1. Grain Size Distribution Documentation of …

1 1. Grain size Distribution Documentation ofCalculationsThe calculations used in the program are fairly simple and for the most part follow ASTM D 422. Thefollowing sections present the equations Moisture ContentMoisture content is calculated with the following formula:M C= 100% Wwt WdtWdt Wt( )Where:MC = the moisture contentWwt= the weight of the moisture specimen with tareWdt= the weight of the dried specimen with tareWt= the weight of the Sieve Test Wash TestP F200=Wts WwashWts 100%( )Where:PF200= the percent of material finer than the #200 sieveWts= the total sample weightWwash= the after-wash weightThe program charts PF200as the #200 percentage if either no further sieve test data are entered ( ,only a #200 wash test is performed), or the sieve test does not include a #200 size Distribution Documentation of Cumulative Weight Retained MethodP F=(1 Wc WctWts) 100%( )Where:PF = the percent finerWc= the cumulative weight retainedWct= the tare weight of the cumulative panWts= the total sample weightAn example calculation .

2 Cumulative weight retained = pan tare = weight = F=(1 ) 100% = Per-Sieve Weight Retained MethodP F= 1 (Wst Wt) +WlsWts 100%( )Where:Wst= the weight of a sieve and its retained materialWt= the weight of the sieveWls= the total amount of material retained on all larger sievesWts= the weight of the total sampleAn example calculation :To calculate the percent finer for the third largest sieve in a sieve nest, we need:Total sample weight = retained + tare for the third largest sieve = weight for the third largest sieve = retained on the larger on the largest + the second F= 1 ( ) + 100% = size Distribution Documentation of Calculationsby GEOSYSTEM SoftwareGrain size Distribution Documentation of CalculationsCalculation Sample SplitsIf the sample is split, the subsequent percent finer values are found as follows:P Ftot=CBT W RDW T( )Where:PFtot= the overall percent finerWR = the weight retained of the split sampleDWT, the post-split sample dry weight, is calculated as follows:DW T=SGDWP Fss P F W( )Where:SGDW = the split gradation dry sample weightPFss= the overall percent finer than the split sievePFW = the percent washed out from the #200 wash test (or 0 if a wash test wasnot performed)CBT, the biased total weight, is calculated as follows:CBT=SGDW+P F W DW T( )An example calculation :PFss= = = = T= + ( ) = F= 2020 GEOSYSTEM Software, size Distribution Documentation of Hydrometer Test Particle SizeP S= 30 v L980 (GS GW) ET( )Where.

3 Ps = the particle size in = the fluid viscosity in centipoisesL = the effective depth in = the specific gravity of the soil particlesGW = the specific gravity of water, corrected for temperatureEt = the elapsed time in minutesFor 152H hydrometers, L, the effective depth, is calculated as follows:L= Rm( )Rm=R+Cm( )Where:Rm = the hydrometer reading corrected for the height of the = the hydrometer reading, taken at the top of the meniscus. (Alt., the hydrom-eter reading taken at the bottom of the meniscus if the meniscus correction isentered as0.)Cm = the meniscus heightFor 151H hydrometers L is calculated with this equation:L= Rm( );Note that the effective depth equation can be changed by the user on a , the fluid viscosity, is calculated as:v=C1 +T (C2 +T (C3 +T (C4 +T C5)))( )Where:T = the fluid temperature, in degrees CelsiusC1 = = = = = size Distribution Documentation of Calculationsby GEOSYSTEM SoftwareGrain size Distribution Documentation of CalculationsCalculation Documentation5GW, the specific gravity of water, is calculated as:GW=C1 +T (C2 +T (C3 +T C4))( )Where:T = the fluid temperature, in degrees CelsiusC1 = = = = example calculation for a 152H hydrometer:ET =8minutesTemp = =34Cm =1GS = =33(=R - Cm)GW = ( calculation not shown)v = ( calculation not shown)L = ( calculation not shown)P S= 30 ( ) 8= 2020 GEOSYSTEM Software, size Distribution Documentation of Percent FinerFor 152H hydrometers, the percent finer than a given opening size is calculated as:P F=Rc aW B 100%( )Where.

4 PF = the percent finerRc = the corrected hydrometer readinga = the specific gravity of solids correction factorWB = the biased hydrometer sample weightFor 151H hydrometers, the calculation is:P F=100 GSW B (GS 1) Rc( )Where:PF = the percent finerRc = the corrected hydrometer readingWB = the biased hydrometer sample weightGS = the soil specific gravityWhen using automatic temperature correction, the corrected hydrometer reading (Rc) is calculated asfollows:Rc=R+Ct+Cc( )Where:R = the actual hydrometer reading (in thousandths for 151H)Cc = the composite correction at 20 degrees Celsius, as entered by the userCt = the composite correctionFor 152H hydrometers, Ct, the composite correction, is calculated as follows:Ct= +T ( +T ( +T ))( )Where:T = the fluid temperature, in degrees CelsiusFor 151H hydrometers, Ct is calculated as:Ct= +T ( +T ( +T ))( )Where:T = the fluid temperature, in degrees size Distribution Documentation of Calculationsby GEOSYSTEM SoftwareGrain size Distribution Documentation of CalculationsCalculation Documentation7 When using the multi-point (linear) temperature correction, the corrected hydrometer reading iscalculated as follows:Rc=R+Ct( )Where:R = the actual hydrometer reading (in thousandths for 151H)Ct = the temperature correction, as interpolated from a linear regression lineconstructed from the pairs of temperature and reading values entered by the userinto the hydrometer correction grid.

5 For test temperatures less than the lowest temperature entered into the correc-tion grid, the program will use the correction value corresponding to the lowestcorrection temperature entered; likewise, for test temperatures higher than thehighest temperature entered into the correction grid, the program will use thecorrection value corresponding to the highest correction temperature specific gravity correction factor is:a= GSGS 1( )Where:GS = the specific gravity of the solidsThe biased sample weight is calculated as:W B=W hs 10000P ss (100 +M h)( )Where:WB = the biased sample weight, in gramsWhs = the air dry hydrometer sample weightPSS = the percent passing the separation sieveMh = the hygroscopic moisture content per ASTM D 422 8An example calculation using a 152H hydrometer:ET =8minutesTemp. = CelsiusR =34GS = = correction pairs: ( at 20 ), ( at 22 ), ( at 25 )By interpolation, Cc at = 2020 GEOSYSTEM Software, size Distribution Documentation of Calculations8Rc= 34 + ( ) = 1= B= 10000100 (100 + )= F= additional calculation , using a 151H hydrometer:ET =15minutesTemp =22 CelsiusR = = = at 22 degrees Celsius = + ( ) = F=100 = size Distribution Documentation of Calculationsby GEOSYSTEM SoftwareGrain size Distribution Documentation of CalculationsCalculation calculation of Fractional ComponentsThe fractional components and percentage diameters (D85, D60,D50, etc.)

6 Are computed by creating acubic spline model of the particle size Distribution curve then solving the model for the curve values atvarious classification coefficients Ccand Cuare calculated as follows:Cc=D30 D30D60 D10( )Cu=D60D10( ) Tables of ConstantsTable : Correction Factor for Specific Gravities Other than when using Hydrometer 2020 GEOSYSTEM Software, size Distribution Documentation of Calculations10 Table : Automatic Temperature Correction Factor as a Function of ,DEG OFWATERVISCOSITYOF WATERTEMP. FOR152 HTEMP. size Distribution Documentation of Calculationsby GEOSYSTEM SoftwareGrain size Distribution Documentation of CalculationsCalculation Documentation11 Table : Effective Depth for 152H and 151H 2020 GEOSYSTEM Software.