It is much easier to measure solid phase data or particle size distribution (PSD) than pore size distribution, therefore it is useful to determine relationship between fractal dimension of the soil particle size distributions (D_PSD) and soil water retention curve ( ${\text{D}}_{\text{SWRC}}$). The present research aims to firstly measure fractal dimension of the soil particle size distribution using three radii 1 (clay), 25 (silt) and 1000 (sand) µm (D_PSD3) and subsequently compare it with fractal dimension obtained from D_PSD, and secondly develop a relationship between ${\text{D}}_{\text{PSD}3}$ and ${\text{D}}_{\text{SWRC}}$. The results showed that the maximum and minimum values for $D_{PSD}$ were 2.93 and 2.65 and for $D_{PSD3}$ were 2.91 and 2.63 and there was no significant difference between ${\text{D}}_{\text{PSD}3}$ and ${\text{D}}_{\text{PSD}}$. A linear relationship between ${\text{D}}_{\text{PSD}3}$ and ${\text{D}}_{\text{SWRC}}$ was developed for some of soils UNSODA databases. The relationship developed here was compared with three present methods to calculate ${\text{D}}_{\text{SWRC}}$ from soil texture including (1) non-linear relationship with clay, (2) logarithmic relationship with clay, and (3) percent of sand, silt and clay for some of the northern soil of Iran. The results indicated that the proposed method in this study, especially in fine-grained soils, can efficiently predict ${\text{D}}_{\text{SWRC}}$ with appropriate precision..

The main objective of the present research is scaling lognormal water retention curves for dissimilar soils. This method requires a reference curve and the amount of water content in a particular suction. The scaling factor in this method equals to the amount of moisture logarithm in a particular suction (e.g. $S{e}_{5000}$) in the reference soil to the amount of water content logarithm in the same suction in the soil. The proposed method was evaluated for 14 different soil samples. The scaling factor obtained by this method was evaluated by the scaling factor obtained from the optimization method ( ${\alpha }_{Opt}$). The results showed that the average scaling factor based on $S{e}_{5000}$ is closest to the average ${\alpha }_{Opt}$ . The water retention curve obtained by the method presented in this research is fitted on the water retention curve obtained from the log-normal model with superior accuracy.