Horizontal Vibration of Pile Foundation in Transversely Isotropic Soil Considering Three-Dimensional Wave Effect

The soil in nature will form anisotropic soil due to the arrangement of soil particles and constitutive elements, resulting in differences in the properties of the soil in the vertical direction and the horizontal direction. The vertical modulus of the soil is often smaller than the horizontal modulus, but the horizontal modulus presents isotropic characteristics. Therefore, it is more suitable to treat this kind of soil as transversely isotropic soil. Considering the influence of soil anisotropy and three-dimensional wave effect, the soil around the pile is regarded as transversely isotropic soil. The horizontal vibration of transversely isotropic soil layer is solved by using the separated variable method, and the analytical solution expression of soil damping factor is obtained. Considering the effect of transversely isotropic soil around the pile on pile foundation, the horizontal dynamic impedance at pile top in transversely isotropic soil is obtained by using the boundary conditions of the problem and the orthogonality of trigonometric function. The results show that the horizontal impedance factor of transversely isotropic soil layer and the horizontal dynamic impedance of pile foundation in transversely isotropic soil can degenerate to homogeneous soil. For transversely isotropic soil, there is a resonance point in the curve of soil impedance factor and dynamic impedance at pile top varying with frequency at low frequency, which is much sharper than that of homogeneous soil. The dimensionless frequencies interval between the resonance points of the horizontal stiffness factor is about 3, and the dimensionless frequencies interval between the resonance points of the damping factor is about 4.The anisotropy of soil has a great influence on the horizontal vibration of pile foundation, which should not be ignored. With the increase of pile length, the influence of pile length on the horizontal vibration of pile foundation in transversely isotropic soil will decrease. When the pile length is more than 100 times of the pile diameter, the influence of pile length on the horizontal dynamic impedance is very small.