###### Abstract  
An analytical model is presented for solving the longitudinal complex impedance of a large-diameter floating pile in viscoelastic surrounding soil with radial heterogeneity and viscous-type damping, taking the effect of three-dimensional wave propagation of soil and lateral inertia of the pile shaft into account. The corresponding analytical solution for longitudinal impedance is also derived and validated via comparisons with existing solutions. The influences of the pile length, Poisson's ratio of the pile shaft and the viscous damping coefficient, as well as the degree and radius of disturbed surrounding soil, on the longitudinal impedance of the pile shaft are examined by performing parametric analyses. It is demonstrated that the proposed analytical model and solution are suitable for the longitudinal vibration problem of a large-diameter pile and radially inhomogeneous surrounding soil, especially when the pile slenderness is low. In addition, the present solution  
inner disturbed zone of surrounding soil as a series of annular sub-layers and combined them with [PERSON]'s plane-strain model for pile-soil vibration. On this basis, [PERSON] et al. [21] and [PERSON] et al. [22] identified the limitations of [PERSON]'s model and proposed a new approach for the longitudinal vibration of piles in hysteretic-damping soil, which considers a completely coupled condition at the sub-layer interface by adopting the complex stiffness method. In addition, [PERSON] et al. [23] further examined the longitudinal impedance of piles in radially inhomogeneous soil with a hysteretic-type damping model, considering the three-dimensional (3D) wave propagation in soil. The aforementioned studies mainly employed the Euler-Bernoulli rod model to describe the dynamic behavior of pile shafts, in which the wave propagation effect of pile shafts in a radial direction was roughly ignored [24; 25]. Instead, the Rayleigh-Love rod model can take account of this radial wave effect, i.e., the lateral inertia effect, by introducing [PERSON]'s ratio into the governing equation [26; 27; 28]. With the combination of the Rayleigh-Love model and the 3D wave propagation theory, [PERSON] et al. [29; 30] proposed a simplified model for the longitudinal dynamic behavior of a large-diameter pile in radially homogenous viscoelastic media by adopting the hysteretic-type damping model. Afterwards, [PERSON] et al. [31] further extended this model to examine the longitudinal vibration of a large-diameter pipe pile in radially homogenous media. Moreover, for the longitudinal vibration problem of piles with radial heterogeneity, [PERSON] et al. [32; 33] investigated the longitudinal vibration characteristics of a large-diameter pile in viscoelastic media with radial heterogeneity and hysteretic-type damping, using [PERSON]'s thin layers model and the wave propagation theory of a 3D continuum, respectively. It has been demonstrated that the hysteretic-type damping model, which is independent of frequency, could be unsatisfactory when the excitation is non-harmonic [34]. In contrast, the viscous-type damping model is suitable for non-harmonic excitation [35; 36]. Hence, [PERSON] et al. [37; 38] presented a new mechanical model and examined the longitudinal impedance of a pipe pile in layered viscoelastic media with radial heterogeneity and viscous-type damping, based on [PERSON]'s plane-strain model. To date, however, little work has been carried out on the longitudinal impedance of a large-diameter floating pile in viscoelastic soil with radial heterogeneity, combining both the viscous-type damping and the 3D wave propagation effect of surrounding soil. The primary aim of this paper is to develop a new analytical model to describe the longitudinal vibration of a large-diameter floating pile in viscoelastic surrounding soil with radial inhomogeneity, taking the effect of 3D wave propagation and lateral inertia of the pile shaft into account.