Simulations of Flexible Buildings in Large Earthquakes

Thomas Heaton (Caltech)Anna Olsen (Caltech)Jing Yang (Caltech)

Masumi Yamada (Kyoto Univ.)

Key Issues

• Modern high-rise buildings and base-isolated buildings have not yet experienced large long-period ground motions (pgd > 1 m).

• Is statistical prediction of long period ground motions technically feasible?

• Will the design of long-period buildings change dramatically in the next 100 years?

Ph.D. Thesis of Anna Olsen, 2008• collected state-of-the-art simulations of crustal

earthquakes• 37 earthquakes, over 70,000 ground motions

– 1989 Loma Prieta (Aagaard et al., 2008)– 1906 San Francisco, with alternate hypocenters (Aagaard et

other al., 2008)– 10 faults in the Los Angeles basin (Day et al., 2005)– Puente Hills fault (Porter et al., 2007)– TeraShake 1 and 2 (K. Olsen et al., 2006, 2007)– ShakeOut, from Chen Ji

• Moment magnitudes between 6.3 and 7.8• Long-period (T > 2 s) and broadband (T > 1 s)• PGD and PGV calculated from vector of north-south

and east-west components

1906 San Francisco Ground Motions

• Magnitude 7.8• Same slip distribution,

three hypocenter locations

• Long-period PGD exceeds 2 m near the fault

• Long-period PGV exceeds 1.5 m

• Simulations by Aagaard and others (BSSA, 2008)

John Hall’s design of a 20-story steel MRF building

•Building U20 1994 UBC zone4 Stiff soil, 3.5 sec. period

•Building J20 1992 Japan code 3.05 sec period

•Both designs consider Perfect welds Brittle welds

Pushover Analysis

•Special attention to P-delta instability•Story mechanism collapse•Frame 2-D fiber-element code of Hall (1997)

0 50 100 150 200 250 3000

5

10

15

20

25

30

35

40Pushover Curves

Bas

e S

hear

(fr

ac o

f bu

ildin

g w

eigh

t)

%

Lateral Roof Displacement cm

U20BU20PU6BU6PJ20BJ20PJ6BJ6P

•Severe damage or collapse in many areas•Stronger, stiffer building (J20) performs better than more flexible building (U20)•Brittle weld buildings 5 times more likely to collapse than perfect-weld buildings•Results summarized in Olsen and others (BSSA, 2008)

Displacements on Base Isolators

•Typical base isolator is 3 sec with a maximum allowed displacement of 40 cm• Nonlinear isolator displacements exceed linear by 20% to 40% (Ryan and Chopra)•Described in Olsen and others (BSSA, 2008)

Collapse Prediction

Collapse

Remain standing

All strong motions recorded at less than 10 km from rupture from M>6

From Masumi Yamada

•Near-source pga’s are log-normal•Same distribution will apply 100 years from now

•Long-period ground motions are not log normal•A few large earthquakes can completely change the distribution•Cannot predict what the shape of this distribution will look like 100 years from now

Ph.D. Thesis of Jing Yang

• Repeat of the giant (M>9) Cascadia earthquake of 1700• Simulate rock ground motions with 2003 Tokachi-Oki M8.3 rock records as

empirical Green’s functions• Include effect of the Seattle basin by a transfer function derived from

teleseismic S-waves transect (Pratt and Brocher, 2006)

Narrow model Wide modelMedium model

Ground Motion Recordings of the M 8.3 Tokachi-oki earthquake

Seattle Basin transfer function for teleseismic S-waves

-1

0

1x 10

-3

EW Rock site: 7295

-1

0

1x 10

-3

EW Soil site: 7335

Vel

cm

/s

Records

Recoverd

0 50 100 150 200-10

0

10

Green's function EW

Time sec

0 2 4 6 8 10 12 14 16 18 20-10

0

10Amplified Green's function EW

Vel

cm

/s

Time sec

Simulated rock and basin ground motions for medium rupture

-100

0

100NS C-Med-15 Med

Rock Vel: 13.8

0 50 100 150 200 250 300 350 400 450 500-100

0

100

vel c

m/s

Soil Vel: 84.1 GF:7295-7335

Time sec

-200

0

200Rock Accn: 161.0

0 50 100 150 200 250 300 350 400 450 500-200

0

200

accn

cm

/s2

Soil Accn: 202.8 GF:7295-7335

Time sec

Roof Displacement U-20 Brittle welds

-100

0

100

26.7 C-Narrow-15 Rock

-100

0

10069.1 C-Wide-23 Rock

Roof Displacements NS U20B

-100

0

100

30.4 C-Med-15 Rock

-200

0

200

Roo

f D

isp

cm

-200

0

200

0 50 100 150 200 250 300 350 400 450 500-200

0

200

Collapse C-Narrow-13 Soil

Time sec

Collapse C-Med-15 Soil

Collapse C-Wide-23 Soil

-100

0

10088.5 C-Wide-23 Rock

Roof Displacements NS U20P

-100

0

100

31.4 C-Med-15 Rock

-100

0

100

27.0 C-Narrow-13 Rock

-200

0

200

Collapse C-Wide-23 Soil

Roo

f D

isp

cm

-100

0

100100.7 C-Med-15 Soil

0 50 100 150 200 250 300 350 400 450 500

-100

0

100 126.8 C-Narrow-13 Soil

Time sec

Roof Displacement U-20 Perfect welds

Conclusions

• Presence of brittle welds significantly degrades performance (2-8 times more likely to collapse)

• Very generally, ground motions with PGD > 0.5-1 m and PGV > 1-2 m/s collapse MRFs

• Although much of the physics of long-period ground motions is understood, statistical prediction might not be meaningful (or possible) … a few earthquakes of unknown source characteristics will determine the fate of long-period buildings.

Model Name

Rock Soil

Wide Med Narrow C-Wide-23 C-Med-15

C-Narrow-

13

PGV cm/s

max 78 39 38 227 222 131 med 43 14 18 290 84 82 min 24 16 6 103 54 25

U20bwIDR (%)

max 2.3 2.6 2.0 CO CO COmed 2.3 0.4 0.4 CO CO COmin 0.7 0.4 0.1 CO CO 1.3

U20pw IDR (%)

max 1.2 1.0 1.4 CO CO COmed 1.8 0.3 0.3 CO 2.4 2.9min 0.5 0.3 0.1 1.7 2.2 0.6

J20bw IDR (%)

max 2.1 2.2 2.5 CO CO COmed 2.6 0.3 0.3 CO CO 4.4

min 0.5 0.2 0.1 CO 4.3 0.3

J20pw IDR (%)

max 1.1 0.5 0.7 CO 6.2 COmed 1.2 0.3 0.3 CO 1.2 0.9

min 0.4 0.2 0.1 1.2 1.0 0.3

20-Story Steel Frame Buildings (UBC94 and 1992 Japan)

Model Name

Rock Soil

Wide Med Narrow Wide Med Narrow

PGV cm/s

max 78 39 38 227 222 131

med 43 14 18 290 84 82

min 24 16 6 103 54 25

U6bw IDR (%)

max 2.0 1.1 0.7 CO CO CO

med 1.2 0.2 0.4 CO 3.5 3.5

min 1.0 0.3 0.1 4.7 3.4 0.6

U6pw IDR (%)

max 2.1 0.8 0.5 CO CO CO

med 1.0 0.2 0.4 CO 1.9 1.8

min 0.9 0.3 0.1 4.7 1.8 0.5

J6bw IDR (%)

max 1.5 0.5 0.3 CO CO CO

med 0.6 0.2 0.2 CO 1.9 1.9

min 0.3 0.2 0.1 3.5 2.0 0.4

J6pw IDR (%)

max 1.4 0.5 0.3 CO 3.8 2.4

med 0.5 0.2 0.2 CO 0.8 1.2

min 0.3 0.2 0.1 2.4 1.1 0.4

6-Story Steel Frame Buildings (UBC94 and 1992 Japan)