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A Hybrid Fractional-Derivative And Peridynamic Model For Water Transport In Unsaturated Porous Media

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  • YUANYUAN WANG

    (State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu 210098, P. R. China†College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, P. R. China§Industrial Engineering Department, University of Padova, via Venezia 1, Padova 35131, Italy)

  • HONGGUANG SUN

    (State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu 210098, P. R. China†College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, P. R. China)

  • TAO NI

    (��State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, 610059 Chengdu, P. R. China§Industrial Engineering Department, University of Padova, via Venezia 1, Padova 35131, Italy)

  • MIRCO ZACCARIOTTO

    (�Industrial Engineering Department, University of Padova, via Venezia 1, Padova 35131, Italy¶Center of Studies and Activities for Space (CISAS)-G. Colombo, via Venezia 15, Padova 35131, Italy)

  • UGO GALVANETTO

    (�Industrial Engineering Department, University of Padova, via Venezia 1, Padova 35131, Italy¶Center of Studies and Activities for Space (CISAS)-G. Colombo, via Venezia 15, Padova 35131, Italy)

Abstract

Richards’ equation is a classical differential equation describing water transport in unsaturated porous media, in which the moisture content and the soil matrix depend on the spatial derivative of hydraulic conductivity and hydraulic potential. This paper proposes a nonlocal model and the peridynamic formulation replace the temporal and spatial derivative terms. Peridynamic formulation utilizes a spatial integration to describe the path-dependency, so the fast diffusion process of water transport in unsaturated porous media can be captured, while the Caputo derivative accurately describes the sub-diffusion phenomenon caused by the fractal nature of heterogeneous media. A one-dimensional water transport problem with a constant permeability coefficient is first addressed. Convergence studies on the nonlocal parameters are carried out. The excellent agreement between the numerical and analytical solutions validates the proposed model for its accuracy and parameter stability. Subsequently, the wetting process in two porous building materials is simulated. The comparison of the numerical results with experimental observations further demonstrates the capability of the proposed model in describing water transport phenomena in unsaturated porous media.

Suggested Citation

  • Yuanyuan Wang & Hongguang Sun & Tao Ni & Mirco Zaccariotto & Ugo Galvanetto, 2023. "A Hybrid Fractional-Derivative And Peridynamic Model For Water Transport In Unsaturated Porous Media," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500809
    DOI: 10.1142/S0218348X23500809
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