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 引用本文: 秦爱芳, 陈光敬, 谈永卫, 孙德安. 非饱和土层一维固结问题的解析解[J]. 应用数学和力学, 2008, 29(10): 1208-1218.
QIN Ai-fang, CHEN Guang-jin, TAN Yong-wei, SUN De-an. Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1208-1218.
 Citation: QIN Ai-fang, CHEN Guang-jin, TAN Yong-wei, SUN De-an. Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1208-1218.

• 中图分类号: TU44

Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils

• 摘要: 对一有限厚度，处于一维受荷状态，表面为透水透气面，底面为不透水不透气面的非饱和土层，依据Fredlund的非饱和土一维固结理论，由液相及气相的控制方程、Darcy定律及Fick定律，经Laplace变换及Cayley-Hamilton数学方法构造了顶面状态向量与任意深度处状态向量间的传递关系；通过引入初始及边界条件，得到了Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解；实现Laplace逆变换，得到了时间域内的解析解；用一典型算例，与差分法结果进行对比，验证了其正确性．
•  [1] Blight G E. Strength and consolidation characteristics of compacted soils[D].Ph D dissertation. England: University of London, 1961. [2] Scott R F.Principles of Soil Mechanics[M].USA:Addison Wesley Publishing Company,1963. [3] Barden L. Consolidation of compacted and unsaturated clays[J].Geotechnique,1965,15(3):267-286. [4] Fredlund D G,Hasan J U. One-dimensional consolidation theory: unsaturated soils[J]. Canadian Geotechnical Journal,1979，17(3):521-531. [5] Fredlund D G, Rahardjo H.Soil Mechanics for Unsaturated Soil[M].New York: John Wiley and Sons, 1993;非饱和土土力学[M].陈仲颐，张在明，陈愈炯，等 译.北京：中国建工出版社，1997. [6] 杨代泉. 非饱和土广义固结理论及其数值模拟与试验研究[D].博士学位论文.南京:南京水科院,1990. [7] 陈正汉. 非饱和土固结的混合物理论(Ⅰ)[J].应用数学和力学,1993,14(2):127-137. [8] 陈正汉. 非饱和土固结的混合物理论(Ⅱ)[J].应用数学和力学,1993,14(8):687-698. [9] 沈珠江. 非饱和土简化固结理论及其应用[J].水利水运工程学报,2003,4:1-6. [10] 殷宗泽,王保田，余湘娟，等. 土工原理[M].北京：中国水利水电出版社，2007，350-364. [11] Lloret A, Alonso E E. Consolidation of unsaturated soils, including swelling and collapse behavior[J].Géotechnique,1980,30(4): 449-477. [12] Ausilio E, Conte E. Settlement rate of foundations on unsaturated soils[J].Canadian Geotechnical Journal,1999，36(5):940-946. [13] Conte E. Consolidation analysis for unsaturated soils[J].Canadian Geotechnical Journal,2004,41(4): 599-612. doi: 10.1139/t04-017 [14] Korn G A, Korn T M.Mathematical Handbook for Scientists and Engineering[M].New York:McGraw-Hill Inc,1968.

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出版历程
• 收稿日期:  2007-10-15
• 修回日期:  2008-08-28
• 刊出日期:  2008-10-15

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