Earthquake-induced poundings of a seismically isolated building with adjacent structures

Engineering Structures 32 (2010) 1937–1951

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Earthquake-induced poundings of a seismically isolated building with adjacent structures Panayiotis C. Polycarpou, Petros Komodromos ∗ Department of Civil and Environmental Engineering, University of Cyprus 75 Kallipoleos Street, P.O. Box 20537, 1678 Nicosia, Cyprus

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Article history: Available online 10 April 2010 Keywords: Poundings Impact Seismic isolation Impact Adjacent structure Moat wall

abstract Past earthquakes have revealed detrimental effects of pounding on the seismic performance of conventional fixed-supported buildings, ranging from light local damage to more severe structural failure. However, the potential consequences of earthquake-induced poundings on seismically isolated buildings can be much more substantial, and, thus, should be assessed. This paper investigates, through numerical simulations, the effects of potential pounding incidences on the seismic response of a typical seismically isolated building. Such impact events may occur either with the surrounding moat wall at the building’s base or against an adjacent building that may stand at a very close distance. A specialized software application has been developed in order to efficiently perform numerical simulations and parametric studies of this problem. The effects of certain parameters, such as the size of the separation distance, the characteristics of the adjacent structures and the earthquake characteristics, have been investigated using the developed software. The simulations have revealed that even if a sufficient gap is provided, with which poundings with the surrounding moat wall at the base of the building could be avoided, this does not ensure that the building will not eventually collide with neighboring buildings due to the deformations of their superstructures. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Seismic isolation technology is an innovative approach of antiseismic design of structures, which has been more widely used in the last few years. The incorporation of seismic isolators aims at the avoidance of damage in the superstructure, in contrast to conventionally designed structures where damage is very likely during strong earthquakes. However, seismically isolated buildings are expected and allowed to experience large displacements relative to the ground during strong earthquake excitations, especially when the latter contain long period impulses [1–3]. In order to accommodate such large displacements, a sufficiently wide clearance must be provided around the building, which is known as ‘‘seismic gap’’. Nevertheless, the width of the provided seismic gap in most cases cannot be unlimited due to practical constraints, especially in cases of retrofitting existing structures. In addition, it is widely accepted that there are several uncertainties about the characteristics of the expected earthquake and the methods that are used to estimate the maximum induced relative displacements of the structure. Therefore, a reasonable concern is the possibility of poundings of a seismically isolated building against either the surrounding

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0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.03.011

moat wall or adjacent buildings during a very strong earthquake. From a research perspective, there is a scientific interest and a practical necessity to investigate thoroughly the complex research problem of earthquake-induced poundings of seismically isolated buildings, since there is an increasing number of seismic isolation applications in earthquake-prone areas. 1.1. Pounding incidences during past earthquakes Although seismic isolation technology began to be implemented in structures only during the last few decades, a case of pounding occurrences, during a strong earthquake, can already be found in the literature [4]. In particular, the base-isolated Fire Command and Control (FCC) building in Los Angeles experienced impacts at its base during the 1994 Northridge earthquake, as it was observed in the recorded strong motion data. The building is a twostory steel frame structure with an isolation system consisting of high damping elastomeric bearings. According to the reconnaissance report, one-sided impact occurred against the concrete entry bridge in the northeast corner of the building. The accelerometers that were attached on each floor of the building recorded an amplification of the acceleration response at the isolation level, in the direction of pounding, from 0.22g, which was the peak ground acceleration, to 0.35g, while in the other direction the ground accelerations were reduced, thanks to seismic isolation, from 0.18g to 0.07g.

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Fig. 1. Damage of a four-story conventional building due to pounding with its adjacent two-story building, during the L’Aquila earthquake in Italy, in April 2009 [12].

Poundings of fixed-supported buildings have been more frequently observed around the world, especially during very strong earthquakes, ranging from light local to heavier damage that might even have initiated collapse [5–9]. After the 1985 Mexico City earthquake, great attention was given to structural poundings, since they had been considered as a leading cause of building collapses, based on an exaggeration concerning the actual damage due to poundings [10]. Although the number of buildings that were severely damaged due to poundings was initially overestimated [11], after reconsideration, a few years later, it was reported that only in 4% of the severely damaged or collapsed buildings, during the Mexico City earthquake, poundings could have played a significant factor [5,10]. Furthermore, it has been observed that the most severe damage due to poundings occurred in cases of unequal heights, different structural systems and different configurations of the adjacent buildings [6]. The photograph in Fig. 1 shows a pounding incidence between two neighboring buildings, as reported from an EERI/PEER reconnaissance team, after the L’Aquila earthquake, which hit central Italy in April 2009 [12]. During that seismic event, the roof of the two-story building hit the adjacent four-story structure causing significant damage to the columns of the latter at that level. Nevertheless, the third and the fourth stories of the building do not seem to experience significant damage. The confinement of the damage of the four-story building at the level of impact indicates the destructive effect of structural poundings. 1.2. Past research studies on poundings Since poundings of conventional fixed-supported buildings have been frequently observed around the world, especially during very strong earthquakes, extensive research work has been conducted regarding that case. Anagnostopoulos [13] was one of the pioneers who used numerical simulations to investigate the problem, considering single-degree-of-freedom (SDOF) systems in series, undergoing the same seismic excitations. Later on, several research studies focused on the numerical or experimental investigation of earthquake-induced poundings of fixed-supported buildings [14–19]. Compared to the extensive research work on poundings of conventional buildings and bridges, very limited research studies have been carried out for poundings of seismically isolated buildings. Tsai [20] and Malhotra [21] were the first two who,

through their similar research studies, analytically investigated the possibility of a seismically isolated building pounding against the surrounding moat wall. Both researchers simulated the superstructure of an isolated building as a continuous shear beam bumping against a stopper at its base, representing the moat wall, in order to investigate, using wave propagation theory, the effects of impact on its seismic response. Tsai observed very high acceleration response during poundings with the surrounding moat wall at the isolation level, while Malhotra concluded that the base shear force increases with the stiffness of the superstructure or retaining wall, while sometimes it becomes higher than the total weight of the seismically isolated building. Matsagar and Jangid [22] also numerically and parametrically examined the case of poundings of seismically isolated multidegree-of-freedom (MDOF) structures, for various types of seismic isolation systems. They concluded that poundings affect the response of a seismically isolated building more when the latter has a flexible superstructure, an increased number of stories or relatively stiff adjacent structures. Komodromos et al. [23] and Komodromos [24] investigated, through parametric analyses, the effects of poundings of a seismically isolated building with the surrounding moat wall, revealing the detrimental effects of structural impact on the effectiveness of seismic isolation. In those research works, the behavior of the seismic isolation system was assumed to be linear elastic, while no other adjacent buildings were considered in the simulations. Recently, Agarwal et al. [25] have examined the case of poundings between two-story buildings that were taken to be either fixed-supported or seismically isolated. In the case of seismically isolated buildings, a sliding isolation system with varying friction was considered. Nevertheless, the case of poundings between a seismically isolated building and a fixed-supported building was not taken into account, while the simulation involved only buildings with two degrees of freedom. Based on the observations from past earthquakes about the detrimental effects of pounding on the seismic response of conventional buildings, it would be interesting to investigate the possibility of poundings of seismically isolated buildings, which exhibit quite different dynamic characteristics from fixedsupported buildings. Furthermore, it is more likely to have more rigorous performance requirements and higher expectations for buildings that utilize an innovative earthquake-resistant design, such as the seismic isolation technology, than for conventionally fixed-supported buildings. Although the previous research on earthquake-induced poundings of seismically isolated buildings that has been described above provides some basic information about the effects of impacts on the response, there is still a need for further investigation of the problem, using more effective modeling approaches and taking into account more influencing parameters. In this paper, a part of an extensive research work concerning the numerical investigation of poundings of seismically isolated buildings with adjacent structures is presented. In particular, using a specially developed software application, a large number of dynamic analyses and parametric studies of seismically isolated buildings pounding with adjacent structures has been performed. From this investigation some indicative results are presented and some useful remarks are derived. 2. Modeling assumptions The modeling of the simulated structures was performed in two dimensions (2D), while the superstructure of the seismically isolated building and the adjacent conventionally fixed-supported buildings are modeled as MDOF systems, with shear–beam behavior and the masses lumped at the floor levels, assuming linear elastic behavior during earthquake excitations.

P.C. Polycarpou, P. Komodromos / Engineering Structures 32 (2010) 1937–1951

Fig. 2. Bilinear inelastic model for the behavior of the seismic isolation system.

2.1. Modeling of the seismic isolation system The behavior of the seismic isolation system is simulated using a bilinear inelastic model, which is a more representative and appropriate model, since it represents satisfactorily the response under cyclic loading of the most commonly used seismic isolation systems, such as the Lead Rubber Bearings (LRB) and the Friction Pendulum Systems (FPS). In the case of the LRB, the bilinear behavior is justified by the yielding of the lead core after the exceedance of a certain shear force level. The three parameters that determine the bilinear inelastic model are the yielding force (fy ), the initial elastic stiffness (K1 ) and the post-yield stiffness (K2 ). For all performed simulations, in the frame of the currently presented work, the values of these parameters were empirically selected, based on the assumption that the corresponding equivalent stiffness would render the fundamental period of the seismically isolated building about three times larger than the corresponding period of the superstructure. The selected values are presented in Fig. 2 along with the pre-described bilinear inelastic model. 2.2. Damping Classical Rayleigh damping has been used for the construction of the viscous damping matrices of the simulated fixed-supported buildings. In the case of seismically isolated buildings undergoing earthquake excitations, the energy dissipation mechanisms of the corresponding MDOF systems are not uniformly distributed, as they may differ significantly between the seismic isolation systems and the superstructures. In such cases, the usage of classical Rayleigh damping for the construction of the damping matrix may not be appropriate [26]. Therefore, in the current study a different approach has been adopted in order to take into account the dissipation of energy in a more appropriate, yet simple, manner. Assuming, initially, a uniformly distributed energy dissipation mechanism along the height of the superstructure, a primary damping matrix C p is constructed, according to Rayleigh damping [26], assuming the viscous damping ratios for the two extreme eigenmodes of the MDOF system to represent the viscous energy dissipation due to the deformation of the superstructure. Then, considering an almost ‘‘rigid body’’ behavior for the superstructure of the seismically isolated building, due to the relatively excessive flexibility at the seismic isolation level, an equivalent SDOF system is formed, using the total mass of the building (mtot ) and the effective stiffness (kiso ) of the isolation system. For this SDOF system, the equivalent viscous damping coefficient is calculated to correspond to the excess in damping that is provided by the seismic isolation system, beyond the uniform viscous damping that is assumed for the entire MDOF system: ciso = 2 · (ζiso − ζsstr ) ·

p

mtot · kiso

(1)

1939

where ζiso and ζsstr are the selected damping ratios for the seismic isolation and the superstructure, respectively. The viscous damping ratio that corresponds to the superstructure is subtracted from the corresponding seismic isolation damping ratio (Eq. (1)), since it has already been taken into account during the construction of the primary viscous damping matrix, using the Rayleigh damping assumption. The final damping matrix C is assembled by superposing the primary damping matrix to the equivalent viscous damping coefficient ciso that corresponds to the supplemental damping provided by the seismic isolation system. In particular, the value of ciso is added to the first element (first row and first column) of the primary damping matrix C p , since the seismic isolation system is located at the base of the building. In the current study a value of supplemental damping ratio ζiso equal to 0.05 has been considered. Nevertheless, the effect of the value of the supplemental viscous damping ratio of the isolation system is examined in Section 7. 2.3. Impact modeling The numerical modeling of impact and the estimation of the impact forces acting on the colliding bodies is an essential topic, not only for cases of structural poundings, but also for other problems involving numerical simulation of impact. In the case of structural poundings, simple impact models, which estimate the impact forces, are usually used by researchers to investigate structural impact [13,27,28]. In the current study, a force-based impact model is used, assuming an impact spring and an impact dashpot exerting, in parallel, impact forces to the colliding structures whenever their separation distances are exceeded. Actually, it is a small variation of the linear viscoelastic impact model that had been initially proposed by Anagnostopoulos [13], in which the tensile forces arisen at the end of the restitution period are omitted and a small plastic deformation is introduced, which increases the available clearance. In particular, when a contact is detected, the impact force is estimated at each time-step using the following formulas [23]: kimp · δ (t ) + cimp · δ˙ (t ) 0



Fimp (t + 1t ) =

when Fimp (t ) > 0 (2) when Fimp (t ) ≤ 0

˙ t ) is the relative where δ(t ) is the interpenetration depth, δ( velocity between the colliding bodies, kimp is the impact spring’s stiffness and cimp is the impact damping coefficient. The later is computed according to the following formulas, provided by Anagnostopoulos [13], based on the conservation of energy before and after impact: cimp = 2 · ξimp

r kimp ·

m1 · m2 m1 + m2

(3)

ln (COR) ξimp = − p . (4) 2 π + (ln (COR))2 In the above formulas, m1 , m2 are the masses of the two bodies and COR represents the coefficient of restitution, which is defined as the ratio of relative velocities after and before impact (0 < COR ≤ 1). The exact value of the impact stiffness term (kimp ) is practically unknown, since its physical meaning is not clearly determined. However, it seems that its value depends on the mechanical properties of the material and the geometry of the contact surface of the colliding bodies. In order to examine the influence of the selected value for the impact stiffness, as well as the value of the coefficient of restitution, on the overall response, a parametric analysis was performed, from which selected results are presented in Section 6. In all presented simulations, the stiffness of the impact spring has been assumed to be 2500 kN/mm, while the coefficient of restitution (COR) has been taken to be equal to 0.7.

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a

b

Fig. 3. Computed maximum impact force in terms of the considered time-step for various values of (a) the impact stiffness and (b) the impact velocity.

2.4. Numerical integration

2.5. Vertical location of impacts

The equations of motion are directly integrated using the Central Difference Method (CDM), computing the displacements at time (t + 1t ). In order to ensure the stability and the accuracy of the CDM, a sufficiently small time-step must be used for the timeintegration, according to the following formula:

Two different configurations of a seismically isolated building are used in the performed simulations. The first case concerns the possibility of the seismically isolated building hitting against the surrounding moat wall, during a strong earthquake excitation, only at the isolation level, whenever the limited width of the seismic gap is exceeded (Fig. 4(a)). In the other case, the seismically isolated building is considered to be adjacent to other conventionally fixedsupported buildings, with the possibility of poundings occurring not only at its base, but also at the upper floors of the buildings due to the deformation of their superstructures (Fig. 4(b)).

1t < 1tcr

2

ωmax

=

Tmin

π

(5)

where ωmax is the maximum eigenfrequency of the system. However, during impacts, ωmax should be the equivalent eigenfrequency of the force-based impact model, which equals

s ωimp =

kimp

(6)

meff

where meff = m 1+m2 . For example, for a kimp = 2500 kN/mm 1 2 and two colliding masses of 250 tons each, the equivalent eigenfrequency of the impact model is equal to 141.42 rad/s. Therefore, according to the above stability criterion (Eq. (5)) of the CDM, the critical time-step is about 1.4 × 10−2 s. In the current study, the time-step is taken to be equal to 2 × 10−5 s, which is much smaller than the aforementioned critical time-step. The selection of a small time-step is also important for the accuracy of the computed impact force when simulating poundings using a ‘‘penalty method’’. This effect is presented in Fig. 3, considering two colliding rigid bodies, each with a mass equal to 300 tons, and the pre-described impact model to compute the impact forces. In particular, the computed impact force is plotted in terms of the size of the time-step in logarithmic scale. It is observed that, as the time-step size increases, the dispersion in the impact force values increases. In addition, for higher values of the impact stiffness or the impact velocity, a smaller time-step is needed to avoid errors in the computed responses. According to the plots, a value of the time-step size smaller than 2 × 10−3 s may provide sufficient accuracy for the particular case. As mentioned previously, the selected value of the time-step size that is used in the conducted analyses in the context of this study is much lower than that limit, avoiding this kind of numerical errors and instabilities in the computed responses. Such small time-steps can be easily used in numerical simulations and parametric studies, considering the significant increase of the computational speed of the available computing resources. m ·m

(a) Poundings with the moat wall This configuration represents the case where the seismic gap is limited and for some reason the relative horizontal displacement at the base of the seismically isolated building exceeds the available clearance, during a strong earthquake. Then, the slab at the isolation level hits against the surrounding moat wall, which is assumed to be rigid and move with the ground during the earthquake excitation. The effective mass of the moat wall, which is used for the estimation of the impact forces, has been considered to be 500 tons. (b) Poundings with adjacent buildings In this configuration, one or two fixed-supported multistory buildings are considered to be located next to a seismically isolated building at the same distance as the surrounding moat wall. Therefore, poundings may occur either with the moat wall at the base of the seismically isolated building or with the adjacent buildings at the levels of the upper floors of their superstructures. For simplicity, it is assumed that the slabs of the neighboring buildings are located at the same levels. Therefore, the impact forces act directly on the concentrated masses of the MDOF systems. Modeling buildings in series, like in this case, requires the simultaneous solution of the equations of motion of the neighboring structures in order to detect potential contacts among the oscillating systems. The selected force-based impact model, as described previously, allows the simulation of more than one impact occurring on the structure simultaneously. 3. Developed software Considering the limited, if any, number of commercial structural analysis software applications that are able to perform dynamic analysis of more than one structures in series, interacting with each other through structural impacts, it was necessary,

P.C. Polycarpou, P. Komodromos / Engineering Structures 32 (2010) 1937–1951

a

1941

b

Fig. 4. Two considered configurations of a seismically isolated building regarding the possible locations of impacts: (a) poundings only at the base; (b) poundings at all floor levels, including the base.

Fig. 5. Relative displacement at the isolation level of the four-story seismically isolated building due to the Kobe earthquake for the two cases of without and with poundings.

for the fulfillment of the aims of this investigation, to develop a specialized software tool in order to be able to perform the required simulations and parametric studies effectively, based on the previously described assumptions. Therefore, a software application has been specifically developed in order to efficiently perform large numbers of dynamic simulations of seismically isolated buildings in series with other structures taking into account potential pounding incidences. In particular, an Object-Oriented Programming (OOP) approach and the Java programming language have been utilized to design and implement a flexible and extendable software application with effective visualization capabilities that can be used in relevant numerical simulations and parametric analyses. Among other features, the developed software enables the user to observe, through appropriate animations, the seismic responses of the analyzed structures in series, facilitating the verification of the results and the understanding of the analysis outcomes. Large numbers of simulations can be performed, varying automatically a certain parameter for each analysis, in order to parametrically investigate its effects on the overall dynamic response. 4. Analyses considering impacts with the surrounding moat wall A four-story building is considered, under the following three different circumstances: (a) fixed-supported, (b) seismically isolated without the possibility of pounding, and (c) seismically

isolated with a seismic gap on either of its sides, to illustrate the pounding effects on its structural response. The superstructure is assumed to have four floors, each with a lumped mass of 320 tons, except for the top floor, where a mass of 250 tons is considered. Each story has a horizontal stiffness of 600 MN/m. The seismically isolated building has an additional mass of 320 tons lumped at the isolation level, while the isolation system’s behavior is simulated using the bilinear inelastic model. The fundamental period of the fixed-supported four-story building is equal to Tfixed = 0.398 s. In order to observe the effects of poundings on response timehistories of the seismically isolated building, dynamic analysis of the building for each of the cases described above was performed, using the 1995 Kobe earthquake record (KJMA Station) as the ground excitation. For the case of poundings, the size of the seismic gap is taken to be equal to 15 cm, which is 10% smaller than the maximum relative displacement (16.74 cm) at the isolation level of the seismically isolated building under the same excitation (Fig. 5). This assumption is based on the uncertainties concerning the characteristics of the design earthquake and the estimation of the maximum design displacement of the seismically isolated building. Fig. 5 presents the displacement time-histories at the base of the seismically isolated building under the Kobe earthquake for the case without poundings and the case of a seismic gap equal to 15 cm, where the base mat unavoidably hits against the surrounding moat wall at two time instances. It is observed that the differences in the two plots are very difficult to be identified. Only a slight reduction of the peak values due to impact is detected.

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Fig. 6. Acceleration time-histories at the top of the seismically isolated building, with and without poundings.

Fig. 7. Peak responses of the four-story seismically isolated building with and without poundings compared with the peak responses of the corresponding fixed-supported building.

In contrast to the relative displacement response, the floor accelerations, as expected, are found to be more sensitive to impact occurrences. Although the width of the clearance is less than 2.0 cm smaller than the maximum relative displacement, the effects of poundings are significant, especially on the acceleration response at the isolation level where impacts occur. Fig. 6 presents the acceleration time-histories at the top floor of the seismically isolated building during poundings, compared to the corresponding time-histories for the case without poundings. High values of the acceleration response are observed at the time of impact. Nevertheless, due to damping, a short time after impact, the response tends to become identical to the corresponding response without poundings. The peak values of the interstory deflections and absolute floor accelerations of the seismically isolated building with impacts are plotted in Fig. 7 and compared with the corresponding values of the fixed-supported and base-isolated building without impact. It is observed that, during poundings, interstory deflections at the upper floors reach the peak values of the deflections of the corresponding fixed-supported building. Consequently, on the particular stories of the superstructure, we observe almost the same shear forces that act on the fixed-supported building with the same structural characteristics. If insufficient strength is provided to the structural elements, taking into account these effects of potential poundings during the design of the superstructure of a seismically isolated building, considerable damage may occur in such cases. Considering the computed peak absolute floor accelerations of the building, the influence of poundings in its response is much more pronounced at the lower floors, where the peak floor accelerations become much higher than those for the corresponding fixed-supported building. Due to poundings with the moat wall,

the structure may experience maximum floor accelerations at the isolation level, where impacts occur, instead of the top floor of the building. It is well known from previous studies [14,16,29] that the acceleration response is highly affected from impact. These high values of floor acceleration that are generated due to poundings can damage sensitive equipment that may be housed in the building. The specially developed software tool provides the ability to create animations of the simulated structures that are subjected to ground excitations. Fig. 8 presents some snapshots that have been created using the developed software, for the case of the aforementioned four-story seismically isolated building, considering a seismic gap that is 15 cm wide. It is observed that poundings excite higher modes of deformation of the seismically isolated building, instead of moving, according to its fundamental mode as an almost rigid body. However, in some cases, more detailed examination of the results is needed to validate the information that is given by the animations. For example, in this case, two impact events are observed in the animation. In particular, the first impact happens at time 8.4 s on the left side and the second at time 8.8 s on the right side of the seismically isolated building (Fig. 8). Nevertheless, in Fig. 9, the time-history data of the impact force indicate that there are three impact events. Specifically, the first pounding event on the left side is followed in very short time by a second smaller impact due to the effect of the deformation of the superstructure and the inertia forces acting at the upper stories in the opposite direction from the impact force. While the impact forces push the base mat apart from the moat wall, the inertia forces of the superstructure are driving the building against the wall. Consequently, the base mat rebounds on the moat wall.

P.C. Polycarpou, P. Komodromos / Engineering Structures 32 (2010) 1937–1951

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Fig. 8. Snapshots of the animated seismically isolated building under the Kobe earthquake, considering a seismic gap equal to 15 cm.

Fig. 9. Impact force time-history at the base of the four-story seismically isolated building under the Kobe earthquake, considering a gap width equal to 15 cm. Table 1 First two natural modes and periods of the fixed-supported structures considered adjacent to the seismically isolated building.

First two eigenmodes: Number of stories T1 (s) T2 (s)

2

3

4

5

6

0.216 0.086

0.306 0.111

0.398 0.139

0.490 0.168

0.58 0.20

5. Analyses considering impacts at all floors A series of dynamic analyses has been conducted in order to investigate the case of having the seismically isolated building adjacent to other fixed-supported buildings, compared to the case of the seismically isolated building standing alone surrounded only by the moat wall. For this reason, five types of fixed-supported buildings which differ only in the number of stories are considered, assuming the same story stiffness and floor mass values as for the superstructure of the seismically isolated building. The first two modes and their corresponding natural periods of the five fixed-supported buildings used in the simulations are presented in Table 1. Five selected earthquake records, which are presented in Table 2, are used in order to examine the effects of the excitation characteristics on the seismic response of the seismically isolated building during poundings. All selected earthquake records are characterized by low-frequency content, in order to induce large relative displacements to the seismically isolated building, since this is one of the most decisive factors for the occurrence of poundings in such structures. The normalized response spectra, i.e. the spectral acceleration divided by the peak ground acceleration, of all five seismic records are plotted together in Fig. 10 The size of the seismic gap is considered to be different for each case of seismic action. In particular, the width of the seismic gap is taken to be 10% smaller than the maximum relative displacement at the isolation level of the seismically isolated building under the specific seismic excitation. The maximum induced relative displacements at the base and the top of the seismically isolated

Table 2 Earthquake records that are used in the simulations. Earthquake

Mw

Station

PGA (g)

Kobe, Japan 1995 Northridge, USA 1994 Northridge, USA 1994

6.9 6.7 6.7

0.821 0.897 0.604

Kocaeli, Turkey 1999 San Fernando, USA 1971

7.4 6.6

0 KJMA 74 Sylmar - Converter Station 24514 Sylmar - Olive View Med FF Sakarya Pacoima Dam, S16

0.628 1.170

building, as well as the displacements of the tops of the fixedsupported buildings, for each earthquake record, are provided in Table 3. Figs. 11 and 12 present the amplification factors of the peak floor accelerations and interstory deflections, respectively, of the four-story seismically isolated building considering poundings with the adjacent structures. The amplification factor is defined as the ratio of the maximum response quantity of interest when poundings occur divided by the corresponding maximum response value without poundings. According to the simulation results, the peak total accelerations as well as the interstory deflections and, therefore, the story shear forces of the seismically isolated building significantly increase due to poundings that occur when the available seismic gap is slightly exceeded. In the specific cases under investigation, the available clearance is only 10% less than what is needed to avoid impact and, nevertheless, the responses are amplified significantly regarding the corresponding responses without poundings. In addition, it is observed that the amplification of the peak floor accelerations is, in general, greater than the amplification of the peak interstory deflections, since the former are much more sensitive to local impacts. The maximum amplification of the acceleration response is usually located (i) at the isolation level (for the case of poundings occurring only with the moat wall), (ii) at the floor that is at the same level with the roof of the adjacent structures or (iii) at the top floor of the seismically isolated building when that is shorter than the neighboring buildings. Moreover, the amplifications of the response of the seismically isolated building with poundings seem to depend on the earthquake characteristics in combination with the number of stories

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Fig. 10. Normalized response spectra of the five selected seismic records, considering a viscous damping ratio of 5%. Table 3 Maximum relative displacements (cm) of the seismically isolated building and the fixed-supported buildings, under the five seismic excitations.

(Base - Top)

(Top)

(Top)

(Top)

(Top)

(Top)

Earthquake excitation

Kobe Northridge (Converter) Northridge (Olive) Sakarya San Fernando

16.74–18.85 31.71–35.25 15.63–17.07 11.40–12.51 26.78–29.52

1.49 1.49 1.18 2.12 3.47

and, consequently, the flexibility of the adjacent buildings. The amplification of the response due to poundings occurring only at the base of the building is more or less the same for all seismic excitations. However, in the case where the seismically isolated building is between other multistory buildings, which have different dynamic responses under each excitation, the amplification curves for each earthquake record have significant dispersions. The worstcase scenario for the seismically isolated building is when the adjacent fixed-supported buildings have fundamental eigenfrequencies in resonance with the dominant frequencies of the earthquake excitation. Another set of parametric analyses was performed in order to examine how the width of the seismic gap affects the response of the seismically isolated building in the six different cases regarding the type of adjacent structures. In particular, the width of the gap between the seismically isolated building and the adjacent structures is varied between 10 and 45 cm, with a step of 0.5 cm, simultaneously on both sides of the building. Fig. 13 presents the maximum responses of the seismically isolated building in terms of the size of the available clearance for the six configuration cases and for the five seismic excitations. It is observed that the response is, in general, decreasing with the increase of the available clearance around the seismically isolated building. However, the variations of some curves indicate that this is not always true, especially for relatively narrow gap sizes in combination with the earthquake characteristics. Specifically, very small widths of the seismic gap, in combination with a strong earthquake ground excitation, do not allow the structure to develop high impact velocities as in cases of wider seismic gaps, leading to relatively milder consequences from potential poundings. Some modern anti-seismic codes suggest the use of the SRSS (Square Root of the Sum of Squares) approach for the determination of the minimum required seismic gap between two adjacent buildings in order to avoid structural poundings during strong

5.57 3.41 3.28 4.50 5.67

11.40 6.43 5.60 5.23 14.61

16.88 10.50 9.75 6.30 13.40

15.22 17.70 13.54 7.51 8.66

earthquakes [30–32]. Relevant research on the investigation of poundings of fixed-supported buildings showed that the SRSS of the maximum displacements of two adjacent buildings can be sufficient [13], while in fewer times it may be insufficient, but with minor impact effects [14,15]. In almost half of the cases that have been analyzed in the current study, a seismic gap, equal to the SRSS of the design peak relative displacements of the adjacent structures, is insufficient under the specific earthquake excitations. Table 4 displays the difference 1d = dRSSS − dReq for each one of the cases of the configurations of the adjacent buildings and for all five q


2

seismic records, where dRSSS = (max diso )2 + max dfixed and dReq is the minimum required seismic gap in order to avoid poundings according to the simulations. The terms max diso and max dfixed represent the maximum horizontal displacement of the seismically isolated building and its adjacent fixed-supported building, respectively, under the same excitation. Therefore, a negative sign of the difference 1d denotes that a seismic gap width equal to dSRSS is insufficient. The computed dSRSS is also plotted in the graphs of Fig. 13 with vertical lines. Considering the type of the adjacent structure, the results indicate that the presence of fixed-supported buildings at close distance to a seismically isolated building significantly affects the response of the latter during poundings. In general, the plots indicate that the amplifications of the peak floor accelerations due to impact are, in general, increasing with the number of stories of the adjacent building. An important observation is that, in such a case, poundings may occur for much wider widths of the seismic gap compared to the case of impacts occurring only at the base with the moat wall. This is justified by the fact that the adjacent multistory buildings have some horizontal flexibility in contrast to the surrounding moat wall, which remains undeformed relative to the ground during the excitation. Therefore, the seismically isolated building may pound against the neighboring buildings at

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Fig. 11. Amplification of the maximum floor accelerations of the seismically isolated building due to poundings with adjacent structures.

Table 4 The difference 1d = dRSSS − dReq (cm), where the negative sign denotes insufficiency. Earthquake excitation

Kobe

−0.09

Northridge (Converter)

0.78

Northridge (Olive)

0.61

Sakarya

0.69

San Fernando

0.72

−0.34 1.91

−0.62 −0.70 1.06

the upper stories, due to the deformation of the superstructures of the buildings in series, before hitting the surrounding moat wall. Fig. 13 also suggests that the peak interstory deflections during poundings for the case of buildings in series are most of the times smaller than those for the case of having impacts only with the moat wall. This indicates that, in most cases, the adjacent buildings act as constrainers, preventing the large horizontal displacements that may take place when the seismically isolated building hits only against the moat wall at the isolation level. The earthquake characteristics and, in particular, the range of predominant periods, in combination with the fundamental periods of the adjacent structures seem to play a significant role in the severity of the structural impact. Specifically, the detrimental effects of poundings are more pronounced when the fundamental periods of the adjacent fixed-supported buildings fall within the predominant periods of the seismic ground motion.

−5.47 −3.17 2.46

−1.44 3.31

−6.70 −7.72

−1.77 −5.06

1.66

0.29

0.01

3.59

0.42

−3.74

A representative example is the case of having five-story fixedsupported buildings adjacent to the seismically isolated building, under the Kobe earthquake record. 6. Influence of the impact parameters As mentioned previously, a series of parametric analyses has been performed in order to examine the influence of selecting different values for the impact parameters, when using the corresponding linear viscoelastic impact model. Considering the case where the four-story seismically isolated building is standing between two same four-story fixed-supported buildings, the impact stiffness and the coefficient of restitution were varied in the ranges 500–5000 kN/mm and 0.1–1.0, respectively. Two cases of seismic gap size were examined and the Kobe earthquake record

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Fig. 12. Amplification of the maximum interstory deflections of the seismically isolated building due to poundings with adjacent structures.

was selected as the imposed seismic excitation. In the first case (Fig. 14), the width of the seismic gap equals 25 cm and poundings occur only at the two top floor levels of the seismically isolated building, while in the second case, where the separation distance equals 15 cm (Fig. 15), poundings occur at all floor levels. The plots in Fig. 14 indicate that the influence of the value of the impact parameters on the interstory deflections is negligible, while a small variation is observed for the acceleration response at the two floors where impacts occur. Specifically, for values of the coefficient of restitution (COR) lower than 0.5, the acceleration increases and reaches its maximum value when the impact becomes highly overdamped. For values greater than 0.5, the acceleration response is almost insensitive to the variation of the COR. On the other hand, the increase of the impact stiffness increases the peak floor acceleration at the impacting floor, while at the rest of the floor levels the acceleration remains almost constant with the variation of kimp . An interesting observation is that the peak floor accelerations at the top floor are more sensitive to the variation of the impact stiffness than that at the third floor, indicating that the rate with which the accelerations increase depends on the impact velocity. This is also shown in Fig. 15, where the rate of the increase of the peak floor accelerations is greater, since the seismic gap’s width is smaller and causes more severe impacts. In addition, in the case of relatively narrow seismic gaps, the interstory deflections are not as insensitive to the variation of the impact parameters as in the first case. Conclusively, the influence of the values of the impact parameters on the overall response during poundings is greater in cases of high impact velocities. The values of the coefficient of restitution and the impact stiffness that were used in the performed simulations are

shown with dotted lines in both figures, indicating the relatively limited influence of their selected values. 7. Influence of supplemental viscous damping Recent studies have shown that the use of supplemental damping devices may reduce the relative displacements at the base of a seismically isolated building under extreme seismic actions that are characterized by near-fault effects [33]. Since the developed software provides the ability of introducing additional damping explicitly at the isolation level, this scenario was also investigated. In order to examine the effect of introducing excessive viscous damping at the isolation level, using special devices such as viscous dampers, some parametric analyses have been conducted. The plots in Fig. 16 provide the maximum relative displacement at the isolation level as well as the peak floor acceleration at the top floor of the four-story seismically isolated building (without considering any pounding) in relation to the supplemental damping ratio of the isolation system. It is observed that the response is substantially decreasing with the increase of the supplemental damping ratio. Consequently, in this case, the possibility of pounding due to insufficiently wide seismic gap is reduced when such supplemental damping devices are implemented. However there is always an upper limit, since excessive damping may lead to increased interstory deflections and absolute floor accelerations of the superstructure [33]. Furthermore, the case with a seismic gap size equal to 10% of the maximum unconstrained displacement of the base of the seismically isolated building was also considered in order

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Fig. 13. Peak responses of the seismically isolated building in terms of the width of the seismic gap. The vertical lines indicate the SRSS of the peak displacements of the neighboring buildings for each earthquake excitation, plotted with the corresponding color and line-type. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to demonstrate the effect of supplemental viscous damping on impact velocity. In Fig. 17, the computed maximum impact velocity of the base of the seismically isolated building is plotted in terms of the supplemental damping ratio. It is observed that the impact velocity decreases substantially with the increase of the supplemental damping, while impacts are avoided after a certain damping ratio value. Therefore, it seems that the use of supplemental viscous damping at the isolation system can be an efficient measure for mitigating the detrimental effects of pounding.

8. Software validation Finally, in order to validate the accuracy of the aforementioned developed software, the commercial analysis software SAP2000 [34] has been used to simulate the previously described four-story seismically isolated building. Since the Central Difference Method is not available in the particular software, Newmark’s method has been selected and used as the time-integration scheme. The Kobe earthquake record has been used as the ground

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Fig. 14. Variation of the response of the seismically isolated building during poundings with adjacent fixed-supported structures, in terms of the COR and the impact stiffness for a 25 cm gap width.

Fig. 15. Variation of the response of the seismically isolated building during poundings with adjacent fixed-supported structures, in terms of the COR and the impact stiffness for a 15 cm gap width.

excitation, while a non-linear time-history analysis has been performed. Fig. 18 demonstrates comparative results of the timehistories of the relative displacements at the seismic isolation level and the absolute accelerations at the top floor of the building, with-

out considering any impact. It is observed that the computed responses from both software applications are very similar, with negligible differences, considering that a different integration scheme and time-step have been used.

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Fig. 16. Effect of supplemental viscous damping on the response of the four-story seismically isolated building without impact.

Fig. 17. Effect of supplemental viscous damping on the maximum value of impact velocity with which the base of the four-story seismically isolated building hits against the surrounding moat wall on the left and on the right side of the building, respectively.

Fig. 18. Validation of the computed results without considering any impacts.

In order to take into account the case of poundings with the surrounding moat wall in the SAP2000 model, two gap elements have been used with a linear stiffness equal to the impact stiffness that is used in the developed software and an opening equal to 15 cm, which corresponds to the width of the seismic gap. Fig. 19 compares the results of the analysis using SAP2000 with the corresponding results from the developed software. It is observed

that, in general, the computed responses are very similar, and the maximum responses are very close. Some variations on the time-history responses exist probably due to the different integration algorithms that are used and the way of constructing the damping matrices. Specifically, SAP2000 uses classical Rayleigh damping, calculating the damping matrix terms based on the viscous damping ratios that are provided

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Fig. 19. Validation of the computed results with impact, considering a seismic gap width equal to 15 cm.

from the user for two extreme eigenmodes of the structure, while the developed software uses non-classical damping, as previously described in Section 2.2. It is worth mentioning that conducting a simulation with SAP2000 requires about 2–3 orders of magnitude more time than conducting the corresponding analysis with the developed software. This significant efficiency allows us to perform large numbers of parametric studies, which could not be performed with commercial software within a realistic time span. 9. Concluding remarks Past earthquakes have revealed that poundings of fixedsupported buildings can cause damage ranging from light local to heavier damage that might even have initiated collapse, especially during very strong earthquakes. Although there is not much experience from poundings of seismically isolated buildings, since it is a relatively recent anti-seismic technology, numerical simulations reveal that poundings may have very detrimental consequences on such buildings. This paper presents some representative results that are selected from a wide range of simulations, which have been performed in order to investigate the effects of poundings with adjacent structures on the response of seismically isolated buildings during very strong earthquakes. The results presented consider only the case of a typical four-story seismically isolated building with specific structural characteristics under different cases of neighboring structures and under a range of different seismic excitations. Summarizing the observations regarding the results, it has been found that poundings occurring either at the base of the seismically isolated building or at its upper floors are particularly unfavorable for the structure, since they significantly increase the peak absolute floor accelerations and the interstory deflections. The parametric analyses show that even if a ‘‘sufficient’’ gap is provided, with which poundings with the surrounding moat wall at the base of the building could be avoided, this does not ensure that the building will not eventually collide with neighboring buildings. It is expected that the superstructures of the neighboring buildings will be considerably deformed during a strong earthquake and the floors will have such horizontal interstory deflections that, in combination with the expected large horizontal relative displacements of the seismically isolated building, unwanted pounding incidences may occur. The results also indicate that the detrimental effects of pounding are more pronounced when the structures adjacent to the seismically isolated building are in

resonance with the seismic excitation. Therefore, it is important to take into account the presence and characteristics of the adjacent buildings on the estimation of the required width of the seismic gap around a seismically isolated building, as the design displacement at its base may not be sufficient as a sole criterion for the determination of the required width of the seismic gap. The SRSS method for the estimation of the required separation distance between a seismically isolated building and its adjacent fixed-supported buildings is found to be insufficient for half of the configurations and earthquake excitations that have been considered in the simulations performed. Moreover, the values of the impact parameters that are used for the estimation of the impact forces have insignificant effects on the response of the seismically isolated building during poundings, except for the cases of very severe impacts. Finally, the implementation of supplemental viscous damping devices seems to mitigate the detrimental effects of pounding, while in some cases the impact is avoided due to the reduction of the maximum horizontal relative displacements of the seismically isolated building. References [1] Taylor AW, Igusa T. Primer on seismic isolation, ASCE task committee on seismic isolation. 2004. [2] Jangid RS, Kelly JM. Base isolation for near-fault motions. Earthq Eng Struct Dyn 2001;30:691–707. [3] Makris N, Chang SP. Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures. Earthq Eng Struct Dyn 2000;29: 85–107. [4] Nagarajaiah S, Sun X. Base-isolated FCC building: impact response in Northridge earthquake. J Struct Eng 2001;127(9):1063–75. [5] Anagnostopoulos SA. Earthquake induced poundings: state of the art. In: Duma, editor. 10th European conference on earthquake engineering. Rotterdam: Balkema; 1995. [6] Bertero VV. Observations on structural pounding. In: Proceedings international conference on Mexico City earthquakes. ASCE; 1986. p. 264–87. [7] Earthquake Engineering Research Institute (EERI). In: Benuska L, editor. Loma Prieta earthquake reconnaissance report. Rep. No. 90–01. Oakland (CA): EERI; 1990. [8] Earthquake Engineering Research Institute (EERI). In: Youd TL, Bardet J-P, Bray JD, editors. Kocaeli, Turkey, Earthquake of August 17, 1999 Reconnaissance Report. Publ. No. 00-03. Oakland (CA): EERI; 2000. [9] Earthquake Engineering Research Institute (EERI). The Nisqually, Washington, earthquake of February 28, 2001 — preliminary reconnaissance report. Oakland (CA): EERI; 2001. [10] Anagnostopoulos SA. Building pounding re-examined: how serious problem is it? 11th world conference on earthquake engineering, Paper no: 2108, 23–28 June 1996, Acapulco (Mexico). [11] Rosenblueth E, Meli R. The 1985 earthquake: causes and effects in Mexico City. Concr Internat (ACI) 1986;8:23–36. [12] Earthquake Engineering Research Institute (EERI). L’Aquila, Italy earthquake clearinghouse–observations from-EERI/PEER team. 2009. http://www.eqclearinghouse.org/italy-090406/. [13] Anagnostopoulos SA. Pounding of buildings in series during earthquakes. Earthq Eng Struct Dyn 1988;16:443–56.

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