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Seismic excitation, which results in large horizontal relative displacements, may cause collisions between two adjacent structures due to insufficient separation distance between them. Such collisions, known as earthquake-induced structural pounding, may induce severe damage. In this paper, the case of pounding between two adjacent buildings is studied by the application of single degree-of-freedom structural models. Impact is numerically simulated with the use of a nonlinear viscoelastic model. Special attention is focused on calculating values of impact forces during collisions which have significant influence of pounding-involved response under ground motions. The results of the study indicate that the impact force time history is much dependent on the earthquake excitation analyzed. Moreover, the peak impact forces during collision depend substantially on such parameters as gap size, coefficient of restitution, impact velocity, and stiffness of impact spring element. The nonlinear viscoelastic model of impact force with the considered relation between the damping coefficient and the coefficient of restitution has also been found to be effective in simulating earthquake-induced structural pounding.

During ground motions, buildings often collide with each other due to different dynamic characteristics, insufficient gap between them, and out-of-phase vibrations [

Anagnostopoulos [

Maison and Kasai [

Jankowski [

Komodromos et al. [

Barros and Khatami [

Furthermore, some more recent numerical analyses have been carried out to study the influence of different parameters in pounding of buildings [

Nevertheless, there is still a need to investigate different models of structural pounding so as to verify their accuracy in the case of different configurations under different earthquake excitations. This concerns especially the values of impact forces during collisions which are often not studied in the analyses (or the analyses are simplified) since the investigations are rather focused on pounding-involved response under ground motions.

The contact element is a special element (usually consisting of a spring and damper) to model impact between two colliding structures, which is widely used to simulate impact force. Impact is parametrically modelled in this way that when relative displacement exceeds the separation distance, the contact element is activated. The general formula for the impact force during collision can be expressed as follows (see [

Impact force versus time and lateral displacement for the linear viscoelastic model.

Impact force versus time and lateral displacement for the nonlinear viscoelastic model.

Impact force versus time and lateral displacement for the Hertzdamp model.

Impact force versus time and lateral displacement for the modified Hertzdamp model.

A parametric study has been conducted in order to verify the effectiveness of the nonlinear viscoelastic model of impact force during structural pounding described by (

Model of interacting structures.

The dynamic equation of motion for such a model can be expressed as [

The dynamic analyses under the Parkfield (1966), San Fernando (1971), Kobe (1995), and El Centro (1940) earthquake records have been performed. These records have different contents of the excitation frequencies, different magnitude of the accelerations, and different time durations. Besides, their place of occurrence and geological conditions close to the epicentre are distinct. San Fernando earthquake had the highest Peak Ground Acceleration (PGA) among the four records discussed. The PGA of the earthquake amounted to 1.164 g, with an epicentre distance less than 12 km. The PGA of the Kobe earthquake was 0.7105 g and it was measured at a distance of 18.3 km. The PGA of the Parkfield earthquake was equal to 0.462 g (measured at a distance of 32 km). Finally, the PGA of the El Centro earthquake was equal to 0.347 g. All mentioned records have been normalized to investigate the effect of earthquake properties on pounding-involved structural response. The examples of the results of the numerical analysis in the form of the lateral displacement time histories under different earthquakes are shown in Figure

Lateral displacement time histories under different earthquakes.

El Centro

Kobe

San Fernando

Parkfield

Impact force time histories for the Kobe and El Centro earthquakes.

Using four different earthquake excitations, the peak lateral displacements, velocities, and accelerations have also been calculated for different structural periods of colliding structures. The results of the analyses are presented in Figure

Peak lateral displacement, velocity, and acceleration with respect to structural period under different earthquakes.

In order to investigate the effect of separation distance between structures, a gap size has been varied from 0 to 8 cm. Figure

Peak impact force with respect to gap size under different earthquakes.

Different values of coefficient of restitution

Peak impact force with respect to coefficient of restitution under different earthquakes.

In order to obtain the responses and compare the results of peak impact forces, different values of impact velocity have been considered from the range 1–25 m/s. The relations between the peak impact force and impact velocity values under different earthquakes are presented in Figure

Peak impact force with respect to impact velocity under different earthquakes.

Stiffness of impact spring element is considered to be one of the most important parameters when the impact force during collision is calculated. The results of the parametric study showing the peak values of impact forces with respect to stiffness of spring are presented in Figure

Peak impact force with respect to impact spring stiffness under different earthquakes.

In this paper, earthquake-induced pounding between two adjacent buildings has been studied by the application of single degree-of-freedom structural models. Impact has been numerically simulated with the use of a nonlinear viscoelastic model. Special attention has been focused on calculating values of impact forces during collisions which have significant influence of pounding-involved response under ground motions.

The results of the study indicate that the impact force time history depends substantially on the earthquake excitation analyzed. Moreover, the peak impact force during collision is much dependent on such parameters as gap size, coefficient of restitution, impact velocity, and stiffness of impact spring element. The nonlinear viscoelastic model of impact force with the considered relation between the damping coefficient and the coefficient of restitution has also been found to be effective in simulating pounding between structures during seismic excitations.

The conclusions of the study can be very valuable for the purposes of accurate modelling the phenomenon of earthquake-induced structural pounding. This concerns especially the issue of determination of the precise values of impact forces during collisions which are often not studied in the analyses (or the analyses are simplified) since the investigations are rather focused on pounding-involved response under ground motions. It can be considered as the most significant element of the analysis described in this paper, as compared to other relevant research studies.

The authors declare that there is no conflict of interests regarding the publication of this paper.