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Vol.11, No.3 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION
September, 2012
Earthq Eng & Eng Vib (2012) 11: 343-358 DOI:
10.1007/s11803-012-0126-0
Earthquake induced pounding between adjacent buildings
considering soil-structure interaction
Sadegh Naserkhaki1, Farah N.A. Abdul Aziz1 and Hassan
Pourmohammad2
1. Department of Civil Engineering, Faculty of Engineering,
Universiti Putra Malaysia, Serdang, Malaysia
2. Department of Civil Engineering, Faculty of Engineering,
Islamic Azad University, Karaj Branch, Karaj, Iran
Abstract: Many closely located adjacent buildings have suffered
from pounding during past earthquakes because they vibrated out of
phase. Furthermore, buildings are usually constructed on soil;
hence, there are interactions between the buildings and the
underlying soil that should also be considered. This paper examines
both the interaction between adjacent buildings due to pounding and
the interaction between the buildings through the soil as they
affect the buildings seismic responses. The developed model
consists of adjacent shear buildings resting on a discrete soil
model and a linear visco-elastic contact force model that connects
the buildings during pounding. The seismic responses of adjacent
buildings due to ground accelerations are obtained for two
conditions: fi xed-based (FB) and structure-soil-structure
interaction (SSSI). The results indicate that pounding worsens the
buildings condition because their seismic responses are amplifi ed
after pounding. Moreover, the underlying soil negatively impacts
the buildings seismic responses during pounding because the ratio
of their seismic response under SSSI conditions with pounding to
those without pounding is greater than that of the FB
condition.
Keywords: adjacent buildings; underlying soil; pounding; seismic
response; fi xed-based (FB); structure-soil-structure interaction
(SSSI)
Correspondence to: Sadegh Naserkhaki, Department of Civil
Engineering, Faculty of Engineering, Universiti Putra Malaysia,
Serdang, MalaysiaTel: +98-26-34425876; Fax: +98-26-34425876 E-mail:
[email protected]
Research Assistant; Senior Lecturer; Assistant ProfessorReceived
November 22, 2011; Accepted May 30, 2012
1 Introduction
Pounding is the impact of the adjacent buildings on each other
when they vibrate out of phase and the separation gap between them
is less than the minimum distance required for them to vibrate
freely due to earthquake excitation. This phenomenon has caused
building damage during most destructive earthquakes. For instance,
pounding-incurred building damage happened during the 1985 Mexico
City and 1989 Loma Prieta earthquakes, as reported by Rosenblueth
and Meli (1986) and Kasai and Maison (1997), respectively. Even for
recent earthquakes, there are several reports of building damage
due to pounding despite great improvements in building codes (Wang,
2008; GRM, 2008, 2009).
Building codes in earthquake-prone areas typically assign
preventive provisions to avoid pounding between the adjacent
buildings (TBC, 1997; INBC, 2005; IBC, 2009). Despite these
building code provisions, the risk of building pounding is still
high because:
Building codes do not consider the out of
phase responses of the adjacent buildings (Kasai et al., 1996;
Hao and Shen, 2001), and changes of the phase difference of seismic
responses due to the underlying soil (Jeng and Kasai, 1996).
Building displacements can be larger than the displacements
considered by building codes due to the underlying soil (Savin,
2003).
Many researchers have attempted to elucidate the effects of
pounding on the seismic responses of the adjacent buildings, but
many aspects of the subject are yet to be determined. The primary
notable contributions in the study of pounding of the adjacent
buildings are the studies conducted by Anagnostopoulos (1988),
Maison and Kasai (1990), Anagnostopoulos and Spiliopoulos (1992)
and Maison and Kasai (1992). Numerical models of the pounding of
the adjacent buildings have been developed, and the effects of
different parameters have been investigated. Pounding signifi
cantly amplifi es the seismic responses of the adjacent buildings,
particularly by increasing the story shear, which could lead to
building damage. The most important conclusion from these studies
is that neglecting pounding effects could result in inappropriate
building design where the pounding potential is high.
More recent studies have attempted to account for different
factors involved in the pounding of the adjacent buildings. Studies
on the effects of the mass distribution on pounding structures
(Cole et al., 2011), pounding of seismically isolated buildings (Ye
et al., 2009;
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344 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
Polycarpou and Komodromos, 2010), eccentric building pounding
(Wang et al., 2009), heavier adjacent building pounding (Jankowski,
2008), mid-column building pounding, (Karayannis and Favvata, 2005)
and corner building pounding (Papadrakakis et al., 1996) are some
examples. Although these studies signifi cantly contribute to the
fi eld, they did not account for the infl uence of the underlying
soil on building pounding.
It is apparent that the underlying soil affects the seismic
responses of buildings, whereas there are a limited number of
studies on seismic pounding that consider the soil effects. The
underlying soil affects the pounding of the adjacent buildings in
two ways: spatially varying earthquakes and the soil-structure
interaction (SSI). Hao et al. (2000) and Hao and Gong (2005)
investigated the seismic responses of the adjacent buildings
subjected to pounding due to spatially varying earthquakes. The
attenuation of waves propagating through the soil and the
associated time lag cause the buildings to experience different
seismic responses. However, the infl uence of the spatial variation
of earthquake ground motions is of secondary importance compared to
the SSI because the adjacent buildings are close to each other.
The SSI and its infl uence on the pounding of the adjacent
buildings have been studied by Rahman et al. (2001), Chouw (2002)
and Shakya and Wijeyewickrema (2009). Rahman et al. (2001) studied
the pounding behavior of two 6-story and 12-story moment-resistant,
reinforced concrete frame structures while considering the soil
effects. In their studies, the adjacent buildings and underlying
soil were modeled using the FEM-BEM method with the RUAUMOKO
software package; the seismic responses to the El-Centro earthquake
were obtained via an inelastic dynamic analysis, and the Hertz
contact force model was used to represent the pounding between the
adjacent buildings. Rahman et al. (2001) found that the shift of
period due to the underlying soil altered the time at which the fi
rst impact occurred, which had consequences on the subsequent
poundings. However, they conservatively did not draw a unique
conclusion; they instead recommended each case be evaluated
individually for its particular confi guration, site condition and
expected seismic hazard.
Chouw (2002) went further by stating that poundings could
amplify the induced fl oor vibrations, while the SSI suppressed the
induced vibrations. Amplifying the fl oor vibrations referred to
higher mode vibrations, which signifi cantly infl uenced the
secondary structures. Unlike previous studies, this research did
not determine how the pounding affects the buildings structural
members. Chouw (2002) also claimed that both the soil and
long-period pulses in the ground excitation could increase the
pounding potential of buildings.
Shakya and Wijeyewickrema (2009) analyzed non-equal story height
buildings considering the underlying soil effects to study the
mid-column pounding of the adjacent buildings. They used the SAP
2000 software
to model the adjacent buildings and the underlying soil. The
buildings were connected by a combination of the Gap element and
the Kelvin-Voigt model. The authors asserted that pounding forces,
interstory displacements and normalized story shears were generally
decreased when the underlying soil was considered.
The seismic responses of the adjacent buildings are generally
subjected to several uncertainties in addition to the unknown
characteristics of the earthquake. With one confi guration of the
adjacent buildings, three fundamental periods are found: two for
either building and one for the pounded buildings. Thus, more
studies are necessary to create a more reliable conclusion. This
research fi rst elucidates the effect of the underlying soil on the
fundamental period of individual and pounded adjacent buildings.
Then it develops an analytical model to analyze the seismic
responses of the adjacent buildings resting on the soil subjected
to earthquake induced pounding. Sinusoidal ground accelerations
with a wide range of periods as well as real earthquake
accelerations are applied to the model, and the resulting responses
are analyzed and discussed. A parametric study is performed, and
the effects of the underlying soil on the seismic responses of the
adjacent buildings subjected to earthquake induced pounding are
investigated.
2 Development of the analytical model
The analytical model comprises two sub-models: (1) the adjacent
buildings resting on the soil, vibrating individually and freely,
and (2) pounding forces, which are combined to create the
analytical model for the pounding of the adjacent buildings resting
on the soil.
2.1 Analytical model of the adjacent buildings resting on the
soil
The adjacent buildings and underlying soil are modeled as shear
buildings and discrete soil, respectively, with a concentrated
mass, a viscous damper and a linear spring, as shown in Fig. 1(a).
The analytical model of the adjacent buildings resting on the soil
is shown in Fig. 1(b). The building and the underlying soil are
connected through interaction forces with equal magnitudes but
opposite directions. These interaction forces come from the
inertial forces that correspond to the masses of the building and
the underlying soil, called the inertial interaction (Clough and
Penzien, 2003; Naserkhaki and Pourmohammad, 2011). Moreover, the
adjacent buildings are coupled through the underlying soil, and the
response of each building affects the other because they are
located in near proximity, termed the structure-soil-structure
interaction" or "SSSI" effect (Padron et al., 2009; Naserkhaki and
Pourmohammad, 2011). The equation of motion for two adjacent
buildings with the SSSI effect consideration due to earthquake
acceleration of ug (t) is proposed by Naserkhaki and Pourmohammad
(2011) as:
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No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
345
M U C U K U M v vbsb bsb bsb bsb bsb bsb bsb + + = +( )bsb fbsb
ug (t)(1)
where Mbsb, Cbsb and Kbsb are the mass, damping and stiffness
matrices, respectively. U Ubsb bsb, , Ubsb, vbsb and vfbsb are the
acceleration, velocity, displacement and the infl uence vectors of
the buildings and underlying soil, respectively. This equation
consists of two sets of equations corresponding to the two
buildings, while these two sets of equations are coupled by the
off-diagonal SSSI components of stiffness and damping matrices. The
fi rst set includes n+2 coupled equations; n for the NDOF for the
left building and 2 for the 2DOF for the underlying soil.
Similarly, the second set includes m+2 coupled equations; m for the
MDOF for the right building and 2 for the 2DOF for the underlying
soil (n>m).
A more tractable version of Eq. (1) is created by its expansion,
Eq. (2). The defi nitions of the variables in Eq. (1) are still
valid for Eq. (2), while the subscripts l and r stand for the left
and right buildings, respectively; b and s denote the building and
underlying soil, respectively; and, bs (sb is the transpose of bs)
and bsb indicate the SSI and the SSSI, respectively. The seismic
responses of the adjacent buildings resting on the soil subjected
to earthquake acceleration are obtained by
Eq. (2); however, the pounding between the adjacent buildings is
not yet involved in this equation.
m m 0 0m m 0 0
0 0 m m0 0 m m
uu
ls lbs
lsb lb
rs rbs
rsb rb
ls
lb
uu
rs
rb
(2)
+
c 0 c 00 c 0 0
c 0 c 00 0 0 c
uuuu
ls bsb
lb
bsb rs
rb
ls
lb
rs
r
bb
+
k 0 k 00 k 0 0
k 0 k 00 0 0 k
uuuu
ls bsb
lb
bsb rs
rb
ls
lb
rs
rb
=
m m 0 0m m 0 0
0 0 m m0 0 m m
0v0
v
ls lbs
lsb lb
rs rbs
rsb rb
lb
rb
+
v0v0
ls
rs
u tg ( )
Fig. 1 Analytical model of adjacent buildings resting on the
soil
Ilncln kln
Ilm mlm
clm klm
Ili mli
cli kli
Il1 ml1
cl1 kl1
Irm mrm
crm krm
Iri mri
cri kri
Irl mrl
crl krl
ml, mlf kbsb mr, mrfkl, klf kbsbf kr, krfcl, clf cbsb cr, crf
cbsbf
ulf+Hnul +uln
ulf+Hmul +ulm
ulf+Hiul +uli
ulf+H1ul +ul1
urf+Hmur +urm
urf+Hiur +uri
urf+H1ur +ur1
Hn
Hm
Hi
H1
u tg ( )(a) Adjacent buildings resting on the soil (b) Discrete
model
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346 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
The matrices and vectors of Eq. (2) corresponding to the left
building are introduced in the following (those corresponding to
the right building are the same as those for the left building,
except that the subscripts l and n are replaced by r and m,
respectively).
mm
mlb =
l
ln
1 0 00
SYM. (3)
klb =
+
+
+
+
k k kk k k
k k
k n
l1 l2 l2
l2 l3 l3
l3 l4
l( -1)SYM.
0 0 00 00 0
kk kk
n n
n
l l
l
(4)
mli and kli are mass and stiffness of ith fl oor of the left
building. clb is Rayleigh damping matrix of the left building
proportional to mass and stiffness matrices.
ulbT = { }u u nl1 l (5) ulbT = { }u u nl1 l (6)ulb
T= { }u u nl1 l (7)
vlbT
= { }1 1 (8)u il , u il and uli are acceleration, velocity and
displacement of ith fl oor of the left building.
mls =+ +
+
= =
= =
m H m I H m
H m m m
ii
nii
n
ii
nf ii
n
l2
li li1 i l1
li1 l l1
(9)
m mlbs lsbT
= =
H m H mm m
n n
n
1 l1 l
l1 l
(10)
cls =
cc f
l
l
00
(11)
kls =
kk f
l
l
00
(12)
Hi is the height of ith fl oor from the center of gravity of the
underlying soil and Ili is mass moment of inertia of the ith fl
oor. Mass components of the discrete soil model (ml and mlf) are
virtual masses of underlying soil plus mass of the rigid foundation
(subscripts and f are the notation for rocking and horizontal
components of soil deformation, respectively). Damping (cl and clf)
and stiffness (kl and klf) coeffi cients of the discrete soil model
are frequency dependent parameters that can be
described in the time domain by the basic constants of soil
including its shear modulus (G), shear wave velocity (Vs) and
Poissons ratio () and the width of the foundation (a).
ulsT = { }u u fl l (13) ulsT = { }u u fl l (14)uls
T= { }u u fl l (15)
vlsT
= { }0 lm f (16)where ul , ul and ul are acceleration, velocity
and displacement corresponding to rocking deformation of the
underlying soil, respectively, and u fl , u fl and ulf are
acceleration, velocity and displacement corresponding to the
horizontal deformation of the underlying soil, respectively
cbsb =
cc f
bsb
bsb
00
(17)
kbsb =
kk f
bsb
bsb
00
(18)
Values of SSSI damping (cbsb and cbsbf) and stiffness (kbsb and
kbsbf) coeffi cients can be obtained from basic constants of soil
as proposed by Mulliken and Karabalis (1998).
2.2 Analytical model of the pounding
Pounding of the adjacent buildings can be simplifi ed as
pounding of different masses corresponding to each building at the
same level. The stereomechanical and contact force models are two
available pounding models in structural analysis. The momentum
conservation principle is used in the former method by considering
the coeffi cient of restitution to model the pounding. One of the
signifi cant infl uence factors is the duration of pounding, which
is ignored in this method, thereby preventing force from being
derived by this method.
However, the contact force model provides the advantages of
considering the pounding duration and pounding force that has been
used widely in the numerical analysis of pounding of the adjacent
buildings. In this force-based model, a spring and a viscous damper
are introduced to model the pounding force. The characteristics of
the associated spring and viscous damper could be either linear or
nonlinear; depending on the linearity and damping, four models have
been proposed: (i) linear elastic; (ii) linear visco-elastic; (iii)
nonlinear elastic; and iv. nonlinear elastic with nonlinear
damping. Additionally, eliminating damping from the linear
visco-elastic and nonlinear elastic with nonlinear damping models
reduces them to the linear elastic and nonlinear elastic models,
respectively. Studies by
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No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
347
Jankowski (2005) and Muthukumar and DesRoches (2006) revealed
that the differences between different contact force models were
not signifi cant; however, the nonlinear elastic with nonlinear
damping, and after that, the linear visco-elastic models, gave more
accurate results. Note that there is a general agreement among
researchers that the contact force model does not signifi cantly
affect the seismic responses of a building.
The advantages of the linear visco-elastic contact force model
are as follows: it is effi cient and practical and provides the
pounding force while considering the energy dissipation during
pounding, thus, it is used in this research. The relationship
between the pounding force and displacement is shown in Fig. 2. Its
only
defi ciency is that it provides tension forces at the end of
pounding with no physical meaning, which is ignorable.
The linear visco-elastic contact force model consists of a
linear spring representing the stiffness of the contact and a
viscous damper representing the energy dissipation during pounding.
Figure 3(a) demonstrates the analytical model of the adjacent
buildings connected by the linear visco-elastic contact force
model. The contact force model is inactive when the buildings
vibrate individually and freely; however, it is activated when the
separation gap is closed, causing the adjacent buildings to pound
together. Pounding forces develop immediately after pounding by the
relationship:
F k u c ui i i i ip sg sg= + (19)where ui and ui are the
relative displacement and relative velocity at the ith fl oor,
respectively, and ksgi and csgi are the contact stiffness and
damping of the ith fl oor, respectively. The relative displacement
is given by
u u H u u u H u u ui f i i f i i i= + +( ) + + +( )l l l r r r
sg(20)
Fig. 2 Pounding force-displacement relationship (Naserkhaki,
2011)
Linear elasticLinear visco-elasticSeparation gap
Poun
ding
forc
e
Relative displacement
Fig. 3 Analytical model of pounding
(a) Linear visco-elastic pounding model (b) Free body diagram of
pounding forces
where usgi is the separation gap at the ith fl oor. In a similar
way, relative velocity is calculated from:
u u H u u u H u ui f i i f i i= + +( ) + +( )l l l r r r
(21)Contact stiffness is a term without a special calculation
procedure. It has been proposed to be proportional to the axial
stiffness of the pounded diaphragm by some authors (Maison and
Kasai, 1990; Maison and Kasai, 1992; Zhu et al., 2002;
Ruangrassamee and Kawashima, 2003; Muthukumar and DesRoches, 2006).
Although other researchers believe that this parameter is better
described by the lateral stiffness of the pounded fl oor, e.g.,
values equal to 50-100 times and 20 times the lateral stiffness of
the pounded fl oor were proposed by Anagnostopoulos (1988) and
Naserkhaki (2011), respectively.
Luckily, a rational method exists to acquire the contact damping
value. It can be determined from the mass and stiffness of the
building in the pounding state, given by Eq. (22) (Anagnostopoulos,
1988):
c k m mm mi i
i i
i isg sg
l r
l r
2=+
(22)
Separation gap
ksgmusgm
usgi
usg1
csgm
ksgi
csgi
ksg1
csg1
ksgm(ulf+Hmul+ulm(urf+Hmur+urm+usgm))
csgm(u
lf+Hmu l+
ulm(
urf+Hm
u r+u
rm))
ksgi(ulf+Hiul+uli(urf+Hiur+uri+usgi))
csgi(u
lf+Hiu l+
uli(
urf+Hi
u r+u
ri))
ksg1(ulf+Hlul+ull(urf+H1ur+ur1+usgi))
csg1(u
lf+Hlu l+
uli(
urf+H1
u r+u
r1))
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348 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
where:
=+
- ln ln 2 2e
e (23)
e is the coeffi cient of restitution, the ratio of the contact
and separation velocities (i.e., the start and end velocity) of the
pounding:
eu uu u
=
( )( )
l r start
l r end
(24)
The coeffi cient of restitution (e) ranges between 1 (pure
elastic) and 0 (pure plastic poundings). Typical values in various
applications for metals are between 0.6 and 1.0 (Nguyen et al.,
1986). Rajalingham and Rakheja (2000) found the coeffi cients of
restitution less than 1.0 and greater than 0.49 are acceptable in
decreasing pounding force while values less than 0.3 are
undesirable in constructive engineering applications. For typical
building material, an interval of 0.5
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No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
349
3 Numerical study
Obtaining the seismic responses of the adjacent buildings during
an earthquake requires solving a second order linear ordinary
differential equation (Eq. (31)). However, this equation is
conceptually nonlinear because its characteristics are changed
periodically from the no-pounding to the pounding states and vice
versa during the analysis. The step by step Newmark (1959) method,
which makes use of integration from the initial to the fi nal
condition for each time step with a linear acceleration history, is
employed for the solution. The equations and solutions were
implemented by a written computer program code to assist with the
analyses. Different time steps were taken during the analyses to
ensure the computational effi ciency of the computer program code;
for the no-pounding state, time steps were 0.02 s, 0.01 s and 0.005
s, depending on the time step for which the earthquake acceleration
was recorded; and for the pounding state, the time step was equal
to 0.001 s, which guarantees the accuracy of the results.
The underlying soil primarily affects the dynamic properties of
the buildings and thus alters the seismic responses of the
buildings. The dynamic properties of the buildings and the seismic
responses of the buildings are studied for four cases:
(1) N-FB, adjacent buildings with FB condition do not pound
together.
(2) P-FB, adjacent buildings with FB condition pound
together.
(3) N-SSSI, adjacent buildings with SSSI condition do not pound
together.
(4) P-SSSI, adjacent buildings with SSSI condition pound
together.
The results are presented and discussed in the following
subsections.
3.1 Dynamic properties of the adjacent buildings
All dynamic characteristic factors of the studied buildings
including height, material, stiffness and mass are combined into
the most signifi cant dynamic property of the building called the
building period, which helps to predict the buildings seismic
behavior during the earthquake. The underlying soil essentially
causes an elongation of the building period. Finding the building
period requires solving the matrix eigenvalue problem:
K M = (33)where M and K are the mass and stiffness matrices,
respectively. Moreover, and are eigenvalues and eigenvectors,
respectively. The eigenvalues i are the roots of the characteristic
equation:
f ( ) = [ ] =det 0K M (34)where f() is a polynomial of order
equal to the number
of DOFs of the building/buildings. The solution method for the
eigenvalue problem must be iterative in nature because it requires
fi nding the roots of the polynomial f(). The inverse vector
iteration method is used in this study to obtain the fundamental
period of the building. Higher modal periods, which contribute less
in building vibration than the fundamental period, are not
presented in this study. The underlying soil increases both the
fundamental and 2nd modal periods, while the rate of change for the
fundamental period is greater than that of the 2nd modal period
(Naserkhaki and Pourmohammad, 2011).
Each building confi guration possesses three distinct
fundamental periods: (1) the fundamental period of the left
building, (2) the fundamental period of the right building and (3)
the fundamental period of the pounded buildings. To obtain the
fundamental period of the left and right buildings in the
no-pounding state, M and K are replaced by Mbsb and Kbsb,
respectively. In the no-pounding state, the adjacent buildings with
the FB condition are vibrating individually and freely, and the
fundamental period of each building is not affected by the other
building. The adjacent buildings with the SSSI condition are
coupled through the soil, so they have interaction through the
underlying soil during the vibration and the fundamental period of
each building is slightly affected by the other building. In the
pounding state, regardless of the FB or SSSI condition, the
adjacent buildings interact together through the pounded fl oors,
so the vibration and the fundamental period of each building is
substantially affected by the other building. When the adjacent
buildings are pounded together, M is again replaced by Mbsb, while
K is replaced by (Kbsb+Kp). To obtain the fundamental period of the
pounded buildings, all components of Kp are effective, meaning that
all adjacent fl oors collide together. The fundamental period of
pounded adjacent buildings is almost equal for both cases of
collision between all adjacent fl oors and the collision between
only the top fl oor of the short building and the adjacent fl oor
of the tall building (i.e., the difference is minor).
The buildings under study here are residential buildings with a
mass of 100 tons per story and a lateral stiffness in compliance
with INBC (2005). The fundamental period of the buildings can be
found from their mass and stiffness. Additionally, a wide range of
soil types are chosen, from soft to hard soils, with a shear wave
velocity ranging from 140 to 750 m/s.
The variation of the fundamental periods of three confi
gurations of the adjacent buildings (i.e., 10-story vs. 8-story,
10-story vs. 6-story, and 10-story vs. 4-story) are shown in Fig.
4. In the fi gure, there are three lines corresponding to each
confi guration; the upper and the lower lines indicate the
variation of the fundamental periods of the no-pounding state of
individual buildings, and the middle line indicates the variation
of the fundamental periods of pounding states in the pounded
buildings.
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350 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
Figure 4 indicates that longer fundamental periods are obtained
for buildings resting on softer underlying soils with lower shear
wave velocities, while the longest fundamental period is referred
to the softest underlying soil. Furthermore, the rate of the
fundamental period increment is higher for the taller buildings,
with the maximum (25%) increment being that of the 10-story
building.
Figure 4 also indicates that the fundamental period of pounded
buildings in the pounding state falls between the fundamental
periods of the individual buildings in the no-pounding state,
regardless of the foundations condition. In the pounding state,
pounded buildings are combined into a new structural system with a
new fundamental period that is stiffer than an individual tall
building but is more fl exible than an individual short building.
This result shows that, after pounding, the tall
buildings fundamental period shifts toward the rigid zone, while
the short buildings fundamental period shifts toward the fl exible
zone. However, the effect of this period shift is smaller for the
tall building than for the short building, particularly if the
latter building is too short. The nearer the fundamental period of
pounded buildings is to the fundamental period of the tall
building, the more the tall building dominates the seismic
responses of buildings during pounding.
3.2 Seismic responses of the adjacent buildings to sinusoidal
excitations
This section discusses the effects of the underlying soil on the
seismic responses of the confi guration of a 10-story building
adjacent to a 5-story building due to ground accelerations without
and with pounding. The buildings are residential buildings with a
mass of 100 tons per story and a lateral stiffness of 171 MN/m.
These properties are adopted from INBC (2005), which gives the
fundamental periods as tabulated in Table 1. These building
properties provide a relatively fl exible behavior for a 10-story
building, whereas a 5-story building exhibits a relatively stiff
behavior; thus, the 10-story building is called the fl exible
building and the 5-story building is called the stiff building.
The contact stiffness is equal to 10,000 MN/m, and the coeffi
cient of restitution is taken as 0.65. When the SSSI condition is
considered, the underlying soil has a shear wave velocity equal to
140 m/s, a shear modulus equal to 32.34 MN/m2 and a Poissons ratio
equal to 0.35. The ground excitations applied to these models are
artifi cial sinusoidal ground accelerations with periods ranging
from 0.1 s to 10 s. This range of excitation period is wide enough
to capture the buildings responses due to any real earthquake (the
seismic responses of the adjacent buildings due to real earthquakes
will be discussed in the next section).
Figures 5 and 6 show the results spectrum of seismic induced
maximum displacements and story shears of the top fl oors of the
buildings, respectively, because the top fl oors experience the
most critical condition. Additionally, the peak displacements and
story shears of the top fl oors of the buildings are summarized in
Tables 2 and 3, respectively, for comparison. The peak response
(displacement/story shear) of each case is the largest response
among all maximum responses of that case and occurs in the
resonance period. The peak responses of the buildings occur within
the ground acceleration periods ranging between 0.5 s and 1.5 s.
Meanwhile, the local peak responses occur at smaller ground
acceleration periods, corresponding to the higher modes of
vibration but with minor, negligible effects for structural
members.
Note that the shift in the peak responses toward the fl exible
zone due to the underlying soil effect is visible in both fi gures.
In the no-pounding cases, the peak responses of the buildings with
the SSSI condition
Fig. 4 Variation of fundamental periods of adjacent buildings
with soil shear wave velocity
-
No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
351
Fig. 5 Maximum displacement of the top fl oor of the buildings
against ground acceleration periods under sinusoidal excitation
Fig. 6 Maximum story shear of the top fl oor of the buildings
against ground acceleration periods under sinusoidal excitation
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Dis
plac
emen
t (m
)
0.160.140.120.100.080.060.040.02
0
Dis
plac
emen
t (m
)
N-FB
P-FB
N-SSSI
P-SSSI
N-FB
P-FB
N-SSSI
P-SSSI
0.1 1 10Period (s), logarithmic scale
(a) Top fl oor of 10-story building
0.1 1 10Period (s), logarithmic scale
(b) Top fl oor of 5-story building
0.1 1 10Period (s), logarithmic scale
(a) Top fl oor of 10-story building
0.1 1 10Period (s), logarithmic scale
(b) Top fl oor of 5-story building
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
Stor
y sh
ear (
MN
)
3.0
2.5
2.0
1.5
1.0
0.5
0
Stor
y sh
ear (
MN
)
N-FB
P-FB
N-SSSI
P-SSSI
N-FB
P-FB
N-SSSI
P-SSSI
Table 1 Fundamental periods of the buildings with different
conditions
Fundamental period (s)10-story individual building Pounded
adjacent buildings 5-story individual building
FB 1.02 0.95 0.53SSSI 1.27 1.11 0.61
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352 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
occur for periods 25% and 15% longer than the period in which
the peak responses of the buildings with the FB condition occur for
the individual fl exible (Figs. 5(a) and 6(a)) and stiff buildings
(Figs. 5(b) and 6(b)), respectively. For the pounding cases, the
peak response of both buildings occurs at periods 17% longer for
the SSSI condition than for the FB condition (Figs. 5 and 6).
Furthermore, Figs. 5 and 6 show that pounding causes a shift in
the peak response toward the rigid zone for the fl exible building,
whereas it shifts toward the fl exible zone for the stiff building.
The shift of the peak responses due to pounding is less remarkable
for the fl exible building compared to the stiff building. The peak
responses of the fl exible building for the pounding case occur in
periods 7% (FB) and 13% (SSSI) shorter than the no-pounding case,
while for the stiff building, the peak responses for the pounding
case occur at periods 79% (FB) and 82% (SSSI) longer than the
no-pounding case because the fl exible building shares larger mass
during pounding than the stiff building.
In addition to the shift in the peak responses, pounding causes
the buildings to experience different values of responses due to
seismic excitations (Figs. 5 and 6; Tables 2 and 3). The peak
displacements are reduced 0.41-fold (FB) and 0.56-fold (SSSI) in
the fl exible building due to pounding (Fig. 5(a)). The comparison
between the SSSI and FB conditions reveals that the underlying soil
causes larger displacements in the building; the increment is up to
1.16-fold and 1.57-fold for the no-pounding and pounding cases,
respectively. The larger displacements of the SSSI buildings are
due to the additional displacements imposed on the fl exible
building by the underlying soil, mostly due to the rocking
component of the underlying
soil for upper stories. Unlike the fl exible building, the peak
displacements of a stiff building are increased 1.17-fold (FB) and
1.55-fold (SSSI) due to pounding (Fig. 5(b)). The peak
displacements of the stiff building are 1.10-fold and 1.46-fold
larger for the no-pounding and pounding cases, respectively, when
considering the underlying soil. While the underlying soil causes
larger displacements in all cases, the rate of increment is greater
for the pounding cases.
The effect of pounding on the story shears of both buildings is
incremental where the buildings experience larger story shears due
to pounding (Fig. 6). The peak story shear is increased 1.34-fold
(FB) and 2.00-fold (SSSI) for the fl exible building and 2.14-fold
(FB) and 2.89-fold (SSSI) for the stiff building due to pounding.
It is notable that the underlying soil develops contradictory
effects on building story shears for the no-pounding and pounding
cases. The story shear is reduced 0.74-fold for the fl exible
building and 0.77-fold for the stiff building for the no-pounding
case, whereas for pounding case, it is increased 1.11-fold for the
fl exible building and 1.03-fold for the stiff building. The
reduction of the story shear for the top fl oors of the buildings
in the no-pounding cases is due to a reduction of the story drift
of the top fl oors because of the rocking component from the
underlying soil. However, pounding suppresses the rocking effect
and causes the buildings to experience larger story drifts and,
thus, larger story shears.
The effects of pounding on the seismic responses of other fl
oors of the buildings in terms of displacement ratio and story
shear ratio are shown in Figs. 7 and 8, respectively
(displacement/story shear ratio of each fl oor refers to the ratio
of its peak displacement/story shear in the pounding case compared
to its peak displacement/story shear in the no-pounding case). In
general, the
Table 3 Peak story shears of the top fl oor of the buildings
Story shear of 10-story (MN) Story shear of 5-story (MN)
No-pounding PoundingRatio of
pounding to no-pounding
No-pounding PoundingRatio of
pounding to no-pounding
FB 2.165 2.893 1.336 1.227 2.628 2.142SSSI 1.608 3.216 1.999
0.941 2.716 2.887Ratio ofSSSI to FB 0.743 1.112 - 0.767 1.033 -
Table 2 Peak displacements of the top fl oor of the
buildings
Displacement of 10-story (m) Displacement of 5-story
(m)No-pounding Pounding Ratio of
pounding to No-pounding
No-pounding Pounding Ratio ofpounding to no-
poundingFB 0.564 0.233 0.413 0.089 0.104 1.168SSSI 0.653 0.365
0.559 0.097 0.151 1.554Ratio ofSSSI to FB 1.157 1.567 - 1.098 1.460
-
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No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
353
results show that the seismic responses of the buildings can be
categorized into following three types, depending on the building
fl oor whose response is of concern:
(1) Above-pounding fl oors for the fl exible building with the
extreme condition at the top fl oor,
(2) Through-pounding fl oors for the fl exible building with the
extreme condition at the mid fl oor,
(3) Through-pounding fl oors for the stiff building with the
extreme condition at the top fl oor.
As shown in Fig. 7(a), the displacement ratios for the fl exible
building are less than one, so it experiences smaller peak
displacements after pounding. The displacement reduction due to
pounding is justifi ed through all fl oors of the fl exible
building and is approximately half of that in the no-pounding case.
Although both the FB and SSSI conditions demonstrate a similar
pattern, the SSSI condition has greater displacement ratios than
the FB condition, meaning that the underlying soil causes larger
displacements in the fl exible building in the pounding case, which
does not favor the fl exible building during pounding.
Despite reducing the displacements, the relative displacements
(i.e., story drifts) are not reduced through
all fl oors of the fl exible building. When the adjacent
buildings pound together, through-pounding fl oors in the fl exible
building are prevented from moving further by the adjacent
building, while its above-pounding fl oors move freely, which
causes a sudden jump between the displacements of the
through-pounding and above-pounding fl oors. While the relative
displacements of the through-pounding fl oors are reduced, this
sudden jump causes a sharp increment of relative displacement in
the above-pounding fl oors, which is like a whiplash behavior.
Because the story shears are produced due to relative
displacements, the story shears of the fl exible building are
decreased in the through-pounding fl oors, while they are
dramatically increased in the above-pounding fl oors (Fig. 8(a)).
The story shear ratios of the fl exible building are greater for
the SSSI than for the FB condition, which means that if the fl
exible building is pounded to the adjacent building, then it
experiences larger story shears because of the underlying soil.
Therefore, the underlying soil is again unfavorable for the fl
exible building.
For the stiff building, both the displacement ratios and story
shear ratios of all fl oors are greater than unit
Fig. 7 Displacement ratios of the buildings after pounding
Fig. 8 Story shear ratios of the buildings after pounding
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement ratio
(a) 10-Story
109876543210
109876543210
Floo
r lev
el
Floo
r lev
el FBSSSI
FBSSSI
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement ratio
(b) 5-Story
-2.5 -1.5 -0.5 0.5 1.5 2.5Story shear ratio
(a) 10-story
109876543210
109876543210
Floo
r lev
el
Floo
r lev
el FBSSSI
FBSSSI
-2.5 -1.5 -0.5 0.5 1.5 2.5Story shear ratio
(b) 5-story
-
354 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
(Figs. 7(b) and 8(b)), meaning that they are amplifi ed after
pounding. The stiff building is pushed away by the fl exible
building during pounding, which not only produces larger
displacements but also creates larger story drifts and,
consequently, larger story shears. Furthermore, the SSSI condition
has greater displacement and story shear ratios than the FB
condition. Therefore, the underlying soil is also detrimental to
the stiff building because it causes it to experience larger
displacement and story shears in the pounding case.
In summary, pounding causes smaller displacements but larger
story shears for the fl exible building. Considering the underlying
soil effect (SSSI condition), the displacements and story shears
produced in the fl exible building due to pounding are both larger
than those in the FB condition. For the stiff building, the
displacements and story shears both are larger in the pounding case
than in the no-pounding case. Both the displacements and story
shears produced in the stiff building due to pounding are amplifi
ed when the underlying soil is considered. Thus, pounding worsens
the adjacent buildings conditions because their responses are
amplifi ed due to the pounding and the rate of amplifi cation is
higher by considering the underlying soil. The effects of pounding
should be considered in the building design and the adjacent
buildings should be modeled together with the underlying soil to
maximize the safety of the building design.
3.3 Responses of the adjacent buildings to real earthquakes
The acceleration records of real earthquakes are applied to the
building confi guration to investigate their seismic responses. The
characteristics of the earthquake records are summarized in Table
4. The results are shown in terms of envelopes of maximum
displacements and story shears of the buildings, the dominant
factors in building seismic design. The structural elements are
then designed to resist the story shear from earthquake excitation
and their displacements are checked to remain in allowable
limits.
The envelopes of maximum displacements and story shears of the
buildings produced due to different earthquakes are shown in Figs.
9 and 10, respectively. Figures 9 (a), (c), (e) and (g) show that
the maximum displacements of the fl exible building are reduced
throughout all fl oors during pounding. The changes in the story
shear are not the same as the changes in the
displacements due to earthquake induced pounding. While the
story shears of the fl exible building are reduced in the through
pounding fl oors, they are increased dramatically in the above
pounding fl oors (Fig. 10 (a), (c), (e) and (g)) due to the
whiplash effect. For the stiff building, the critical condition
happens in the no-pounding side of the building where both the
displacements (Fig. 9 (b), (d), (f) and (h)) and story shears (Fig.
10 (b), (d), (f) and (h)) are increased because the fl exible
building pushes the stiff building away during pounding. The
patterns of seismic responses are similar for both the FB and SSSI
conditions; however, Figures 9 and 10 show that the SSSI condition
provides larger values of responses, particularly after
pounding.
Though the patterns of seismic responses for the buildings are
similar, each building demonstrates a unique response to each
earthquake with different values and ratios of responses. The top
fl oor of the fl exible building on the pounding side and the top
fl oor of the stiff building on the no-pounding side suffer the
most from earthquake induced pounding, leading to a discussion of
these fl oors responses in the following paragraphs.
The top fl oor of the fl exible building with the FB condition
experiences the largest displacement of 0.12 m after pounding under
the El Centro earthquake while it experiences the largest
displacement of 0.18 m after pounding under the Kobe earthquake if
its condition is changed to SSSI. The maximum displacement ratio of
the top fl oor of the fl exible building with the FB condition is
0.73 under the Victoria earthquake, while for the SSSI condition
this ratio is 0.74 under the El Centro earthquake. The largest
story shear produced at the top fl oor of the fl exible building
after pounding is 2.22 MN for the FB condition and 2.52 MN for the
SSSI condition, both under the El Centro earthquake. The maximum
story shear ratio of the top fl oor of the fl exible building is
3.36 for the FB condition and 4.88 for the SSSI condition under the
Victoria earthquake and the El Centro earthquake, respectively.
The Loma Prieta earthquake causes the largest displacement of
0.10 m for the FB condition and 0.13 m for the SSSI condition at
the top fl oor of the stiff building after pounding. The maximum
displacement ratio of the top fl oor of the stiff building is 1.17
for the FB condition under the El Centro earthquake and 1.39 for
the SSSI condition under the Kobe earthquake. The largest story
shear of the top fl oor of the stiff building is 1.63 MN for the FB
condition after pounding, which is
Table 4 Characteristics of records of earthquakes
Earthquake Year Record/Component PGA (g) Site condition
(USGS)Kobe 1995 KOBE/KAK090 0.345 DEl Centro 1940 IMPVALL/I-ELC180
0.313 CVictoria, Mexico 1980 VICT/CPE315 0.587 BLoma Prieta 1989
LOMAP/G01090 0.473 A
-
No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
355
Fig. 9 Envelopes of maximum displacements of the buildings under
different real earthquakes
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(a) Kobe (10-story)
Floo
r lev
el
Floo
r lev
el N-FBP-FBN-SSSIP-SSSI
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)(b) Kobe (5-story)
Floo
r lev
el
Floo
r lev
el-2.5 -1.5 -0.5 0.5 1.5 2.5
Displacement (m)(c) El Centro (10-story)
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(d) El Centro (5-story)
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(e) Victoria (10-story)
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(f) Victoria (5-story)
Floo
r lev
el
Floo
r lev
el
Floo
r lev
el
Floo
r lev
el
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(g) Loma Prieta (10-story)
-2.5 -1.5 -0.5 0.5 1.5 2.5Displacement (m)
(h) Loma Prieta (5-story)
-
356 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11
Fig. 10 Envelopes of maximum story shears of the buildings under
different real earthquakes
-6 -3 0 3 6Story shear (MN)
(a) Kobe (10-story)
Floo
r lev
el
Floo
r lev
el
N-FBP-FBN-SSSIP-SSSI
-6 -3 0 3 6Story shear (MN)(b) Kobe (5-story)
Floo
r lev
el
Floo
r lev
el
-6 -3 0 3 6Story shear (MN)
(c) El Centro (10-story)
-6 -3 0 3 6Story shear (MN)
(d) El Centro (5-story)
-6 -3 0 3 6Story shear (MN)
(e) Victoria (10-story)
-6 -3 0 3 6Story shear (MN)
(f) Victoria (5-story)
Floo
r lev
el
Floo
r lev
el
Floo
r lev
el
Floo
r lev
el
-6 -3 0 3 6Story shear (MN)
(g) Loma Prieta (10-story)
-6 -3 0 3 6Story shear (MN)
(h) Loma Prieta (5-story)
-
No.3 Sadegh Naserkhaki et al.: Earthquake induced pounding
between adjacent buildings considering soil-structure interaction
357
produced under either the El Centro earthquake or the Loma
Prieta earthquake. The largest story shear of the top fl oor of the
stiff building with the SSSI condition is 1.98 MN after pounding
under the El Centro earthquake. The maximum story shear ratio of
the top fl oor of the stiff building is 1.88 for the FB condition
and 3.44 for the SSSI condition, both under the Kobe
earthquake.
Not only do the values of the maximum displacements and story
shears increase but the ratios also increase when the underlying
soil is considered. These increments happen for all earthquakes,
although the rate of increment is different for each earthquake.
Although the pattern of the earthquake induced response of
buildings is the same, the underlying soil has a unique effect for
each building confi guration. Each case possesses three distinct
fundamental periods (i.e., two for either individual building and
one for pounded buildings); the underlying soil shifts each
fundamental period to a new one. Thus, different responses are
expected under the same earthquake because of different foundation
conditions (i.e., FB and SSSI), which increases the uncertainty of
the problem. Therefore, each case must be evaluated specifi cally
considering the buildings together with the underlying soil since
ignoring the underlying soil can underestimate the design and lead
to detrimental consequences.
4 Conclusions
This study develops a numerical model of the adjacent buildings
resting on the soil with the buildings connected by the
visco-elastic contact force model during pounding. The contact
force model is activated when the buildings pound together. The
dynamic properties of the adjacent buildings as well as their
seismic responses are presented and discussed in this paper.
Each building confi guration possesses three distinct
fundamental periods; two for either building and one for the
pounded buildings where the fundamental period of the pounded
buildings falls between the individual fundamental periods of the
buildings, closer to the tall and fl exible building. The
underlying soil causes a lengthening of all three fundamental
periods.
The seismic responses of the adjacent buildings subjected to
sinusoidal ground accelerations as well as the accelerations of
different earthquakes are calculated. The results show that
pounding causes smaller displacements but larger story shears in
the fl exible building, while the displacements and story shears
are increased in the stiff building due to pounding. The underlying
soil (SSSI) increases the displacements and story shears produced
in both buildings due to pounding compared to those seen under the
FB condition. In conclusion, pounding worsens the adjacent
buildings conditions, which is amplifi ed by the underlying soil.
Pounding effects should be considered in the building design and
the buildings should be modeled together with the underlying soil
to create the safest design
profi le; ignoring the effects of the underlying soil may result
in unrealistic and unconservative designs with detrimental
consequences.
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358 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11