变荷载下双曲线模型修正土体一维固结理论

 假定土体本构关系满足双曲线模型，把利用该模型得出的孔隙比e和有效应力s ¢的双曲线关系应用到一维单层均质地基固结理论的研究中，通过假定土体的初始有效应力沿深度均匀分布和渗透系数的降低与压缩系数的减小成正比，推导出任意荷载作用下一维非线性固结理论的方程。对于所得到的非线性偏微分方程，通过x-s ¢代换化成线性偏微分方程，并按照具体的初始和边界条件采用分离变量法求出土体有效应力s ¢和超静孔隙水压力u的解，由此分别推导出按沉降定义的平均固结度Us和按平均孔隙水压力定义的平均固结度Up的表达式。采用MATLAB语言编制相应的计算程序，结合具体算例与已有的修正非线性固结理论解的结果进行对比来论证本修正的正确性。计算结果表明：固结度随着时间的增长而增长，其增长速率逐渐减小；Us值稍大于Up值；2种修正的计算结果中存在微小的差异，其原因是在推导固结方程时采用了不同的本构模型以及不同的对渗透系数变化规律的假定。

ONE-DIMENSIONAL CONSOLIDATION THEORY BASED ON HYPERBOLA MODEL UNDER TIME-DEPENDENT LOADING FOR SATURATED SOIL

It is supposed that the constitutive relation of soil is the hyperbola model. The hyperbolic relationship between e and s ¢，which was achieved from this model，is applied to the study on one-dimensional nonlinear consolidation of one-layered and homogeneous saturated soil. With the assumptions that the decrease of the hydraulic conductivity is proportional to the decrease of the compression conductivity and the distribution of initial effective pressure does not vary with depth，the one-dimensional nonlinear partial differential consolidation equation，which is under arbitrary loading，is deduced. With the x -s ¢ transform，the nonlinear partial differential equation is changed into a linear one. According to the idiographic initial condition and the boundary conditions，the equation is then solved by using the variable separation method. Then the effective stress of soil and the excess water pore pressure can be achieved. So the correlation approach of the average consolidation degree，which is defined according to the settlement，and the correlation approach of the average consolidation degree that is defined according to the excess pore pressure are both deduced. The relevant computer program has been developed by MATLAB language. The results using this program are gained with the data from a specific example and the nonlinear consolidation theory with the same data. Both of the results are drawn in two charts. By comparing the curves from the charts，it is found that the differences between the two results are very small，which shows the rationality of this theory. The calculation shows that the consolidation degrees increase with the increment of time；and the value of the Us is a little bigger than that of the Up. When the consolidation equation is deduced，the different relationships between e and can be obtained. The different changing laws of hydraulic conductivity are adopted，and it clearly displays that the small differences in the results with the two different theories.