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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 hv = velocity head (KE) hp = pressure head (SE)**

he = elevation head (PE) h = total head = hv + hp + he (Bernoulli) units of LENGTH

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**Heads in a tank of water…**

B

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**Head loss l head loss = Dh = h1 – h2**

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

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

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

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

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

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

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**Hydrostatic pore water pressure**

Depth, z zw zw1 zw2

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**One dimensional flow SOIL Flow is in one direction**

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

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**Flowrate through soil SOIL Flowrate = Q [m3/sec]**

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

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**Darcy’s Law Assumptions: flow is laminar**

soil properties do not D with time Cross-sectional area to flow Hydraulic conductivity “permeability” [cm/s] Hydraulic gradient

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

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**k fluid soil Measure of a soil-fluid system’s resistance to flow**

depends on soil fluid 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 SOIL TYPICAL VALUES [cm/s] gravel 101 – 102 sands 10-3 – 100 silts**

10-8 – 10-3 clays 10-10 – 10-6 Probably soil’s most varying parameter (largest numerical range)

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**Lab testing sand clay “seam” k1 = 10-2 k2 = 10-6**

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

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**Lab testing (constant head test)**

Dh A L Measure Q Figure 7.11 (text)

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In-situ testing Slug test Pumping test

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**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 USE THESE UNITS! k = [cm/sec] C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1) D10 = [mm]

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**Example Compute seepage loss (Q) through the sand seam el. = 167.3m**

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

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**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 Q = kiA = m3/sec = 41.5 m3/hr

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