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Geotechnical Engineering and Applications

– CE 3413 –

Jie Huang, Ph.D., PE

University of Texas-San Antonio

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Topic – 7

Permeability & Seepage (Chapter 7 & 8)

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Chapter 7 Permeability Bernoulli Equation (7.1) Darcy’s Law (7.2) Permeability (hydraulic conductivity) (7.3) Tests for permeability (7.4) Equivalent permeability in stratified soil (7.8)

Lab testing (7.4)

Field testing (7.9)

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Bernoulli’s Equation

Pressure head

Velocity head

Elevation head

Total head

Even though the units of these heads are the same as the units of length, they represents the energy.

Unit: inches, feet, yards

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Hydraulic Gradient Point A:

Point B:

Hydraulic gradient (In reality it is the energy loss per unit flow distance).

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Darcy’s Law

Permeability (hydraulic conductivity)

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Application of Darcy’s Law

(Darcy’s Law)

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Darcy’s Law

Real velocity (seepage velocity)

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Permeability

•Fluid viscosity •Pore size distribution •Grain size distribution •Void ratio •Roughness of mineral particles •etc.

K= f(fluid, viscosity, size distribution, void ratio,……)

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Typical Permeability Values

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Lab Tests for Permeability

Constant Head Test Falling Head Test

Constant Head Test

constant

Given: Flow distance, L Cross-section area, A Water head, h Measurements: Time, t Volume of water, Q

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Falling Head Test Given: Flow distance, L Cross-section area, A Standpipe cross-section, a

Measurements: Time, t Water head, h1 and h2

L

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Falling Head Test Given: L, A, a

Measurements: t, h1, h2

L

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Exercise Ask: q

Given: the sketch

Equivalent Hydraulic Conductivity in Stratified Soil

SW, k1

SP, k3 SC, k2

MH, k4

Flow perpendicular to layers

SW, k1

SP, k3 SC, k2

MH, k4

Flow parallel to layers

Then, how to use Darcy’s law,

How to determine k

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Flow Perpendicular to Layers

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Flow Parallel to Layers

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Exercises

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Field Tests for Permeability Pumping from Wells

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1: Underlain by Impermeable Layer

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2: Confined by Impermeable Layer

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Chapter 8 Seepage Laplace Equation for continuity (8.1) Continuity Equation to solve simple problems (8.2) Flow net (8.3) Seepage calculation from flow net (8.4) Uplift pressure under hydraulic structures (8.7)

Laplace Equation of Continuity Governing equation:

Continuity equation

&, if (isotropic)

Using Continuity Equation to Solve Simple Problem

(A1 and A2 are constants .)

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Flow Net

Flow line: the path water “particle” travels

Equipotential line: a line along which the water heads are equal

Principle of flow net: flow lines are perpendicular to equipotential lines

Flow Net Components

Equipotential line

Flow line

After Philip Bedient Rice University

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Flow Net Formulation

Nf: number of flow channels Nd: number of potential drops

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How to Draw Flow Net Drawing Method:

1. Draw to a convenient scale the geometry of the flow field.

2. Establish constant head and no-flow boundary conditions

3. Draw one or two flow lines and equipotential lines near the boundaries.

4. Sketch intermediate flow lines and equipotential lines by smooth curves

adhering to right-angle intersections and square grids. Where flow direction is a

straight line, flow lines are an equal distance apart and parallel.

5. Continue sketching until a problem develops. Each problem will indicate

changes to be made in the entire net. Successive trials will result in a

reasonably consistent flow net.

6. In most cases, 5 to 10 flow lines are usually sufficient. Depending on the

number of flow lines selected, the number of equipotential lines will

automatically be fixed by geometry and grid layout. After Philip Bedient Rice University

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Non-square Grid Flow Net (square grids)

(rectangular grids)

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Example

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Questions!!!