This paper investigates the consolidation behavior of multi-layered viscoelastic soils considering groundwater. First, the fractional Merchant viscoelastic model is introduced to describe the behavior of multi-layered viscoelastic soils considering groundwater. Later, the governing equations are extended to a viscoelastic medium by virtue of the elastic-viscoelastic corresponding principle in the Laplace-Hankel domain. According to the extended precise integration method, the soil layer is divided into a series of layer units. Then the relationship between general stress vector and general displacement vector on the top and bottom planes is established. Every two adjacent layer units are combined into one layer in each computational iteration. The solutions in the Laplace-Hankel domain are obtained by considering the boundary conditions, and numerical inversion is performed to obtain the solutions in the physical domain. The practicability of the present method is assessed by comparing the numerical results with those in the existing literature and done by ABAQUS. Finally, the effects of groundwater table, properties of the soils above groundwater table, load depth, viscoelastic parameters, and soil stratification are investigated.

Geo-materials naturally display a certain degree of anisotropy due to various effects such as deposition. Besides, they are often two-phase materials with a solid skeleton and voids filled with water, and commonly known as poroelastic materials. In the past, despite numerous studies investigating the vibrations of strip foundations, dynamic impedance functions for multiple strip footings bonded to the surface of a multi-layered transversely isotropic poroelastic half-plane have never been reported in the literature. They are first presented in this paper. All strip foundations are assumed to be rigid, fully permeable, and subjected to three types of time-harmonic loadings. The dynamic interaction problem is investigated by using an exact stiffness matrix method and a discretization technique. The flexibility equations are established by enforcing the appropriate rigid body displacement boundary conditions at each footing-layered soil interface. Numerical results for dynamic impedance functions of two-strip system are presented to illustrate the influence of various effects on dynamic responses of multiple rigid strip foundations.