Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions
来源期刊：中南大学学报(英文版)2013年第8期
论文作者：梅国雄 CHEN Qi-ming(陈启明)
文章页码：2239 - 2244
Key words：consolidation; boundary condition; pore water pressure; consolidation degree
Abstract: Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation’s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general boundary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.
MEI Guo-xiong(梅国雄)1, CHEN Qi-ming(陈启明)2
(1. College of Transportation Engineering, Nanjing University of Technology, Nanjing 210009, China;
2. Louisiana Transportation Research Center, Louisiana State University, Baton Rouge 70808, USA)
Abstract:Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation’s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general boundary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.
Key words:consolidation; boundary condition; pore water pressure; consolidation degree
