引用本文: 田沛博, 梁英杰. 膨胀性土壤中水分反常吸附的分形导数模型1)[J]. 力学与实践, 2022, 44(2): 317-321.
TIAN Peibo, LIANG Yingjie. FRACTAL DERIVATIVE MODEL OF WATER ANOMALOUS ADSORPTION IN SWELLING SOIL1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 317-321.
 Citation: TIAN Peibo, LIANG Yingjie. FRACTAL DERIVATIVE MODEL OF WATER ANOMALOUS ADSORPTION IN SWELLING SOIL1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 317-321.

## FRACTAL DERIVATIVE MODEL OF WATER ANOMALOUS ADSORPTION IN SWELLING SOIL1)

• 摘要: 本文基于物质坐标,构建了膨胀性土壤中水分吸附的时间分形导数模型,其中物质坐标建立了土壤含水率与空间坐标的联系,并推导了膨胀性土壤中水分的累积吸附量。分形导数模型对应水分的累积吸附量为时间分形导数的阶数和扩散系数的函数。分形导数的阶数能够用于吸附过程的分类,表征介质的非均质性。本文结合黑土和砂土中水分累积吸附,验证了该模型模拟膨胀性土壤中水分累积吸附的可行性,比传统的整数阶导数模型的模拟精度高。

Abstract: In this paper the fractal derivative model of water adsorption in swelling soil was constructed based on the material coordinates, which correlates the moisture content with the spatial position. The cumulative adsorption of water in swelling soil was also derived. The cumulative adsorption in swelling soil underlying the fractal derivative model is a function of the fractal derivative of time and the diffusion coefficient. The fractal derivative order can be used to classify the adsorption process and to characterize the heterogeneity of soil. The feasibility of the fractal derivative model is verified by analyzing the experimental data of the water cumulative adsorption in the black soil and sand, and the proposed model exhibits higher accuracy than the traditional integer order model.

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