Estimation of Secured Distance between Neighboring Buildings
to Avoid Seismic Pounding
Daigoro Isobe1 and Kenta Takatera2
1

Division of Engineering Mechanics and Energy, University of Tsukuba
Tennodai 1-1-1, Tsukuba-shi, Ibaraki 305-8573, JAPAN
isobe@kz.tsukuba.ac.jp
2Graduate School, University of Tsukuba
Tennodai 1-1-1, Tsukuba-shi, Ibaraki 305-8573, JAPANs1011181@u.tsukuba.ac.jp
Abstract
In this study, some seismic pounding analyses are performed on two neighboring buildings
with different heights using a finite element code based on the adaptively shifted integration(ASI)-Gauss technique. Elastic limit distances of each building are estimated by applying
various sine waves with different natural periods. Furthermore, a story drift angle of 1/100,
which is an allowable plastic limit stated in the Building Standard Law, is added to each
elastic limit distance to estimate the secured distance between the buildings. The secured
distance between 8-story and 12-story steel frame buildings, for example, became 1,150 mm
by summing both elastic and plastic limit distances. The numerical results clearly showed theeffect of the secured distance compared to those of shorter distances.
Introduction
Seismic pounding phenomena, particularly the collision of neighboring buildings underlong-period ground motion, are becoming a more significant issue. For example, the Nuevo
Leon buildings in the Tlatelolco district of Mexico City, which consisted of three similarbuildings built consecutively with narrow expansion joints between them, collapsed due toseismic pounding in the 1985 Mexican earthquake [1].
In this study, some seismic pounding analyses are performed on two neighboring buildings
with different heights using a finite element code based on the adaptively shifted integration(ASI)-Gauss technique [2]. The numerical code provides a higher computational efficiency
than the conventional code for this type of problem and enables us to address dynamic
behavior with strong nonlinearities, including phenomena such as member fracture andelemental contact. Contact release and re-contact algorithms are implemented in the code tounderstand the complex behaviors of structural members during seismic pounding and thecollapse sequence.
Elastic limit distances of each building are estimated by applying various sine waves withdifferent natural periods. Furthermore, an allowable plastic limit stated in the BuildingStandard Law, which is a story drift angle of 1/100, is added to each elastic limit distance toestimate the secured distance between the buildings. Some numerical examples with various
distances in between are performed under Atsuma wave, which was observed in 2003
Tokachi-oki Earthquake, to confirm the seismic pounding phenomena and the resulting
damages of the buildings.

- 464 -Column and beamsFloors

48 m
32 mYZX(a) 8-story model(b) 12-story model

Figure 1: Numerical models
Numerical models and conditions
Two building models with different heights are constructed to perform some seismic
pounding analyses. One of the models is an 8-story, 3-span steel building designed with abase shear coefficient of 0.232, and the other is a 12-story, 3-span steel building designedwith a base shear coefficient of 0.167, as shown in Fig. 1. Their floor heights are 4 m andspan lengths are 6 m. The columns and beams are made of SS400 steel and a floor load of 800
kgf/m2 is applied on all floors. In both models, the members are modeled with four linear
Timoshenko beam elements per member. The total number of elements are 1,856 for theformer model and 2,784 for the latter model. The 12-story steel building models with theirbase shear coefficients of 0.083 (50 % of the original model), 0.125 (75 %), 0.210 (125 %),0.250 (150 %), 0.330 (200 %) are also constructed. The natural periods to X-axis direction,
elastic and plastic limit deformations are obtained as shown in Table 1. It is clear that thenatural periods of 12-story models depend upon their base shear coefficients, however, there
are no significant difference in elastic limit deformations between them.
Table 1: Natural periods, elastic and plastic limit deformations of each model
Base shear coefficient
Natural period [s]Elastic limit
deformation [mm]Plastic limit
deformation [mm]8-story model
0.232
1.24

0.083
2.69

0.125
2.11

12-story model
0.167
0.210
1.79
1.57

0.250
1.41

0.330
1.20

138

192

208

209

213

211

320

209
480

The acceleration record data of Atsuma wave, which is used as an input seismic wave, isshown in Fig. 2. Figure 3 shows its acceleration response spectrum, and Table 2 shows themaximum acceleration and predominant period of the seismic wave. The predominant periodof the seismic wave in EW direction (which is X-axis direction in the models) nearly matcheswith the natural period of the 12-story model with a base shear coefficient of 0.167.

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Response spectrum [gal]1000(a) EW

100

100.1

EWNSUD1
Period [s]10Figure 3: Acceleration response spectrumof Atsuma wave(b) NS

Table 2: Maximum acceleration andpredominant period of Atsuma wave(c) UDFigure 2: Input seismic wave (Atsuma wave)

Max. acceleration [gal]Predominant period [s]

EW
380.6
1.95

NS249.3
1.90

UD
100.1
0.20

We define the sum of elastic limit deformations of both models as the elastic limit distance,
the sum of plastic limit deformations as the plastic limit distance, and the sum of both elastic
and plastic limit distances as the elasto-plastic limit distance. In this case, the elastic limit
distance can be estimated as 350 mm, the plastic limit distance as 800 mm, and theelasto-plastic limit distance as 1,150 mm, respectively, according to Table 1. The two models
shown in Fig. 1 are placed with these distances between them as shown in Table 3. We
applied a 17 % Atsuma wave to see the behaviors of two neighboring models which only
deform elastically, when excited independently. Then we applied a 100 % Atsuma wave tosee the effects of three limit distances between two models.
Table 3: Distance between two models for each input wave
Input seismic wave
17 % Atsuma wave
100 % Atsuma wave

Distance between two models [mm]100，350
350，800，1150

Numerical results and summary
There were no plastic deformations occurred or collisions between two models observed in
the case when the distance between two models was set to its elastic limit distance, 350 mm,
and 17% Atsuma wave was applied. However, the shorter distance 100 mm made the twomodels collide sequentially and many elements in both models yielded in the process.

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For the 100 % Atsuma wave as an input, the rate of yielded elements in each case became asshown in Table 4. The rates of yielded elements in 8-story and 12-story models when excitedindependently were 30.5 % and 39.0 %, respectively. However, the rates became larger (andin greater rate in 8-strory model) as the distance between two models became shorter. Even amember fracture occurred in elastic and plastic limit distance cases. Figure 4 shows thebehaviors of the models at moment of impact, when elastic limit distance is adopted as thedistance between both models. fy in the figure indicates yield function value and elements
colored in red means that they are yielded. The 12-story model deformed largely as it nearlymatches the predominant period of the input wave and many plastic elements could beobserved. The 8-story model, on the other hand, deformed locally at the uppermost story,
which indicates the occurrence of some local collisions near the location.
The numerical results indicate that the elasto-plastic limit distance should be taken as aclearance between two buildings to avoid any excessive, serious damages. However, furtherinvestigation should be taken to see the effects of building sizes, strengths, seismic waves andso on.
Table 4: Rate of yielded elements and presence of member fracture in each case

Independent model
Elasto-plastic limit distance
1150 [mm]Plastic limit distance800 [mm]Elastic limit distance
350 [mm]

8-story model
Rate of yielded
Memberelements [%]fracture
30.5
None

12-story model
Rate of yielded
Memberelements [%]fracture
39.0
None

35.5

None

39.7

None

38.3

None

41.3

Yes

46.7

Yes

42.6

None

1.00
0.90
0.80
0.67

0.34

0.00

Figure 4: Moment of impact (49.1 s, 100% Atsuma wave, elastic limit distance 350 mm)
References[1] D. Isobe, T. Ohta, T. Inoue and F. Matsueda: Seismic Pounding and Collapse Behavior ofNeighboring Buildings with Different Natural Periods, Natural Science, Vol. 4, No. 8A,
pp.686-693, 2012.
[2] K. M. Lynn and D. Isobe: Finite element code for impact collapse problems of framedstructures, International Journal of Numerical Methods in Engineering, Vol.69, No. 12,
pp.2538-2563, 2007.

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