Vertical–Horizontal–Rocking Vibrations of Rigid Foundations of Arbitrary Shape on Poroelastic Layer

The vertical–horizontal–rocking vibrations of rigid foundations of arbitrary shape resting on a poroelastic layer are studied in this paper. The poroelastic layer consists of a finite thickness overlying a rigid base. A foundation is subjected to time-harmonic vertical, horizontal and moment loading. The interaction problem is formulated by employing a discretization technique based on the rigid body displacement boundary conditions at the soil–foundation contact surface and the displacement influence functions of a poroelastic layer. The discretization method used in this paper yields a flexibility equation system for the contact traction at the soil–foundation contact area. Selected numerical results for the vertical, horizontal, and rocking compliances of rigid foundations of arbitrary shape are presented to portray the effects of the foundation shape, the finite thickness of a poroelastic layer, and the poroelastic properties on the dynamic interaction problem. The results show that the influences of the foundation shape, the finite thickness of a poroelastic layer, and the poroelastic properties are significant on the vertical, horizontal, and rocking compliances.