عنوان مقاله [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.