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

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## Abstract

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.

## Keywords

Friction Sliding base Instantaneous frequency Instantaneous amplitude Restitution coefficient## List of Symbols

*a*A constant in Formula (2)

- COR
Coefficient of restitution

*F*_{b}Friction load between the block and ground

*F*_{n}Normal load

*k*A constant in Formula (2)

*g*Gravitational acceleration (9.81 m/s

^{2})*m*_{b}Block mass

*N*Instantaneous vertical reaction

*V*Relative velocity of the contacting surfaces

*t*_{impact}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

*α*A constant in Formula (1)

*u*_{b}Block velocity just before hitting the ground

*u*_{g}Ground velocity just before the block hits the ground

*v*_{b}Block velocity after the hitting the ground

*v*_{g}Ground velocity just after the block hits the ground

*μ*Friction coefficient of the layer

*µ*_{s}Static friction coefficient

*µ*_{max}The maximum coefficients of friction

*µ*_{min}The minimum coefficients of friction

## Notes

### Acknowledgments

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.

## References

- 1.Rahgozar MA (2015) Accounting for soil nonlinearity in three-dimensional seismic structure-soil structure-Interaction analyses of adjacent tall buildings structures. Int J Civil Eng 13(3):213–225Google Scholar
- 2.Shakib H, Atefatdoost GR (2014) Minimizing the torsional response of asymmetric wall-type systems considering soil-structure interaction. Int J Civil Eng 12(1):14–24Google Scholar
- 3.Davoodi M, Sadjadi M (2015) Assessment of near-field and far-field strong ground motion effects on soil-structure SDOF system. Int J Civil Eng 13(3):153–166Google Scholar
- 4.Naderzadeh A (2009) Application of seismic base isolation technology in Iran. Menshin 63:40–47Google Scholar
- 5.Kelly J (1986) Aseismic base isolation: review and bibliography. Soil Dyn Earthq Eng 4(3):202–216CrossRefGoogle Scholar
- 6.Constantinou M, Mokha A, Reinhorn A (1990) Teflon bearings in base isolation. II: modeling. J Struct Eng ASCE 116(2):455–474CrossRefGoogle Scholar
- 7.Westermo B, Udwadia F (1983) Periodic response of a sliding oscillator system to harmonic excitation. Earthq Eng Struct Dyn 11:135–146CrossRefGoogle Scholar
- 8.Younis CJ, Tadjbakhsh IG (1983) Response of sliding rigid structure to base excitation. J Eng Mech ASCE 110(3):417–432CrossRefGoogle Scholar
- 9.Ahmadi G (1983) Stochastic earthquake response of structures on sliding foundation. Int J Eng Sci 21(2):93–102CrossRefzbMATHGoogle Scholar
- 10.Su L, Ahmadi G (1988) Response of frictional base isolation systems to horizontal–vertical random earthquake excitations. Probab Eng Mech 3(1):12–21CrossRefGoogle Scholar
- 11.Su L, Ahmadi G (1992) Probabilistic responses of base-isolated structures to El Centro 1940 and Mexico City 1985 earthquakes. Eng Struct 14(4):217–230CrossRefGoogle Scholar
- 12.Fan F-G, Ahmadi G, Tadjbakhsh IG (1990) Multi-story base-isolated buildings under a harmonic ground motion—Part I: a comparison of performances of various systems. Nucl Eng Des 123:1–16CrossRefGoogle Scholar
- 13.Fan F-G, Ahmadi G, Mostaghel N, Tadjbakhsh IG (1991) Performance analysis of aseismic base isolation systems for a multi-story building. Soil Dyn Earthq Eng 10:152–171CrossRefGoogle Scholar
- 14.Matsui K, Iura M, Sasaki T, Kosaka I (1991) Periodic response of a rigid block resting on a footing subjected to harmonic excitation. Earthq Eng Struct Dyn 20:683–697CrossRefGoogle Scholar
- 15.Vafai A, Hamidi M, Ahmadi G (2001) Numerical modeling of MDOF structures with sliding supports using rigid-plastic link. Earthq Eng Struct Dyn 30:27–42CrossRefGoogle Scholar
- 16.Hamidi M, El Naggar MH, Vafai A (2003) Response of structures supported on SCF isolation systems. Earthq Eng Struct Dyn 32:1555–1584CrossRefGoogle Scholar
- 17.Hamidi M, El Naggar MH, Vafai A, Ahmadi G (2003) Seismic isolation of buildings with sliding concave foundation (SCF). Earthq Eng Struct Dyn 32:15–29CrossRefGoogle Scholar
- 18.Khoshnoudian F, Haghdoust V (2009) Response of pure-friction sliding structures to three components of earthquake excitation considering variations in the coefficient of friction. Sci Iran Trans A Civil Eng 16(6):429–442Google Scholar
- 19.Liaw TC, Tian QL, Cheung YK (1988) Structures on sliding base subjected to horizontal and vertical motion. J Struct Eng ASCE 114:2119–2129CrossRefGoogle Scholar
- 20.Shakib H, Fuladgar A (2003) response of pure-friction sliding structures to three components of earthquake excitation. Comput Struct 81:189–196CrossRefGoogle Scholar
- 21.Takahashi Y, Iemura H, Yanagawa S, Hibi M (2004) Shaking table test for frictional isolator. In: Proceeding of 13th world conference on earthquake engineering, Vancouver, CanadaGoogle Scholar
- 22.Iemura H, Taghikhany T, Takahashi Y, Jain S (2005) Effect of variation of normal force on seismic performance of resilient sliding isolation systems in highway bridges. Earthq Eng Struct Dyn 34:1777–1797CrossRefGoogle Scholar
- 23.American Society of Civil Engineers (1994) Minimum design loads for buildings and other structures, vol. 7. American Society of Civil Engineers, RestonCrossRefGoogle Scholar
- 24.Iranian Code of Practice for Seismic Resistant Design of Buildings (2015) Standard No. 2800, Road, Housing and Urban Development Research Center of I. R. IranGoogle Scholar
- 25.Bruneau M, Uang CM, Sabelli SR (2011) Ductile design of steel structures. McGraw Hill Professional, New YorkGoogle Scholar
- 26.Mokha AS, Constantinou MC, Reinhorn AM (1993) Verification of friction model of teflon bearings under triaxial load. J Struct Eng ASCE 119:240–261CrossRefGoogle Scholar
- 27.Chowdhury MA, Helali M (2008) The effect of amplitude of vibration on the coefficient of friction for different materials. Tribol Int 41:307–314CrossRefGoogle Scholar
- 28.Chowdhury MA, Helali M (2009) The frictional behavior of materials under vertical vibration. Ind Lubr Tribol 61(3):154–160CrossRefGoogle Scholar
- 29.Misiti M, Misiti Y, Oppenheim G, Poggi JM (1996) Wavelet toolbox. The MathWorks Inc., NatickzbMATHGoogle Scholar