Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, Japan

UNCERTAINTIES OF LONG-PERIOD GROUNDMOTION AND ITS IMPACT ON BUILDINGSTRUCTURAL DESIGN
Izuru TAKEWAKI1, Kohei FUJITA2 and Shinta YOSHITOMI3
1

Professor, Department of Architecture and Architectural Engineering, Kyoto University,
Kyoto, Japan, takewaki@archi.kyoto-u.ac.jp
2
Graduate Student, Department of Architecture and Architectural Engineering, Kyoto University,
Kyoto, Japan, fm.fujita@archi.kyoto-u.ac.jp
3
Asst. Professor, Department of Architecture and Architectural Engineering, Kyoto University
Kyoto, Japan, yoshitomi@archi.kyoto-u.ac.jp

ABSTRACT: On March 11, 2011, Japan was shaken by the 2011 off the Pacific coast of
Tohoku earthquake (the Great East Japan Earthquake). This paper reports some aspectsof this earthquake and its impact on building structural design. It was reported that
long-period ground motions were induced in Tokyo, Nagoya and Osaka. The responseof high-rise buildings to the recorded ground motions during this earthquake and thesimulated ground motions provided by the Japanese Government is discussed from theviewpoint of resonance and critical excitation.
Key Words: Great East Japan earthquake, long-period ground motion, resonance, criticalexcitation, earthquake input energy, passively controlled structure

INTRODUCTION
The most devastating earthquake in Japan after the 1923 Great Kanto earthquake occurred on March
11, 2011 (AIJ 2011a, b, USGS 2011). The moment magnitude was 9.0 and this is the largest so far inJapan. The earthquake resulted from the thrust faulting near the subduction zone plate boundary
between the Pacific and North America Plates (AIJ 2011a, b, USGS 2011). Nearly 20,000 people
were killed or are still missing by that earthquake and the subsequent monster tsunami as of November
1, 2011.
Because super high-rise buildings in mega cities in Japan had never been shaken by theso-called long-period ground motions with high intensities, the response of high-rise buildings to suchlong-period ground motions is one of the most controversial subjects in the field ofearthquake-resistant design in Japan (MLIT 2010). The issue of long-period ground motion and its
effect on building structural design was initially brought up in Mexico, USA and Japan during
1980-1990s (for example Earthquake Spectra 1988, Heaton et al. 1995, Kamae et al. 2004, Ariga et al.

1005

2006).
This paper discusses the response of assumed super high-rise buildings (40 and 60-story) inTokyo during this earthquake through the comparison with the reported fact. The issue of
long-period ground motion and its impact on building structural design are also discussed by using thesimulated long-period ground motions provided in December, 2010 by the Japanese Government (theMinistry of Land, Infrastructure, Transport and Tourism (MLIT)) (MLIT 2010). Two 40-story steelbuildings are subjected to these simulated long-period ground motions. It is further demonstrated
that the high-hardness rubber dampers with high damping capacity (Tani et al. 2009) are extremely
effective for the reduction of response level and response duration.
Furthermore the criticality and uncertainty of the long-period ground motions are investigatedbased on the theory of critical excitation (Drenick 1970, Takewaki 2004, 2006, 2008a). The credible
bounds of input energy responses are obtained by using the robust critical excitation method with theconstraints on acceleration and velocity powers. It is shown that the long-period ground motions
with a large power in a long-period range are controlled primarily by the velocity power and theground motion recorded in Tokyo during the 2011 off the Pacific coast of Tohoku earthquake actually
included long-period wave components.

RESPONSE SIMULATION OF SUPER HIGH-RISE BUILDINGS
Fig.1 shows the velocity waveforms of the long-period ground motion recorded at K-NET, Shinjuku
station (TKY007). It can be observed that the maximum ground velocity attains about 0.25(m/s) andthe ground shaking continues for more than several minutes. The corresponding velocity response
spectra are shown in Fig.2. The corresponding ones of the Japanese seismic design code for 5%
damping are also plotted in Fig.2. It is understood that these ground motions include long-period
components up to 10 seconds.

Fig.1 Long-period ground motion at K-NET, Shinjuku station (TKY007) (NIED 2011b)

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0.01(small damping)0.05(medium damping)0.20(large damping)displacement

Response ratio

Fig.2 Velocity response spectra of ground motions at TKY007 (NIED 2011b) (Takewaki et al. 2011)

Resonant caseNon-resonant caseh=0.02h=0.01(Takewaki 2006)

h=0.005

time

(a)
(b)
Fig.3 (a) Response amplification in resonant and random cases, (b) damping effect in resonanceIn order to investigate the influence of this ground motion on high-rise buildings, two assumedbuildings of 40 and 60 stories have been treated. The buildings have a plan of 40 m × 40 m (equally
spaced 36 columns; span length.8 m) and one planar frame is taken as the object frame. The uniform
story height is 4 m. The floor mass per unit area is assumed to be 800 kg/m2. The damping ratio istaken as 0.01 in accordance with the well-accepted database. The detail of member size and its
material property are shown in the reference (Takewaki et al. 2011). The 40-story building has thefundamental natural period of 4.14s and the 60-story building has that of 5.92s. Furthermore, it iswell accepted that the passive dampers are very effective in the reduction of earthquake response inhigh-rise buildings. The 2011 off the Pacific coast of Tohoku earthquake may be the first plate-type
earthquake to have affected super high-rise buildings in mega cities. For the purpose of clarifying themerit of visco-elastic dampers (high-hardness rubber dampers with high damping capacity (Tani et al.
2009)), the buildings of 40 and 60 stories without and with these high-hardness rubber dampers havebeen subjected to the long-period ground motion recorded at K-NET, Shinjuku station (TKY007).
It may be useful to note that the amplification by damping can be expressed by
1/ hfor resonant long-period ground motion(1a)1.5 / (1 + 10 h ) for non-resonant conventional ground motion (ratio to h=0.05)(1b)This implies that the high sensitivity of the response to damping in resonant long-period groundmotions (Fig.3).

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40

40

without high-hardness
35 rubber dampers

35

30

30

25

25

story

story

Fig.4 shows the maximum story displacements and interstory drifts of two 40-story buildings of
T1=4.14s without and with high-hardness rubber dampers to the ground motion at Shinjuku station(TKY007) (frame response: elastic or plastic). On the other hand, Figs.5(a) and (b) illustrate themaximum story displacements and interstory drifts of a 60-story building of T1=5.92s to the groundmotion at Shinjuku station (TKY007) (frame response: plastic, without or with high-hardness rubber
dampers). Fig.5(c) presents the time history of the story displacement at top.
It has been reported recently (Asahi newspaper 2011) that a 54-story steel building(height=223m: fundamental natural period=6.2s (short-span direction), 5.2s (long-span direction))
retrofitted with new-type passive oil dampers including the supporting bracing system in Shinjuku,
Tokyo experienced the top displacement of 0.50(m) during the 2011 off the Pacific coast of Tohoku
earthquake. The vibration duration was reported to be over 13 minutes. It was also explained thatthat building would have attained the top displacement of 0.7(m) if the passive dampers would nothave been installed. This fact corresponds well to the result explained above.
There is another report that a 55-story super high-rise building in Osaka (height=256m: T1=5.8s(long-span direction), 5.3s (short-span direction)) was shaken severely regardless of the fact that
Osaka is located far from the epicenter (about 800km) and the JMA instrumental intensity was 3 in
Osaka. Afterwards the natural periods were found to be longer ones reflecting the flexibility ofpile-ground systems. It should be pointed out that the level of velocity response spectra of groundmotions observed here (first floor) is almost the same as that at the Shinjuku station (K-NET) in Tokyoand the top-story displacement are about 1.4m (short-span direction) and 0.9m (long-span direction).
Fig.6 shows the ground acceleration, ground velocity and top-story displacement. It can be observedthat a clear resonant phenomenon occurs during about eight cycles. This implies the need of
consideration of long-period ground motions in the seismic resistant design of super high-risebuildings in mega cities even though the site is far from the epicenter. The seismic retrofit using
hysteretic steel dampers and oil dampers is being planned.

20
elastic NS
elastic EW
plastic NS
plastic EW

10
5

10
5

0
0 100 200 300 400 500 600
maximum story displacement (mm)

0

40

40

35 without high30 hardness
rubber dampers
25

35

story

30

0
0

25
20

with high-hardness
rubber dampers

15

15

5

elastic NS
elastic EW
plastic NS
plastic EW

0 100 200 300 400 500 600
maximum story displacement (mm)20

10with high-hardness
rubber dampers

15

15

story

20

10

elastic NS
elastic EW
plastic NS
plastic EW

5
0
0

5
10 15 20 25 30
maximum interstory drift (mm)elastic NS
elastic EW
plastic NS
plastic EW

510 15 20 25 30
maximum interstory drift (mm)Fig.4 Maximum story displacement and interstory drift of an assumed 40-story building of T1=4.14s toground motion at Shinjuku station (TKY007) (frame response: elastic or plastic)1008

(c) GM at Chiyoda-ku

Fig.5 Maximum displacement and interstory drift of an assumed 60-story building of T1=5.92s to GM
at K-NET, Shinjuku station (TKY007) (frame response: plastic, without or with high-hardness rubber
dampers) (Takewaki et al. 2011)
Long-period ground motion of about
8 cycles is resonant with building

0.0

Ground acceleration

Shear wave velocity (km/s)
1.0 2.0 3.0 4.0

-0.2
-0.4

Height above sea level (km)8 cycles of 6-7 seconds

Ground velocity

-0.6
-0.8
-1.0
-1.2
-1.4

earthquake
bedrock-1.6-1.8

Top displacement-2.0

Fig.6 Ground acceleration, velocity and top-story displacement of a 55-story building in OsakaRESPONSE OF HIGH-RISE BUILDINGS TO PREDICTED LONG-PERIOD GROUNDMOTIONS
Simulated long-period ground motions
On December 21, 2010, the Japanese Government made a press release to upgrade theregulation for high-rise buildings under long-period ground motions. The Ministry of Land,
Infrastructure, Transport and Tourism (MLIT) selected and specified 9 areas in Osaka, Nagoya andTokyo (see Fig.7). Areas 1-4 exist in Tokyo, areas 5-7 in Nagoya and areas 8, 9 in Osaka. MLIT
provided simulated long-period ground motions in each area based on the advanced theory of groundmotion generation. It was found that large velocity waves appear in later times and the velocity
spectra in 2-8 seconds have relatively large magnitudes. It should be remarked that this project was
conducted before the present Tohoku earthquake and a revision of the simulation is under preparation
together with the inclusion of the simultaneous occurrence of three great earthquakes predicted in WestJapan.

1009

OsakaNagoyaTokyo(Area 8, 9)(Area 5-7)
(Area 1-4)
Fig.7 Zoning areas in Osaka, Nagoya and Tokyo (MLIT 2010)
Response simulation of high-rise buildings without and with high-hardness rubber dampers
In order to investigate the influence of the simulated ground motions in areas 1-9 on the
response of high-rise buildings, two assumed buildings of 40 stories have been used. The parametersof the buildings are the same as those stated above. The stiffness of beams has been evaluated as
double the original stiffness for the building frame of T1=3.6s and as 1.5 times the original stiffness forthe building frame of T1=4.14s. The model of T1=3.6s is a slightly stiff building model and themodel of T1=4.14s is a slightly flexible model. Only the latter one has been treated above. For the
purpose of clarifying the merit of visco-elastic dampers (high-hardness rubber dampers (Tani et al.
2009) as in the previous case), the buildings of 40 stories without and with these high-hardness rubber
dampers have been subjected to the simulated long-period ground motions. One damper unit consistsof rubber thickness=15mm and rubber area=0.96m2. ‘Damper single’ includes 2 damper units atevery story and ‘damper double’ includes 4 damper units at every story. The ‘damper double’ hasbeen treated above.
Fig.8 illustrates the comparison of the time histories of the top displacement of the 40-story
buildings of T1=3.6s without and with high-hardness rubber dampers (damper double, frame response;elastic) under a simulated long-period ground motion in area 5 (Nagoya area). It can be observedthat the high-hardness rubber dampers are able to damp the building vibration in an extremely shorter
duration compared to the building without those dampers.
The comparison of the top displacements of the 40-story buildings of T1=3.6(s) (elastic orelastic-plastic, without or with dampers) has been made under the simulated long-period groundmotion in area 5. It has been observed that the elastic-plastic response of the building frame
decreases the response level to some extent. It has also been seen that the high-hardness rubber
dampers can damp the vibration so quickly. It has been confirmed that this quick vibration reduction
rate can be achieved also by viscous dampers like oil dampers so long as an appropriate amount of
dampers is provided. The P-delta effect of columns has also been investigated. It has been madeclear that the P-delta effect of columns has a small influence on the response in this case.
Fig.9 shows the ground acceleration, ground velocity and top-story displacement. It can beobserved that a clear resonant phenomenon occurs during about three cycles and intensive vibration of
the building corresponds well to the velocity wave of the ground motion, not the acceleration wave of
that. This is a special character of the response of high-rise buildings under long-period groundmotions.

1010

150
100
50
0
-50
-100
-150
0

Groundacceleration
50

100

150

200 250
time (s)

20

300

350

400

Building intensive response begins
almost after the end of groundacceleration.

velocity (cm/s)

0Groundvelocity

-10
-20
50

1500

100

150

200 250
time (s)

300

350

400

Top building
displacement

1000
500
0
-500

no damper
damper single
damper double

-1000
-1500

Characteristic of long-period
ground motion

area05100

top displacement (mm)area050

50

20

area05

10
0
-10
-20
100

Top displacement (mm)velocity (cm/s)

2

acceleration (cm/s )Fig.8 Time histories of top-story displacement of an assumed 40-story building

110

120
130
time (s)

140

150

140

150

1500
1000
500
0
-500

-1000

no damper
damper single
damper double

-1500
100

110

120

130

Time (s)100 150 200 250 300 350 400
time (s)Fig.9 Ground acceleration, velocity and top displacement of an assumed 40-story building in Nagoya
NEW PARADIGM OF EARTHEQUAKE RESISTANT DESIGN FOR GROUND MOTIONSINCLUDING LONG-PERIOD GROUND MOTION
In order to respond to the issue of long-period ground motions, a new paradigm is desired.
There are various buildings in a city. Each building has its own natural period and its original
structural properties. When an earthquake occurs, a variety of ground motions are induced in the city.
The combination of the building natural period with the predominant period of the induced groundmotion may lead to disastrous phenomena in the city (see Fig.10). Many past earthquake
observations demonstrated such phenomena repeatedly. Once a devastating earthquake occurs, somebuilding codes are revised and upgraded. However, it is true that this repetition never resolves all theissues and new serious problems occur. In order to overcome this problem, a new paradigm has to beposed. The concept of "critical excitation" (Drenick 1970, Takewaki 2004, 2006, 2008a) and thestructural design based upon this concept can become one of such new paradigms (Takewaki 2006).
Earthquake inputs are uncertain both in epistemic and aleatory sense even with the present
knowledge and it does not appear easy to predict forthcoming events precisely (Geller et al. 1997,
Stein 2003, Aster 2012). Near-field ground motions (Northridge 1994, Kobe 1995, Turkey 1999 and
Chi-Chi, Taiwan 1999) and the Mexico Michoacan motion in 1985 have some peculiar, unpredictablecharacteristics. It is also true that the civil, mechanical and aerospace engineering structures areoften required to be designed for disturbances including inherent uncertainties due mainly to their"low rate of occurrence". It is said in fact that the return period of the earthquake of March 11 isabout 1,000 years. Worst-case analysis combined with proper information based on reliable physical1011

data is expected to play an important role in avoiding difficulties induced by such uncertainties.
Approaches based on the concept of "critical excitation" seem to be promising.
The most critical issue in the seismic resistant design is the resonance. One of the promising
approaches to this phenomenon is to shift the natural period of the building through seismic control(Takewaki 2009) and to add damping in the building. However it is also true that the seismic control
is under development and more sufficient time is necessary to respond to uncertain ground motions.
It is believed that earthquake has a bound on its magnitude and the earthquake energy radiatedfrom the fault has a bound (Trifunac 2008). The problem is to find the most unfavorable groundmotion for a building or a group of buildings (see Fig.10). The Fourier spectrum of a ground motion
acceleration has been proposed at the rock surface depending on the seismic moment M 0 , distanceR from the fault, etc. (for example Boore 1983).

A(ω ) = CM 0 S (ω , ωC ) P (ω , ωmax ) exp(−ω R /(2 β Qβ ) / R(2)

Such spectrum may have uncertainties. One possibility or approach is to specify the acceleration orvelocity power as a global measure and allow the variability of the spectrum.
The problem of ground motion variability is very important and tough. Code-specified design
ground motions are usually constructed by taking into account the knowledge from the pastobservation and the probabilistic insights. However, uncertainties in the occurrence of earthquakes(or ground motions), the fault rupture mechanisms, the wave propagation mechanisms, the groundproperties, etc. cause much difficulty in defining reasonable design ground motions especially forimportant buildings in which severe damage or collapse has to be avoided absolutely (Takewaki 2006,
Geller et al. 1997, Stein 2003, Aster 2012).
A significance of critical excitation is supported by its broad perspective. In general there are
two classes of buildings in a city. One is the important building which plays an important role during
and after disastrous earthquakes. The other is ordinary building. The former one should not getdamaged during an earthquake and the latter one may be damaged partially especially for criticalexcitation larger than code-specified design earthquakes. Just as the investigation on limit states ofstructures plays an important role in the specification of response limits and performance levels of
structures during disturbances, the clarification of critical excitations for a given structure or a groupof structures appears to provide structural designers with useful information in determining excitation
parameters in a risk-based reasonable way. It is expected that the concept of critical excitation
enables structural designers to make ordinary buildings more seismic-resistant and seismic-resilient.

critical excitation ?
critical excitation Z
critical excitation A
critical excitation C
critical excitation D
critical excitation B

low-rise RC bld wood house

med-rise RC bld

base-isolated bld

high-rise bld

Fig.10 Structure-dependent critical excitation

1012

nuclear-power
plant

The total input energy is an appropriate quantity for evaluating the demand of earthquake
ground motions (Housner 1959, Akiyama 1985, Takewaki 2004). Fig.11 presents the credible
bounds of input energy for JMA Kobe NS during Hyogoken-Nanbu earthquake 1995, Petrolia NS
during Cape Mendocino earthquake 1992, Ofunato NS during Miyagiken-oki earthquake 1978 andVina del Mar NS during Chile earthquake 1985. It is seen that the property of the uniform risk stillholds. On the other hand, Fig.12 shows those for ground motions recorded at K-NET, Shinjuku
station (TKY007) and Fig.13 illustrates those for ground motions recorded in Osaka bay area. It canbe found that the ratio of actual input energy to the bound is large. This implies that the groundmotion of March 11 includes wave components in a broad period range.
20
2

Hyogoken-Nanbu 1995,
JMA Kobe NS
h=0.0520
15
10

Near-fault Rock Motion

5
0

0

1

2

3

actual input energy
credible bound (acc)credible bound (vel)

2

2

25

input energy per unit mass (m /s )actual input energy
credible bound (acc)credible bound (vel)2

input energy per unit mass (m /s )30

15Cape mendocino 1992,
Petrolia NS
h=0.05

10

0

4

Near-fault Soil Motion

5

0

1

natural period (s)
1

3

4

40
2

Miyagiken-oki 1978,
Ofunato NS
h=0.05

0.5
Long-duration Rock Motion
0.25

00

1

2

3

actual input energy
credible bound (acc)credible bound (vel)

2

2

0.75

input energy per unit mass (m /s )actual input energy
credible bound (acc)credible bound (vel)2

input energy per unit mass (m /s )2natural period (s)30Long-duration Soil Motion
10

0

4

Chile 1985,
Vina del Mar NS
h=0.0520

0

1natural period (s)

2

3

4

natural period (s)Fig.11 Credible bound of input energy for various types of ground motions (near-fault rock motion,near-fault soil motion, long-duration rock motion, long-duration soil motion) (Takewaki 2004)
20.0

15.0

10.0

5.0

0.0

0

2

4
6
Natural period (s)actual input energy
credible bound(acceleration constraint)
credible bound(velocity constraint)

2 2

Input energy per unit mass (m /s )actual input energy
credible bound(acceleration constraint)
credible bound(velocity constraint)

2 2

Input energy per unit mass (m /s )

20.0

15.0

10.0

5.0

0.0

8

0

2

4
6
Natural period (s)Fig.12 Credible bound of input energy for ground motion recorded at K-NET,
Shinjuku station (TKY007)

1013

8

20.0

15.0

10.0

5.0

0.0

0

1

2

3 4 5 6Natural period (s)7Actual Input Energy
credible bound (acceleration constraint)
credible bound (velocity constraint)

2 2

Input energy per unit mass (m /s )Actual Input Energy
credible bound (acceleration constraint)
credible bound (velocity constraint)

2 2

Input energy per unit mass (m /s )

20.0

8

15.0

10.0

5.0

0.0

0

1

2

3 4 5 6Natural period (s)78

Fig.13 Credible bound of input energy for ground motion recorded in Osaka bay area
CONCLUSIONS
The following conclusions have been obtained.
(1) The 2011 off the Pacific coast of Tohoku earthquake is the most devastating earthquake in Japanafter the 1923 Great Kanto earthquake in terms of the damaged area and loss cost. This
earthquake may be the largest inter-plate earthquake which affected mega cities after theconstruction of super high-rise buildings. However this earthquake may not be the mostinfluential one. This fact has been confirmed from the comparison with the result using thesimulated ground motions provided by the Japanese Government.
(2) The ground motion recorded at K-NET, Shinjuku station (TKY007), Tokyo contains fairly large
long-period wave components and has a frequency content of broad band (2-6 seconds). Thiscan be observed from not only the velocity response spectra (and Fourier spectra) but also theearthquake input energy spectra taking into account of the concept of critical excitation.
(3) The region of short natural period in the input energy spectrum can be controlled by the credible
bound for the acceleration constraint and the region of long period by the credible bound for thevelocity constraint (Takewaki 2004, 2006). The introduction of both credible bounds enables theconstruction of a reliable bound with uniform risk in all the natural period range. Especially thecredible bound (Takewaki 2004, 2006) for the velocity constraint can control the bound of input
energy from the long-period ground motion and this bound plays a role for overcoming thedifficulties caused by uncertainties on period and duration of long-period ground motions.
(4) Visco-elastic dampers (high-hardness rubber dampers with high damping capacity) and viscousdampers (oil dampers) are able to damp the building vibration during long-period ground motionsin an extremely shorter duration compared to the building without those dampers. It has been
made clear that the safety is not the only target and the functionality together with theconsideration of psychological aspects of residents has to be protected appropriately.
(5) The word ‘unexpected issue’ is often used in Japan after this great earthquake. It may be true thatthe return period of this class of earthquakes at the same place could be 500-1000 years and theuse of this word may be acceptable to some extent from the viewpoint of the balance (or trade-off)
between the construction cost and the safety. However, the critical excitation method is expected
to enhance rationally the safety level of building structures under uncertain circumstances byexpecting the unexpected (Aster 2012).
(6) The concepts of redundancy, robustness (Takewaki 2008b, AIJ 2011c) and resilience (Committee
on Nat. Earthq. Resilience Res., Implementation, and Outreach (2011)) and their relationship may
be a key factor for designing building structures with greater earthquake resilience.

1014

ACKNOWLEDGMENTS
This paper includes an extended version of the preliminary report (Takewaki 2011) and also part of thepaper (Takewaki et al. 2011b). Part of the present work is supported by the Grant-in-Aid for
Scientific Research of Japan Society for the Promotion of Science (No.20656086, 21360267). This
support is greatly appreciated. The use of ground motion records at K-NET, Building ResearchInstitute of Japan and Nikken Sekkei Co. is also highly appreciated. The ground motions provided
by PEER Center (1998) are also appreciated.

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