Study on Two-Dimensional Water Flow over and through Anisotropic Soil
Publication: Journal of Engineering Mechanics
Volume 146, Issue 9
Abstract
The two-dimensional (2D) hydraulic analysis of water flow down a slope is crucial. Contrary to past studies, not only the anisotropy of soil but also the vertical component of flow velocity are considered in this study. The flow field is divided into two regions, namely, the water layer and the anisotropic soil layer. By regarding soil as an anisotropic and permeable porous medium, the viscous flow theory and poroelastic theory are employed to govern the surface flow and subsurface flow, respectively. When considering the anisotropy of soil, hydraulic conductivity is supposed to be a second order tensor, and the momentum equations for the porous medium flow in the soil layer should be derived through a new method. Based on the presumption of velocity type, the distributions of horizontal and vertical velocity and pressure could be acquired by an analytical approach by the differential transform method. The results show that both the horizontal and vertical components of flow velocity increase with the anisotropy degree, whereas the pore water pressure decreases with the anisotropy degree. The streamlines in surface water flow depend on higher anisotropy degree. The infiltration rate for sand estimated by the present solution is feasible when compared with previous research result.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This study was financially supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST 103-2313-B-005 -007 -MY3. In the meanwhile, this manuscript was mostly edited by Wallace Academic Editing.
References
Arikoglu, A., and I. Ozkol. 2006. “Solution of differential-difference equations by using differential transform method.” Appl. Math. Comput. 181 (1): 153–162.
Bear, J. 1988. Dynamics of fluids in porous media, 136–148. New York: Dover Publications.
Biot, M. A. 1956a. “Theory of propagation elastic waves in a fluid saturated porous solid. I: Low-frequency range.” J. Acoust. Soc. Am. 28 (2): 168–178. https://doi.org/10.1121/1.1908239.
Biot, M. A. 1956b. “Theory of propagation elastic waves in a fluid saturated porous solid. II: High-frequency range.” J. Acoust. Soc. Am. 28 (2): 179–191. https://doi.org/10.1121/1.1908241.
Chan, A. W., and S. T. Hwang. 1991. “Anisotropic in-plane permeability of fabric media.” Polym. Eng. Sci. 31 (16): 1233–1239. https://doi.org/10.1002/pen.760311613.
Deng, C., and D. M. Martinez. 2004. “Viscous flow in a channel partially filled with a porous medium and with wall suction.” Chem. Eng. Sci. 60 (2): 329–336. https://doi.org/10.1016/j.ces.2004.08.010.
Desseaux, A. 1999. “Influence of a magnetic field over a laminar viscous flow in a semi-porous channel.” Int. J. Eng. Sci. 37 (14): 1781–1794. https://doi.org/10.1016/S0020-7225(99)00003-8.
Hillel, D. 1980. Application of soil physics. New York: Academic press.
Hsieh, P. C., and P. Y. Hsu. 2018. “Hydraulic analysis of a two-dimensional water flow down a hillslope.” J. Eng. Mech. 144 (5): 04018020. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001432.
Hsieh, P. C., J. S. Yang, and Y. C. Chen. 2012. “An integrated solution of the overland and subsurface flow along a sloping soil layer.” J. Hydrol. 460–461 (Aug): 136–142.
Iwanek, M. 2008. “A method for measuring saturated hydraulic conductivity in anisotropic soils.” Soil Sci. Soc. Am. J. 72 (6): 1527–1531. https://doi.org/10.2136/sssaj2007.0335.
Jagdale, S., and P. T. Nimbalkar. 2012. “Infiltration studies of different soils under different soil conditions and comparison of infiltration models with field data.” Int. J. Adv. Eng. Technol. 3 (2): 154–157.
Makungo, R., and J. O. Odiyo. 2011. “Determination of steady state infiltration rates for different soil types in selected areas of Thulamela municipality.” In Proc., 15th SANCIAHS National Hydrology Symp. Grahamstown, South Africa: Rhodes Univ.
Rashidi, M. M., and S. M. Sadri. 2010. “Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the differential transform method.” Int. J. Contemp. Math. Sci. 5 (15): 711–720.
Song, C. H., and L. H. Huang. 2000. “Laminar poroelastic media flow.” J. Eng. Mech. 126 (4): 358–366. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:4(358).
Szabo, B. A., and I. W. McCaig. 1968. “A mathematical model for transient free surface flow in nonhomogeneous or anisotropic porous media.” J. Am. Water Resour. Assoc. 4 (3): 5–18. https://doi.org/10.1111/j.1752-1688.1968.tb05759.x.
Wang, X., F. Thauvin, and K. K. Mohanty. 1998. “Non-darcy flow through anisotropic porous media.” Chem. Eng. Sci. 54 (12): 1859–1869. https://doi.org/10.1016/S0009-2509(99)00018-4.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 9 • September 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 5, 2019
Accepted: Apr 22, 2020
Published online: Jun 26, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 26, 2020
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