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Coupling effects of porosity and particle size on seepage properties of broken sandstone based on fractional flow equation

Studying the seepage properties of broken rock is important for understanding the behavior of engineering projects and preventing seepage disasters from occurring. Therefore, a test system was developed to test the seepage properties of broken rock under different porosities and particle sizes. A nonlinear seepage equation of broken rock was developed based on the Forchheimer equation and the theories of fraction calculus. The influence of the coupling mechanism of the porosity and particle size on the seepage properties of broken rock was analyzed. The results show that the nonlinear seepage equation can describe the nonlinear seepage properties of broken rock well. The relations between the permeability and the porosity and particles size can all be represented through an exponential function. It is thought that watercourses are developed in broken rock with high porosity and large particle size, which shows a stronger hydraulic conductivity capability; however, the inertial potential energy of a non-Darcy flow is relatively small.
PAPER REVISED: 2018-09-11
PAPER ACCEPTED: 2018-11-07
  1. Feng, M.M., Experimental investigation on seepage property of saturated broken red sandstone of continuous gradation. Bulletin of Engineering Geology and the Environment, 77(2018),3,pp.1167-1178
  2. Darcy,H., Les FontainesPubliques de la Vile de Dijon, Victor Dalmond, Paris, 1856
  3. Dupuit, J.,EtudesTheoriques et Pratiques sur le Mouvement des Eaux,Dunod, Paris, 1863
  4. Forchheimer,P. H.,Wasserbewegungdurch Boden. Z. Ver. Deutsch. Ing.,45(1901), pp. 1782-1788
  5. Goodman, R. E., An Introduction to Rock Mechanics,Engineering Geology, 19(1980), 1, pp. 72-74
  6. Zoback, M. D., et al.,Note on the deformational behavior and permeability of broken granite, International Journal of Rock Mechanics and Mining Sciences &Geomechanics Abstracts,13(1976), 10, pp. 291-294
  7. Pradip, K. G.N., et al.,Non-Darcy converging flow through coarse granular media,Journal of the Institution of Engineers (India), Civil Engineering Division, 76(1995), pp. 6-11
  8. Legrand.J.,Revisited Analysis of Pressure Drop in Flow through broken Rocks. Journal of Hydraulic Engineering, 128(2002), 11, pp. 1027-1031
  9. Ma.D,et al., An Experimental Investigation of Permeability Measurement of Water Flow in broken Rocks. Transport in Porous Media, 105(2014), 3, pp. 571-595
  10. Wang, M.L.,etal.,Effect of Water on the Consolidation of broken Rock Salt, Engineering Mechanics, ASCE, 2015, pp. 531-534
  11. Yang, X. J.,General Fractional Derivatives: Theory, Methods and Applications, New York: CRC Press, 2019
  12. Yang, X.J.,et al.,Fundamental solutions of the general fractional-order diffusion equations,Mathematical Methods in the Applied Sciences,41(2018), 18, pp. 9312-9320
  13. Yang, X.J.,New rheological problems involving general fractional derivatives with nonsingular power-law kernels. Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science,19(2018), 1, pp. 45-52
  14. Yang, X.J.,et al., A new fractional derivative involving the normalized sinc function without singular kernel. European Physical Journal,226(2017), s21, pp. 3567-3575
  15. Yang, X.J., et al., Anomalous diffusion models with general fractional derivatives within the kernels of the extended mittag-leffler type functions. Romanian Reports in Physics, 69(2017), 4, pp. 115
  16. He, J. H., Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics & Engineering,167(1998), 1-2, pp. 57-68
  17. Choudhary, A., A fractional model of fluid flow through porous media with mean capillary pressure. Journal of the Association of Arab Universities for Basic & Applied Sciences, 21(2015), pp. 59-63
  18. Liu,Q.,et al,. Numerical simulation for the 3D seepage flow with fractional derivatives in porous media. Ima Journal of Applied Mathematics, 74(2009), 2, pp. 201-229
  19. Wang, R., et al., The study on non-Darcy seepage equation of low velocity flow. SCIENTIA SINICA Physica, Mechanica&Astronomica, 47 (2017), 6,pp.064702
  20. Wu J.Y., et al., Aggregate gradation effects on dilatancy behavior and acoustic characteristic of cemented rockfill. Ultrasonics,92(2019), 2, pp. 79-92
  21. Wu, J.cY.,et al., The length of pre-existing fissures effects on the mechanical properties of cracked red sandstone and strength design in engineering. Ultrasonics, 82(2018),1,pp.188-199
  22. Wu, J.Y., et al.,Particle size distribution of aggregate effects on mechanical and structural properties of cemented rockfill: Experiments and modeling. Construction and Building Materials, 193(2018), pp. 295-311
  23. Miao, X.X., et al., Seepage Theory of Mining Strata. Science Press, Beijing, 2004
  24. Kilbas, A. A. A., et al., Theory and applications of fractional differential equations. 204. Elsevier Science Limited, 2006