تخمین منحنی مشخصه آب خاک با استفاده توزیع اندازه ذرات بر پایه روش فرکتال

نوع مقاله : مقالات پژوهشی

نویسندگان

• محمدمهدی چاری ¹
• بیژن قهرمان ¹
• کامران داوری ¹
• علی اصغر خشنود یزدی ²

¹ دانشگاه فردوسی مشهد

² دانشکده کشاورزی شیروان

https://doi.org/10.22067/jsw.v0i0.34661

چکیده

به دست آوردن منحنی رطوبتی در آزمایشگاه زمان بر و پرهزینه می باشد. به این دلیل پژوهش گران روش هایی را ارائه کرده اند که به کمک آن‌ها بتوان منحنی مشخصه را به آسانی به دست آورد. یکی از این روش ها، استفاده از هندسه فرکتال می باشد. از آن‌جا که به دست آوردن داده های فاز جامد یا توزیع اندازه ذرات (PSD) آسان تر از توزیع اندازه منافذ می باشد، تعیین رابطه بین بعد فرکتال توزیع اندازه ذرات (DPSD) و بعد فرکتال منحنی رطوبتی (DSWRC) می تواند مفید واقع شود. از طرفی در بسیاری از داده های خاک، اطلاعات کاملی از منحنی دانه بندی نیز موجود نمی باشد و تنها سه جزء (درصد رس، سیلت و شن) از آن اندازه گیری می شود. این پژوهش با هدف تعیین DPSD با استفاده از داده های زود یافت خاک و همچنین ایجاد رابطه ای بین DPSD و DSWRC انجام گردید. برای این کار 54 نمونه خاک از مناطق شمالی ایران انتخاب و به شش کلاس بافتی لوم، لوم رسی، رسی، لوم رس شنی، لوم سیلتی و لوم شنی تقسیم بندی شد. DPSD با استفاده از روش بسط داده شده منحنی دانه بندی (Dm1) و روش استفاده از سه نقطه (شن، سیلت و رس) (Dm2) به دست آمد. نتایج نشان داد که بعد فرکتال توزیع اندازه ذرات به دست آمده با هر دو روش اختلاف معنی داری با یکدیگر ندارند. DSWRC نیز با استفاده از داده های مکش-رطوبت به دست آمد. نتایج حاکی از این بود که هر سه بعد فرکتال وابسته به بافت خاک بوده و با افزایش مقدار رس خاک مقدار آن افزایش می یابد. هم‌چنین روابط رگرسیون خطی بین Dm1 و Dm2 با DSWRC با استفاده از 48 نمونه خاک ایجاد گردید که به ترتیب دارای ضریب تعیین 902/0 و 871/0 بودند. سپس بر اساس روابط به دست آمده، از چهار روش : 1- Dm1= DSWRC ، 2-استفاده از معادله رگرسیونی به دست آمده با Dm1 ، 3- Dm2= DSWRC و 4- استفاده از معادله رگرسیونی به دست آمده با Dm2 برای بیان DSWRC استفاده گردید. مدل ها برای تعیین درصد رطوبت خاک در مکش های مختلف با توجه به شاخص های آماری ریشه مربع میانگین خطاهای نرمال شده، میانگین خطا، نسبت خطای متوسط هندسی و راندمان مدل‌سازی مورد ارزیابی قرار گرفت. نتایج نشان داد که به استثناء خاک لوم شنی در سایر خاک ها دقت روش ها مناسب بوده است. به طورکلی این پژوهش کارایی روش فرکتال را برای شبیه سازی منحنی رطوبتی با استفاده از داده زود یافت خاک با موفقیت اثبات کرد.

کلیدواژه‌ها

• رس
• بعد فرکتال اندازه ذرات
• منحنی رطوبتی
• مدل سازی

20.1001.1.20084757.1394.29.3.9.6

عنوان مقاله [English]

Estimating Soil Water Retention Curve Using The Particle Size Distribution Based on Fractal Approach

نویسندگان [English]

• M.M. Chari ¹
• B. Ghahraman ¹
• K. Davary ¹
• A. A. Khoshnood Yazdi ²

¹ Ferdowsi University of Mashhad

² Shirvan University

چکیده [English]

Introduction: Water and soil retention curve is one of the most important properties of porous media to obtain in a laboratory retention curve and time associated with errors. For this reason, researchers have proposed techniques that help them to more easily acquired characteristic curve. One of these methods is the use of fractal geometry. Determining the relationship between particle size distribution fractal dimension (DPSD) and fractal dimension retention curve (DSWRC) can be useful. However, the full information of many soil data is not available from the grading curve and only three components (clay, silt and sand) are measured.In recent decades, the use of fractal geometry as a useful tool and a bridge between the physical concept models and experimental parameters have been used.Due to the fact that both the solid phase of soil and soil pore space themselves are relatively similar, each of them can express different fractal characteristics of the soil .
Materials and Methods: This study aims to determine DPSD using data soon found in the soil and creates a relationship between DPSD and DSWRC .To do this selection, 54 samples from Northern Iran and the six classes loam, clay loam, clay loam, sandy clay, silty loam and sandy loam were classified. To get the fractal dimension (DSWRC) Tyler and Wheatcraft (27) retention curve equation was used.Alsothe fractal dimension particle size distribution (DPSD) using equation Tyler and Wheatcraft (28) is obtained.To determine the grading curve in the range of 1 to 1000 micron particle radius of the percentage amounts of clay, silt and sand soil, the method by Skaggs et al (24) using the following equation was used. DPSD developed using gradation curves (Dm1) and three points (sand, silt and clay) (Dm2), respectively. After determining the fractal dimension and fractal dimension retention curve gradation curve, regression relationship between fractal dimension is created.
Results and Discussion: The results showed that the fractal dimension of particle size distributions obtained with both methods were not significantly different from each other. DSWRCwas also using the suction-moisture . The results indicate that all three fractal dimensions related to soil texture and clay content of the soil increases. Linear regression relationships between Dm1 and Dm2 with DSWRC was created using 48 soil samples in order to determine the coefficient of 0.902 and 0.871 . Then, based on relationships obtained from the four methods (1- Dm1 = DSWRC, 2-regression equationswere obtained Dm1, 3- Dm2 = DSWRC and 4. The regression equation obtained Dm2. DSWRC expression was used to express DSWRC. Various models for the determination of soil moisture suction according to statistical indicators normalized root mean square error, mean error, relative error.And mean geometric modeling efficiency was evaluated. The results of all four fractalsare close to each other and in most soils it is consistent with the measured data. Models predict the ability to work well in sandy loam soil fractal models and the predicted measured moisture value is less than the estimated fractal dimension- less than its actual value is the moisture curve.
Conclusions: In this study, the work of Skaggs et al. (24) was used and it was amended by Fooladmand and Sepaskhah (8) grading curve using the percentage of developed sand, silt and clay . The fractal dimension of the particle size distribution was obtained.The fractal dimension particle size of the radius of the particle size of sand, silt and clay were used, respectively.In general, the study of fractals to simulate the effectiveness of retention curve proved successful. And soon it was found that the use of data, such as sand, silt and clay retention curve can be estimated with reasonable accuracy.

کلیدواژه‌ها [English]

• clay
• Fractal dimension of particle size
• Fractal dimension retention curve
• Modeling

مراجع

1- Bird N.R.A., Bartoli F., and Dexter A.R. 1996. Water retention models for fractal soil structures. Eur Journal Soil science, 47: 1 – 6.

2- Bird N., Perrier E. and Rieu M. 2000. The water retention curve for a model of soil structure with pore and solid fractal distributions. Eur Journal Soil science, 55:55–63

3- Brooks R. H. and Corey A. T. 1964. Hydraulic propertes of porous media.Colorado State University, Fort Collins. Hydrology Paper No. 3 , 27pp

4- Campbell G.S. 1974. A simple method for determining unsaturated hydraulic conductivity from moisture retention data. Soil science, 177, 311 –314.

5- De Gennes P.G. 1985. Partial filling of fractal structure by a wetting fluid. In: Adler, D., et al., (Ed.) Physics of Disordered Materials. Plenum, New York, pp. 227 – 241.

6- Ersahin S., Gunal H., Kutlu T., Yetgin B., and Cuban S. 2006. Estimating specific surface area and cation exchange capacity in soils using fractal dimension of particle‐size distribution. Geoderma, 136:588‐597.

7- Filgueira R. R., Pachepsky Ya. A., Fournier L. L., Sarli G. and Aragon A. 1999. Comparison of fractal dimensions estimated from aggregate mass-size distribution and water retention scaling. Soil Science Society, 164: 217-223.

8- Fooladmand H.R., and Sepaskhah A.R. 2006. Improved estimation of the soil particle-size distribution from textural data. Biosystems Engineering, 94:133–138.

9- Ghanbarian-Alavijeh B., and Hunt A.G. 2012. Estimation of soil-water retention from particle-size distribution: Fractal approaches. Soil Science. Vol 177: 321-326

10- Ghilardi P., Kai A., and Menduni G. 1993. Self-similar heterogeneity in granular porous media at the representative element volume scale. Water Resour Research, 29: 1205 – 1214.

11- Haghverdi A., Cornelis W.M., and Ghahraman B. 2012. A pseudo- continuous neural network approach for developing water retention pedotransfer function with limited data. Journal of hydrology. 442: 46-54

12- Huang G., and Zhang R. 2005. Evluation of soil water retention curve with the pore-solid fractal model. Geoderma. 127:52-61.

13- Huang G., Zhang R. and Huang Q. 2006. Soil water retention curve with a fractal method. Pedosphere, 16(2) : 137-146.

14- Khoshnood Yazdi A. 1996. Soil moisture curves of the physical properties of soils in Iran. Msc thesis.Tehran university.140p.( in Persian)

15- Kravchenko A., and Zhang R. D. 1998. Estimating the soil water retention from particle-size distributions: A fractalapproach. Soil Science. 163: 171-179

16- Perfect E., McLaughlin N.B., Kay B.D. and Topp G.C. 1998. Reply to the comment on bAn improved fractal equation for the soil water retention curveQ . Water Resour. Research. 34: 933 – 935.

17- Perrier E., and Bird N. 2002. Modeling soil fragmentation: The pore solid fractal approach. Soil Tillage Research. 64:91–99.

18- Perrier E., Rieu M., Sposito G. and de Marsily G. 1996. Models of water retention curve for soils with fractal pore size distribution. Water Resour Research. 32: 3025 – 3031.s

19- Rawls W.J., and Brakensiek D.L. 1985. Prediction of soil water properties for hydrologic modeling. In: Jones, E., Ward, T.J. (Eds.), Watershed Manage. Eighties. Proceedings of the Sym-posium of ASAE, Denver, pp. 293–299.

20- Rieu M. and Sposito G. 1991a. Fractal fragmentation, soil porosity and soil water properties: I. Theory. Soil Science Society America Journal, 55: 231 – 1238.

21- Rieu M. and Sposito G. 1991b. Fractal fragmentation, soil porosityand soil water properties: II. Applications. Soil Science Society America Journal, 55: 1239 – 1244.

22- Saxton K.E., Rawls W.J., Romberger J.S. and Papendick R.I. 1986. Estimating generalized soil-water characteristics from texture. Soil Science Society America Journal, 50:1031–1036.

23- Schaap M.G., Nemes A. and van Genuchten M.Th. 2004. Compar-ison of models for indirect estimation of water retention and available water in surface soils. Vadose Zone Journal, 3: 1455–1463.

24- Skaggs T. H., Arya L. M., Shouse P. J. and Mohanty B. P. 2001. Estimating particle-size distribution from limited soil texture data. Soil Science Society America Journal, 65: 1038-1044.

25- Toledo P.G., Novy R.A., Davis H. T., Scriven L.E. 1990. Hydraulic conductivity of porous media at low water content. Soil Science Society America Journal, 54: 673–679.

26- Tyler S.W., and Wheatcraft S.W. 1989. Application of fractal mathematics to soil water retention estimation. Soil Science Society America Journal, 53: 987-996.

27- Tyler S.W., and Wheatcraft S.W. 1990. Fractal processes in soil water retention. Water Resour Research, 26:1047–1054.

28- Tyler S.W., and Wheatcraft S.W. 1992. Fractal scaling of soil-particle size distributions: analysis and limitations. Soil Science Society America Journal, 56: 362–369.

29- Van Genuchten M.T. 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898.

30- Vereecken H., Maes J., Feyen J. and Darius P. 1989. Estimating the soil moisture retention characteristic from texture, bulk density and carbon content. Soil Science, 148: 389–403.

31- Wosten J.H.M., Pachepsky Y.A. and Rawls W.J. 2001. Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics. Journal of Hydrology, 251: 123–150.