Analytical solution to vertical vibration of cast-in-place concrete large-diameter pipe piles by considering 3D wave effect of soils

Considering 3D wave effect of soils and soil-pile coupled vibration, treating the pile as one-dimensional rod and the soils as three-dimensional axisymmetric viscoelastic medium, the frequency-domain vertical dynamic response of PCC pile in viscoelastic soils is investigated. The potential functions are adopted to decouple the governing equations for the soils. The analytical solutions of soils in frequency domain are obtained by using the Laplace transform technique and the separation of variables. Under the assumption of perfect contact between the pile and the soils, the pile response is derived. The solution is compared with that of solid pile to verify the rationality. Furthermore, this solution is compared with the simplified solution to verify the correctness of the simplified solution. Moreover, the effects of the stiffness coefficient of pile, pile length and pile radius on the complex stiffness are analyzed. The oscillation amplitudes and resonant frequencies of the complex stiffness of the pile decrease steeply with the increase of its stiffness coefficient. The oscillation amplitudes of the complex stiffness of the pile without inner soils are larger than those with outer and inner soils, and those without the outer soils are larger than those without inner soils. The oscillation amplitudes and resonant frequencies of the complex stiffness of the pile decrease steeply with the increase of the pile length. When the pile length increases to a critical value, the effect trends to vanish. The oscillation amplitudes of the complex stiffness of the pile increase with the increase of the outer radius or decrease of the inner radius.