Particle Size of Fine-Grained Soils
The screening process cannot be used for fi ne-grained soils—silts and clays—because of their extremely small size. The common laboratory method used to determine the size distribution of fi ne-grained soils is a hydrometer test (Figure ). The hydrometer test involves mixing a small amount of soil into a suspension and observing how the suspension settles in time. Larger particles will settle quickly, followed by smaller particles. When the hydrometer is lowered into the suspension, it will sink into the suspension until the buoyancy force is suffi cient to balance the weight of the hydrometer.
Hydrometer in soil–water suspension.
The length of the hydrometer projecting above the suspension is a function of the density, so it is possible to calibrate the hydrometer to read the density of the suspension at different times. The calibration of the hydrometer is affected by temperature and the specifi c gravity of the suspended solids. You must then apply a correction factor to your hydrometer reading based on the test temperatures. Typically, a hydrometer test is conducted by taking a small quantity of a dry, fi ne-grained soil (approximately 50 grams) and thoroughly mixing it with distilled water to form a paste. The paste is placed in a 1-liter glass cylinder, and distilled water is added to bring the level to the 1-liter mark. The glass cylinder is then repeatedly shaken and inverted before being placed in a constant-temperature bath. A hydrometer is placed in the glass cylinder and a clock is simultaneously started. At different times, the hydrometer is read. The diameter D (cm) of the particle at time tD (seconds) is calculated from Stokes’s law as
where m is the viscosity of water [0.01 gram/(cm.s) at 208C], z is the depth (cm), rw is the density of water (1 gram/cm3), g is the acceleration due to gravity (981 cm/s2), and Gs is the specifi c gravity of the soil particles. For most soils, Gs < 2.7.
In the application of Stokes’s law, the particles are assumed to be free-falling spheres with no collision. But the mineral particles of clays are platelike, and collision of particles during sedimentation is unavoidable. Also, Stokes’s law is valid only for laminar fl ow with Reynolds number , where v is velocity, D is the diameter of the particle, gw is the unit weight of water, m is the dynamic viscosity of
water at 208C, and g is the acceleration due to gravity) smaller than 1. Laminar fl ow prevails for particle sizes in the range 0.001 mm , Ds , 0.1 mm. By using the material passing the No. 200 sieve (average particle size ,0.075 mm), laminar fl ow is automatically satisfi ed for particles less than 0.001 mm.
Particles smaller than 0.001 mm are colloids. Electrostatic forces infl uence the motion of colloids, and Stokes’s law is not valid. Brownian motion describes the random movement of colloids. The results of the hydrometer test suffi ce for most geotechnical engineering needs. For more accurate size distribution measurements in fi ne-grained soils, other, more sophisticated methods are available (e.g., light-scattering methods). The dashed line in Figure shows a typical particle size distribution for fine-grained soils.