Research on unsaturated seepage problems based on fractional order derivative
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摘要: 非饱和渗流问题广泛存在于煤炭工程领域。 现有实验表明,均方位移与时间成非线性关 系,但经典的Richards方程未考虑这一情况。 针对这一问题,本文通过引入时间分数阶导数,结 合两种水力传导系数对新的Richards方程进行了数值求解。 在此基础上,分析了时间分数阶 Richards方程中的相关参数对含水量曲线的影响,并对已有论文的实验数据进行了拟合。 结果 表明,新的模型能够描述反常扩散条件下的非饱和渗流问题。Abstract: Unsaturatedseepagephenomenonwidelyexistsincoalengineering*Theexperimentalshows thatthereisa nonlinear relationship between mean square displacement and time,while the classic Richardsequationfailstocharacterize*Tosolvethis,weintroducedtime⁃fractionalorderintoclassice⁃ quationbyinvolvingtwoformsofhydraulicconductivitysoastogettime⁃fractionalRichardsequation andnumerical results were obtained*Furthermore,the effect of the parameters in the time⁃fractional Richardsequationonthewatercontenthasbeendiscussedinthispaperandthefittingresultshave beenappliedtotheexperimentalresultsfromformerpaper*Thefittingresultsshowthatthenewmodel canfitbettertotheseepageprocessinunsaturatedporousmedia*
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