变荷载下基于指数形式渗流的一维固结分析

One-dimensional consolidation analysis considering exponential flow law and time-depending loading

建立了考虑指数形式渗流以及变荷载条件下的一维固结微分方程,采用相对稳定的Crank-Nicolson差分格式获得控制方程的差分解答并验证了计算程序的可靠性。结果表明,当指数大于1时,较小时间因子下固结速率比达西渗流快,较大时间因子下固结速率比达西渗流慢;而当指数小于1时,较小时间因子下固结速率比达西渗流慢,较大的时间因子下固结速率比达西渗流快。在土层厚度相同的情况下,指数大于1时作用于土层的荷载越小,固结速率越慢;基于指数形式渗流,传统一维固结理论中室内土样固结与实际地基土层固结之间的相似关系不再成立;加荷速率越快,则土层的固结速率越快。

The differential equation governing one-dimensional consolidation was modified to consider exponential flow law and time-depending load.Finite difference solution was acquired by Crank-Nicolson difference scheme which was relatively stability.The reliability of difference programming was verified by comparing the results with analytic solutions.The results show that,if the exponent is greater than 1,the rate of consolidation is faster than the case of Darcy＇s flow at short time factor,slower than the case of Darcy＇s flow at long time factor.On the contrary,if the exponent is less than 1,the rate of consolidation is slower than the case of Darcy＇s flow at short time factor,faster than the case of Darcy＇s flow at long time factor.If the exponent is greater than 1,the less the load,the slower the consolidation rate for the same soil layer.At the case of exponential flow law,the classical similitude between consolidation of laboratory samples and that of field layers is not satisfied.The faster the loading rate,the faster the consolidation rate.