Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTHE 2010 MAULE AND THE 2011 GREAT EAST
JAPAN EARTHQUAKES-LESSONS LEARNED FOR
THE SEISMIC DESIGN OF STRUCTURES
Mario E. RODRIGUEZ1
1Professor, Instituto de Ingenieria, National University of Mexico,Mexico, Mexico City, mrod@servidor.unam.mx

ABSTRACT: Some ground motions recorded in the 2010 Maule, the 2011 Great East Japan and the1985 Mexico Earthquakes are used in this paper for analyzing the structural response of typical buildings
using simple models. Lateral displacements of structures, hysteretic energy response spectra and ameasure of earthquake damage are calculated in this paper using the selected records. From results foundin the analysis conducted in this paper, seismic design implications for structures are discussed. It isfound that structures on soft soil need to have special seismic design considerations.

Key Words: Damage parameter, seismic design, Great East Japan earthquake, 2010
Chile Earthquake, earthquake engineering.

INTRODUCTION
The recent 2010 Chile and 2011 Great East Japan earthquakes had high magnitudes, 8.8 and 9.0,
respectively. It is relevant to evaluate the observed response of structures during these strong earthquakes
along with results from response spectra analysis using recorded ground motions. In this paper, results from
response spectra analysis and a measure of seismic damage corresponding to the 2010 Chile and 2011
Great East Japan earthquakes are calculated. As a comparison, these parameters are also evaluated for the1985 Mexico City earthquake. Results from the evaluation of these parameters are used to discuss someseismic design implications for structures.

EARTHQUAKE GROUND MOTIONS AND OBSERVED BUILDING BEHAVIOR
In this study four accelerograms recorded in three earthquakes are analyzed. These earthquakes inchronological order are 1985 Mexico City, 2010 Chile, and 2011 Japan. Table 1 shows typicalcharacteristics of the earthquake ground motions that have been used, which include Magnitude Ms,
epicentral distance, soil type at the recording site, peak ground acceleration, PGA (g), where g is theacceleration of gravity, peak ground velocity, PGV (cm/s), and the abbreviations used for the records
selected.
Building behavior observed during these earthquakes is documented in the literature. According toa review of this information, the most destructive earthquakes were the ones experienced in Mexico1304

City (1985) and Chile (2010).
Table 1 Earthquake Data

Comp.

Abbr.

Epic.
Dist.
(km)

Ms
(Mw)

PGA
(g)

Year

1234

2010 Concepcion
NSCON-1
D65
8.80.40
2011
Tsukidate
NSMYG004
C
125.9
9.0
2.73
2011
SendaiNS
MYG013
C
126.1
9.01.55
1985
SCTEW
SCT
Soft soil
400
8.1
0.17
*ASCE 7-05 Site Classification: C (Vs= 360 to 760 m/s), D (Vs= 180 to 360 m/s)

ChileJapan
Japan
MexicoStationSite*ClassNo Earthq.

PGV(cm/s)
6894
7561

APPROXIMATE LATERAL DISPLACEMENT ANALYSIS OF STRUCTURES
A simple approach is chosen here for the evaluation of lateral displacements, which uses SDOF
systems to analyze global displacements of multistory buildings. A constant deflected shape isassumed for the seismic analysis of multistory buildings and the roof displacement,  , is selected asresponse parameter of an equivalent SDOF system (Saiidi and Sozen, 1981).
The maximum roof drift ratio in a multistory building, Drm , is defined as.

Drm H(1)where  m is the maximum roof displacement and H is the height of the building.
Considering a regular building with n floors and a constant story height, h , the following
expression can be written:

H  nh(2)

In addition, the fundamental period of a building, T , and n can be related byTn

(3)

The parameter  depends of the type of structure. For structural wall buildings on firm soil as those
designed according to the Chilean and Japanese practice, results from small amplitude ambientvibration tests suggest a value of  equal to 20 (Rodriguez and Aristizabal, 1999). For typical framebuildings on firm soil constructed before 1985 in Mexico City a value of 10 has been suggested for (Rodriguez and Aristizabal, 1999). Lower values of  should be used for buildings in soft soil asthat of the Mexico City case. A valued of 1.3T has been suggested for evaluating the SSI period,
where T is evaluated considering the fixed-base case (Rodriguez and Aristizabal, 1999). A reductionof lateral stiffness should be considered when analyzing the response of buildings during earthquakes.
As an approximate procedure, it is assumed in this study that the effective fundamental period of abuilding is equal to 2 times the fundamental period of vibration obtained from small amplitude
vibration tests. Thus, when evaluating Drm , the previous discussed values should be affected by thefactor

2 . According to this discussion, a value of  equal to 14 it is assumed in this paper when1305

analyzing buildings in Japan. For Chile, considering that the analyzed ground motion was obtained ina type of soft soft soil, a value of  equal to 14/1.3=10.8. For Mexico City, considering framebuildings on soft soil, a value of 5.4 is used.
The seismic response of a building is related here to the response of a SDOF system with a lateraldisplacement u and yielding displacement u y . A basic assumption of this procedure is that thefundamental circular frequency,  , and the maximum global displacement ductility ratio  m , in themultistory building are equal to the circular frequency and maximum displacement ductility ratio ofthe SDOF system, respectively. With these assumptions,  m and u y can be related by means of theparameter  using the following expression:mm u y(4)when performing a global seismic analysis of regular building structures, parameter  can beapproximated to 5/4 (Sozen, 1997).
Combining Eqs (1)-(4), Eq (1) can be written as:

Drm m  u yTh(5)Displacement u of the SDOF system was computed for given ductility displacement ratios, (1,2,4) and considering a fraction of critical damping,  , equal to 0.02, using the RUAUMOKO
computer program (Carr, 2011) and the Takeda hysteresis rule, with a stiffness, ku , defined as:ku  ko  0.5

(6)

where ko is the initial stiffness of the system. The reloading stiffness parameter was taken equal to0.5.
Figure 1 shows plots of Drm spectra using the above discussed values for the parameters
involved in Eq (5) and considering h  3m . An inspection of inelastic results shows that in general
the highest roof drift ratios correspond to frame systems responding to the SCT Mexico City record,with the highest demands in the period range of about 1.2-2.5 s, that is buildings in the range of 7-14stories. Results found using the Concepcion record (CON-1), recorded in the area of highest building
damage in the city of Concepcion, show that the highest roof drift ratios correspond to wall buildingsin the period range of about 0.9-2.2 s, see Fig. 1, that is buildings in the range of 10-24 stories. In bothcases, Mexico City and Concepcion, the highest rate of building damage was observed in the above
mentioned range of number of stories.
For the 2011 Japan earthquake, results using the Sendai record indicate maximum values of Drmof about 0.01 in the range of 0.5-1.0 s, that is in the range of 7-14 stories. For the Tsukidate record,
maximum values of Drm , from 0.01 to 0.015, were calculated in the range of 0.1-0.3 s, that is in therange of 1-4 stories.

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Sendai
0.04

0.03

0.03

0.02

Drm

Drm

Tsukidate
0.04

Duc 1
Duc 2

0.01

0.02

Duc 1
Duc 2

0.01

Duc 4

Duc 4
0.00

0.00
00.5

1

1.5

22.5300.5

1T (s)2

2.5

3T (s)a)Tsukidateb) Sendai

CON-1

SCT

0.04

0.08

0.03

0.06

0.02

DrmDrm

1.5

Duc 1

0.04

Duc 1

Duc 20.01

Duc 20.02

Duc 4

Duc 4
0.00

0.00
00.5

1

1.5

2

2.5

0

3

0.5

1

1.5

2

2.5

3T (s)

T (s)c) Concepciond) SCT

Fig. 1 Drm spectra for 4 earthquake ground motion records

SEISMIC RESISTANCE
By specifying a displacement ductility ratio,  , for an inelastic SDOF system for a given earthquake
record, the seismic resistance, C y , is defined as:

Cy RyMg(7)

where Ry is the yielding resistance and M is the mass of the structure.
Figure 2 shows results of the evaluation of C y for the Tsukidate, Sendai and Concepcion records,
which were calculated using elastic and inelastic analysis of the same SDOF system above described.
As shown in Fig. 2, the maximum demand of elastic seismic resistance for the Tsukidate record ranged
from 5g to about 17g in the period range 0.1-0.3 s, whereas the maximum demand of elastic seismic
resistance for the Sendai record led to values of about 1.5g to 3.7g in the period range 0-1.1 s.
Resistance to the elastic C y demands in the low range of periods such as that of the Tsukidate casecan be explained considering low values of mass for typical structures such as those for housing in thisperiod range. Therefore, in the case of the Tsukidate record it is expected an elastic behavior ofstructures in this low range of periods. Figure 2 shows C y demands for the Concepcion record. As
seen there, maximum inelastic demands of C y ranged from about 0.5g to 0.7g in the range 0.15 to0.7s.

1307Sendai

204153CyCyTsukidate

10Duc 1
Duc 252Duc 1
Duc 21Duc 4

Duc 4
000.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

T (s)

1.5

2.0

2.5

3.0

T (s)

a) Tsukidateb) Sendai
CON-1
2.0Cy

1.5
1.0

Duc 1
Duc 2

0.5

Duc 4

0.0
0

0.5

11.5

2

2.5

3T (s)c) Concepcion

Fig. 2

CY spectra for 3 earthquake ground motion records

PARAMETER FOR MEASURING SEISMIC DAMAGE
For a MDOF structure with fundamental circular frequency  and height H , the parameter I d(Rodriguez, 1994) for measuring seismic damage is defined as:Id  2 EH( H Drd ) 2(8)where EH is the hysteretic energy per unit mass dissipated by the SDOF system representing theMDOF system, and Drd is the maximum roof drift ratio in a building associated to an acceptablebuilding performance in a strong earthquake. In this paper it is assumed the value of 0.015 forparameter Drd , for both wall and frame buildings.

A parametric form of the product  H for regular buildings has been proposed by Rodriguez(1994):

 H  2  h(9)Figure 3 shows results of the evaluation of I d for the cases of  equal to 2 and 4 for the selectedearthquake ground motions. The assumed values for  and h for evaluating I d were those used1308

for the previous discussed evaluation of Drm . Results shown in Fig. 3 indicate that the highest
damage parameter correspond to the SCT record (Mexico City, 1985). However, results using theConcepcion record indicate also high values of the damage parameter, particularly in the range of
1-1.8 s, that is in the range of about 10 to 20 stories. It is of interest that the peak value of I d for theSCT record is only about 50% higher that the peak value corresponding to the Concepcion record.
Furthermore, the shape of the I d spectra for the Concepcion record has some similarities to that ofthe demands of I d for the SCT record, see Fig. 3, which suggests a type of soft soil in the areas
where the mentioned accelerograms were recorded. The above discussed computed values of I d andshape of the I d spectra for the SCT and Concepcion records explain the important building damage orcases of failures observed in the 1985 Mexico and 2010 Chile earthquakes in Mexico City andConcepcion, respectively.
Maximum I d values for the case of the Sendai record are equal to about 1.0, see Fig. 3, which isa value much lower than the maximum values for I d obtained using the SCT and Concepcion
records, which suggests for the Sendai case expected building damage much lower than that observedin the 1985 Mexico and 2010 Chile earthquakes. It is of interest that for the Tsukidate record
parameter I d ranges from about 1 to 3.7 in the period range 0.1-0.25 s. However, as mentioned
before, for typical structures in this low range of periods, such as those for dwellings, due to their low
levels of mass it is expected elastic response. Therefore, the demands of hysteretic energy in this casewould be null.
Sendai

Tsukidate

44

Duc 2

2

Id6

Id6

Duc 22

Duc 4

Duc 4
00
0.0

0.5

1.0

1.5

2.0

2.5

0.0

3.0

0.5

1.0

1.5

2.0

2.5

3.0

T (s)T (s)a) Tsukidateb) Sendai

CON-1

SCT664IdId4

Duc 22

Duc 4

Duc 22Duc 40000.5

11.5

22.5

0

30.5

11.5

2

2.5

3T (s)

T (s)c) Concepciond) SCT

Fig. 3 Measure of seismic damage for 4 earthquake ground motion records

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CONCLUSIONS
A seismic damage parameter formerly proposed by the author is used in this study to evaluate seismic
damage using data from the recent 2010 Chile and 2011 Great East Japan earthquakes. For comparison
with results from this evaluation, seismic damage is also evaluate for the case of 1985 Mexico Cityearthquake.
Results from the evaluation show an acceptable correlation with global building damage observedin the earthquakes studied. It is also found that is relevant controlling lateral displacements, mainly
roof drift ratio of buildings, for minimizing seismic damage.
The 2010 Chile earthquake also showed the importance of properly considering soil properties forthe seismic design of buildings since buildings in a type of soft soil in Concepcion had computed
values of the proposed seismic damage parameter that were comparable to those corresponding to theMexico City case not only in maximum values of this parameter but also in the shape of the spectra forthe damage parameter. A number of RC structural wall buildings on this type of soil in Concepcion
either collapsed or had severe structural damage during the 2010 Chile earthquake.
The computed values of the damage parameter for the case of the analyzed ground motions
recorded in the 2011 Great East Japan earthquake were in general significantly lower than thosecorresponding to the 2010 Chile, 2011 Great East Japan and 1985 Mexico City earthquakes, which isin agreement with the observed building damage in these earthquakes.
The above conclusions suggest that the proposed damage parameter can be used as a useful andsimple tool for an innovative seismic design approach and for evaluating expected seismic
performance of existing regular structures.

ACKNOWLEDGMENTS
The author acknowledge the assistance of his formerly graduate students for developing the proposed
damage index, and the support of the Instituto de Ingenieria, UNAM, Mexico City, to carry out thisresearch.

REFERENCES
Carr, A. (2011), “RUAUMOKO, Computer Program Library”, University of Canterbury, Departmentof Civil EngineeringRodriguez, M. E. (1994), “A Measure of the Capacity of Earthquake Ground Motions to DamageStructures”, Earthquake Engineering & Structural Dynamics, Nº 23, pp. 627-643.
Rodriguez, M. E. and Aristizabal J.C. (1999) “Evaluation of a Seismic Damage Parameter”,
Earthquake Engineering & Structural Dynamics, Nº 28, pp. 463-477.
Saiidi M. and Sozen M. (1981), “Simple nonlinear analysis of RC structures”, Journal StructuralDivision, ASCE, Vol 197, pp 937-952.
Sozen M. (1997), “Drift-driven design for earthquake resistance of reinforced concrete”,
EERC-CUREe Symposium in Honor of Vitelmo Bertero, Report UCB/EERC-97/05, EERC,
University of California, Berkeley.

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