Parametric investigation for rigid circular foundations undergoing vertical and torsional vibrations

•The vibrating sources include seismic excitations and forced vibrations.•Dominant dimensionless parameters for the dynamic foundation response are studied.•The dynamic responses are investigated in the dimensionless analysis.

This study derives the vertical and torsional responses of a rigid circular foundation resting on unbounded soil. The rigid foundation is subjected to vertical incident P-waves, torsional incident waves, vertical harmonic forces, and harmonic torques, respectively. The solutions of the proposed method are found to agree well with existing solutions of previous research. Results of dimensionless parameter analysis show that the vertical response of the rigid surface foundation can be simplified to a function of the Poisson ratio, the dimensionless frequency and mass ratio, and that the torsional response can be further simplified to a function of dimensionless frequency and mass ratio. As the dimensionless mass ratio increases, the vertical and torsional responses increase at low frequencies but decrease at high frequencies, while the fundamental frequency of the foundation-soil system also decreases. As the Poisson ratio increases, the vertical response increases at low frequencies but increases at high frequencies, while the fundamental frequency of the system increases. As the damping ratio of the viscoelastic half-space increases, the vertical and torsional responses rapidly decrease, and the fundamental frequency of the system slightly decreases. The study found significant characteristics of dynamic responses for the foundation undergoing vertical and torsional vibrations, which can provide helpful physical insights for foundation designs.