1 One Dimensional Seepage

8/10/2019 1 One Dimensional Seepage

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Priyantha Jayawickrama, Ph.D.

Associate Professor

One-Dimensional SeepagePermeability and Darcys Law

Texas Tech UniversityDepartment of Civil and Environmental Engineering


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CE 5321-001: Advanced Soil Engineering 2

References

Chapters 17, 18 and 19,

Lambe and Whitman, John Wiley

Chapter 17: One-dimensional flowChapter 18: Two-dimensional flow

Chapter 19: Soil Permeability and Filter

Requirements


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Permeability and Seepage

Why would geotechnical engineers be

concerned with this topic?

What applications come to mind?

What are the principles governing this

process?


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Subsurface Water

Vadose Zone

(zone of aeration)

Ground Surface

capill ary fr inge Water Table

(Phreatic Surface)

Zone of Phreatic Water

(zone of saturation)


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Artesian Conditions

Confined

sandstone

aquifer

Impermeable

shale

Non-flowing

well

Artesian pressure

surface


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Seepage Illustration:Loop 287, Lufkin, TX


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Roadbed Excavation in Sandy Soilk 1 x 10 -4cm/sec


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High Head: Dewatering Required(grid of French drains)


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Antilley Road Bridge, Abilene


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Antilley Road Bridge,Abilene

30-ft

100.1-ft92.3-ft

79.9-ft

61.6-ft

67.3-ft

61.4-ft

70.0-ft

Seepage location


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CE 5321-001: Advanced Soil Engineering

11

To Estimate Seepage Loss

Seepage through the body of the dam


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To Estimate Seepage LossSeepage through the body of the dam and the foundation soil


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To Estimate Seepage LossSeepage through the body of the dam and the foundation soil

Anisotropic Soil


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To Estimate Pore WaterPressures


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15

15

To Estimate Pore Water Pressures


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16

16

To Evaluate Quicksand Conditions


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17Dewatering Excavations

Other ApplicationsDewatering System Design
http://images.google.com/imgres?imgurl=http://www.godwinpumps.com/images/Wellpointphoto.jpg&imgrefurl=http://www.godwinpumps.com/wellpoint.html&h=253&w=400&sz=33&tbnid=LbTzrFXsfrcJ:&tbnh=75&tbnw=120&hl=en&start=10&prev=/images%3Fq%3Ddewatering%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN


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Other ApplicationsDrainage System Design

Pavement Drainage


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Drainage behind Retaining Walls



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21



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H

b

d

w

1

2 3

4

P



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Flow through soil and rockmaterial Soil and rock are porous

materials

Fluid flow takes place through

interconnected void spacesbetween particles and notthrough the particlesthemselves

No soil or rock material isstrictly impermeable


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Question

What causes flow of waterthrough soil?

Answer:

A difference in TOTAL HEAD

We will focus on Water Movement withinSaturated Soils!


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Total Head = pressure head +elevation head

soil

No Flow!

5ft 5ft


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soil

Flow from left to right!

5ft

9ft



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soil

Flow from left to right!



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5ft

5ft7ft



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Comments re: Total Head

A differencein to tal headis required to cause

movement of water through soil.

Total head is measured in units of length;e.g., feet or meters; not psf, kPa, etc.

Darcys Law, governing fluid flow through a

porous medium, takes this one step further:


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Pressure Head, hp= pressure/w

Elevation Head, he= distance from

datum

Total head = hp+ he

Velocity head is negligibly small, e.g.at flux = 2ft/min, velocityhead=0.00002 ft.

Total Head


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How do you estimate flow rate ?

Flow rate will be controlled by Difference in total head between Point A & Point B

Distance between Point A & Point B

Type of Soil

5ft

5ft7ft

A

B


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Some Definitions

Quantity of Flow, Q Cu.ft

Flow Rate, q = Q/t Cu.ft/min

Flux, v = q/A Cu.ft/min/sq.ft = ft/min

5ft

5ft7ft

A

B


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Some Definitions

Hydraulic Gradient, i (no units)

L

h

L

HHi

AB

BA

5ft

5ft7ft

A

B


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Darcys Law

k= coefficient of permeability

i = hydraulic gradient (i < 5, laminar flow)

L

hi

A

tQ

A

qv

)/(

ikv


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Darcys Law; Applications

Elev. 0 ft

Elev. 30 ft

12ft

57ft

Confined Aquifer

Very low

permeable

soil


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Coefficient of Permeability

k= coefficient ofpermeability, or

hydraulic conductivity

k depends on the poresize in the soil


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Some typical k - values

uniform coarse sand .. k = 4 x 10 -1cm/sec

clean sand & gravel.. k = 1 x 10 -2cm/sec

silty sand . k = 1 x 10 -4cm/sec

sandy clay .. k = 5 x 10 -6cm/sec

Compacted clay .. k = 1 x 10 -7cm/sec


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Order of Magnitude ofk - values

Uniform coarse sand is1000 times more

permeable thansilty sand

Silty sand is 1000 times more permeable thanCompacted clay

Coarse Sand . Drainage Layers

Compacted Clay . Liner Material for Ponds


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Empirical relationships toestimate permeability, k

21010Dk

2155.3 Dk


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Grain Size Distribution Curves


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Head DistributionBelow Ground Water Table


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Head DistributionAbove Ground Water Table


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Calculation of Pressure Head inSeepage Conditions


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Oil Refinery Site, Kawasaki, Japan

Previously, for static ground water conditions

(Chapter 16, Lambe and Whitman)

Now modified for steady seepage conditions

See Handout

Calculation of Effective Stress underSeepage Conditions


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+4

-11

-21

-36

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C l l i f Eff i S d


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Calculation of Effective Stress underSeepage Conditions


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Calculating Seepage Force


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Calculating Seepage Force

This is what you havewhen upward seepage

is occurring

This is what you wouldhave had under staticwater conditions

The differencerepresents the energylost due to seepage


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Calculating Seepage Force, iw

L


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Consider:

Boundary water forces + Total weights

OR seepage forces + submergedweights

Seepage force/volume = iw

Force Equilibrium


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Evaluating Quick Conditions


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Evaluating Quick Sand Conditions

wstwv hqba

:00 sqandaWhen

wtv hbb )(

wwtv hb )(

0: vc andiiconditionsquickFor

w

sub

w

wt

c

cwwtb

hihb

)(,thereforeand)(0


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FOS against Quick SandConditions

w

sub

w

wt

c

cb

hi

)(

Factor of Safety against quicksand conditions, F

actual

c

i

iF

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1 One Dimensional Seepage