非饱和土本构关系的混合物理论(Ⅱ)——线性本构方程和场方程

基金项目: 国家自然科学基金资助项目(59678003);陕西省教育厅专项科研计划项目(01JK178)

Constitutive Relation of Unsaturated Soil by Use of the Mixture Theory(Ⅰ)-Nonlinear Constitutive Equations and Field Equations

1.
Science College, Xi'an University of Architecture & Technology, Xi'an 710055, P. R. China;
2.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P. R. China

摘要: 通过对非饱和土非线性本构方程和场方程的线性化,推导出了非饱和土的线性本构方程和场方程.把线性方程表示为与Biot饱和多孔介质方程相似的形式;证明了Darcy定律对非饱和土的适用性;说明了Biot饱和多孔介质方程是这些线性方程的特例.所有这些都表明用混合物理论处理非饱和土本构问题的正确性.
- 混合物理论 /
- 非饱和土 /
- 线性本构方程 /
- 线性场方程 /
- Darcy定律 /
- Biot方程
Abstract: The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
- mixture theory /
- unsaturated soil /
- linear constitutive equation /
- linear field equation /
- Darcy’s law /
- Biot’s equations

[1]	黄义,张引科.非饱和土本构关系的混合物理论(Ⅰ)——非线性本构方程和场方程[J].应用数学和力学,2003,24(2):111-123.
[2]	Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33(4):1482-1498.
[3]	Fredlund D G,Rahardjo H.非饱和土土力学[M].陈仲颐,张在明,陈愈炯,等译.北京:中国建筑工业出版社,1997,126-146.
[4]	Lloret A,Alonso E E.Consolidation of unsaturated soils including swelling and collapse behavior[J].Geotechnique,1980,30(4):449-457.
[5]	陈正汉.非饱和土固结的混合物理论[D].博士学位论文,西安:陕西机械学院,1991,40-47.
[6]	Biot M A.Theory of propagation of elastic wave in a fluid saturated porous solid Ⅰ:Low-frequency range[J].J Acoust Soc Am,1956,28(2):168-178.
[7]	Biot M A.Theory of propagation of elastic wave in a fluid saturated porous solid Ⅱ:Higher-frequency range[J].J Acoust Soc Am,1956,28(2):179-191.
[8]	吴世明.土介质中的波[M].北京:科学出版社,1997,62-98.
[9]	Biot M A.General theory of three-dimensional consolidation[J].J Appl Phys,1941,12(1):155-164.
[10]	Bowen R M.混合物理论[M].许慧已,董务民译.南京:江苏科学技术出版社,1983,98-170.