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Estimating Soil Water Retention Curve from Particle-Size Distribution Data Based on Polydisperse Sphere Systems

T. P. Chan and R. S. Govindaraju*

School of Civil Engineering, Purdue University, 500, Stadium Mall Drive, West Lafayette, IN 47907-2501


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Fig. 1. Schematic of the polydisperse sphere systems in two dimensions: (left) impenetrable hard spheres and (right) overlapping spheres.

 


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Fig. 2. Particle-size distributions: (a) with constant {sigma}y and varying µy (thicker lines for µy = 2, thinner line for µy = 4); (b) with constant µy and varying {sigma}y (thicker lines for {sigma}y = 0.5, thinner line for µy = 0.8). The cumulative mass fraction (cmf) is plotted as dash–dot line. cdf, cumulative distribution function; pdf, probability density function.

 


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Fig. 3. Particle-size distribution of Beerse podzol II sand (code no. 4061) plotted on a normal probability scale (y axis). Data points falling on a straight line follow a lognormal distribution. The solid line represents the best-fit curve given by Eq. [29].

 


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Fig. 4. Measured and estimated cumulative mass fractions for all 119 sandy soils. The dashed line is a linear regression of the data points. The R2 and RMSE imply the goodness of fit of the dashed line.

 


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Fig. 5. Comparison of the proposed totally impenetrable spheres (TIS) and fully penetrable spheres (FPS) models' (a) effective pore-size distribution and (b) water retention curve.

 


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Fig. 6. The water retention curves of the totally impenetrable sphere models with varying {sigma}y.

 


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Fig. 7. Estimated and measured normalized water contents for all 119 soils. The scaling factor {alpha} is treated as a fitting parameter in obtaining the totally impenetrable spheres (TIS) and fully penetrable spheres (FPS) model estimates. VG, van Genuchten model.

 


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Fig. 8. Wagram sand (code no. 1142): (a) measured particle-size distribution data and the lognormal distribution fit (solid line); (b) measured water retention curve and the proposed models with fitted {alpha}. Considerable change in the water content occurs in the high saturation range, perhaps indicating a secondary pore system. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model; and VG, van Genuchten model.

 


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Fig. 9. Scaling factor {alpha} vs. the mean parameter µy and the standard deviation parameter {sigma}y of the lognormal distribution. The dashed line indicates the theoretical value of {alpha}. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model.

 


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Fig. 10. Estimated and measured normalized water contents for all 119 soils. The scaling factor {alpha} is fixed at 4. A wider scatter of data points is expected as a result. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model.

 


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Fig. 11. The RMSE of the totally impenetrable spheres (TIS) model prediction on water retention data vs. the mean parameter µy of the lognormal particle-size distribution.

 


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Fig. 12. The measured and estimated soil water retention curves of Troup loamy sand (code no. 1012) (a) with fitted {alpha} and (b) with theoretical {alpha}. The fitted {alpha} value is higher than the theoretical one. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model; and VG, van Genuchten model.

 


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Fig. 13. The measured and estimated soil water retention curves of Kootwijk sand (code no. 4520) (a) with fitted {alpha} (b) with theoretical {alpha}. The proposed TIS model does not match the shape of the measured retention curve very well. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model; and VG, van Genuchten model.

 


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Fig. 14. The measured and estimated soil water retention curves of Beerze podzol II sand (code no. 4061) (a) with fitted {alpha} (b) with theoretical {alpha}. The TIS model provides a very good fit to the data. TIS, totally impenetrable spheres model; FPS, fully penetrable spheres model; and VG, van Genuchten model.

 





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