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Published byJudah Batterton Modified about 1 year ago

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Flow through Soils (ch7)

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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

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Heads h v = velocity head (KE) h p = pressure head (SE) h e = elevation head (PE) h = total head = h v + h p + h e (Bernoulli) units of LENGTH

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Heads in a tank of water… A B

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Head loss 1 2 l h2h2 h1h1 Fluid flows from point of high total head to point of low total head head loss = Dh = h 1 – h 2

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

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

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

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Pore water pressures u hydrostatic = u h = due to hydrostatic condition only u excess = u e = due to additional processes

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Hydrostatic pore water pressure z w1 z w2 Depth, z zwzw

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

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Flowrate through soil What is the flowrate through a soil? SOIL Concrete dam Flowrate = Q [m 3 /sec]

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

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L hh A Measure Q Figure 7.11 (text) Finding k

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

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k Units are in cm/sec but k = velocity

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k sands silts clays SOIL TYPICAL VALUES [cm/s] gravel 10 1 – 10 2 10 -3 – 10 0 10 -8 – 10 -3 10 -10 – 10 -6 Probably soil’s most varying parameter (largest numerical range)

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

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L hh A Measure Q Figure 7.11 (text) Lab testing (constant head test)

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Slug test Pumping test In-situ testing

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k pore size Hazen’s Correlation ~ (pore diameter) 2 (pore diameter) ~ D 10 For loose clean sands with 0.1mm < D 10 < 3mm and C u < 5 k = [cm/sec] C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1) D 10 = [mm] USE THESE UNITS!

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

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Solution Q = kiA k = 4x10 -2 cm/sec i = h/L = (167.3m – 165m) / 256m = 0.009 A = (3.2 m) (1000 m) = 3200 m 2 Q = kiA = 0.0115 m 3 /sec = 41.5 m 3 /hr

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