Static and dynamic displacements of foundations on heterogeneous multilayered soils

An analytical-numerical formulation is presented for dynamic and static analysis of strip foundations on an elastic isotropic medium consisting of heterogeneous layers. Each layer is characterized by an S-wave velocity that increases or decreases linearly with depth, a constant material density, a constant Poisson’s ratio equal to l/4 and a constant linearlyhysteretic critical damping ratio. The solution, based on a transformation that uncouples the wave equations in closed-form, is ‘exact’ in that it properly accounts for the true boundary conditions at the layer interfaces and the surface. Results are presented for two characteristic soil profiles (halfspace and stratum on rigid rock) in the form of normalized load-displacement ratios as functions of key dimensionless factors that influence the foundation behaviour during static and dynamic vertical, horizontal or moment loading. An interesting equivalence is established between a heterogeneous and a homogeneous halfspace, both having the same moduli at a depth equal to the foundation halfwidth (for translational motions) or to l/2 the foundation halfwidth (for rotation), i.e. for low frequency factors, the two media yield displacements of about the same average level, although the occurrence of resonance phenomena due to total wave reflection in the heterogeneous medium leads to fluctuations of the corresponding curves around the mean values. Cet article pr&.ente une formulation analytiquenumerique pour l’analyse dynamique et statique de fondations continues sur un milieu isotrop tlastique form6 de couches hCt&og&es. Chaque couche est

[1]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[2]  J. Enrique Luco.  Vibrations of a rigid disc on a layered viscoelastic medium , 1976 .

[3]  VERTICAL VIBRATION OF A RIGID CIRCULAR FOUNDATION ON GIBSON SOIL , 1972 .

[4]  F. Molenkamp,et al.  Dynamic displacements of offshore structures due to low frequency sinusoidal loading , 1980 .

[5]  Ravindra N. Gupta,et al.  Reflection of elastic waves from a linear transition layer , 1966 .

[6]  Kausel Bolt,et al.  Forced vibrations of circular foundations on layered media. , 1974 .

[7]  R. E. Gibson,et al.  The analytical method in soil mechanics , 1974 .

[8]  R. E. Gibson.  SOME RESULTS CONCERNING DISPLACEMENTS AND STRESSES IN A NON-HOMOGENEOUS ELASTIC HALF-SPACE , 1967 .

[9]  D. L. Holl,et al.  STRESS TRANSMISSION IN EARTHS , 1941 .

[10]  D. Burmister,et al.  The General Theory of Stresses and Displacements in Layered Soil Systems. II , 1945 .

[11]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[12]  George Gazetas,et al.  Forced Vibrations of Strip Footings on Layered Soils , 1976 .

[13]  M. Kassir,et al.  Displacements and Stresses in Nonhomogeneous Solid , 1974 .

[14]  R. E. Gibson,et al.  Surface Settlement of a Deep Elastic Stratum Whose Modulus Increases Linearly with Depth: Erratum , 1974 .

[15]  F. E. Richart,et al.  Vibrations of soils and foundations , 1970 .

[16]  M. Kassir,et al.  A Rigid Punch in Contact With a Nonhomogeneous Elastic Solid , 1974 .

[17]  A. O. Awojobi,et al.  PLANE STRAIN AND AXIALLY SYMMETRIC PROBLEMS OF A LINEARLY NONHOMOGENEOUS ELASTIC HALF-SPACE , 1973 .

[18]  A. Awojobi.  The settlement of a foundation of Gibson soil of the second kind , 1975 .

[19]  J T Christian,et al.  Rigid circular plate resting on a nonhomogeneous elastic halfspace , 1973 .

[20]  S. Lekhnitskii.  Radial distribution of stresses in a wedge and in a half-plane with variable modulus of elasticity , 1962 .