考虑边界排水时间效应的软土一维非线性固结近似解答

为了考虑实际工程中，土层边界的排水性状是一个随时间连续变化的过程，基于经典的非线性压缩和非线性渗透关系，研究考虑排水边界时间效应时固结系数随时间变化的土体一维非线性固结问题。通过分离变量法和Laplace变换技术，获得该固结问题的近似解答；再将该文解退化并与既有差分解答进行对比，从而验证近似解答正确性。基于所得解，探讨了压缩指数与渗透指数比值Cc/Ck、最终有效应力与初始有效应力比值Nq及界面参数α、β对土体固结特性的影响。结果表明：在连续排水条件下，土体内的不排水对称面的位置与界面参数有关，并且随时间会发生变化；当Cc/Ck>1时，在固结前期，土体的沉降速率随着Nq值的增大而增大，而在固结后期则相反。排水边界的界面参数取值对反映边界排水速率影响很大，因此工程中计算地基固结速率时有必要确定界面参数取值。

APPROXIMATE SOLUTION FOR ONE-DIMENSIONAL NONLINEAR CONSOLIDATION THEORY OF SOIL CONSIDERING THE TIME EFFECT OF BOUNDARY DRAINAGE

In order to consider the fact that the drainage behavior of soil boundary is a continuous process with time in practice, it studied the one-dimensional nonlinear consolidation problem of soil with time-dependent consolidation coefficient considering the time effect of boundary drainage, and the classical nonlinear relationships in terms of the compression and permeability of soils were introduced. The approximate analytical solution for the consolidation problem was obtained by means of variable separation and Laplace transformation, and then the present solution was verified through a degeneration and comparison with existing solutions. Based on the present solution, the influences of the ratio of compression index to permeability index (N_q), the ratio of final effective stress to initial effective stress (C_c/C_k) and interface parameters (α and β) on the consolidation behaviors were discussed in detail. The results show that, under the continuous drainage boundary, the location of the undrained plane in soil is dependent on the interface parameters and varies with time; when C_c/C_k>1, with the increase of N_q, the settlement rate increases in the early consolidation stage, while the opposite is true in the later stage. The value of interface parameter of drainage boundary has great influence on reflecting the drainage rate, so it is necessary to determine the value of interface parameters when calculating the consolidation rate of foundation in engineering.