Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System

KOU Lei; BAI Yun

doi:10.3879/j.issn.1000-0887.2016.01.007

Volume 37 Issue 1

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KOU Lei, BAI Yun. Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System[J]. Applied Mathematics and Mechanics, 2016, 37(1): 84-96. doi: 10.3879/j.issn.1000-0887.2016.01.007

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Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System

doi: 10.3879/j.issn.1000-0887.2016.01.007

KOU Lei¹,
BAI Yun²

¹School of Water Conservancy & Environment, Zhengzhou University,Zhengzhou 450002, P.R.China;²Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P.R.China

Received Date: 2015-10-14
Rev Recd Date: 2015-11-28
Publish Date: 2016-01-16

Abstract

Abstract

Based on the basic viscoelastic equations of Biot consolidation in the Cartesian coordinate system and in view of the viscoelasticity of soft soil skeleton, the analytical solutions to 3D problems and plane strain problems of Biot consolidation in the integral transform domain were obtained through the FourierLaplace transform and the decoupling transform according to the differential equation theory and the matrix theory, and in turn the corresponding element stiffness matrixes were derived. The global stiffness matrixes for Biot consolidation 3D problems and plane strain problems of multilayered viscoelastic foundations were assembled with the matrix matching method, and the solutions to the corresponding problems of multilayered viscoelastic foundations in the transform domain were obtained in the solution of the algebraic equations for the global stiffness matrixes. The solutions in the physical domain were acquired through the inverse FourierLaplace transform. The validity of the proposed method was examined in the comparison of the present results of 2 examples, where viscoelastic Biot consolidation was reduced to elastic Biot consolidation, with the previous reference solutions. The analytical stiffness matrixes provide a theoretical base for Biot consolidation of multilayered viscoelastic foundations.
- Cartesian coordinate system,
- multilayered viscoelastic foundation,
- Biot consolidation,
- analytical stiffness matrix method

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References(18)

References

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