Soil–structure interaction for a SDOF oscillator supported by a flexible foundation embedded in a half-space: Closed-form solution for incident plane SH-waves

Abstract A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the special case of a rigid foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with more flexible foundation, the radiation damping is smaller, the foundation response is larger, especially for obliquely incident waves, while the structural relative response is smaller, and the system frequency shifts towards lower frequencies. This simple model may be helpful to obtain insight into the effects of soil–structure interaction for a slim structure on an extended flexible foundation.

[1]  J. E. Luco,et al.  Strong earthquake motion and site conditions: Hollywood , 1970, Bulletin of the Seismological Society of America.

[2]  Nien-Chien Tsai.  MODAL DAMPING FOR SOIL-STRUCTURE INTERACTION , 1974 .

[3]  Maria I. Todorovska,et al.  Plain strain soil–structure interaction model for a building supported by a circular foundation embedded in a poroelastic half-space , 2006 .

[4]  Mihailo D. Trifunac,et al.  Two-dimensional, antiplane, building-soil-building interaction for two or more buildings and for incident planet SH waves , 1975 .

[5]  D T Mihailo,et al.  FULL-SCALE EXPERIMENTAL STUDIES OF SOIL-STRUCTURE INTERACTION , 2001 .

[6]  Vlado Gicev,et al.  Translation, torsion, and wave excitation of a building during soil–structure interaction excited by an earthquake SH pulse , 2015 .

[7]  Apostolos S. Papageorgiou,et al.  Analysis of recorded earthquake response and identification of a multi-story structure accounting for foundation interaction effects , 1991 .

[8]  Mihailo D. Trifunac,et al.  Two-dimensional translation, rocking, and waves in a building during soil-structure interaction excited by a plane earthquake SV-wave pulse , 2016 .

[9]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[10]  J. Avilés,et al.  Effects of wave passage on the relevant dynamic properties of structures with flexible foundation , 2002 .

[11]  Mihailo D. Trifunac,et al.  Antiplane response of a dike with flexible soil-structure interface to incident SH waves , 2001 .

[12]  Gin-Show Liou,et al.  EFFECT OF FLEXIBILITY ON IMPEDANCE FUNCTIONS FOR CIRCULAR FOUNDATION , 1994 .

[13]  Mihailo D. Trifunac,et al.  The system damping, the system frequency and the system response peak amplitudes during in‐plane building‐soil interaction , 1992 .

[14]  Ralf Peek,et al.  Parametric study of vertical vibrations of circular flexible foundations on layered media , 1993 .

[15]  Mihailo D. Trifunac,et al.  Antiplane dynamic soil-bridge interaction for incident plane SH-waves , 1977 .

[16]  Mihailo D. Trifunac,et al.  Contact stresses and ground motion generated by soil‐structure interaction , 1977 .

[17]  Mihailo D. Trifunac,et al.  Antiplane response of a dike on flexible embedded foundation to incident SH-waves , 2001 .

[18]  Paul C. Jennings,et al.  Soil-structure interaction during the San Fernando earthquake , 1975, Bulletin of the Seismological Society of America.

[19]  Maria I. Todorovska,et al.  In-plane foundation-soil interaction for embedded circular foundations , 1993 .

[20]  Vincent W. Lee,et al.  Out-of-plane (SH) soil-structure interaction: Semi-circular rigid foundation revisited , 2014 .

[21]  Dimitris L. Karabalis,et al.  Dynamic analysis of 3‐D flexible embedded foundations by a frequency domain BEM‐FEM , 1988 .

[22]  J. E. Luco,et al.  Torsional Response of Rigid Embedded Foundation , 1976 .

[23]  Mihailo D. Trifunac,et al.  Interaction of a shear wall with the soil for incident plane SH waves , 1972 .

[24]  Jacobo Bielak,et al.  Dynamic behaviour of structures with embedded foundations , 1974 .

[25]  Maria I. Todorovska,et al.  Effects of the wave passage and the embedment depth for in-plane building-soil interaction , 1993 .

[26]  J. Enrique Luco,et al.  Dynamic Interaction of a Shear Wall with the Soil , 1969 .

[27]  Jacobo Bielak,et al.  Modal Analysis for Building-Soil Interaction , 1976 .

[28]  Mihailo D. Trifunac,et al.  A note on the dynamic response of rigid embedded foundations , 1975 .

[29]  Jia Fu,et al.  Effects of the site dynamic characteristics on soil-structure interaction (I): Incident SH-Waves , 2013 .

[30]  J. E. Luco,et al.  Dynamic response of flexible rectangular foundations on an elastic half‐space , 1981 .

[31]  R. Rajapakse,et al.  Dynamic response of elastic plates on viscoelastic half space , 1989 .

[32]  Michio Iguchi,et al.  Vibration of Flexible Plate on Viscoelastic Medium , 1982 .

[33]  Y. J. Lin.  Dynamic Response of Circular Plates Resting on Viscoelastic Half Space , 1978 .

[34]  Maria I. Todorovska,et al.  Effects of rainfall on soil–structure system frequency: Examples based on poroelasticity and a comparison with full-scale measurements , 2006 .

[35]  Mihailo D. Trifunac,et al.  Experimental evidence for flexibility of a building foundation supported by concrete friction piles , 1999 .