Abstract
The time‐dependent behaviour of saturated soils under static and dynamic loading is generally attributed to the flow‐dependent and viscous behaviour of pore fluid. However, the intrinsic energy dissipative effects from the flow‐independent viscoelastic behaviour of solid skeleton are not always considered. In this study, the effect of flow‐independent viscoelastic behaviour on the seismic amplification of ground soil in vertical and horizontal directions is studied based on a two‐phase poroviscoelastic model. A generalized Kelvin–Voigt model is used to define the effective stress in the soils, and the compressibilities of both solid skeleton and pore fluid are considered. The seismic‐induced dynamic displacements are analytically derived and are shown to depend on soil layer thickness, soil properties, and ground motion parameters. The formulation neglecting the viscoelastic behaviour of solid skeleton could overestimate both the vertical and horizontal motion amplifications at the surface of ground soil. In addition, the seismic responses of viscoelastic soils are demonstrated to be closely related to the saturation state of surface soil.
Highlights
The seismic waves propagating in the isotropic Earth are associated with the vibrating direction of the substrate bedrock
The study on the amplification effect of vertical motion is quiet limited. is is perhaps due to the fact that the engineering structures are sufficiently resistant to the vertical earthquake action, which has smaller magnitude but becomes more obvious in high frequency range [15]. e phenomenon of structural damage under the action strong vertical earthquake has been continuously observed [16, 17], and ignoring the effect of vertical motion may lead to underestimation of ground motion site response [18]
A set of parametric analysis is carried out to analyze the influence of critical parameters on the seismic wave propagation and the motion amplification in the viscoelastic soil layer
Summary
Soil is a so-called damping material as a part of energy of the wave which will dissipate during the propagation [31]. e viscoelasticity of soil skeleton is described by Kelvin–Voigt model and the stress-strain relationship is [32]. Where σi′j is the effective stress, δij is Kronecker delta, μe and λe are Lameelastic moduli, λv and μv are the dilatant constant and shear constant of the viscoelastic soil, e denotes the volumetric strain of solid skeleton, and the strain εij is expressed as εij. 1, where Ks, Kb, and Kf are the bulk moduli of solid grains, solid skeleton, and pore fluid, respectively. Where b is the coefficient representing the resisting forces from the fluid-solid coupling and could be expressed as (η/K), where η denotes the fluid viscosity and K is the permeability in the unit m2. It is noted that the third term at the right side of equation (7) could reveal the viscous coupling which involves viscous resisting forces between the pore fluid and solid skeleton.
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