一维固结微分方程及固结度的解析计算

Analytical Calculation of One-dimensional Consolidation Differential Equation and Consolidation Degree

用标准的数学物理方法详细推导一维渗流固结微分方程的傅里叶级数解,并用Mathematica绘制了压力分布的三维图,直观地展示了渗流固结过程中压力随深度和时间变化的物理规律.讨论了固结度实用公式的理论依据.结果表明:不同的边界条件决定了不同的物理进程;当t=0时,固结微分方程的级数解不适用于排水面;固结度两个实用公式的最佳转换点是Ut=0.5,而不是Ut=0.6.

The series solution of one-dimensional consolidation differential equation is derived in great details by using the standard methods of mathematical Physics. The three-dimensional image of the pressure distribution is drawn. Theoretical basis for the practical formula of degree of consolidation is discussed. The results show that： the different boundary conditions determine the different physical processes.When t =0, the series solution of the consolidation differential equation is not suitable for the surface of drainage.The optimal switching point of two practical formulas for degree of consolidation is Ut =0.5, instead of Ut=0.6.