连续排水边界下非线性饱和土体一维热固结解析解

为探究受温度影响的非线性饱和土体的一维固结特性，基于孔隙比变化是由有效应力和温度引起的假设，根据热平衡方程和连续性方程建立考虑热效应的一维非线性固结方程。采用分离变量法及Laplace变换获得连续排水边界下考虑土体非线性的一维热固结问题的解析解，通过与现有两种解析解对比，验证此解答的正确性。基于所得解答，详细讨论热扩散系数与固结系数比值、温度增量、界面参数及非线性参数对土体固结特性的影响。结果表明：温度增量越大或界面参数越大时，土体的固结速率越快；按沉降定义的固结速率随非线性参数的增大而增大，而按孔压定义的固结速率随非线性参数的增大而减小；热扩散系数与固结系数的比值较大时，前期热固结速率明显快于不考虑温度作用的固结速率，采用热加固法处理地基时，有必要先测定热扩散系数和固结系数，以确定是否适合采用热加固法。

Analytical solution for one-dimensional thermal consolidation of nonlinear saturated soils based on continuous drainage boundary

The one-dimensional consolidation process of nonlinear saturated soils affected by temperature was investigated. Based on the assumption that the change in void ratio is caused by effective stress and temperature, a one-dimensional nonlinear consolidation equation considering thermal effects was established according to the heat balance equation and the continuity equation. An analytical solution for the one-dimensional thermal consolidation problem considering soil nonlinearity under continuous drainage boundary was derived by utilizing separated variable method and Laplace transform, and the reasonableness of the present solution was assessed by comparing with two existing analytical solutions. On the basis of the present solution, the influences of the ratio of thermal diffusion coefficient to consolidation coefficient, as well as the temperature increment, interface parameter, and nonlinear parameter on the consolidation behavior of soil were analyzed in detail. Results show that the larger the temperature increment or the larger the interface parameter was, the faster the consolidation rate of soil was. The consolidation rate defined by settlement increased with the increase in nonlinear parameter, while that defined by pore pressure decreased with the increase in nonlinear parameter. When the ratio of thermal diffusion coefficient to consolidation coefficient was large, the early thermal consolidation rate was obviously faster than that without considering temperature. Therefore, it is necessary to first measure the thermal diffusion coefficient and consolidation coefficient to determine whether the thermal consolidation method is suitable for foundation treatment.