Permeability versus degree of saturation for various sands (courtesy of John Wiley & Sons, Inc. 200 ) e. Hydraulic Gradient. The hydraulic gradient (2-16) where H = head loss L = length over which head loss occurs 2-13
EM 1110-2-1901 30 Sep 86 at which permeability is measured can have a significant influence on the coefficient of permeability computed from Darcy's law under certain condi- tions. The maximum hydraulic gradient for which laminar flow occurs for a particular soil at a given density may be determined in the laboratory by plotting the discharge velocity (2-17) versus the hydraulic gradient as shown in figure 2-8. A straight line relationship indicates laminar flow (2-18) while deviations from the straight line at high gradients indicate turbulent flow. Darcy's law for a fine sand, as shown in figure 2-8, is valid only for the hydraulic gradient less than 2 for the loose state and 4.5 for the dense state. For soils larger than a fine sand, Darcy's law is valid for progres- sively smaller hydraulic gradients (Burmister 1948 and Burmister 1955). f. Particle Size. For cohesive soils, the permeability increases with increases in clay mineral size and increase in void ratio (ratio of the volume of voids to the volume of solid particles in the soil mass) as shown in figure 2-9 (Yong and Warkentin 1966). (l) For cohesionless soils, the size and shape of the soil particles influence the permeability. Allan Hazan conducted tests on filter sands for use in waterworks and found that for uniform loose clean sands the permeability was given by (Taylor 1948) (2-19) where k - coefficient of permeability in cm per second D 10 = particle size in cm at which 10 percent of the material is finer by weight (also known as Hazen's effective size) (1) As shown in table 2-2, the exchangeable cation present influences the permeability of clay minerals at constant void ratio (Scott 1963). The permeabilities are much smaller when the exchangeable cation is sodium which is one of the reasons why sodium montmorillonite is used to seal reservoirs. 2-14
EM 1110-2-1901 30 Sep 86 Figure 2-8. Determination of maximum hydraulic gradient for which laminar flow occurs for a fine sand (courtesy of American Society for Testing and Materials 147 ) Hazen's experiments were made on sands for which 0.1 mm < D 10 < 0.3 mm and the uniformity coefficient, C u < 5 , where where C u = uniformity coefficient D 60 = particle size at which 60 percent of the material is finer by weight (2-20) The coefficient 100 is an average of many values which ranged from 41 to 146, but most of the values were from 81 to 117. Equation 2-19 makes no allowance for variations in shape of the soil particles or void ratio. 2-15
EM 1110-2-1901 30 Sep 86 a. Edge view sketch to show relative size and shape of clay particles (dimension not shown in length) b. Permeability versus void ratio for various clay minerals Figure 2-9. Influence of particle size and void ratio on permeability of clay minerals (courtesy of Macmillan 294 ) 2-16
EM 1110-2-1901 30 Sep 86 Table 2-2. Coefficients of Permeability for Different Exchange Cations and Void Ratios for Two Clay Minerals a
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