Analytical solution to one-dimensional consolidation in unsaturated soils under sinusoidal cyclic loading
来源期刊：中南大学学报(英文版)2015年第2期
论文作者：FENG Jun(冯君) WU Xi-yong(巫锡勇) ZHU Bao-long(朱宝龙) YANG Qi-xiang(杨期祥)
文章页码：646 - 653
Key words：unsaturated soil; analytical solution; one-dimensional consolidation; excess pore-water pressure; excess pore-air pressure; settlement; sinusoidal cyclic loading
Abstract: An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund’s one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained 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 excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.
FENG Jun(冯君)1, WU Xi-yong(巫锡勇)1, ZHU Bao-long(朱宝龙)2, YANG Qi-xiang(杨期祥)1
(1. Department of Geological Engineering, Southwest Jiaotong University, Chengdu 610031, China;
2. School of Civil Engineering and Architecture, Southwest University of Science and Technology,
Mianyang 621010, China)
Abstract:An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund’s one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained 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 excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.
Key words:unsaturated soil; analytical solution; one-dimensional consolidation; excess pore-water pressure; excess pore-air pressure; settlement; sinusoidal cyclic loading
