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Flow through Soils (ch7)

Flow through Soils (ch7). Energies. Kinetic E (velocity) Strain E (fluid pressure) Potential E (elevation) Head : convert each form of energy into the equivalent potential energy and express it as the corresponding height . units of LENGTH. Heads. h v = velocity head (KE)

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Flow through Soils (ch7)

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  1. Flow through Soils(ch7)

  2. Energies Kinetic E (velocity) Strain E (fluid pressure) Potential E (elevation) Head:convert each form of energy into the equivalent potential energy and express it as the corresponding height. units of LENGTH

  3. Heads hv = velocity head (KE) hp = pressure head (SE) he = elevation head (PE) h = total head = hv + hp + he (Bernoulli) units of LENGTH

  4. Heads in a tank of water… A B

  5. h1 2 h2 1 l Head loss Fluid flows from point of high total head to point of low total head head loss = Dh = h1 – h2

  6. Hydraulic gradient Rate at which the total head changes along a length

  7. Heads in soils Since velocity is slow through soils, we neglect the velocity head. Thus,

  8. hp Pressure head at A. Soil piezometer A The “pore water pressure” at A is

  9. Pore water pressures uhydrostatic = uh = due to hydrostatic condition only uexcess = ue = due to additional processes

  10. zw1 zw zw2 Depth, z Hydrostatic pore water pressure

  11. One dimensional flow Flow vectors: parallel of equal magnitude SOIL Flow is in one direction

  12. Flowrate through soil What is the flowrate through a soil? Concrete dam Flowrate = Q [m3/sec] SOIL

  13. Cross-sectional area to flow Hydraulic conductivity “permeability” [cm/s] Hydraulic gradient Darcy’s Law Assumptions: flow is laminar soil properties do not D with time

  14. Dh A L Finding k Measure Q Figure 7.11 (text)

  15. fluid soil k Measure of a soil-fluid system’s resistance to flow depends on Void size Fabric (structure) Void continuity Specific surface (drag) Viscosity Mass density

  16. k Units are in cm/sec but k = velocity

  17. TYPICAL VALUES [cm/s] SOIL 101 – 102 gravel k sands 10-3 – 100 10-8 – 10-3 silts clays 10-10 – 10-6 Probably soil’s most varying parameter (largest numerical range)

  18. Soil specimens sand clay “seam” 1 sand 2 Lab testing k1 = 10-2 k2 = 10-6 k – precision is on the order of +/- 50% or more! Report values to one decimal place.

  19. Dh A L Lab testing (constant head test) Measure Q Figure 7.11 (text)

  20. In-situ testing Slug test Pumping test

  21. USE THESE UNITS! Hazen’s Correlation k a pore size ~ (pore diameter)2 (pore diameter) ~ D10 For loose clean sands with 0.1mm < D10 < 3mm and Cu < 5 k = [cm/sec] C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1) D10 = [mm]

  22. el. = 167.3m clay el. = 165m clay sand seam 256 m 3.2 m Example Given: ksand = 4x10-2 cm/sec reservoir length (into board) = 1000 m Compute seepage loss (Q) through the sand seam

  23. Q = kiA = 0.0115 m3/sec = 41.5 m3/hr Solution Q = kiA k = 4x10-2 cm/sec i = Dh/L = (167.3m – 165m) / 256m = 0.009 A = (3.2 m) (1000 m) = 3200 m2

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