基于不对称连续排水边界的太沙基一维固结方程及其解答

Terzaghi's one-dimensional consolidation equation and its solution based on asymmetric continuous drainage boundary

在Terzaghi一维固结理论的基础上,提出了一个从透水到不透水的双面不对称连续排水边界条件,建立了广义Terzaghi固结理论,并给出其解答。对其解答进行分析发现:修正后的固结方程的边界条件能严格满足其初始条件;通过变化边界条件中的参数,可以得到包括Terzaghi一维固结理论解答在内的连续解,从而弥补了Terzaghi固结理论只能考虑透水和不透水这两种极端情况的不足;通过调整边界条件中的参数,还可以用来模拟实际土层上下两面透水性不同的情况;对其结果进行级数项数的研究,固结系数取不同值时,级数取一项或多项,均能满足精度要求。所以该理论把Terzaghi一维固结理论推广到了更为一般的情况,而且其结果可以很方便地推广到工程应用中。

The problems of traditional one-dimensional consolidation theory are analyzed.An asymmetric continuous drainage boundary which has two surfaces from pervious to impervious is put forward.The solutions based on these conditions are given.The boundary conditions of the modified consolidation equation meet their initial conditions strictly.The degradation solutions show that the equation is well-posed,continuous and has its physical meanings.The studies on terms in series of calculating solutions show that only one term in series in calculation process can meet the precision requirement well for a larger consolidation degree,and that more terms in series can meet the precision requirement when the consolidation degree is smaller.So the results calculated by the equation can extend to engineering application conveniently.