The problems involving scattering and refracting of plane strain wave by a cylinder in fluid-saturated soils are studied in this paper. The theoretical solutions for the amplitudes of scattering and refracting are derived on the basis of modified Blot's theory for two-phase medium in engineering, in which the compressibility of soil grains and the viscous coupling effect between the skeletal frame and the pore fluid are taken into account. Moreover, the amplitude equations of potential function are presented when the fluid-saturated soil cylindrical inclusion is degenerated into cylindrical cavity, rigid cylinder, single phase elastic cylinder and single phase fluid cylinder.

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By applying Yin and Graham’s one-dimensional (1-D) equivalent-time rheological model, which can predict both primary and secondary settlement, the expressions for calculating the long-term subsoil settlement under rectangular or semi-sinusoidal repeated loading of low amplitude are obtained without considering the fluid–solid coupling. A property has been proven that ultimate settlement of clay is independent of stress increasing history under 1-D conditions. According to this property, the expressions are derived considering the solid–fluid coupling to approximately calculate the long-term total settlement and the long-term settlement of soft subsoil clay after construction of the road embankment. Because the expressions of the long-term settlement are analytical solutions in the present paper, they can not only avoid cumulative calculation errors in the numerical analysis, but also have more solid theoretical foundations than empirical equations.

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