

Accuracy of mapped fault trace–

Complexity of fault geometry–

Cell size (structure footprint size)

•

Fault specific application using detailed fault trace

•

A large number of cross-line profiles for map generation

After Tim Dawson (2004)

Partition of Fault Displacement

Displacement is partitioned among branches based on local geological evidence.

Without partition Partitioned

0

50

100

150

200

-500 -300 -100 100 300 500

Disp

lace

men

t (cm

)

Distance to Main Fault Trace (m)

Main Trace (70%)Branch 1 (20%)Branch 2 (10%)Combined

0

50

100

150

200

-500 -300 -100 100 300 500

Disp

lace

men

t (cm

)

Distance to Main Fault Trace (m)

Application to the Hayward Fault

•

Rupture of the Northern and Southern Hayward Fault segments

•

A characteristic, M 7.0 earthquake occurring once every 140 years

•

Modeled fault trace (in yellow) is defined by about 70 points selected in GIS based on:–

Alquist-Priolo

traces–

Jim Lienkaemper

traces

Fault Displacement Hazard Near Three 580 Crossings

Partition (Main Trace , Branch)

(90%, 10%)

(95%, 5%)

(100%, single trace)

0

50

100

150

200

-500 -300 -100 100 300 500 700

Disp

lace

men

t (cm

)

Distance to Main Fault Trace (m)

1st Crossing: Inferred Complex2nd Crossing: Inferred Complex3rd Crossing: Approximate

10% in 50 years25×25 m2 cell size

Fault Displacement Hazard Map Near Hayward

10% in 50 years25x25 m2

cell size

26 cross-line profiles

Partition of Displacement at

Selected LocationsMain Trace Branch 1 Branch 2

1 75% 5% 20% 2 90% 10% -3 95% 5% -4 90% 10% -5 85% 10% 5% 6 95% 5% -

580

238

Effect of Cell Size

3rd Highway 580 crossing10% in 50 years

Wells and Coppersmith (1993):

Modification:

)(

)(

1]|0[ bMa

bMa

eeMsrP +

+

+=≠

cellsofnumbertotalrupturewithcellratio =0

50

100

150

200

-200 -100 0 100 200

Dis

plac

emen

t (cm

)

Distance to Fault (m)

25x2550x50100x100150x150200x200Infinite

Cell Size (m2)0

0.2

0.4

0.6

0.8

1

4.5 5.5 6.5 7.5 8.5 9.5

Prob

abili

ty of

on-F

ault

Sufa

ce R

uptu

reEarthquake Magnitude

25x25 (0.74)50x50 (0.87)100x100 (0.90)150x150 (0.87)200x200 (0.93)Wells & Coppersmith (1993)

Estimate of On-Fault Displacement•

Wells and Coppersmith (1994)

•

Geological average or seismological average? What do they mean and how are they calculated?

MDave 9.032.6)(log10 +−=

)9.032.6(10)/(),( Mave ADDDlD +−×=

2004 data and regression:(normalized to seismological AD?)

0479.0)/(*9406.1)/(*4165.2/ 2 ++−= LlLlADD

2009 revision:(normalized to geological AD)

0.0

0.1

1.0

10.0

0.000 0.100 0.200 0.300 0.400 0.500

Norm

alize

d Av

erag

e Di

spal

cem

ent,

D/AD

Normalized distance, x/ L

D/AD = 1 x/ l ≥ 0.25D/AD = 3.8 (x/L)+0.05 x/L < 0.25σ =0.58

l/L

l/L

On-Fault Slip Distribution

Wesnousky

(2008):Asymmetric curves fit better than symmetric curves

Can we incorporate variation in the degree of asymmetry in PFDHA?

Probability Profiles

0%

10%

20%

30%

40%

-250 -200 -150 -100 -50 0 50 100 150 200 250

Prob

abili

ty of

D ≥

100 c

m

Distance to Fault (m)

25x25

50x50

100x100

150x150

200x200

Cell size (m2)3rd Highway 580 crossing

Multiple Probabilities

0

100

200

300

400

-200 -150 -100 -50 0 50 100 150 200

Disp

lace

men

t (cm

)

Distance to Fault (m)

10% (475 yrs)5% (975 yrs)2% (2475 yrs)

25x25 m2 cell50 yr probability

Summary

1.

Lateral extent of estimated zone of fault displacement increases with increasing uncertainty in fault location and increasing complexity of mapped fault traces

2.

Need continuous effort in augmenting fault displacement data and updating regression relations

3.

PFDHA is consistent with PSHA and may be a valuable tool in design