饱和土体中的长时间渗流特性研究具有重要意义。引入Riemann-Liouville(R-L)分数阶导数对达西定律进行修正(以下称修正渗流模型),以描述长时间渗流过程中土体渗透率的演化现象。文献数据拟合结果表明:修正渗流模型能更好的描述流体速度随时间的非线性变化,且由修正渗流模型反演出的反常渗透系数数值也在合理范围之内。将修正渗流模型代入一维Biot固结方程组,推导了R-L分数阶扩散方程。采用显(时间域)-隐(空间域)差分格式对上述方程进行了离散并编制了相应的计算程序,且通过算例验证了程序的正确性。在此基础上,探讨了修正渗流模型参数对饱和土体一维固结过程的影响。结果表明:分数阶阶次体现了土体渗透率衰减的程度,阶次越高,渗透率越低,固结速度越慢。此外,与渗透系数一样,反常渗透系数增大会加快土体的固结速度,但对土体固结速度的影响占主导地位。

The long-term seepage characteristics of fluid flow in saturated soil are of significant importance. The Riemann-Liouville (R-L) fractional derivative was adopted to modify classical Darcy"s law (hereinafter referred to as modified seepage model) to describe the evolution of soils’ permeability during the long-term seepage process. Data fitting of experimental results given in published literature show that the modified seepage model could more accurately describe the nonlinear evolution of fluid velocity with time. Moreover, the anomalous permeability coefficient value obtained with the modified seepage model is found to be reasonable. The R-L fractional diffusion equation was derived by integrating the modified seepage model into the one-dimensional Biot consolidation model. The explicit (time domain)-implicit (space domain) difference method was employed to discretized the above equation, and the correctness of the algorithm was verified through numerical example. On this basis, the influence of the modified seepage model parameters on the one-dimensional consolidation process of saturated soil was investigated. The results show that fractional order reflects the degree of soil permeability decay. The higher the fractional order, the lower the soil permeability, which leads to a further decrease in the consolidation rate; Additionally, similar to the permeability coefficient , an increase in the abnormal permeability coefficient also accelerates the consolidation rate of saturated soils. However, it is the permeability coefficient plays the dominant role.

国家自然科学基金(12272284)；陕西省教育厅科学研究计划重点项目(重点实验室项目)(23JS033)