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Analytical solutions describing the consolidation of a multi-layered soil under circular loading

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Abstract

Analytical solutions describing the consolidation of a multi-layered soil under circular loading are presented. From the governing equations of saturated poroelastic soil in a cylindrical coordinate system, the eighth-order state-space equation of consolidation is obtained by eliminating the variation of time t using the Laplace transform together with the technique of Fourier expansions with respect to the coordinate θ and the Hankel transform with respect to coordinate r. The solution of the eighth-order state-space equation is derived directly by using the Laplace transform and its inversion of the z-domain. Based on the continuity between layers and the boundary conditions, the transfer-matrix method is utilized to derive the solutions for the consolidation of a multi-layered soil under circular loading in the transformed domain. By the inversion of the Laplace transform and the Hankel transform, the analytical solutions in the physical domain are obtained. A numerical analysis based on the solutions is carried out by a corresponding program.

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Authors and Affiliations

  1. Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Zhi Yong Ai & Quan Sheng Wang

  2. Department of Civil, Environmental and Architectural Engineering, The University of Kansas, Lawrence, KS, USA

    Jie Han

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  1. Zhi Yong Ai
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  2. Quan Sheng Wang
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  3. Jie Han
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Correspondence to Zhi Yong Ai.

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Ai, Z.Y., Wang, Q.S. & Han, J. Analytical solutions describing the consolidation of a multi-layered soil under circular loading. J Eng Math 66, 381–393 (2010). https://doi.org/10.1007/s10665-009-9299-6

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