Simulation of the response of base-isolated buildings under ...

Vol.11, No.3

EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION

Earthq Eng & Eng Vib (2012) 11: 359-374

September, 2012

DOI: 10.1007/s11803-012-0127-z

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility Sayed Mahmoud1,2†, Per-Erik Austrell1† and Robert Jankowski3‡ 1. Department of Construction Sciences, Division of Structural Mechanics, Lund University, Sweden 2. Faculty of Engineering at Mataria, Helwan University, Cairo, Egypt 3. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Poland

Abstract: The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil. However, it is often customary to idealize the soil as rigid during the analysis of such structures. In this paper, seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted. The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots. In the analysis, a large number of parametric studies for different earthquake excitations with three different peak ground acceleration (PGA) levels, different natural periods of the building models, and different shear wave velocities in the soil are considered. For the isolation system, laminated rubber bearings (LRBs) as well as high damping rubber bearings (HDRBs) are used. Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions: (1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures; (2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs; (3) although the peak response is affected by the incorporation of soil flexibility, it appears insensitive to the variation of shear wave velocity in the soil; (4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building, indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions, base isolations and shear wave velocities; (5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories, especially for earthquakes with low and moderate PGA levels; and (6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications, especially at the level of the lower stories.

Keywords: base-isolated buildings; rubber bearings; earthquakes; soil-structure interaction

1 Introduction Seismic isolation is a strategy to reduce the seismic forces acting on structures. Isolation systems applied in base-isolated buildings are generally effective due to their flexibility and energy dissipation characteristics. Flexibility in the horizontal direction will lower the fundamental frequency of the building below the range of frequencies which dominate general earthquake input. Providing a method for energy dissipation reduces the seismic energy transmitted to the system during earthquakes so that the structural response will also be reduced. Correspondence to: Robert Jankowski, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Poland Tel: +48 58 3472200; Fax: +48 58 3471670 E-mail: [email protected] † Assistant Professor; ‡Associate Professor Received January 3, 2012; Accepted June 4, 2012

A number of base isolation systems have been proposed and their effects on the dynamic behavior of structures have been thoroughly reviewed by many authors (Kelly, 1997, 1998, 1999; Naeim and Kelly, 1999; Chopra, 1995; Buckle and Mayes, 1990; Jangid and Datta, 1995; Rao and Jangid, 2001; Jangid and Kelly, 2001). A simple isolation system is based on the concept of sliding between the base of the structure and the ground. This well known pure-friction (PF) base isolation system assumes that a low level of friction limits the transfer of shear across the isolation interface. However, two of the most commonly used isolation systems consist of laminated rubber bearings (LRBs) and high damping rubber bearings (HDRBs). The analysis and solution of large isolation base displacement as well as isolation base acceleration problems associated with isolated structures have been investigated (see, Jangid, 1995; Barbat et al., 1995; Jangid and Banerji, 1998; Morales, 2003). LRBs are often used with passive dampers to control the excessive base displacements. On

360


the other hand, the application of HDRBs is considered as one of the most promising among several methods of seismic isolation. Different models have been used to simulate the behavior of HDRB in the horizontal direction (see, for example, Yoshida, 2002). Jankowski (2003) considered a nonlinear rate dependent model of HDRB to accurately simulate the structural response over the entire time of the earthquake excitation. However, most of the previous research on the performance of seismically isolated buildings has been focused on the dynamic behavior of sliding structures based on the PF system subjected to harmonic support motion (Mostaghel et al., 1983; Westermo and Udwadia, 1983; Jangid, 1997; Calio et al., 1998), to earthquake excitations (Toki et al., 1981; Liaw et al., 1988; Constantinou and Kneifati, 1987; Ryan, 2004; Hino et al., 2008), to long-period ground motions (Ariga et al., 2006) and to randomly moving foundations (Constantinou and Tadjbakhsh, 1983, 1984). Moreover, Takewaki (2008) investigated and revealed the robustness of base-isolated high-rise buildings to code-specified ground motions. The energy concepts in the analysis of base-isolated structures subjected to earthquake motions in the time and frequency domains have been introduced by several authors (Austin and Lin, 2004; Takewaki and Fujita, 2009; Yamamoto et al., 2011). A review of the above cited papers indicates that the analyses ignore the influence of soil-structure interaction (SSI) on the dynamic response of structures. Moreover, the isolated bases of the analyzed structures were usually modelled as PF base isolation systems. Seismic design of isolated structures is often based on the rigid base assumption and interaction with the soil-foundation system is ignored. Ignoring the SSI effects may lead to incorrect structural response assessment since it has been recognized that it may have a significant impact on the dynamic system response, especially in cases involving heavier structures and soft soil conditions (see Gazetas and Dobry, 1984; Kavvadas and Gazetas, 1993; Nikolaou et al., 2001). Two general methods are available to rationally incorporate SSI effects into structural analysis (see e.g., Wolf, 1994). The first one is a direct method in which the structure and a portion of the base soil are both incorporated into a finite element mesh. This approach has a number of drawbacks, including the need for a large model, energy absorbing boundaries and detailed soil properties. In the second method, known as a substructure method, the structure and the soil are analyzed separately. A simplified model, which is typically composed of one or more springs or spring-damper combinations to approximate the behavior of the soil, is coupled with the structural model at its base. The most common analytical model is the one in which the soil domain is considered to be a homogeneous elastic half-space. For dynamic SSI problems, several studies proposed lumped-parameter models (see Wolf 1994, 1997; Wolf and Somaini, 1986; De Barros and Luco, 1990; Wu

Vol.11

and Chen, 2001; Wu and Lee, 2002, 2004) to simulate unbounded soil so that these models can be used directly in the time domain analysis. Quite extensive research has been conducted in order to investigate the influence of SSI effects on the response of isolated bridge structures (Zheng and Takeda, 1995; Vlassis and Spyrakos, 2001; Tongaonkar and Jangid, 2003; Jangid, 2004; Kunde and Jangid, 2006; Soneji and Jangid, 2008). However, very limited research has been carried out on the response of isolated buildings with SSI effects. Spyrakos et al. (2009) investigated the importance of considering soil flexibility on the system damping, frequency and mass ratios of an isolated building modelled as a SDOF system. A series of analytical expressions in the frequency domain have been derived in order to investigate the conditions under which the SSI affects the response of base-isolated structures subjected to harmonic ground motions (see Spyrakos et al., 2009). On the other hand, Takewaki (2005a,b) developed a new frequency domain method to evaluate the earthquake input energy to a structurepile system to horizontal earthquake motions. Attempts to examine the seismic response of low-rise buildings through adequate idealization of the structure and subsoil medium can also be found in Dutta and Rana (2010). Although the above cited papers consider SSI effects on the expected structural response, it has been found that most of them have been focused on the response of bridge structures, which exhibit quite different dynamic characteristics comparing to isolated buildings. In the case of buildings, only one type of base isolation system has been considered in the analyses. In addition, the isolated structures have been modelled as SDOF systems or only harmonic excitations have been considered in the study. The aim of this study is to evaluate the effects of base isolation in conjunction with SSI on the seismic response behavior of isolated buildings in the time domain. To achieve this objective, a large number of simulations for SDOF and multi degree-of-freedom (MDOF) systems with different base-isolation systems (linear LRBs and nonlinear HDRBs) subjected to three different real ground motion records has been performed. The responses in terms of accelerations, velocities and displacements with and without SSI effects have been analyzed versus different structural natural periods and regarding the use of linear and nonlinear base-isolation systems. Also, the sensitivity of the response has been investigated for a variety of soil properties in terms of different shear wave velocities in the soil and mass densities.

2 Modelling and idealization 2.1

Base-isolated building models

Base-isolated buildings modelled as SDOF and MDOF systems are described in this subsection. The

No.3

Sayed Mahmoud et al.: Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility 361

models take into account rocking and swaying motion (see Jankowski, 2009). 2.1.1. SDOF base-isolated building model Figure 1 shows the idealized SDOF mathematical model for the isolated building of height h1. A top mass m1 is connected with a rigid mat of mass mb through massless columns with stiffness k1 and damping c1 . 2.1.2. MDOF base-isolated building model The MDOF mathematical model for the isolated building (three-story structure) with the mass mi (i=1,2,3) of each story lumped at the floor level and a base mass mb is shown in Fig. 2. The height, stiffness and damping coefficient for each story is denoted as hi, ki and ci, respectively.

remains elastic and the nonlinearities are localized at the isolation levels. The most commonly used isolation system is composed of elastomeric bearings (Simo and Kelly, 1984). Rubber and steel plates are the basic components of this type of bearings. They are characterized by high damping capacity, horizontal flexibility and high vertical stiffness. 2.2.1. Linear model of isolation system Laminated rubber bearings (LRBs) are one type of elastomeric bearings. They exhibit the parallel action of a linear spring and damper. The restoring force developed in the LRB can be described as:

2.2 Base isolation idealization

where kb, cb, ub and ub are the stiffness, damping coefficient, displacement and velocity of the LRB system, respectively. The isolation period Tb, in terms of the stiffness coefficient and the total mass Mt of the base-isolated building (including the base mass), can be written as:

Fb = kb ub + cb ub

Base isolation of structures provides a reliable and cost-effective measure to mitigate their damage. It allows the superstructure to behave very much like a rigid body where the displacements are concentrated at the level of the isolation devices, i.e., the superstructure

Mt kb

Tb = 2π h

u0

m1

u1

1

h1

b =



ug

kr

Ch

Cr

Fig. 1 Idealized SDOF mathematical model

h3

u0

m3

u3 m3

k3 c3 m2 k2

mb

h3

u2

m1 k1 ub

c1

mb

ug kh ch

k3 c3

kr cr

Fig. 2 Idealized MDOF mathematical model

kb = a1 + a2 (ub ) 2 + a3 (ub ) 4 +

(3)

a6 a4 + cosh 2 (a5ub ) cosh(a7 ub ) cosh(a8ub )

(4a)

m2 k2 c2

u1

h1

c1

h1 h2

c2 m1 k1

h2

cb 2 M t b

2.2.2. Nonlinear model of isolation system High damping rubber bearings (HDRBs) are another type of elastomeric bearings used in the present study for the isolation devices. In order to simulate the behavior of HDRBs, a nonlinear strain rate dependent model (see Jankowski, 2003) is applied. The model describes the behavior of the bearing by a nonlinear elastic spring-dashpot element. The restoring force in the HDRB is computed as in Eq. (1), where kb and cb can be determined at a given time based on the actual values of displacement ub and velocity ub using the following formulas (Jankowski, 2003):

ub

kh

(2)

On the other hand, the damping ratio ξb can be related to the damping coefficient, total mass and the isolation base angular frequency ωb by the formula:

k1

c1

(1)

cb =

a9 + a10 (ub )

2

a112 + (ub ) 2

(4b)

where a1–a11 are parameters of the model which are obtained by fitting the experimental data using the method of least squares. 2.3 Soil modelling The considered building models are assumed to be founded on an elastic half-space without slippage between the model base and the soil. The soil flexibility


 gG

ch = 0.576kh rh

(5)

G  BL2 1 − 0.3  cr = kr rr 1 +  gG kr =

where kh and ch are stiffness and damping coefficients of the swaying spring-damper, kr and cr are the counterparts of the rocking spring-damper, v is the Poisson’s ratio of the soil, βx and βφ are the constants of swaying and rocking spring-dampers (depending on the ratio L/B), rh and rr denotes the equivalent radii of isolated foundation for swaying and rocking spring-dampers, respectively; γ is the density of soil, g refers to the acceleration of gravity and G is the shear modulus which depends on of the shear wave velocity Vs and can be calculated as (Whitman and Richart, 1967):  (Vs ) G= g

(6)

FFT Amplitude

Acceleration (g)

0 -0.2 0

2

4 6 Time (s)

8

10

0.2 0 -0.2 0

2

4 6 Time (s)

8

10

20 30 40 Frequency (Hz)

50

0.6 0.4 0.2 00

10

10


50

1.5 FFT Amplitude

0.5 0 -0.5 -1.0 -1.5

0.1

0.8

N.Palm Springs (PGA=0.59g)

0.4

0.2

0

Chi Chi (PGA=1.13g) 0

5

10

15 20 Time (s)

25

30

1.0 0.5 0

0

10

(7)

where M, C, and K are the mass, damping and

0.3

0

FFT Amplitude

Acceleration (g)

MU + CU + KU + Fb = − MRUg

El Centro (PGA=0.34g)

0.6

Acceleration (g)

The general equations of motion for the isolated system with consideration of the SSI can be written as:

2

0.2

-0.4

3 Governing equations of motions

0.4

0.4

-0.4

The effects of SSI on the response time history of the considered building models have been studied under three different ground motions with three different PGA levels: the El Centro earthquake (1940-05-18, PGA=0.34g), the N. Palm Springs earthquake (1986-0708, PGA=0.59g) and the Chi-Chi (Taiwan) earthquake (1999-09-20, PGA=1.13g). These earthquake records were selected considering that they are characterized by the low-frequency contents in order to induce larger structural response. Acceleration time histories, Fourier transform signals and acceleration response spectra for 5% of critical damping for the selected ground motions are represented in Fig. 3. The maximum ordinates of the pseudo-acceleration are 2.545, 3.070 and 3.381 occurring at periods of 0.25 s, 0.30 s and 0.90 s, for the El Centro, N. Palm Springs and Chi-Chi (Taiwan) earthquake, respectively. This implies that the selected earthquakes are near-fault ground motions.


50

Spectral acceleration (g)

kh = 2(1 − )G  x BL ,

Vol.11

2.4 Earthquake modelling

1.0


allows for horizontal translation and rocking at the structure’s base. For a foundation of length L and width B, the spring stiffness and damping coefficients of swaying and rocking effects, which represent the SSI, are computed using the following expressions (see Whitman and Richart, 1967):

1.5


362

4

0.8 0.6 0.4 0.2 0

0

1

2 3 Period T1 (s)

4

5

0

1

2 3 Period T1 (s)

4

5

1

2 3 Period T1 (s)

4

5

1.0 0.5 0

3 2 1 0

0

Fig. 3 Acceleration time histories (left column), Fourier transform signals (mid column) and acceleration response spectra for 5% of critical damping (right column) for the El Centro earthquake (upper line), N. Palm Springs earthquake (mid line) and Chi-Chi earthquake (bottom line)

No.3


stiffness matrix of the isolated building, respectively; R is an influence matrix; U , U and U represent the acceleration, velocity and displacement vectors, respectively; Ug is the ground acceleration vector and Fb denotes vector containing the forces accumulated in the isolation bearing. 3.1 SDOF building model The model of the isolated building using the SDOF system is shown in Fig. 1. Applying Eq. (7) to the system gives the following expressions for the matrices and vectors: 0 ⎛ m1 ⎜ 0 mb M =⎜ ⎜ m1 mb ⎜ ⎝ m1h1 0

m1 mb m1 + mb m1h1

⎛ k1 −k1 0 ⎜ −k k1 0 K =⎜ 1 ⎜ 0 0 kh ⎜ 0 0 0 ⎝

⎛1 ⎜ 0 R=⎜ ⎜0 ⎜ ⎝0

0 1 0 0

m1h1 ⎞ ⎛ c1 −c1 0 ⎟ ⎜ −c c1 0 0 ⎟ , C =⎜ 1 ⎜ 0 m1h1 ⎟ 0 ch ⎜ 2⎟ m1h1 ⎠ 0 0 ⎝ 0

0⎞ ⎟ 0⎟ 0⎟ ⎟ kr ⎠

0⎞ ⎟ 0⎟ , 0⎟ ⎟ cr ⎠

(8a)

0 0 ⎞ ⎛ u1 ⎞ ⎛ u1 ⎞ ⎛0⎞ ⎛ u1 ⎞ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜  ⎟ 0 0 ⎟  ⎜ ub ⎟  ⎜ u2 ⎟ ub ⎟ f ⎜ , U= , U= , Fb = ⎜ b ⎟ ,U = ⎟ ⎜ u0 ⎟ ⎜ u0 ⎟ ⎜0⎟ ⎜ u0 ⎟ 1 0 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 0 1 h1 ⎠ ⎝  ⎠ ⎝ ⎠ ⎝0⎠ ⎝  ⎠ (8b)

where u1 and ub is the displacement of the superstructure and the isolation bearing, respectively; u0 and φ describe the soil horizontal translation and rocking movements. The corresponding velocities and accelerations are denoted with dots (derivatives with respect to time). 3.2 MDOF building model The model of the isolated building (three-story structure) using the MDOF system is shown in Fig. (2). Similarly, the elements for the matrices and vectors in Eq. (7) can be written as: ⎛ m1 ⎜ ⎜ 0 ⎜ 0 ⎜ 0 M =⎜ ⎜ ⎜ m1 ⎜ ⎜ ⎜⎜ m1h1 ⎝

0 m2 0 0

0 0 m3 0

0 0 0 mb

m1 m2 m3 mb

m2

m3

mb

mb + ∑ mi

3

i =1

3

m2 h2

m3 h3

0

∑m h i =1

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ 3 ⎟ mi hi ⎟ ∑ ⎟ i =1 ⎟ 3 mi hi2 ⎟⎟ ∑ i =1 ⎠ m1h1 m2 h2 m3 h3 0

i i

(9a)

⎛ c1 + c2 ⎜ ⎜ −c2 ⎜ 0 C =⎜ ⎜ −c1 ⎜ 0 ⎜⎜ ⎝ 0 ⎛ k1 + k2 ⎜ ⎜ −k2 ⎜ 0 K =⎜ ⎜ −k1 ⎜ 0 ⎜⎜ ⎝ 0

⎛1 ⎜ ⎜0 ⎜0 ⎜ ⎜0 R = ⎜0 ⎜ ⎜ ⎜ ⎜0 ⎜ ⎜ ⎝

0 1 0 0 0

−c2 c2 + c3 −c3

0 −c3 c3

0 0 0

0 0 0

−k2 k 2 + k3 − k3

0 − k3 k3

0 0 0

0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0

−c1

0 0 0 0 ch

0 0 c1 0 0

−k1 0 0 k1 0 0

0 0 0 0 0 kh 0

0⎞ ⎟ 0⎟ 0⎟ ⎟ 0⎟ 0⎟ ⎟ cr ⎟⎠ 0⎞ ⎟ 0⎟ 0⎟ ⎟ 0⎟ 0⎟ ⎟ kr ⎟⎠

(9b)

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ 3 ⎟ mi hi ⎟ ∑ i =1 ⎟ 3 2 ⎟ mi hi ⎟ ∑ i =1 ⎠ 0 0 0 0 0

⎛ u1 ⎞ ⎛ u1 ⎞ ⎛ u1 ⎞ ⎛0⎞ ⎜  ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ u2 ⎟ ⎜ u2 ⎟ ⎜ u2 ⎟ ⎜0⎟ ⎜ u3 ⎟ ⎜ u3 ⎟ ⎜ u3 ⎟ ⎜0⎟ U = ⎜ ⎟ , U = ⎜ ⎟ , U = ⎜ ⎟ , Fb = ⎜ ⎟ ⎜ ub ⎟ ⎜ ub ⎟ ⎜ ub ⎟ ⎜ fb ⎟ ⎜ u ⎟ ⎜ u ⎟ ⎜u ⎟ ⎜0⎟ ⎜⎜ 0 ⎟⎟ ⎜⎜ 0 ⎟⎟ ⎜⎜ 0 ⎟⎟ ⎜⎜ ⎟⎟ ⎝  ⎠ ⎝  ⎠ ⎝ ⎠ ⎝0⎠

(9c)

where ui and hi (i=1,2,3) is the displacement and height of the ith story of the building.

4 Solution procedures for the equations of motion The solution of Eq. (7) is performed using the finite element toolbox CALFEM (Computer Aided Learning of the Finite Element Method). The function ‘step2’ is utilized for the time integration procedure at equal time steps. The procedure is governed by the coefficients γ and β, the time integration constants for the Newmark family methods (see, for example, Chopra, 1995). In this study, the constant average acceleration approach with γ = 0.5 and β = 0.25 is applied over a small time interval to achieve an unconditional stability.

364


5 Response analysis and results Numerical simulations have been conducted in order to investigate the effects of soil flexibility on the response of base-isolated buildings with different natural periods. In the analysis, different sandy soil types (see Wei et al., 1996; Uniform Building Code Volume 2, 1997) and earthquake motions have been used. Due to space limitations, representative results for one soil type with different shear wave velocities are presented. The soil properties characterized by the shear wave velocities and densities are shown in Table 1. The comparative performance of the building isolated by LRBs and HDRBs, with modelling the isolation devices to behave as a linear and nonlinear system, has been investigated. Table 1 Soil types with different densities and shear wave velocities Soil density γ (103kg/m3) 1.89

Shear wave velocity Vs(m/s)

1.94

220

2.00

255

2.07

275

2.20

500

2.80

1000

3.00

1500

2

4 6 Time (s)

8

10

0

2

4 6 Time (s)

8

4 6 Time (s)

8

10

1

5

0 -1 0

2

4 6 Time (s)

8

5 0 -5 2

4 6 Time (s)

8

10

0

5

10

15 20 Time (s)

25

30

25

30

25

30

Without SSI

-5

With SSI

0

5

10

15 20 Time (s)

40

10 0 -10 -20

With SSI

0

-10

10

Without SSI

-1

10

20

10

-10 0

2

0

2

-2

10

0

1

-2

Acceleration (m/s2)

-2

Acceleration (m/s2)

Velocity (m/s)

-1

Acceleration (m/s2)

Velocity (m/s)

1 0

0

-0.5

Chi-Chi (PGA=1.13g)

2

Velocity (m/s)

-0.2 0

N.Palm springs (PGA=0.59g) Displacement (m)

Displacement (m)

0

-0.4

Figure 4 shows the response characteristics for the base-isolated building modelled as an SDOF system with and without SSI. The building superstructure fundamental period, damping ratio and mass are: T1=1s,

0.5

0.2

The isolated buildings have been excited by a suite of ground motion records. The selected earthquake excitations used in the parametric study are shown in Fig. 3. The records are intended to encompass low, moderate and high PGA levels to better understand the effect of SSI under different earthquake excitations. A numerical study has been carried out using lumped mass models of the base-isolated building under consideration to calculate the response quantities of interest in terms of displacements, velocities and accelerations. The above response quantities are important since story accelerations developed in the superstructure are proportional to the forces exerted due to earthquake ground motion and the bearing displacements are crucial in the design of isolation systems. Moreover, two key factors that engineers must address when designing a seismic-resistant structure are interstory drift and floor acceleration. Interstory drift beyond certain levels will cause severe damage to nonstructural elements (e.g., partitions, ceilings and windows) and may cause light fixtures to fall. High floor accelerations can damage equipment and machinery. 5.1 SFOF model


0.4 Displacement (m)

196

Vol.11

0

2

4 6 Time (s)

8

10

20 0 Without SSI

-20 -40

With SSI

0

5

10

15 20 Time (s)

Fig. 4 SSI effects on displacement (upper line), velocity (mid line) and acceleration (bottom line) time histories of SDOF system isolated by the LRB system under the El Centro (left column), N. Palm Springs (mid column) and Chi-Chi (right column) earthquakes


Base displacement (m)

El Centro PGA = 0.34 g

0.1 0 -0.1 0

1

2

3

4

5 6 Time (s)

7

8

9

10

0.2 N.Palm springs PGA=0.59g

0.1 0 -0.1 -0.2

0

1

2

3

4

5 6 Time (s)

7

8

9

10

1.0 Chi-Chi PGA=1.13g

0.5 0 -0.5 -1.0

0

5

10

15 Time (s)

20

25

30


Without SSI

0.2

-0.2

between the two plots are too small to be identified. Only a slight increase in the peak values due to incorporation of soil flexibility is detected. This implies that considering the flexibility of soil does not affect the response of the flexible base-isolation system. It has also been found that the peak base displacements obtained by ignoring the effect of underlying soil are: 0.1519, 0.1882 and 0.8033 m, while for the case where the SSI effect is considered, the corresponding values have been recorded to be: 0.1524, 0.1883 and 0.8040 m for the El Centro, N. Palm Springs and Chi-Chi earthquake, respectively. This confirms the fact that the flexibility of soil affects the stiff superstructure response and is unable to influence the behavior of the flexible baseisolation system. Similarly, velocity and acceleration time histories at the base of the isolated building under different earthquakes considered in this study confirm the previous results concerning the displacement time histories with and without SSI. Figure 6 shows the peak displacement, velocity and acceleration responses for the linear isolation system with LRBs for different structure natural periods with and without SSI effects under different earthquakes. Note that when the structural period increases, the peak response of the isolated building, ignoring SSI effects, increases as well. However, the influence of the soil flexibility on the peak responses has been found to be considerably different for the various ground motions considered. For earthquakes with a low PGA level, the peak displacement and velocity increase as the system natural period increases, while the peak acceleration is not significant. For ground motions with a moderate PGA level (i.e., N. Palm Springs earthquake), the building peak responses remain nearly unchanged,




ξ1=0.05 and m1=30×103 kg. The story height is h1=3.5 m. For the isolation system, the natural period and the viscous damping ratio of the LRB system are Tb = 2 s and ξb=0.1, respectively. The base mass is mb=90×103 kg. The stiffness of swaying and rocking springs and the damping coefficients of dashpots have been evaluated using the formula given by Eq. (5). The soil mass density and Poisson's ratio are: γ=1.89×103 kg/m3 and v=0.3. The shear wave velocity is taken as Vs=196 m/s. The radii of equivalent circular foundation for swaying and rocking have been estimated and found to be of equal values rh=rr=4m (see Takewaki, 2005a,b). Figure 4 shows the story displacement, velocity and acceleration time histories of the building modelled as an SDOF system isolated by the LRB system with and without SSI under the El Centro, N. Palm Springs and Chi-Chi earthquakes. Note that the displacement, velocity and acceleration values are higher when SSI is considered. The peak values of story acceleration of 4.835, 8.684 and 20.156 m/s2 without SSI increase up to 7.045, 12.404 and 32.119 m/s2 under the El Centro earthquake, N. Palm Springs and Chi-Chi (Taiwan) earthquake, respectively. However, the capacity demand for the superstructure increases due to increased superstructure accelerations when soil flexibility is considered. Moreover, Fig. 4 shows that taking the soil into account does not lead to any major time delay for the response concerning the lower frequency content, suggesting that the influence of soil damping in this case is small. This is due to the relatively small damping in soil compared to that in the isolated building. Displacement time histories at the base of the isolated building under three earthquakes are shown in Fig. 5 with and without SSI. Note that the differences


No.3

With SSI

0.2 El Centro PGA = 0.34 g

0.1 0 -0.1 -0.2

0

1

2

3

4

5 6 Time (s)

7

8

9

10

7

8

9

10

0.2 N.Palm Springs PGA=0.59g

0.1 0 -0.1 -0.2

0

1

2

3

4

5 6 Time (s)

1.0 Chi-Chi PGA=1.13g

0.5 0 -0.5 -1.0

0

5

10

15 Time (s)

20

25

30

Fig. 5 SSI effects on displacement time histories at the base of the isolated building under three earthquakes


El Centro (PGA=0.34g) Without SSI With SSI

0.6 0.4 0.2 00

0.5

1.0 T1 (s)

1.5

2.0

0.3 0.2

0

0.5

1.0 T1 (s)

1.5

2.0

Without SSI With SSI 0

0.5

1.0 T1 (s)

1.5

Without SSI With SSI 0.5

1.0 T1 (s)

1.0 0.5

Chi-Chi (PGA=1.13g)

2.0 1.5 1.0 0.5

0

0.5

1.0 T1 (s)

1.5

2.0

00

0.5 0.5

1.0 1.0 (s) TT1 (s)

1.5 1.5

2.02.0

0

0.5

1.0 T1 (s)

1.5

2.0

0

0.5

1.0 T1 (s)

1.5

2.0

6 5 4 3

1

6

2 0

1.5

2.0

8

4

Peak velocity (m/s)

0.5

Vol.11

7

1.5

2.0

14 12 10 8 6

0

0.5

1.0 T1 (s)

1.5

2.0

Peak acceleration (m/s2)


Peak velocity (m/s)

1.0

0

0.4

2.0


Peak velocity (m/s)

1.5

N.Palm Springs (PGA=0.59g)

0.5

Peak displacement (m)

0.8



366

35 30 25 20 15

Fig. 6 SSI effects on peak displacement (upper line), velocity (mid line) and acceleration (bottom line) responses for the isolated SDOF system against natural periods under different earthquakes. With linear LRBs

except for the slight increase in the peak displacement as the natural period increases. For earthquakes with a high PGA level (i.e., Chi-Chi earthquake), a slight increasing trend can be observed for the peak response curves as the structural natural period increases, and as the natural period continues to increase, a sharp decreasing trend occurs. Figure 7 shows the results for nonlinear HDRBs with and without SSI. Note that the SSI effects induce a larger peak response when compared to the linear LRBs, particularly under moderate and strong earthquakes (e.g., the N. Palm Springs and Chi-Chi earthquakes). Regardless of the overestimation of the peak responses due to the use of nonlinear base isolation, it has been found that for earthquakes with low and moderate PGA levels, the peak response follows almost the same trend as for the system with linear base isolation. For ground motions with high PGA (Chi-Chi earthquake), an increasing trend can be observed as the natural period increases, especially for peak displacement and velocity curves. With further increase in the building period, the peak response of the SSI system with a nonlinear base keeps constant values, differing from the responses observed for the linear base system with SSI. The isolation effects on the seismic response of the studied buildings is examined next. Figures 8–10 show the peak displacement and acceleration amplification factors (AF) as compared between the non-isolated and isolated buildings with respect to the structural natural period under the El Centro, N. Palm Springs and Chi-Chi

earthquakes with different shear wave velocities in the soil (specified in Table 1). Note that, for the non-isolated building, variations in shear wave velocities considerably affect the peak response AF, especially for low structural natural periods. Moreover, when the soil conditions become soft, i.e., the shear wave velocity decreases, the corresponding peak displacement AF increases while the peak AF for the acceleration decreases. It is also worth noting that the PGA levels have been found to be important in affecting the peak acceleration. Figure 8 shows that, for the El Centro earthquake with PGA=0.34g, the peak acceleration AF appears to be below the unit for lower shear wave velocities and slightly above the unit for higher velocity values. For the N. Palm Springs earthquake (see Fig. 9), where the PGA level is larger than the El Centro earthquake, the values for the peak acceleration AF exceed unit, except for the lowest shear wave velocity. On the other hand, for high PGA levels represented by the Chi-Chi earthquake (see Fig. 10), the peak acceleration AF is higher than unit for all considered shear wave velocities in the soil. It is worth noting that for high shear wave velocities (i.e., in the case of buildings resting on very dense, rock and hard rock soils), the displacements and accelerations AF are near to the unit for which the assumption of a rigid base soil can be accepted. Figures 8-10 also show that the response of the base-isolated building is not altered by the shear wave velocity variations, although it is highly affected by the soil flexibility. The simulation results indicate that when



Without SSI With SSI

0.4 0.3 0.2 0.1 0

0

0.5

1.0 T1 (s)

1.5

2.0

0.4

0.5

1.0 T1 (s)

1.5

2.0

0.5

0

0.5

1.0 T1 (s)

Without SSI With SSI 1.5 2.0

10

2.0 1.5 1.0

0

0.5

1.0 T1 (s)

1.5

2.0

4 0

Without SSI With SSI 0.5

1.0 T1 (s)

1.5

2.0

10

5

2 1 0

0.5

1.0 T1 (s)

1.5

2.0

0

0.5

1.0 T1 (s)

1.5

2.0

0

0.5

1.0 T1 (s)

1.5

2.0

10 8 6 4

60

0

0.5

1.0 T1 (s)

1.5

2.0


6


15

8

3

12 Peak velocity (m/s)

1.0


0.6

0.2 0

Chi-Chi (PGA=1.13g)

4

2.5 Peak velocity (m/s)

Peak velocity (m/s)

1.5

0

N.Palm springs (PGA=0.59g)

0.8



0.5


No.3

50 40 30 20

Fig. 7 SSI effects on peak displacement (upper line), velocity (mid line) and acceleration (bottom line) responses for the isolated SDOF system against natural periods under different earthquakes. With nonlinear HDRBs

1.3 1.2 1.1 1.0 0 0.2 0.4

2.1 1.9 1.8 1.7 1.6 1.5 1.4 1.3

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

1.04

2.00

1.02

1.95

1.00 0.98 0.96 0.94 0.92 0.90 0 0.2 0.4

Isolated building Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

2.0

Peak acceleration AF

Peak displacement. AF

Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

1.4

0.9


El Centro PGA=0.34g


Non-isolated building

1.5

0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

1.90 1.85 1.80 1.75 1.70 1.65

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

1.60

Fig. 8 Peak displacement and acceleration amplification factors versus structural natural period for different shear wave velocities in the soil for the non-isolated (left) and isolated (right) buildings (under the El Centro earthquake)

368


Vol.11

N. Palm Springs PGA=0.59g Non-isolated building

1.40

1.20 1.15 1.10 1.05 1.00


Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 0.96 0.94

0 0.2 0.4


1.30

0 0.2 0.4

1.8 1.6

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

1.4 1.2 1.0 0.8

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)



1.35 1.25

Isolated building

2.0

0 0.2 0.4

2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

Fig. 9 Peak displacement and acceleration amplification factors versus structural natural period for different shear wave velocities in the soil for the non-isolated (left) and isolated (right) buildings (under the N. Palm Springs earthquake) Chi-Chi PGA=1.13g Non-isolated building Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

1.6 1.4 1.2 1.0

1.6 1.4 1.2 1.0

1.25

2.0

1.20

1.9

1.15 1.10 1.05 1.00 0.95

Vs=196 Vs=220 Vs=255 Vs=275 Vs=500 Vs=1000 Vs=1500

1.8

0.8

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)



0 0.2 0.4

Isolated building

2.0 Peak displacement. AF


1.8

0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

1.8 1.7 1.6 1.5 1.4 1.3

0 0.2 0.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 T1(s)

Fig. 10 Peak displacement and acceleration amplification factors versus structural natural period for different shear wave velocities in the soil for the non-isolated (left) and isolated (right) buildings (under the Chi-Chi earthquake)

No.3


the natural period of the building decreases, the peak displacement and acceleration AF considerably increase. For all the considered shear wave velocities in the soil, the peak response of the isolated building is uniformly amplified. Similar trends have been observed for all the earthquakes considered. 5.2 MDOF model In order to investigate a more realistic example, the three-story building modelled as an MDOF system (see Jankowski 2008 for the details on its structural properties) is considered in this section. The superstructure is assumed to have three floors, each has a lumped mass of 25×103 kg and a horizontal stiffness of 3.46×106 N/m, and consequently the building has a fundamental period of Tn=1.2 s (see Jankowski, 2008; Mahmoud and Jankowski, 2010). The damping coefficients for the building stories are c1=c2=c3=6.609×104 kg/s with a damping ratio of 5%. The stories are assumed to be of equal height h1=h2=h3=3.5 m. The isolated building model has a base of mass mb=90×103 kg lumped at the isolation level. The soil properties, in terms of mass density, Poisson’s ratio and shear wave velocity, are: γ =1.89×103 kg/m3, v=0.3 and Vs=196 m/s, respectively. Similar to the case of the base-isolated building modelled as a SDOF system, the radii of equivalent circular foundation for swaying and rocking have been considered to be of equal values rh = rr = 4 m. To explore the effects of soil flexibility on the Without SSI With SSI

-0.2 0

2

4 6 Time (s)

8

10

0.5

Velocity (m/s)

0 -0.5 -1.0 0

2

4 6 Time (s)

8

10

5 0 -5 -10

0 -0.2 -0.4 0

2

4 6 Time (s)

8

10

0

2

4 6 Time (s)

8

10

0.3 0.1 -0.1 -0.3 -0.5

0

2

4 6 Time (s)

8

10

-2 0

2

4 6 Time (s)

8

10

2

4 6 Time (s)

8

10

1

1

0

0

-1 -2 0

2

4 6 Time (s)

8

10

5 0 -5 -10

-1

10

10 Acceleration (m/s2)

Acceleration (m/s2)

10

0.2

Acceleration (m/s2)

Velocity (m/s)

1.0

Displacement (m)

0


0.5

Velocity (m/s)

0.2

-0.4


0.4 Displacement (m)

Displacement (m)

0.4

response time histories of the isolated buildings, dynamic analysis for the building modelled as a MDOF system (shown in Fig. 2) has been performed under the 1940 El Centro, 1986 N. Palm Springs and 1999 Chi-Chi earthquake records. Figures 11–13 present the displacement, velocity and acceleration time histories for the first, second and the third story of the isolated building considering SSI effects, as compared with the time histories for the case without SSI effects. Note that high values of the response of the stories are observed with the incorporation of soil flexibility under all the considered ground motions with different PGA levels. Moreover, it has been found that the response values are proportional to the PGA levels as can be clearly seen in the presented figures. In particular, the effects of SSI on the isolated building response increase the number of significant cycles of large amplitude acceleration for the stories in the isolated building, especially for earthquakes with low and moderate PGA. The influence of SSI on the peak responses of isolated buildings is analyzed using two different base isolation systems for the MDOF model shown in Fig. 2. The LRB system, as a representative of the linear model, together with the HDRB system, as a type of the nonlinear model, are used. The peak values of the displacement, velocity and acceleration time histories of the stories of the isolated building with the use of linear and nonlinear base-isolation systems incorporating SSI effects are plotted in Fig. 14 for different earthquake records. As

0

2

4 6 Time (s)

8

10

5 0 -5 -10

0

Fig. 11 Displacement (upper line), velocity (mid line) and acceleration (bottom line) time histories for the first (left column), second (mid column) and third (right column) stories of the isolated building with and without SSI effects under the El Centro earthquake


Without SSI With SSI Displacement (m)

0.5

0.2 0 -0.2 -0.4

0

2

4 6 Time (s)

8

10

-0.1 -0.3 -0.5 0

2

4 6 Time (s)

8

10

0.3 0.1 -0.1 -0.3 -0.5

0

2

4 6 Time (s)

8

10

-2 0

2

4 6 Time (s)

8

10

2

4 6 Time (s)

8

10

2

1

1

0 -1 -2 0

2

4 6 Time (s)

8

10

0 -1 -2 0

2

4 6 Time (s)

8

10

-10 0

2

4 6 Time (s)

8

10

Acceleration (m/s2)

Acceleration (m/s2)

0

10 0 -10 -20

0 -1

20

20

10

-20

Velocity (m/s)

2

1

20 Acceleration (m/s2)

0.1

Vol.11


0.5

0.3

2 Velocity (m/s)

Velocity (m/s)

Displacement (m)

0.4

Without SSI With SSI Displacement (m)

370

0

2

4 6 Time (s)

8

10

10 0 -10 -20

0

Fig. 12 Displacement (upper line), velocity (mid line) and acceleration (bottom line) time histories for the first (left column), second (mid column) and third (right column) stories of the isolated building with and without SSI effects under the N. Palm Springs earthquake

0 -1 -2

0

5

10

15 20 Time (s)

25

30

1 0 -1 -2

0

10

20

30

1 0 -1 -2

5

0

0

0

-5 10

15 20 Time (s)

25

-5 -100

30

40

5

10

15 20 Time (s)

25

30

-20 5

10

15 20 Time (s)

25

30

Acceleration (m/s2)

Acceleration (m/s2)

0

0

5

10

15 20 Time (s)

25

30

0

5

10

15 20 Time (s)

25

30

20 0 -20 -40

0

5

10

15 20 Time (s)

25

30

-5 -10

40

40

20

-40

Velocity (m/s)

5

5

0

Time (s)

5

-10 0

Acceleration (m/s2)

Displacement (m)

Displacement (m)

1


2

2

Velocity (m/s)

Displacement (m)

2

Velocity (m/s)



0

5

10

15 20 Time (s)

25

30

20 0 -20 -40

Fig. 13 Displacement (upper line), velocity (mid line) and acceleration (bottom line) time histories for the first (left column), second (mid column) and third (right column) stories of the isolated building with and without SSI effects under the Chi-Chi earthquake

No.3


expected, the upper stories induce peak displacement, velocity and acceleration responses higher than the lower ones. Considering the effect of the base-isolation system on the structural response, it has been found that the incorporation of the soil flexibility is much more pronounced when the isolated base is modelled as a nonlinear one, except for the case of ground motion with low PGA represented by the El Centro earthquake. In further analysis, the peak response of the isolated building system shown in Fig. 2 with soil flexibility Linear isolator Nonlinear isolator 3

2

0.15 0.20 Peak displacement (m)

2

1 0.4

0.25

3

3 Story number

Story number

0.5

0.6 0.7 0.8 0.9 Peak velocity (m/s)

2

1 3.5

1.0

2

1 0.20

0.25 0.30 0.35 Peak displacement (m)

Story number

Story number

N. Palm Springs (PGA=0.59g)

2

1 0.5

0.40

3 Story number

2

1 0.5

1.0 1.5 Peak displacement (m)

1.0 1.5 Peak velocity (m/s)

1 6.0

2.0

6.5 7.0 Peak acceleration (m/s2)

7.5

20 25 Peak acceleration (m/s2)

30

3

2

1 3.0

2.0

5.0

2

3 Chi-Chi (PGA=1.13g)

4.0 4.5 Peak acceleration (m/s2)

3

3

Story number

Story number

El Centro (PGA=0.34G)

1 0.1

Story number

Linear isolator Nonlinear isolator

Linear isolator Nonlinear isolator

3

Story number

effects has been normalized with respect to the peak response when the soil flexibility is not taken into account. Figure 15 presents the amplification factors for peak displacements and accelerations for the building modelled as a MDOF system under three different ground motions considered in this study. Note that the use of a linear LRB base-isolation system leads to higher displacement and acceleration amplifications due to SSI when compared to the isolated building with a nonlinear HDRB base-isolation system. Moreover, differences in

3.5

4.0 4.5 5.0 5.5 Peak velocity (m/s)

2

1 15

6.0

Linear isolator

4

Nonlinear isolator

3 2 1 1

2 Story number

Nonlinear isolator

3 2 1 1

2 Story number

4 3 2 1 1

2 3 Story number El Centro (PGA=0.34g)

Linear isolator

4

Nonlinear isolator

3 2 1 1

2 Story number

3

5

4 3 2 1 0

5

0

3

5 Acceleration AF

Acceleration AF

4

0

3

5

0

Linear isolator

Acceleration AF

0

5

Displacement AF

5

Displacement AF

Displacement AF

Fig. 14 Peak displacement (left column), velocity (mid column) and acceleration (right column) time histories of the stories of the isolated building with the use of linear and nonlinear base systems incorporating SSI effects under different earthquakes

1

2 3 Story number N. Palm Spring (PGA=0.59g)

4 3 2 1 0

1

2 3 Story number Chi-Chi (PGA=1.13g)

Fig. 15 Peak displacement (upper) and acceleration (bottom) amplifications for the MDOF building model with linear and nonlinear isolation systems under different earthquakes

372


peak response amplifications between the two linear and nonlinear base-isolation systems are more pronounced in the lower stories as can be seen in Fig. 15. Differences between the story displacement amplifications with the use of linear and nonlinear base-isolation systems are much smaller at higher stories, particularly for earthquakes with moderate and high PGA. It has been noticed that, for all the considered ground motion records used to excite the SDOF and MDOF isolated building model, the numerical results obtained for the case with and without SSI inclusion in terms of response time-histories, peak response and response amplification factor are proportional to the spectral accelerations of the ground excitations shown in Fig. 3 (i.e., the higher the earthquake spectral acceleration, the higher the response quantities of the isolated-base buildings).

6 Conclusions Contrary to previous research, this study has focused on the seismic response behavior of buildings modelled as SDOF and MDOF systems isolated by two different systems (linear LRBs and nonlinear HDRBs) with and without SSI effects. Moreover, the records from real earthquakes with different PGA levels (1940 El Centro, 1986 N. Palm Springs and 1999 Chi-Chi ground motions) have been used in the analysis. The isolated buildings have been considered to have different natural periods. Different densities and shear wave velocities in the soil have also been investigated. From the results of the present study, the following conclusions can be drawn: (1) Numerical simulations demonstrate that soil flexibility may considerably influence the earthquakeinduced response of base-isolated buildings. (2) Considering the flexibility of soil affects the stiff superstructure response and is unable to influence the behavior of the flexible base-isolation system. (3) The influence of SSI on the response of baseisolated buildings is more significant for structures with longer natural periods, particularly for earthquakes with high PGA. (4) The use of HDRBs for the isolation system induces higher structural peak responses with SSI when compared to LRBs. (5) The response of non-isolated buildings is sensitive to the variations in shear wave velocity in the soil, especially for low structural natural periods. On the other hand, the response of isolated buildings seems to be insensitive to the shear wave velocity variations. (6) The number of significant cycles of large amplitude accelerations for the isolated MDOF building has been increased due to the incorporation of SSI, revealing that some additional high frequency components in the structure response of the isolated MDOF building were induced due to SSI. (7) For the MDOF isolated building system, the

Vol.11

soil flexibility has a much more pronounced effect on the isolation system consisting of HDRBs, except for the ground motion with low PGA. (8) A linear LRB base-isolation system provides larger structural response amplification factors due to SSI when compared to the building with a nonlinear HDRB base-isolation system under all ground motions considered. It has been assumed in the study described in this paper that the responses of buildings’ superstructures stay within the elastic range during the time of the earthquake. However, under severe ground motions with high PGA levels, the structure may enter into the nonlinear range. Further studies are therefore required to verify the influence of this aspect on the structural behavior of isolated buildings.

References Ariga T Kanno YI and Takewaki I (2006), “Resonant Behavior of Base-isolated High-rise Buildings under Long-period Ground Motions,” The Structural Design of Tall and Special Buildings, 15: 325–338. Austin M and Lin WJ (2004) “Energy Balance Assessment of Base-isolated Structures,” Journal of Engineering Mechanics, ASCE, 130: 347–358. Barbat AH, Rodellar J, Ryan EP and Molinares N (1995), “Active Control of Nonlinear Base-isolated Buildings,” Journal of Engineering Mechanics, ASCE, 121: 676–684. Buckle IG and Mayes RL (1990), “Seismic Isolation: History, Application and Performance: A World Overview,” Earthquake Spectra, 6: 161–202. Calio I, Greco A and Santini A (1998). “A Parametric Study of Sliding Multistory Buildings under Harmonic Excitations,” Proceedings of the Eleventh European Conference on Earthquake Engineering, Rotterdam: A.A. Balkema. Chopra AK (1995), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice-Hall, Englewood Cliffs (NJ), USA. Constantinou MC and Kneifati MC (1987), “Dynamics of Soil-base Isolated Structure Systems,” Journal of Structural Engineering, ASCE, 114: 211–221. Constantinou MC and Tadjbakhsh IG (1983), “Probabilistic Optimum Base Isolation of Structures,” Journal of the Structural Division, ASCE, 109: 676– 689. Constantinou MC and Tadjbakhsh IG (1984), “The Optimum Design of a Base Isolation System with Frictional Elements,” Earthquake Engineering and Structural Dynamics, 12: 203–214. De Barros, FCP and Luco JE (1990). “Discrete Models for Vertical Vibrations of Surface and Embedded Foundations,” Earthquake Engineering and Structural

No.3


Dynamics, 19: 289–303. Dutta SC and Rana R (2010), “Inelastic Seismic Demand of Low-rise Buildings with Soil-flexibility,” International Journal of Non-linear Mechanics, 31: 419–432. Gazetas G and Dobry R (1984), “Horizontal Response of Piles in Layered Soils,” Journal of Geotechnical Engineering, ASCE, 110: 20–40. Hino J, Yoshitomi S, Tsuji M and Takewaki I (2008), “Bound of Aspect Ratio of Base-isolated Buildings Considering Nonlinear Tensile Behavior of Rubber Bearing,” Structural Engineering & Mechanics., 30: 351–368. Jangid RS (1995), “Optimum Isolator Damping for Minimum Acceleration Response of Base-isolated Structures,” Australian Civil Engineering Transactions, 37: 325–331. Jangid RS (1997), “Response of Pure Friction Sliding Structures to Bi-directional Harmonic Ground Motion,” Engineering Structures, 19: 97–104. Jangid RS (2004), “Seismic Response of Isolated Bridges,” Journal of Bridge Engineering, 9: 156–166. Jangid RS and Banerji P (1998), “Effects of Isolation Damping on Stochastic Response of Structures with Non-linear Base Isolators,” Earthquake Spectra, 14: 95–114. Jangid RS and Datta TK (1995), “Seismic Behavior of Base Isolated Buildings: A-state-of-the-art-review,” Proceedings of the ICE - Structures and Buildings, 110: 186–203. Jangid RS and Kelly JM (2001), “Base Isolation for Near-fault Motions,” Earthquake Engineering and Structural Dynamics, 30: 691–707. Jankowski R (2003), “Nonlinear Rate Dependent Model of High Damping Rubber Bearing,” Bulletin of Earthquake Engineering, 1: 397−403. Jankowski R (2008), “Earthquake-induced Pounding between Equal Height Buildings with Substantially Different Dynamic Properties,” Engineering Structures, 30: 2818−2829. Jankowski R (2009), “Non-linear FEM Analysis of Earthquake-induced Pounding between the Main Building and the Stairway Tower of the Olive View Hospital,” Engineering Structures, 31: 1851−1864. Kavvadas M and Gazetas G (1993), “Kinematic Seismic Response and Bending of Free-head Piles in Layered Soil,” Geotechnique, 43: 207–222. Kelly JM (1997), Earthquake-resistant Design with Rubber, Springer, New York, USA. Kelly JM (1998), “Seismic Isolation as an Innovative Approach for the Protection of Engineering Structures,” Proceedings of the Eleventh European Conference on Earthquake Engineering, Rotterdam, A.A. Balkema. Kelly JM (1999), “Progress of Applications and

Development in Base Isolation for Civil and Industrial Structures in the United States,” Proceedings of the International Post-SMiRT Conference Seminar, Cheju, Korea, I: 71–84. Kunde MC and Jangid RS (2006), “Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges,” Journal of Bridge Engineering, 11: 109–121. Liaw TC, Tian QL and Cheung YK (1988), “Structures on Sliding Base Subjected to Horizontal and Vertical Motion,” Journal of Structural Engineering, ASCE, 114: 2119–2129. Mahmoud S and Jankowski R (2010). “Poundinginvolved Response of Isolated and Non-isolated Buildings under Earthquake Excitation,” Earthquakes and Structures, 1: 231–252. Morales CA (2003), “Transmissibility Concept to Control Base Motion in Isolated Structures,” Engineering Structures, 25: 1325–1331. Mostaghel N, Hejazi M and Tanbakuchi J (1983), “Response of Sliding Structure to Harmonic Support Motion,” Earthquake Engineering and Structural Dynamics, 11: 355–366. Naeim F and Kelly JM (1999), Design of Seismic Isolated Structures. Wiley: New York, USA. Nikolaou S, Mylonakis G, Gazetas G and Tazoh T (2001), “Kinematic Pile Bending during Earthquakes: Analysis and Field Measurements,” Geotechnique, 51: 425–440. Rao PB and Jangid RS (2001), “Performance of Sliding Systems under Near-fault Motions,” Nuclear Engineering and Design, 203: 259–272. Ryan KL (2004), “Estimating the Seismic Response of Base-isolated Buildings Including Torsion, Rocking and Axial-load Effects,” Ph.D dissertation, University of California, Berkeley, 248 pages. Simo, J.C. and Kelly, J.M. (1984). “The analysis of Multi-layer Elastomeric Bearings,” Journal of Applied Mechanics, ASME, 51: 256-263. Soneji BB and Jangid RS (2008), “Influence of Soilstructure Interaction on the Response of Seismically Isolated Cable-stayed Bridge,” Soil Dynamics and Earthquake Engineering, 28: 245–257. Spyrakos CC, Koutromanos IA and Maniatakis CA (2009), “Seismic Response of Base-isolated Buildings Including Soil-structure Interaction,” Soil Dynamics and Earthquake Engineering, 29: 658–668. Takewaki I (2005a), “Bound of Earthquake Input Energy to Soil-structure Interaction Systems,” Soil Dynamics and Earthquake Engineering, 25: 741–752. Takewaki I (2005b), “Frequency Domain Analysis of Earthquake Input Energy to Structure-pile Systems,” Engineering Structures, 27: 549–563. Takewaki I (2008), “Robustness of Base-isolated Highrise Buildings under Code-specified Ground Motions,”

374


The Structural Design of Tall and Special Buildings, 17: 257–271. Takewaki I and Fujita K (2009), “Earthquake Input Energy to Tall and Base-isolated Buildings in Time and Frequency Dual Domains,” The Structural Design of Tall and Special Buildings, 18: 589–606. Toki K, Sato T and Miura F (1981), “Separation and Sliding between Soil and Structure during Strong Ground Motion,” Earthquake Engineering and Structural Dynamics, 9: 263–277. Tongaonkar NP and Jangid RS (2003), “Seismic Response of Isolated Bridges with Soil-structure Interaction,” Soil Dynamics and Earthquake Engineering, 23: 287–302. Uniform Building Code Volume 2 (1997). Vlassis AG and Spyrakos CC (2001), “Seismically Isolated Bridge Piers on Shallow Soil Stratum with Soil-structure Interaction,” Computers and Structures, 79:2847–2861. Wei BZ, Pezeshk S, Chang TS, Hall KH and Liu HP (1996), “An Empirical Method to Estimate Shear Wave Velocity of Soils in the New Madrid seismic zone,” Soil Dynamics and Earthquake Engineering, 15: 399–408. Westermo B and Udwadia F (1983), “Periodic Response of a Sliding Oscillator System to Harmonic Excitation,” Earthquake Engineering and Structural Dynamics, 11: 135–146. Whitman RV and Richart FE (1967), “Design Procedures for Dynamically Loaded Foundations,” Journal of Soil Mechanics and Foundations, Division, ASCE, 93 (SM6). Wolf JP (1994), Foundation Vibration Analysis Using Simple Physical Models, Prentice-Hall, Englewood Cliffs (NJ), USA.

Vol.11

Wolf JP (1997), “Spring-dashpot-mass Models for Foundation Vibrations,” Earthquake Engineering and Structural Dynamics, 26: 931–949. Wolf JP and Somaini DR (1986), “Approximate Dynamic Model of Embedded Foundation in Time Domain,” Earthquake Engineering and Structural Dynamics, 14: 683–703. Wu WH and Chen CY (2001), “Simple LumpedParameter Models of Foundation Using Mass-springdashpot Oscillators,” Journal of the Chinese Institute of Engineering, 24: 681–697. Wu WH and Lee WH (2002), “Systematic Lumpedparameter Models for Foundations Based on Polynomialfraction Approximation,” Earthquake Engineering and Structural Dynamics, 31: 1383–1412. Wu WH and Lee WH (2004), “Nested Lumpedparameter Models for Foundation Vibrations,” Earthquake Engineering and Structural Dynamics, 33: 1051–1058. Yamamoto K, Fujita and I Takewaki (2011), “Instantaneous Earthquake Input Energy and Sensitivity in Base-isolated Building,” the Structural Design of Tall and Special Buildings, 20: 631–648. Yoshida J (2002), “Finite Element Modeling for the High Damping Rubber Bearing,” 3rd DIANA World Conference, pp. 375–384. Zheng J and Takeda T (1995), “Effects of Soil-structure Interaction on Seismic Response of PC Cable-stayed Bridge,” Soil Dynamics and Earthquake Engineering, 14: 427–437.