基于指数形式渗流定律的软土一维固结分析

One-dimensional consolidation analysis considering exponential flow law for soft clays

在土中渗流服从指数形式渗流定律的前提下,对软黏土一维固结理论进行分析研究。首先建立考虑指数形式渗流定律的软黏土一维固结微分方程。然后采用相对稳定的Crank-Nicolson差分格式对控制方程进行时间、空间离散,得到了差分方程及其解答,并且将差分计算结果与退化到达西渗流的Terzaghi理论解析解和指数为1.5时的短时间解析解相对比,验证计算程序的可靠性。通过计算分析考虑指数渗流定律情况下的软土地基的一维固结性状,结果表明:考虑指数形式渗流情况下(指数大于1),固结速率在较小的时间因子下要比Terzaghi理论快,而在较大的时间因子下比Terzaghi理论慢,这种现象随着指数值的增大越来越显著;荷载的等效水头与土层厚度的比值对固结性状有显著的影响,比值越小,则固结速率越慢。最后,讨论了达西渗流在实际工程中的适用范围。

Based on an exponential flow law for soft soils, the theory of one-dimensional consolidation was investigated. The differential equation governing one-dimensional consolidation was developed with exponential flow law. Difference equation and numerical solutions were obtained by the relatively stable Crank-Nicolson scheme. The reliability of the difference code was verified by comparing （a） the results of FDM with that of Terzaghi＇ s analytical solution, in which the exponential flow law was degenerated to Darcy＇ s law; （b） the results of FDM with that of a short term analytical solution for the case when the exponent equals 1.5. One-dimensional consolidation behavior considering exponential flow law was investigated. The results show that, if the exponent is greater than one, the rate of consolidation is faster than that predicted by Terzaghi＇ s solution with short time factor, and slower than that of Terzaghi＇ s solution with long time factor. This phenomenon becomes more remarkable with increase of the exponent. The ratio of the equivalent head of external load to the thickness of a soil layer imparts a great influence on the consolidation rate. The smaller the ratio is, the slower the rate of consolidation. Applicability of Darcy＇ s flow in practice is discussed.