连续排水边界下双层地基一维非线性固结解析解

杨晓燕　宗梦繁　吴文兵　梅国雄　蒋国盛

摘    要：基于Davis和Raymond土体一维非线性固结的假设，通过引入连续排水边界条件研究了瞬时荷载下的双层地基一维非线性固结问题. 利用变量代换及分离变量法得到连续排水边界条件下双层地基一维非线性固结问题的解析解，通过退化为Xie双面排水解答驗证了本文解析解的正确性. 基于所得解析解，对不同界面参数以及非线性参数对土体固结特性的影响进行了分析. 结果表明：连续排水边界条件下，按沉降定义的平均固结度解答（Us）始终大于按孔压定义的平均固结度解答（Up），且两者的差别随着非线性参数Nσ值的增大而增大. 连续排水边界条件下Us随Nσ值的增大而增大，而Up随Nσ值的增大而减小. 与Xie双面排水解答相比，连续排水边界下Nσ值对Up的影响较小. 此外，土层界面参数对土体固结有较大影响.

关键词：非线性固结;连续排水边界;双层地基;界面参数;解析解

中图分类号： TU 43                        文献标志码：A

Analytical Solution for One-dimensional Nonlinear Consolidation of

Double-layered Soil Based on Continuous Drainage Boundary

YANG Xiaoyan1，ZONG Mengfan1，WU Wenbing1，2，3， MEI Guoxiong1，2，3，JIANG Guosheng1?

（1. Faculty of Engineering，China University of Geosciences，Wuhan 430074，China;

（2. College of Civil Engineering and Architecture，Guangxi University，Nanning 530004，China;

3. Key Laboratory of Engineering Disaster Prevention and Structural Safety

of Ministry of Education，Guangxi University，Nanning 530004，China）

Abstract：Based on the assumptions of one-dimensional nonlinear consolidation of soil proposed by Davis and Raymond， the one-dimensional nonlinear consolidation problem of double-layered soil under constant loading is investigated by introducing the continuous drainage boundary condition. The analytical solution for the one-dimensional nonlinear consolidation of doubled-layered soil is derived by means of variable substitution method and separation of variables method. The rationality of the present solution is also verified by comparing with Xies solution. Based on the present solution， the effect of different interface parameter and nonlinear parameter on consolidation behavior of soil is analyzed. The results show that， under the continuous drainage boundary condition， the solution of the average consolidation degree，Us，defined as the settlement，is always larger than that of the average consolidation degree， Up， defined as the pore pressure， and the difference between Us and Up increases with the increase of Nσ（the ratio of final effective pressure to initial effective pressure）. In the continuous drainage boundary condition， the Us increases with the increase of Nσ， while the Up decreases with the increase of Nσ. Compared with the Xies solution， the influence of Nσ value on Up is smaller in the continuous drainage boundary. In addition， the soil interface parameters have a great influence on soil consolidation.

Key words：nonlinear consolidation;continuous drainage boundary;double-layered soil;interface parameter; analytical solution

由于地基的成层性和非线性，双层地基的一维非线性固结研究具有重要的理论和工程意义. Davis和Raymond[1]基于e-lgσ′关系，假定固结过程中渗透系数kv与压缩系数mv同步变化且自重应力沿深度保持不变，得到kv和mv随深度及时间变化的土体一维非线性固结理论. 由于一维非线性固结求解的复杂性，现有的土体一维非线性固结解析解相对较少，其中成层地基一维非线性固结解析解仍然很少，Xie等[2-4]基于Davis和Raymond的假定，推导出双层地基瞬时加载……