1CE5101 Lecture 2

Darcys Law and Soil Permeability

byProf Harry Tan14 Aug 2013

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2Outline Soil and Ground Water Conditions Unsaturated and Saturated Soils Balance Equations What is Darcys Law? Permeability Lab Measurement of k Field Measurement of k

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3Soil and Ground Water Soil are products of weathering forming:

Residual Soils (weathered in place) Transported Soils (displaced by wind or

water) Physical weathering produce soil particles

of gravels, sands and silts Chemical weathering produce clay

minerals Kaolin, Illite and Montmorillonite (bentonite)

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4Ground water All soils are permeable (porous medium)

and water flow through interconnected pores of void spaces

Saturated soils when voids are completely filled with ground water

Unsaturated soils when voids are partially filled with water and air in the form of occluded bubbles held by tension capillary stresses

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5Ground Water Table Pressure of pore water is measured relative to

atmospheric pressure Pa (taken as zero pore pressure)

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

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

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

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

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6Unsaturated/Saturated Soils

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7Unsaturated/Saturated Soils

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8Unsaturated/Saturated Soils

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9Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Unsaturated/Saturated Soils

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Types of GWT Hydrostatic Seepage Perched WT Artesian WT

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Hydrostatic GWT

whu *1=

whu *2=

GWTunsaturated

Saturated soil

h1

h2

whu *1=

Soil is saturated below GWT GWT is dependent on local climate; balance of precipitation, evaporation and plant evapo-transpiration GWT is also affected by construction activities, especially excavations

Above WT, pore water held at negative pressure by capillary tension; smaller pores give higher capillary rise; in general degree of saturation decrease with height

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Perched GWT Occur locally, contained by soil of low

permeability above normal GWT

GWTClay lens

Perched WT

Sandy Soils

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Artesian GWT

GWTClayey Soils Cap or Aquiclude

Sandy Soils ( Confined Aquifer)

Artesian PWP

GWT

Inclined soil layer of high permeability is confined locally by overlying clayey soil; the pressure in the artesian layer is governed by a higher WT at a distant location where layer is unconfined

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

balance equations If heat not important, 3rd equation is

ignored for flows in soils8/14/2013

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Continuity Equation

P vx

x1 x1+vxt

VsVv

e

e

en

=

+=

1

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x

z

y

A

H G

FE

D C

B

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Darcys Law (Conservation of momentum of fluid flow)

x

FD

FD is drag force of soil skeleton on flowing water

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Permeability

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Permeability

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PermeabilityClay Silt Sand Gravel Cobble Fine Medium Coarse Fine Medium Coarse Fine Medium Coarse 60

1 m/s

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Measurements of Permeability Laboratory Methods

Constant head test Falling head test Hydraulic cell Test

Field Methods Steady state field pumping tests Falling head bore hole tests Rapid test

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Constant head permeameterSteady state test

Flow rate q=Q/tHydraulic gradient i=h/l

Darcys law: v=ki or q=vA = kiA

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Example 1 Constant head test

oC KT10 1.29915 1.13320 1.00025 0.90630 0.80840 0.670

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

Kk w

=

K=absolute permeability in m2

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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 when inflow and outflow < 10% difference

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Example 3 Hydraulic cell test

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Hydraulic cell permeameter horizontal kSteady state is assumed when inflow and outflow < 10% differenceTheory see pumping test

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Field Permeability Steady State Pumping Tests in Confined Aquifer

Confined aquifer: i=dh/dr and A=2rDPumping rate low enough to keep drawdown above top of acquifer8/14/2013

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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 Aquifer

Confined aquifer: i=dh/dr and A=2rDPumping rate low enough to keep drawdown above top of acquifer8/14/2013

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Field Permeability Steady State Pumping Tests in Unconfined Aquifer

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Field 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 Tests

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Rapid Field Test

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