有限土层轴对称Biot固结的一个新的解析解

艾智勇; 王全胜

有限土层轴对称Biot固结的一个新的解析解

同济大学地下建筑与工程系;岩土及地下工程教育部重点实验室,上海 200092

基金项目: 国家自然科学基金资助项目(50578121)

详细信息

作者简介:
艾智勇(1966- ),男,江西余江人,副教授,博士(联系人.Tel:+86-21-65982201;Fax:+86-21-65985210;E-mail:zhiyongai@tongji.edu.cn).

中图分类号: TU43；O343
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出版历程
- 收稿日期: 2008-06-15
- 修回日期: 2008-10-27
- 刊出日期: 2008-12-15

A New Analytical Solution for Axisymmetric Biot’s Consolidation of a Finite Soil Layer

Department of Geotechnical Engineering;Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, P. R. China

摘要

摘要: 提出一个新的解析方法来研究有限土层的轴对称Biot固结．从轴对称Biot固结的控制方程出发，结合Laplace变换的微分性质，建立了Laplace和Hankel变换域内有限土层地基表面(z=0)和任意深度z处基本变量之间的关系．然后结合有限土层的边界条件，推导出Laplace和Hankel变换域内任意一点的解析解．通过进行Laplace逆变换和Hankel逆变换得到了物理域内的解．编制了计算程序，并对有限土层轴对称固结进行了数值分析．
- 轴对称Biot固结 /
- 有限土层 /
- Laplace变换 /
- Hankel变换
Abstract: A new analytical method is presented to study the axis-symmetric Biot's consolidation of a finite soil layer.Starting from the governing equations of axis-symmetric Biot's consolidation,and based on the property of the Laplace transform,the relationship of basic variables for a point of a finite soil layer was established between the ground surface(z=0) and the depth z in the Laplace and Hankel transform domain.Combined with the boundary conditions of the finite soil layer,the analytical solution of any point in the transform domain can be obtained.The actual solution in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.The numerical analysis for the axis-symmetric consolidation of a finite soil layer was carried out by program.
- axisymmetric Biot’s consolidation /
- finite soil layer /
- Laplace transform /
- Hankel transform

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参考文献(13)

[1]	Biot M A. General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164. doi: 10.1063/1.1712886
[2]	McNamee J, Gibson R E.Displacement functions and linear transforms applied to diffusion through porous elastic media[J].Quarterly Journal of Mechanics and Applied Mathematics,1960,13(1): 98-111. doi: 10.1093/qjmam/13.1.98
[3]	McNamee J, Gibson R E.Plane strain and axially symmetric problem of the consolidation of a semi-infinite clay stratum[J].Quarterly Journal of Mechanics and Applied Mathematics,1960,13(2): 210-227. doi: 10.1093/qjmam/13.2.210
[4]	Schiffman R L, Fungaroli A A. Consolidation due to tangential loads[A].In: Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering[C].Toronto:University of Toronto Press,1965,1: 188-192.
[5]	Christian J T, Boehmer J W. Plane strain consolidation by finite elements[J].Journal of the Soil Mechanics and Foundations Division, ASCE,1970,96(4): 1435-1457.
[6]	Cheng A H D, Liggett J A.Boundary integral equation method for linear porous-elasticity with applications to soil consolidation[J].International Journal for Numerical Methods in Engineering,1984,20(2): 255-278. doi: 10.1002/nme.1620200206
[7]	Booker J R, Small J C.Finite layer analysis of consolidation Ⅰ[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(2):151-171. doi: 10.1002/nag.1610060204
[8]	Booker J R, Small J C.Finite layer analysis of consolidation Ⅱ[J].International Journal for Numerical and Analytical Methods in Geomechanics,1982,6(2): 173-194. doi: 10.1002/nag.1610060205
[9]	Booker J R, Small J C.A method of computing the consolidation behavior of layered soils using direct numerical inversion of Laplace transforms[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(4): 363-380. doi: 10.1002/nag.1610110405
[10]	Talbot A. The accurate numerical inversion of Laplace transforms[J].Journal of Institute of Mathematics and Its Application,1979,23(1): 97-120. doi: 10.1093/imamat/23.1.97
[11]	Sneddon I N.The Use of Integral Transform[M].New York: McGraw-Hill, 1972.
[12]	Ai Z Y, Yue Z Q, Tham L G,et al.Extended Sneddon and Muki solutions for multilayered elastic materials[J].International Journal of Engineering Science,2002,40(13): 1453-1483. doi: 10.1016/S0020-7225(02)00022-8
[13]	Ai Z Y, Cheng Z Y, Han J.State space solution to three-dimensional consolidation of multi-layered soils[J].International Journal of Engineering Science,2008,46(5):486-498. doi: 10.1016/j.ijengsci.2007.12.003

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有限土层轴对称Biot固结的一个新的解析解

作者简介:
艾智勇(1966- ),男,江西余江人,副教授,博士(联系人.Tel:+86-21-65982201;Fax:+86-21-65985210;E-mail:zhiyongai@tongji.edu.cn).

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A New Analytical Solution for Axisymmetric Biot’s Consolidation of a Finite Soil Layer

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有限土层轴对称Biot固结的一个新的解析解

作者简介: 艾智勇(1966- ),男,江西余江人,副教授,博士(联系人.Tel:+86-21-65982201;Fax:+86-21-65985210;E-mail:zhiyongai@tongji.edu.cn).

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出版历程

A New Analytical Solution for Axisymmetric Biot’s Consolidation of a Finite Soil Layer

计量

出版历程

目录

作者简介:
艾智勇(1966- ),男,江西余江人,副教授,博士(联系人.Tel:+86-21-65982201;Fax:+86-21-65985210;E-mail:zhiyongai@tongji.edu.cn).