非等温分布条件下考虑半透水边界时饱和黏土的一维固结解析解

温度的变化会导致土体的物理力学性质改变，且在一些实际工程中，饱和黏土会处于非等温分布状态。为此，针对非等温分布条件下饱和黏土的一维固结问题，考虑了更具普遍性的半透水边界，通过某些假定推导了单级线性加荷形式下饱和黏土一维固结控制方程，并利用分离变量法求解得到了控制方程的解析解。通过将所提解析解分别与已有解析解和有限差分解展开对比分析，验证了所提解答的正确性。基于所提解析解，利用某一算例分析了温度梯度、半透水边界参数及加荷时间对固结性状的影响。结果表明：温度梯度 M 越大，土体的渗透性越大，土体的固结速率越快；半透水边界参数 R1和 R2越大，相同时间内土体的超孔隙水压力越小，土体的平均固结度越大；土体的平均固结度随加荷时间 tc 的增大而减小，这主要是由于加荷阶段所施加的外荷载小于最终荷载，但加荷时间tc的延长可一定程度减小土体中产生的最大超孔隙水压力。

Analytical solution for one-dimensional consolidation of saturated clay considering partial drainage boundary under non-isothermal distribution condition

The variation of temperature will lead to the change of physical-mechanical properties of the soil, and in some engineering cases, saturated clay will be subjected to non-isothermal distribution condition. Therefore, to address the one-dimensional consolidation problem of saturated clay under non-isothermal distribution condition, a one-dimensional consolidation governing equation under single-stage linear loading is derived by some assumptions, in which the more general partial drainage boundary is considered. In addition, the analytical solution for governing equation is obtained by using separation variable method. By comparing the proposed analytical solution with the existing analytical solution and the finite difference solution, the correctness of the proposed analytical solution is verified. Based on the proposed analytical solution, the effects of temperature gradient, partial drainage boundary parameters and loading time on the one-dimensional consolidation behaviors of saturated clay are analyzed with an example. The results show that the larger the temperature gradient is, the greater the permeability of the soil becomes, and the faster the consolidation rate of the soil gets. The larger the partial drainage boundary parameters are, the smaller the excess pore water pressure of the soil at the same time becomes, and the larger the average consolidation degree of the soil gets. The average consolidation degree of the soil decreases with the increase of loading time, which is mainly due to the external loading applied to the soil in the loading stage is smaller than the final loading, but the extension of loading time can reduce the maximum excess pore water pressure in the soil to a certain extent.