循环荷载下非饱和黏弹性地基一维固结特性分析
收稿日期: 2016-02-29
网络出版日期: 2017-12-30
基金资助
国家自然科学基金资助项目(41372279); 上海市自然科学基金资助项目(13ZR1416200)
Analysis of one-dimensional consolidation characteristics of viscoelastic unsaturated soils under cyclic loads
Received date: 2016-02-29
Online published: 2017-12-30
秦爱芳, 吕康立 . 循环荷载下非饱和黏弹性地基一维固结特性分析[J]. 上海大学学报(自然科学版), 2017 , 23(6) : 937 . DOI: 10.12066/j.issn.1007-2861.1799
This paper presents a semi-analytical solution to one-dimensional consolidation in viscoelastic unsaturated soils with a finite thickness under arbitrary loads. It is based on the Fredlund’s one-dimensional consolidation theory for unsaturated soil. The excess poreair and pore-water pressures and settlement in the Laplace-transform domain were obtained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. The top surface of soil is permeable to water and air, and the bottom impermeable to water and air. On this basis and by introducing three kinds of cyclic loads, semi-analytical solutions are obtained in the time domain using the Crump and Durbin method to perform Laplace inversion. Finally, the relevant behavior of one-dimensional consolidation for the viscoelastic unsaturated soil is discussed.
Key words： cyclic load; one-dimensional consolidation; viscoelastic; unsaturated soil
[1] Blight G E. Strength and consolidation characteristics of compacted soils [D]. London: University of London, 1961.
[2] Scott R F. Principles of soil mechanics [M]. Massachusetts: 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 soils [M]. New York: John Wiley and Sons, 1993.
[6] 王奎华, 谢康和, 曾国熙. 双面半透水边界的一维黏弹性固结理论[J]. 岩土工程学报, 1998, 20(2): 34-36.
[7] 蔡袁强, 徐长节, 袁海明. 任意荷载下成层黏弹性地基的一维固结[J]. 应用数学和力学, 2001, 22(3): 307-313.
[8] 蔡袁强, 梁旭, 郑灶锋, 等. 半透水边界的黏弹性土层在循环荷载下的一维固结[J]. 土木工程学报, 2003, 36(8): 86-90.
[9] 谢康和, 周瑾, 董亚钦. 循环荷载作用下地基一维非线性固结解析解[J]. 岩土力学与工程学报, 2006, 25(1): 21-26
[10] Shan Z D, Ling D S, Ding H J, et al. Analytical solution for the 1D consolidation of unsaturated multi-layered soil [J]. Computers and Geotechnics, 2014, 57: 17-23.
[11] Zhou W H, Zhao L S. One-dimensional consolidation of unsaturated soil subjected to timedependent loading with various initial and boundary conditions [J]. International Journal of Geomechanics, 2014, 14(2): 291-301.
[12] Liem H, Behzad F. Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading [J]. Computers and Geotechnics,
2015, 67: 1-16.
[13] Qin A F, Chen G J , Tan Y W, et al. Analytical solution to one dimensional consolidation in unsaturated soils [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1329-1340.
[14] Qin A F, Sun D A, Tan Y W. Analytical solution to one-dimensional consolidation in unsaturated soils under loading changed exponentially with time [J]. Computers and Geotechnics, 2010, 37(1): 233-238.
[15] 秦爱芳, 罗坤, 孙德安. 非饱和土黏弹性地基一维固结特性分析[J]. 上海大学学报(自然科学版), 2010, 16(2): 203-209.
[16] Korn G A, Korn T M. Mathematical handbook for scientists and engineerings [M]. New York: McGraw-Hill Inc, 1968.
[17] Durbin F. Numerical inversion of the Laplace transforms: an efficient improvement to Dubner and Abate’s method [J]. The Computer Journal, 1974, 17(4): 371-376.
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