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Movement of Water Through Soils

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

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Movement of Water Through Soils

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  1. Movement of WaterThrough Soils • Hydraulic Conductivity • Laboratory Tests • Empirical Relations • Field Tests • Flow Nets • Capillary Rise

  2. 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

  3. Water Flow Through Soils Dh=ha-hb i = Dh/L Fig 5.1 in Text

  4. Water Flow Through Soils Fig 5.2 in Text

  5. Darcy’s Law • Assumes laminar flow • Discharge velocity is directly related to the product of hydraulic conductivity times hydraulic gradient • v = k i

  6. Discharge vs Seepage Velocity • Discharge Velocity,v – Factitious velocity of flow through gross cross-sectional area of soil (v = ki) • Seepage Velocity,vs – Factitious velocity of flow through void spaces in soil (vs = v/n)

  7. Discharge vs Seepage Velocity Fig 5.3 in Text

  8. Hydraulic Conductivity • Hydraulic conductivity of soils related to several soil factors: • Fluid viscosity • Grain-size distribution • Pore-size distribution • Void ratio • Degree of saturation

  9. 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

  10. 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

  11. Constant Head Test Fig 5.4 in Text

  12. 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)

  13. Constant Head Test • k = Q L / A h t • Tests can be conducted at varying hydraulic gradients to assess impact of head differential on flow regime

  14. Falling Head Test Fig 5.5 in Text

  15. Falling Head Test • k = (aL/At) ln (h1/h2) • k = 2.303 (aL/At) log (h1/h2)

  16. 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

  17. 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

  18. Tavenas, et al., 1983 US Dept of Navy, 1971

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