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 Pushover Curves

40 35 30 • Special attention to P delta instability 25 • Story mechanism collapse • Frame 2-D fiber-element 20 code of Hall (1997) 15 10 5 0 0 50 100 150 200 Lateral Roof Displacement cm 250 U20B U20P U6B U6P J20B J20P J6B J6P 300

•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

Narrow model Medium model Wide model • • • 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)

Ground Motion Recordings of the M 8.3 Tokachi-oki earthquake

Seattle Basin transfer function for teleseismic S-waves

0 -10 0 10 0 -10 0 1 x 10 -3 EW Rock site: 7295 0 x 10 -3 EW Soil site: 7335 0 2 Green's function EW 4 50 Amplified Green's function EW 6 8 100 Time sec 10 Time sec 12 150 14 16 Records Recoverd 18 200 20

Simulated rock and basin ground motions for medium rupture

NS C-Med-15 Med

100 Rock Vel: 13.8

0 Soil Vel: 84.1 GF:7295-7335 0 -100 0 200 0 50 100 150 200 250 Time sec 300 Rock Accn: 161.0

350 400 450 500 Soil Accn: 202.8 GF:7295-7335 0 -200 0 50 100 150 200 250 Time sec 300 350 400 450 500

Roof Displacement U-20 Brittle welds

100 0

Roof Displacements NS U20B

69.1 C-Wide-23 Rock 0 30.4 C-Med-15 Rock 0 26.7 C-Narrow-15 Rock Collapse C-Wide-23 Soil 0 0 Collapse C-Narrow-13 Soil 0 -200 0 Collapse C-Med-15 Soil 50 100 150 200 250 Time sec 300 350 400 450 500

Roof Displacement U-20 Perfect welds

100 0

Roof Displacements NS U20P

88.5 C-Wide-23 Rock 0 31.4 C-Med-15 Rock 0 27.0 C-Narrow-13 Rock Collapse C-Wide-23 Soil 0 100.7 C-Med-15 Soil 0 -100 100 0 -100 0 126.8 C-Narrow-13 Soil 50 100 150 200 250 Time sec 300 350 400 450 500

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.

20-Story Steel Frame Buildings (UBC94 and 1992 Japan ) Rock Soil Model Name max PGV cm/s med min U20bw IDR (%) U20pw IDR (%) max med min max med min Wide 78 43 24 2.3

2.3

0.7

1.2

1.8

0.5

Med 39 14 16 2.6

0.4

0.4

1.0

0.3

0.3

Narrow 38 C-Wide-23 C-Med-15 227 222 C Narrow 13 131 18 6 2.0

0.4

0.1

1.4

0.3

0.1

290 103 CO CO CO CO CO 1.7

84 54 CO CO CO CO 2.4

2.2

82 25 CO CO 1.3

CO 2.9

0.6

J20bw IDR (%) max med 2.1

2.6

2.2

0.3

2.5

0.3

CO CO CO CO CO 4.4

min 0.5

0.2

0.1

CO 4.3

0.3

J20pw IDR (%) max med 1.1

1.2

0.5

0.3

0.7

0.3

CO CO 6.2

1.2

CO 0.9

min 0.4

0.2

0.1

1.2

1.0

0.3

6-Story Steel Frame Buildings (UBC94 and 1992 Japan ) Rock Soil Model Name max PGV cm/s med min max U6bw IDR (%) med min U6pw IDR (%) max med min J6bw IDR (%) J6pw IDR (%) max med min max med min Wide 78 43 24 2.0

1.2

1.0

2.1

1.0

0.9

1.5

0.6

0.3

1.4

0.5

0.3

Med 39 Narrow 38 14 16 18 6 1.1

0.2

0.3

0.8

0.2

0.3

0.5

0.2

0.2

0.5

0.2

0.2

0.7

0.4

0.1

0.5

0.4

0.1

0.3

0.2

0.1

0.3

0.2

0.1

Wide 227 290 103 CO CO 4.7

CO CO 4.7

CO CO 3.5

CO CO 2.4

Med 222 Narrow 131 84 54 82 25 CO 3.5

3.4

CO 1.9

1.8

CO 1.9

2.0

3.8

0.8

1.1

CO 3.5

0.6

CO 1.8

0.5

CO 1.9

0.4

2.4

1.2

0.4