Transcript Document
Movement of Water Through Soils Hydraulic Conductivity Laboratory Tests Empirical Relations Field Tests Flow Nets Capillary Rise Hydraulic Conductivity Bernoulli’s Equation Total Head is calculated as a summation of pressure, velocity, and elevation heads h = (u/gw) + (v2/2g) + Z Velocity head (v2/2g) typically neglected Water Flow Through Soils Dh=ha-hb i = Dh/L Fig 5.1 in Text Water Flow Through Soils Fig 5.2 in Text Darcy’s Law Assumes laminar flow Discharge velocity is directly related to the product of hydraulic conductivity times hydraulic gradient v=ki Discharge vs Seepage Velocity Discharge Velocity,v – Factitious velocity of flow through gross crosssectional area of soil (v = ki) Seepage Velocity,vs – Factitious velocity of flow through void spaces in soil (vs = v/n) Discharge vs Seepage Velocity Fig 5.3 in Text Hydraulic Conductivity Hydraulic conductivity of soils related to several soil factors: Fluid viscosity Grain-size distribution Pore-size distribution Void ratio Degree of saturation Hydraulic Conductivity Table 5.1 (p 96) Typical Values Clean Gravel – 100 to 102 cm/sec Coarse Sand – 10-2 to 100 cm/sec Fine Sand – 10-3 to 10-2 cm/sec Silty Sand – 10-5 to 10-3 cm/sec Clays - < 10-6 cm/sec Laboratory Measures Constant Head Test Suitable for clean sands and gravels with relatively high hydraulic conductivities Falling Head Test Suitable for dirty sands and fine grained silts and clays with appreciably lower hydraulic conductivity Constant Head Test Fig 5.4 in Text Constant Head Test q = Q/t = k i A Q = captured volume of water (cc) T = time of capture (sec) k = hydraulic conductivity (cm/sec) i = hydraulic gradient (cm/cm) A = cross-sectional area of flow (cm2) Constant Head Test k=QL/Aht Tests can be conducted at varying hydraulic gradients to assess impact of head differential on flow regime Falling Head Test Fig 5.5 in Text Falling Head Test k = (aL/At) ln (h1/h2) k = 2.303 (aL/At) log (h1/h2) Empirical Relations Hazen’s equation – developed for loose, clean filter sands with fairly uniform gradation (Cu -> 1) k (cm/sec) = D102 (mm) Casagrande – developed for fine to medium clean sands k = 1.4 e2 k0.85 Empirical Relations Equations 5.19 to 5.24 in Text Be careful whenever using empirical relationships – examine basis for relationship and limits of observations used interpolations/extrapolations Tavenas, et al., 1983 US Dept of Navy, 1971