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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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Environmental Engineering Lecture Note Week 10 (Transport Processes) Joonhong Park Yonsei CEE Department 2016. 5. 11 CEE3330 Y2013 WEEK3.

Environmental Engineering Lecture Note Week 10 (Transport Processes) Joonhong Park Yonsei CEE Department 2016. 5. 11 CEE3330 Y2013 WEEK3.

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