矿业科学学报 (Feb 2019)

Research on unsaturated seepage problems based on fractional order derivative

  • Wang Rui,
  • Zhou Hongwei,
  • Zhuo Zhuang

DOI
https://doi.org/10.19606/j.cnki.jmst.2019.01.003
Journal volume & issue
Vol. 4, no. 1
pp. 17 – 22

Abstract

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Unsaturated seepage phenomenon widely exists in coal engineering.The experimental shows that there is a nonlinear relationship between mean square displacement and time,while the classic Richards equation fails to characterize.To solve this,we introduced time-fractional order into classic equation by involving two forms of hydraulic conductivity so as to get time-fractional Richards equation and numerical results were obtained.Furthermore,the effect of the parameters in the time-fractional Richards equation on the water content has been discussed in this paper and the fitting results have been applied to the experimental results from former paper.The fitting results show that the new model can fit better to the seepage process in unsaturated porous media.

Keywords