# The University of Toledo Soil Mechanics Laboratory

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1 The University of Toledo Soil Mechanics Laboratory 1 Grain Size Distribution Hydrometer Analysis Introduction The hydrometer analysis, also called sedimentation method, is used to determine the grain size distribution for the fraction of soil that is smaller than the No. 10 (2.00 mm) sieve. Fine soil particles are dispersed by soaking the soil sample in a dispersing agent and by rapid stirring to neutralize the charges between the soil particles. The test uses a Type 152H hydrometer calibrated to give the mass of solids with specific gravity equal to 2.65 in suspension and the settling velocity of the dispersed soil particles. The soil grain diameter D (mm) is computed by application of Stokes Law, a theoretical equation for the terminal settling velocity of spheres in a fluid, according to the following equations. v 2 9 G G s 1 2 D 2 (1) D 30 v 980 G s G 1 (2) where v = settling velocity of the fluid, water plus dispersing agent G s = specific gravity of the soil solids G 1 = specific gravity of the water and dispersing agent solution = absolute viscosity of the suspending fluid which depends on the temperature Since the soil particles are particles are not spheres, the hydrometer analysis gives the diameters of spheres that would be settling at the same velocity as the soil particles. This approximation to the particle size distribution is useful for such engineering purposes as estimating the percentage of fine grained particles and the percentage of clay sized particles. Apparatus 1. Balance capable of measuring to 0.1 g 2. Evaporating dish 3. Mechanical mixer and mixing cup to assist in dispersing the soil 4. Type 152H hydrometer which reads grams of soil per 1000 ml. of slurry ml. cylinders, ml. glass sedimentation cylinder 6. Rubber stopper 7. Thermometer 1 ASTM D (Reapproved 1998) Hydrometer Analysis 1

3 Calculations For Type 152H hydrometers, the velocity v is equal to L/T, and Equation 2 is written as D where K L /T (3) K = a constant depending on the specific gravity of the solids and the temperature of the fluid (mm x (min/cm) 1/2 ), given in the Table 1; L = effective depth in cm. of the hydrometer which is the distance from the surface of the suspension to the center of the hydrometer bulb (cm); T = elapsed time (min). For Type 152H hydrometers, the effective depth can be given as L = R (4) where R is the reading on the hydrometer in grams of solids per liter of suspension. The effective depth is the distance that the soil has settled that can then be used to calculate velocity. The equation for the percentage of the soil remaining in suspension is P = (R c a / M s ) x 100% (5) R c = Actual hydrometer reading - zero correction, Cz + temperature correction, C T (6) where the zero correction is obtained as described in laboratory step (1) above and C T, given in the Table 1, is a factor that accounts for variation in the density of the soil-water suspension for different temperatures. a = correction factor required when the specific gravity of the soil grains is not equal to 2.65 and given by the following equation 1.65 Gs a 2.65 Gs 1 M s = oven dry mass in g of the soil sample dispersed in preparation step (2). Results Complete the Table 2 on the next page using Equations 3 though 7 and temperature dependent constants provided in Table 1. The grain size distribution is plotted on Figure 1, since the particle diameter and percent of soil in suspension, equivalent to the percent finer, are computed. (7) Hydrometer Analysis 3

4 Table 1 Temperature Dependent Fluid Constants K (ASTM Type 152H Hydrometer) Temperature Specific Gravity of Soil, G s o C C T Table 2 Calculation Sheet for Hydrometer Analysis Hydrometer Analysis Group Date Soil Description Oven Dry Soil Mass, M s Specific Gravity, G s Zero Correction, C z Specific Gravity Correction, a Elapsed Hydrometer Corrected Percent Time Reading Temp. L D Reading, Finer, min R ( o C) (K) (cm) (mm) C T R c P Hydrometer Analysis 4

5 100% 80% Percent Finer 60% 40% 20% 0% Particle Diameter, mm Figure 1 Grain Size Distribution of Fine-Grained Soil Conclusions Is the grain size distribution curve representative of the type of soil tested in the laboratory? How would it affect the results if the test were conducted when the temperature was 5 o C higher? What is the percent finer than the # 200 sieve (0.075 mm) and the percent finer than 0.002mm (clay particles)? What correction would be required if the soil was first sieved and it was determined that the hydrometer sample included only 60% of the total soil sample, i. e. the other 40% was larger in diameter than any of the grain diameters measured? Hydrometer Analysis 5

6 1000-ml Cylinders Hydrometer Thermometer And Timer Rubber Stopper Picture 1!000-ml Cylinders and Hydrometer Mixer and Mixing Cup Evaporating Dish Picture 2 Mixer and Mixing Cup Hydrometer Analysis 6

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