کاربرد هندسه فرکتال و مدل لوله‌های موئین در برآورد تابع هدایت هیدرولیکی خاک

نوع مقاله: مقاله پژوهشی

نویسندگان

1 کاندیدای دکتری آبیاری و زهکشی؛ دانشگاه فردوسی مشهد

2 استاد گروه مهندسی آب، دانشکده کشاورزی، دانشگاه فردوسی مشهد

چکیده

در این تحقیق بر مبنای هندسه فرکتال و مدل لوله­های موئین خاک، تابع هدایت هیدرولیکی خاک مدل­سازی شد. مدل پیشنهادی تابعی از قطر منافذ، طول ظاهری مسیر جریان، بعد فرکتالی منفذ و بعد فرکتالی لوله­های موئین معوج می­باشد. در این تحقیق روابط مربوط به محاسبه بعد فرکتالی منفذ و بعد فرکتالی لوله موئین معوج برای جریان غیراشباع به عنوان تابعی از میزان رطوبت خاک ارائه شده است. از مزایای این مدل نداشتن ثابت تجربی است. برای محاسبه قطر منافذ خاک از مدل منحنی مشخصه رطوبتی ون­گنوختن استفاده شد. به منظور ارزیابی مدل ارائه شده از اطلاعات مربوط به 40 نمونه خاک با 11 بافت مختلف در محدوده­ی شن، لوم و رس از بانک خاک UNSODA استفاده شد. نتایج ارزیابی (RMSE بین 9-E3/1 تا 5-E2/6، GMER بین 006/0 تا 13/3 و GSDER بین 998/0 تا 48/8) [A1] بیانگر انطباق خوب تابع هدایت هیدرولیکی خاک مدل شده براساس فرکتال با مقادیر گزارش­شده هدایت هیدرولیکی خاک بود.



 [A1]این اعداد در متن انگلیسی ذکر نشده است.

کلیدواژه‌ها


عنوان مقاله [English]

Estimation of Soil Hydraulic Conductivity Function Based on Fractal Geometry and the Capillary Tube Models

نویسندگان [English]

  • S. Omidi 1
  • B. Ghahraman 2
1 PhD Candidate of Irrigation and Drainage, Ferdowsi University of Mashhad
2 Professor of Irrigation and Drainage, Ferdowsi University of Mashhad
چکیده [English]

In this study, soil hydraulic conductivity function was modeled based on fractal geometry and capillary tube models. The proposed model is expressed as a function of the pore diameter, apparent flow path length, pore fractal dimension and tortuosity fractal dimension. In this study, the relationships concerning calculation of the pore fractal dimension and tortuosity fractal dimension for unsaturated flow was presented as a function of the soil water content. The advantage of this model is lack of empirical constants. Van Genuchten soil water retention curve was used to calculate the pore diameters. In this research, the model was evaluated by using 40 soil samples with 11 different soil textures covering sandy, loam, and clay from the UNSODA database. Results of comparison of unsaturated hydraulic conductivity estimated with fractal model presented in this study and the reported amounts of Van Genuchten model showed that the root mean square error (RMSE) of van Genuchten model was less than the fractal model, while the ratio of geometric mean error (GME) and standard deviation error of fractal geometry model was less than the van Genuchten model. Van Genuchten model had the highest coefficients of variation, with the exception of RMSE parameters. In terms of GMER and GSDER, fractal model was more reliable than the van Genuchten model.

کلیدواژه‌ها [English]

  • Soil database UNSODA
  • Pore fractal dimension
  • Tortuosity fractal dimension
  1. Agnese C., Blanda F., Drago A., Iovino M., Minacapilli M., Provenzano G., Rallo G., and Sciortino M. 2007.Assessing the agro hydrological SWAP model to simulate soil water balance in typical Mediterranean crops. Geophysical Research Abstracts 9, 08146.
  2. Binley A., Cassiani G., Middleton R., and Winship P. 2002. Vadose zone flow model parameterisation using cross-borehole radar and resistivity imaging. Journal of Hydrology, 267 (3-4): 147-159.
  3. Binley A., Winship P., Middleton R., Pakar M., and West J. 2001. High- resolution characterization of vadose zone dynamics using cross- borehole radar. Water Resour. Research. 37: 2639-2652.
  4. Burdine N.T. 1953. Relative permeability calculations from pore-size distribution data. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers.198: 71–77. (Trans. Am. Inst. Min. Metall. Pet. Eng)
  5. Crawford J. W., Baveye P., Grindord P., and Rappoldt C. 1999. Application of fractals to soil Properties, landscape patterns, and solute transport in porous media in Assessment of non-point source pollution in the vadose zone, Geophysical monograph. 108: 151- 164, American Geophysical Union.
  6. Crawford J.W. 1994. The relationship between structure and the hydraulic conductivity of soil. European Journal of Soil Science. 45: 493-501.
  7. Denn M. M. 1980. Process Fluid Mechanics. Prentice-Hall, England cliff, New Jersey.
  8. Dubreuil-Boisclair C., Gloaguen E., Marcotte D., and Giroux B. 2011. Heterogeneous aquifer characterization from ground-penetrating radar tomography and borehole hydrogeophysical data using nonlinear Bayesian simulations. Geophysics. 76 (4): 13-25.
  9. Elliot T.R., Reynolds W.D., and Heck R.J. 2010. Use of existing pore models and X-ray computed tomography to predict saturated soil hydraulic conductivity. Geoderma. 156 (3-4): 133-142.
  10. Finsterle S., and Faybishenko B. 1999. Inverse modeling of a radial multistep outflow experiment for determining unsaturated hydraulic properties. Water Resources Research. 22: 431-444.
  11. Fuentes C., Vauclin M., and Parlange J.I. 1996. A note on the soil–water conductivity of a fractal soil. Transport in Porous Media. 23: 31–36.
  12. Gueting N., Vienken T., Klotzsche A., van der Kruk J., Vanderborght J., Caers J., Vereecken H., and Englert A. 2017. High resolution aquifer characterization using cross hole GPR full-waveform tomography: Comparison with direct-push and tracer test data, Water Resour. Res., 53: 49–72.
  13. Hilal M. H. and Anwar N. M. 2016. Vital role of water flow and moisture distribution in soils and the necessity of a new out-look and simulation modeling of soil- water relations. Journal of America science. 12 (7):6- 18.
  14. Hudson D. B., Wierenga P. J. and Hills R. G. 1996. Unsaturated hydraulic properties from upward flow into soil cores. Soil Science Society of America Journal. 60: 388-396.
  15. Mandelbrot B. 1975. Stochastic models for the earth’s relief, the shape and fractal dimension of coastlines and the number area rule for islands. Proc. National Acad. Sc USA. 72 (10): 2825-2828.
  16. Meng F.G., Zhang H.M., Li Y.s., Zhang X.W., and Yang F.G. 2005. Application of fractal permeation model to investigate membrane fouling in membrane bioreactor. Journal of Membrane Science. 262: 107-116.
  17. Mualem Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research. 12:513– 22.
  18. Nasta P., Huynh S., and Hopmans J. W. 2010. Simplified Multistep Outflow Method to Estimate Unsaturated Hydraulic Functions for Coarse-Textured Soils. Soil Science Society of America Journal. 75 (2): 418-425.
  19. Naveed M., Moldrup P., Schaap M.G., Tuller M., Kulkarni R., Vogel H.J., de Jonge L. W. 2016. Prediction of biopore- and matrix-dominated flow from X-ray CT-derived macropore network characteristics. Hydrol. Earth Syst. Sci., 20: 4017–4030.
  20. Nemes A., Schaap M.G., Leij F.J., and Wösten J.H.M. 2001. Description of the unsaturated soil hydraulic database UNSODA version 2.0. Journal of Hydrology. 251(3–4): 151–162.
  21. Rieu M., and Sposito G. 1991. Fractal fragmentation, soil porosity, and soil water properties: I. Theory. Soil Science Society of America Journal. 55: 1231–1238.
  22. Schindler U., Müller L., and Eulenstein F. 2017. Hydraulic performance of horticultural substrates-1. Method for measuring the hydraulic quality indicators. Horticulture Journal. 3, 5: 1-7.
  23. Schindler U., Durner W., von Unold G., and Müller L. 2010. Evaporation method for measuring unsaturated hydraulic properties of soils: extending the measurement range. Soil Science Society of America Journal. 74: 1071-1083.
  24. Shepard J. S. 1993. Using a fractal model to compute the hydraulic conductivity function. Soil Science Society of America Journal. 57: 300-306.
  25. Shi Y., Cheng S., and Quan S. 2012. Fractal-based theoretical model on saturation and relative permeability in the gas diffusion layer of polymer electrolyte membrane fuel cells. Journal of Power Sources. 209: 130-140.
  26. Sriboonlue V., Srisuk K., Konyai S., and Khetkratok N. 2006. Unsaturated Hydraulic Conductivity for Upward Flow in Soil. Proceedings of the 4th International Conference on Unsaturated Soils. April 2–6. Carefree, Arizona, USA.
  27. Stolte J., Freijer J.L., Bouten W., Dirksen C., Halbertsma J.M., Van Dam J.C., Van Den Berg J.A., Veerman G.J., and Wosten J.H.M. 1994. Comparison of six methods to determine unsaturated soil hydraulic conductivity. Soil Science Society of America Journal. 58: 1596–1603.
  28. Tsai C.H., and Yeh G.T. 2012. Retention Characteristics for Multiple-Phase Fluid Systems. Terrestrial, Atmospheric and Oceanic Sciences. 23 (4), DOI code: 10.3319/TAO.2012. 02.14.01(Hy).
  29. Tyler S.W., Wheatcraft S.W. 1990. Fractal process in soil water retention. Water Resources Research. 26: 1047–54.
  30. van Genuchten M.Th., Leij F. J., and Yates S.R. 1991. The RETC code for quantifying the hydraulic functions of unsaturated soils. (Available at http://www.pc-progress.cz/Pg_RetC.htm; verified 14 may. 2014). Report No. EPA/600/2–91/065. R.S. Kerr Environmental Research Laboratory. U. S. Environmental Protection Agency, Ada, Oklahoma.
  31. Wheatcraft S. W., and Tyler S.W. 1988. An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resources Research 24: 566–578.
  32. Xu Y.F. 2004. Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution. Computers and Geotechnics. 31: 549–557.
  33. Xu Y.F., Dong P. 2004. Fractal approach to hydraulic properties in unsaturated porous media. Chaos, Solitons and Fractals. 19: 327–337.
  34. Yu B.M. 2005. Fractal character for tortuous stream tubes in porous media. Chinese Physics Letters. 22 (1): 158-160.
  35. Yu B.M. and Cheng P. 2002. A fractal permeability model for bi-dispersed porous media. International Journal of Heat and Mass Transfer. 45: 2983-2993.
  36. Yu B.M. and Li J.H. 2001. Some fractal characters of porous media. Fractals. 9: 365-372.
  37. Yu B.M., Lee L.J., and Cao H.Q. 2002. A fractal in-plane permeability model for fabrics. Polymer composites. 23: 201-221.
  38. Zhou Q. Y., Shimada J., and Sato A. 2001. Three-dimensional spatial and temporal monitoring of soil water content using electrical resistivity tomography. Water Resources Research. 37: 273-285.