Analytical Study on the Impedance of Radial Heterogeneous Viscoelastic Soil with Two Different Methods

The influence of the vertical and horizontal impedances of soil radial heterogeneity was studied theoretically based on the series convergence and transfer matrix methods. The soil around the pile was assumed to be composed of two homogeneous soil zones in three-dimensional axisymmetric space, that is, a disturbed inner boundary zone and an outer semi-infinite undisturbed zone. Moreover, the shear moduli of the inner perturbed and the outer unperturbed zones were correlated with a specific parabolic function. Then, the soil vertical and horizontal impedances in the radially inhomogeneous boundary zone were derived based on the series convergence and transfer matrix methods using the stress and displacement continuity conditions and the infinite boundary condition. Finally, the impedance errors and applicable range of two methods are discussed. The main findings can be categorized as: (1) when analysing a soil radial heterogeneous site, the influence of the shear modulus ratio of the inner and outer zones, the ratio of the thickness of boundary zone to the pile radius, soil density and pile radius should be taken into account; (2) when 0.8≤Gi/G0≤1.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.8 \le G_{i} /G_{0} \le 1.0$$\end{document} and 1≤tm/r0≤4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \le t_{m} /r_{0} \le 4$$\end{document}, the error between the series convergence method and transfer matrix method is within 10%, while the error is approximately 15% when 0.4≤Gi/G0≤0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.4 \le G_{i} /G_{0} \le 0.7$$\end{document}.