Calculation Following the Fit of the Grain-size Distribution

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Two algorithms are initiated following the fitting of the grain-size equation to experimental data. The first algorithm calculates %clay, %silt, %sand, %coarse, D10, D20, D30, D50, and D60 based on the equation representing the grain-size distribution. The second algorithm re-classifies the soil based on the equation of the grain-size equation.


The unimodal or bimodal equations can be used as the basis for these calculations. The fit used as the basis for these calculations is determined by selecting the fit with the highest R2 value.


Calculation of % clay, % silt, % sand, % coarse, D10, D20, D30, D50, and D60

 One of the benefits of the two grain-size equations presented is that conventional physical variables can be computed from the fitted curves. The most commonly used variables are % clay, % sand, and % silt. Also used are particle diameter variables such D10, D20, D30, D50, and D60. The equations presented are of the form, Pp(d) where d is particle diameter (mm). The % clay, % silt, and % sand can therefore be a read off of the curve by selecting the appropriate diameter size. The particle diameter sizes used depend upon the criteria associated with the various classification methods. For example, the USDA classification boundaries are 0.002, 0.05, and 2.0 mm for percent clay, percent silt, and percent sand, respectively. The USCS classification uses boundaries of 0.002, 0.075, and 4.75 mm for percent clay, percent silt, and percent sand, respectively. The particle size divisions can be determined for any classification method by substituting into the equations the appropriate diameters as shown in Figure 1.

Figure 1 Determination of the soil fractions (i.e., %clay, %silt, and %sand) when using the unimodal equation


The diameter variables must be read off of the curve in an inverse manner. The particle size diameter answers the question, “What particle diameter has 10 percent of the total mass smaller than this size?”. Taking the inverse of either the unimodal or bimodal equation is difficult. A half-length algorithm is used to read diameters off the grain-size curve. An initial guess of the particle diameter is selected and the correction distance is progressively halved until the iteration process yields a minimal error. The results of this process can be seen in Figure 2.


Figure 2 Determination of the percent passing for any particle size, d, for a unimodal grain-size distribution


The current soil is automatically classified following the fit of the grain-size distribution with an equation. The % clay, % silt, % sand, % coarse, D10, D20, D30, D50, and D60 variables calculated from the best-fit equation are used as the basis to classify the soil by the USCS and the USDA methods.