International Journal of Civil Engineering

, Volume 15, Issue 2, pp 287–298 | Cite as

Seismic Behavior of Sliding Base Isolation Systems, Regarding Restitution Factor and Variable Friction Coefficient

  • Majid MohammadiEmail author
Research Paper


Sliding foundation is a technique to suppress seismic loads applied to structures. There are many studies showing that sliding foundations are efficient especially for low rise buildings; however, most of them have ignored the effects of vertical components of the earthquake records on the behavior of such bases. This paper focuses on influences of sliding foundations on seismic behavior of low rise buildings, for real cases. For this purpose, vertical component of earthquakes is considered as well as inherent properties of foundation material such as coefficient of restitution (COR). Furthermore, variation of friction coefficient during the earthquake is considered. COR is utilized to consider bouncing of the structure after separation of the foundation, occurred for extreme downward vertical accelerations (greater than gravitational acceleration). Variation of friction coefficient is considered based on a new study, showing that the coefficient of friction depends on instantaneous amplitude and frequency of the vertical excitation. The obtained results show that vertical component of earthquake affects the behavior of the sliding base substantially. It is also demonstrated that providing material for the sliding base with higher COR is advantageous in decreasing structural acceleration response. Furthermore, the coefficient of friction is really lower than the regularly assumed values and, therefore, leads to smaller structural acceleration response but mostly greater residual displacements.


Friction Sliding base Instantaneous frequency Instantaneous amplitude Restitution coefficient 

List of Symbols


A constant in Formula (2)


Coefficient of restitution


Friction load between the block and ground


Normal load


A constant in Formula (2)


Gravitational acceleration (9.81 m/s2)


Block mass


Instantaneous vertical reaction


Relative velocity of the contacting surfaces


Time duration of the impact

\( X_{\text{b}} \)

Block absolute horizontal displacement

\( X_{\text{g}} \)

Ground absolute horizontal displacement

\( \dot{X}_{\text{b}} \)

Block horizontal velocity

\( \dot{X}_{\text{g}} \)

Ground horizontal velocity

\( {\ddot{X}}_{\text{b}} \)

Block horizontal acceleration

\( {\ddot{X}}_{\text{g}} \)

Ground horizontal acceleration

\( Y_{\text{b}} \)

Block absolute vertical displacement

\( Y_{\text{g}} \)

Ground absolute vertical displacement

\( {\ddot{Y}}_{\text{b}} \)

Block vertical acceleration

\( {\ddot{Y}}_{\text{g}} \)

Ground vertical acceleration


A constant in Formula (1)


Block velocity just before hitting the ground


Ground velocity just before the block hits the ground


Block velocity after the hitting the ground


Ground velocity just after the block hits the ground


Friction coefficient of the layer


Static friction coefficient


The maximum coefficients of friction


The minimum coefficients of friction



This research study has been accomplished by financial support of International Institute of Earthquake Engineering and Seismology under the Grant No. 7385 and their contribution is highly appreciated.


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Copyright information

© Iran University of Science and Technology 2017

Authors and Affiliations

  1. 1.International Institute of Earthquake Engineering and Seismology (IIEES)TehranIslamic Republic of Iran

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