darcy law and soil permeability

CE5101 Lecture 2CE5101 Lecture 2

Darcy’s Law and Soil P biliPermeability

bybyProf Harry Tan

A 2011Aug 2011

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O tlineOutline

• Soil and Ground Water Conditions• Unsaturated and Saturated Soils• Balance Equations• Balance Equations• What is Darcy’s Law?y• Permeability • Lab Measurement of k

Fi ld M t f k• Field Measurement of k

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Soil and Gro nd WaterSoil and Ground Water

• Soil are products of weathering forming:R id l S il ( th d i l )– Residual Soils (weathered in place)

– Transported Soils (displaced by wind or water)

• Physical weathering produce soil particlesPhysical weathering produce soil particles of gravels, sands and siltsCh i l th i d l• Chemical weathering produce clay minerals – Kaolin, Illite and Montmorillonite (bentonite)

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Gro nd aterGround water

• All soils are permeable (porous medium) and water flow through interconnectedand water flow through interconnected pores of void spaces

• Saturated soils when voids are completely filled with ground waterfilled with ground water

• Unsaturated soils when voids are partially fill d ith t d i i th f ffilled with water and air in the form of occluded bubbles held by tension capillary y p ystresses

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Gro nd Water TableGround Water Table• Pressure of pore water is measured relative toPressure of pore water is measured relative to

atmospheric pressure Pa (taken as zero pore pressure)pressure)

• The water table (GWT) or phreatic surface is the level at Pa or zero pore pressurelevel at Pa or zero pore pressure

• Atmospheric pressure = 1 bar or 14.7 psi or 100 kPa)kPa)

• Below the WT, the soil is assumed to be fully saturated (positive pore water pressure)saturated (positive pore water pressure)

• Above the WT, the soil is unsaturated (negative pore water pressure or pore water tension orpore water pressure or pore water tension or suction) where we have capillary water in Vadose Zone

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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Unsat rated/Sat rated SoilsUnsaturated/Saturated Soils

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T pes of GWTTypes of GWT

• Hydrostatic• Seepage• Perched WT• Perched WT• Artesian WT

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Hydrostatic GWTHydrostatic GWTAbove WT, pore water held at negative pressure by capillary tension; smaller pores give higher capillary rise;

whu *2

capillary tension; smaller pores give higher capillary rise; in general degree of saturation decrease with height

w2

GWTunsaturated h2 • Soil is saturated below GWT

• GWT is dependent on local

h *1

Saturated soil

pclimate; balance of precipitation, evaporation and plant evapo-transpiration

whu *1soil

h1

plant evapo-transpiration

• GWT is also affected by construction activities,

whu *1

,especially excavations

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Perched GWTPerched GWT

• Occur locally, contained by soil of low bilit b l GWTpermeability above normal GWT

Perched WT

GWTClay lens

Sandy Soils

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Artesian GWTArtesian GWTInclined soil layer of high permeability is confined locally by overlying y g p y y y y gclayey soil; the pressure in the artesian layer is governed by a higher WT at a distant location where layer is unconfined

GWTGWT

GWTClayey Soils – Cap or Aquiclude Artesian PWP

Sandy Soils ( Confined Aquifer)

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Balance Eq ationsBalance Equations

Fluid Mechanics• Balance of Mass (Continuity)• Balance of Momentum• Balance of Momentum• Balance of Energy (Heat)gy ( )• Most physical problems need the 1st two

balance equations• If heat not important 3rd equation is• If heat not important, 3rd equation is

ignored for flows in soils21

Contin it Eq ationContinuity Equatione

VVve

een

1

P v

Vs

P vx

x1 x1+vx∆t

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yH G

D C

x

FE

zA B

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Darcy’s Law (Conservation of y (momentum of fluid flow)

x

FD is drag force of soil skeleton on flowing water

FD

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PermeabilityPermeability

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PermeabilityPermeability

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PermeabilityClay Silt Sand Gravel Cobble Fine Medium Coarse Fine Medium Coarse Fine Medium Coarse <0.0020.002 mm 0.002

0.006 0.02 0.06 0.2 0.6 2 6 20 >60

<10-9 m/s

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

>1 m/s

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Meas rements of PermeabilitMeasurements of Permeability

• Laboratory Methods– Constant head test– Falling head testFalling head test– Hydraulic cell Test

• Field MethodsSteady state field pumping tests– Steady state field pumping tests

– Falling head bore hole tests– Rapid test

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Constant head permeameterConstant head permeameterSt d t t t tSteady state test

Fl Q/Flow rate q=Q/t

Hydraulic gradient i=h/l

Darcy’s law: v=ki or q=vA = kiA

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Example 1 – Constant head test

Temperature correction due to effect on viscosity of water η, which increase with higher temperature

Kk w

2

oC KT

K=absolute permeability in m2

10 1.29915 1.13320 1.00025 0.90630 0 80830 0.80840 0.670

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Falling head permeameter

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Example 2 – Falling head test

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Hydraulic cell permeameter – vertical k

Steady state is assumed whenSteady state is assumed when inflow and outflow < 10% difference

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Example 3 – Hydraulic cell testExample 3 Hydraulic cell test

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Hydraulic cell permeameter – horizontal k

Steady state is assumed when inflow and outflow < 10% differenceinflow and outflow < 10% difference

Theory – see pumping test

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Field Permeability Steady State Pumping Tests in Confined AquiferConfined Aquifer

Confined aquifer: i=dh/dr and A=2πrD

P i t l h t k d d b t f if44

Pumping rate low enough to keep drawdown above top of acquifer

Pumping Test in Confined Aquifer

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Example 4 – Pumping Test in Confined Aquifer

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Example 4 – Pumping Test in Confined Aquifer

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Field Permeability Steady State Pumping Tests in Unconfined AquiferUnconfined Aquifer

Confined aquifer: i=dh/dr and A=2πrD

P i t l h t k d d b t f if48

Pumping rate low enough to keep drawdown above top of acquifer

Field Permeability Steady State Pumping Tests in Unconfined AquiferUnconfined Aquifer

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Field Permeability Steady State Pumping Tests inField Permeability Steady State Pumping Tests in Unconfined Aquifer

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Example 5 Pumping Tests in Unconfined Aquifer

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Example 5 Pumping Tests in Unconfined Aquifer

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Borehole TestsBorehole Tests

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Rapid Field Test

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