A BEM–FEM model for the dynamic analysis of building structures founded on viscoelastic or poroelastic soils

This paper presents a time-harmonic boundary element–finite element three–dimensional model for the dynamic analysis of building structures founded on viscoelastic or poroelastic soils. The building foundation and soil domains are modelled as homogeneous, isotropic, viscoelastic or poroelastic media using boundary elements. The foundation can also be modelled as a perfectly rigid body coupled to soil and structure. The buildings are modelled using Timoshenko beam finite elements that include the torsional eccentricity of non-symmetrical buildings. The excitation model includes far-field plane seismic waves of P, S or Rayleigh type for viscoelastic soils and P1 and S type for poroelastic soils. Modelling foundation and structure as rigid body and Timoshenko beam respectively conveys important benefits such as a significant reduction in the number of degrees of freedom in the problem, which allows to study problems involving several building structures and the interactions between them with acceptable computational effort. Results are presented for validation purposes first, and for studying the influence of modelling the soil as a viscoelastic or poroelastic region afterwards. Results involving structure–soil–structure interaction are also presented for illustration purposes.

[1]  Juan José,et al.  Efectos de los fenómenos de interacción interacción incluyendo factores espaciales y sedimentos de fondo en la respuesta sísmica de presas bóveda , 2002 .

[2]  José Domínguez,et al.  Boundary element approach for dynamic poroelastic problems , 1992 .

[3]  I. C. Simpson,et al.  On the interaction of rayleigh surface waves with structures , 1978 .

[4]  J. Domínguez.  Boundary elements in dynamics , 1993 .

[5]  J. Vega,et al.  On soil-structure interaction in large non-slender partially buried structures , 2013, Bulletin of Earthquake Engineering.

[6]  Rafael Gallego,et al.  DYNAMIC STIFFNESS OF FOUNDATIONS ON SATURATED POROELASTIC SOILS , 1997 .

[7]  J. Enrique Luco,et al.  Dynamic structure-soil-structure interaction , 1973, Bulletin of the Seismological Society of America.

[8]  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 .

[9]  J. E. Luco,et al.  Response of structures to nonvertically incident seismic waves , 1982 .

[10]  Juan J. Aznárez,et al.  Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams , 2004 .

[11]  J. Enrique Luco,et al.  Soil-structure interaction effects on the seismic response of tall chimneys , 1986 .

[12]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[13]  R. Skalak,et al.  On uniqueness in dynamic poroelasticity , 1963 .

[14]  Juan J. Aznárez,et al.  Be analysis of bottom sediments in dynamic fluid-structure interaction problems , 2006 .

[15]  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 .

[16]  Andrew N. Norris,et al.  Radiation from a point source and scattering theory in a fluid-saturated porous solid , 1985 .

[17]  J. Domínguez,et al.  Effects of Space Distribution of Excitation on Seismic Response of Arch Dams , 2002 .

[18]  S D Townley,et al.  SEISMOLOGICAL SOCIETY OF AMERICA. , 1923, Science.

[19]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[20]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[21]  Werner Wagner,et al.  Shear correction factors in Timoshenko's beam theory for arbitrary shaped cross-sections , 2001 .

[22]  John L. Tassoulas,et al.  Seismic Response of Gravity Dams. II: Effects of Sediments , 1991 .

[23]  S. Timoshenko,et al.  X. On the transverse vibrations of bars of uniform cross-section , 1922 .

[24]  G. Schmid,et al.  Dynamic structure-soil-structure interaction by FEM and BEM , 1992 .

[25]  Anil K. Chopra,et al.  Period formulas for moment-resisting frame buildings , 1997 .

[26]  Anil K. Chopra,et al.  Elastic Earthquake Analysis of a Class of Torsionally Coupled Buildings , 1977 .

[27]  Juan J. Aznárez,et al.  Dynamic impedances of piles and groups of piles in saturated soils , 2005 .

[28]  J. Kosmatka,et al.  An improved two-node timoshenko beam finite element , 1993 .

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