解Biot固结方程的有限元方法

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The Application of the Finite Element Method to Solving Biot’s Consolidation Equations

1.
Shanghai Institute of Computing Technique, Shanghai;
2.
Institute of Hydraulic Research, Yellow River Water Conservancy Commission, Zhengzhou;
3.
East China College of Hydraulic Engineering, Nanjing

摘要: 饱和土固结的Biot理论^[1]将固结过程作为一个弹性体应力和孔隙流流动的耦合问题,和Terzhigi理论^[2]相比,它更能确切地反映固结机理.本文用经典变分原理导得固结问题一般的Biot有限元方程,具有明确的物理意义.这一结果已用来分析巴家咀土坝的固结过程,计算结果和工程实践一致.

Abstract: Biot's theory of consolidation of saturated soil.regards the consolidation process as a coupling problem between stress of elastic body and flow of fluid existing in pofes^[1]. It can more precisely reflect the mechanism of consolidation than Terzhigi's theory^[2]. In this article, we obtain the general Biot's finite element equations of consolidation with classical variational principles. The equations have clear physical meaning and have been applied to analysing the consolidation of Bajiazui earth dan. The computational results are in accord with engineering practice.

[1]	Biot,M.A,General theory of three-dimensional consolidation.J.Appl.Phys.,vol.12,(1941).
[2]	Terzhagi,K.and R.B.Peck,Soil mechanics in engineering practice,Wiley,(1948).
[3]	Sandhu,R.S.and E.L.wilson,Finite element analysis of seepape in elastic media.J.Engg.Mech.Div.ASCE,Vol.95,(1969).
[4]	Hwang,C.T.,N.R.Morgenstern,and D.W.Murray,On solutions of plane strain consolidation problems by finite element methods.Canadian Geotechnical Journal,8,(1971).
[5]	殷宗泽、徐鸿江、朱泽民,饱和土平面固结问题有限单元法,华东水利学院学报,1,(1978).
[6]	鹫津久一狼,《弹性学の变分原理概论》,东京,(1972).