Flownet Seepage

Sepaage and flownets

Lecture 4

References

Braja M Das, Principal of Geotechnical Engineering, fourth edition, PWS Publishing Company, 1998, BostonMuni Budu, Soil Mechanics and Foundations, 2ndedition, John Wiley & Sons, 2007, USAR.F. Craig, Soil Mechanics, (English & terjemahan Prof.Dr.Ir Budi S Supandji)Cernica, J.N., Soil Mechanics, John Wiley & Sons,1995Holtz, R.D., Kovacs, W.D., An introduction to Geotechnical Engineering, Prentice Hall, N.J., 1981

Laplace equations

The assumptions :Darcys law is validThe soil is homogeneous and saturatedThe soil and water are imcompressibleNo volume change occurs

Laplace equations of continuity A B

Impermeable soil layerWater incompressible and no vol. change :Flow x direction

Flow z direction

Laplace equations of continuity A B

Impermeable soil layer

Darcys law : Isotrpic soil kx=kz

Simple flow S F Flow in Z direction

A1 dan A2 are constant;

For flow through layer 1 :

Simple flow S F Flow in Z direction

A1 dan A2 are constant;

For flow through layer 2 :

From condtion 2:

Simple flow S F from and

Flow of layer 1 = flow of layer2

Simple flow S F Example

H1 = 300mm, H2 = 500mm, h1=600mm at z=200mm and h=500mm

Determine h at z=600 mm

Solution Z=200mm hence

Because z=600mm is located in soil layer 2 hence,

h = 179.9 mm

Water In

)h =hA - hB

Head Loss orHead Difference or Energy Loss

hA

hB

i = Hydraulic Gradient

(q)Water

out

Datum

hA

W.T.

hB

)h = hA - hB

W.T.

Impervious Soil

Impervious Soil

ZA

Datum

ZB

q = v . A = k i A = k AhL

Three different scenarios (a) Static (b) Flow-up (c) Flow-down

Stresses due to Flow

12


X

soil

hw

L

Static Situation (No flow)

z

v = whw + satz

u = w (hw + z)

v ' = ' z

At X,

14 ft

3 ft

12 ft

In Flow

Out Flow 2 ft

4 ft

Datum

3 ft

3 ft

8 ft

Piezometer

A

B

C

D

u =

6 x

62.4

u =

14 x

62.

4

No Seepage

Buoyancy

Ws

Ws

Ws

Ws

Ws

Stresses due to FlowDownward Flow

hw

L

flow

X

soil

z

v = whw + satz

w hw + w(L-hL)(z/L)

v ' = ' z + wiz

At X,

hLu = w hw

u = w (hw+L-hL)

as for static case

= w hw + w(z-iz)

= w (hw+z) - wiz

Reduction due to flow

Increase due to flow

u =

10 ft

3 ft

12 ft

In Flow

Out Flow

2 ft

4 ft

Datum

3 ft

3 ft

8 ft

Piezometer

A

B

C

D

u =

6 x

62.4

-

u

u =

17 x

62.

4

Downward Seepage

Buoyancy - Seepage Force

Ws

Ws

Ws

Ws

Ws

Seepage Force

16


flow

Upward Flow

hw

LX

soil

z

v = whw + satz

w hw + w(L+hL)(z/L)

v ' = ' z - wiz

At X,

hL

u = w hw

u = w (hw+L+hL)

as for static case

= w hw + w(z+iz)

= w (hw+z) + wiz

Increase due to flow

Reduction due to flow

u =

17 ft

3 ft

12 ft

In Flow

Out Flow 2 ft

4 ft

Datum

3 ft

3 ft

8 ft

Piezometer

A

B

C

D

u =

6 x

62.4

+

u

u

u =

17 x

62.

4

Upward Seepage

Buoyancy + Seepage Force

Ws

Ws

Ws

Ws

Ws

18

Quick Condition in Granular SoilsDuring upward flow, at X:

v ' = ' z - wizflow

hw

LX

soil

z

hL

= izw

w '

Critical hydraulic gradient (ic)

If i > ic, the effective stresses is negative.

i.e., no inter-granular contact & thus failure.

- Quick condition

Flow nets

To construct a flownet The Equipotensial lines intersect the flow line at right angle The flow elemens formed aproximate squares

Flownet is a combination of flow lines and equipotensial lineA flow line is a line along which water particle will travel from upstream to downstream.An equipotensial line is line along which the potensial head at all points is equal

Seepage Terminology

concrete dam

impervious strata

soil

Stream/flow line is simply the path of a water molecule.

datum

hL

TH = 0TH = hL

From upstream to downstream, total head steadily decreases along the stream line.

Seepage TerminologyEquipotential line is simply a contour of constant total head.

concrete dam

impervious strata

soil

datum

hL

TH = 0TH = hL

TH=0.8 hL

FlownetA network of selected stream lines and equipotentiallines.

concrete dam

impervious strata

soil

curvilinear square

90

Equipotential Lines

Flow Element

Principles of the Flow Net

Piezometer

)h = head loss = one drop

Datum

1

2

3

4

5

Principles of the Flow Net

Equipotential LinesTotal heads along this line are the same

Flow Element

Seepage calculation from flow net 1 Square

From Darcys law v=k i A

and

where H= head difference between upstream and down streamNd = number of potential drops

Seepage calculation from flow net cont

2 Rectangular

or

Seepage calculation from flow net cont

Flow channels 1&2 have square elements

Flow channel 3 has elemenrectangular b/l=0.38

Flow nets in anisotropic soil

4.

For anisotropic soil kx kz

To construct the flow net use the following procedures:1. Adopt vertical scale (z axis) fro drawing the cross section2. Adopt horisontal scale (x axis) such that horisontal scale =

kz/kx3. Plot the vertical section through the permeable layer

parallel to the direction of flow 4. Draw the flow net for the permeable layer on the section

obtained from step 3; with flow line intersecting equipotential line at right angles and the elements as approximate squares

The rate of seepage can be calculated :

where H =total head loss,Nf dan Nd = number of flow channels and potensial

drops

Quantity of Seepage (Q)

d

fL N

NkhQ = .per unit length normal to the plane

# of flow channels

# of equipotential drops

impervious strata

concrete dam

hL

head loss from upstream to downstream

Heads at a Point X

impervious strata

concrete dam

datum

X

z

hL

TH = hL TH = 0

Total head = hL - # of drops from upstream x h

h

Elevation head = -z

Pressure head = Total head Elevation head d

L

Nh

=

Uplift pressure under hydraulic structures

Assuming kx = kz = k Nd =7 H=21ft Head loss for each potensial

drop = H/Nd=3 Uplift pressure at a =

(Pressure head at a) x w[(21+6)-3]x w =24 w

Uplift pressure at b =[27-(2)(3)] w= 21 w

Uplift pressure at f =[27-(6)(3)] w = 9 w

Weir

Uplift force under hydraulic structures

Seepage through an earth dam on impervious base

Flow through a homogeniuos earth dam constructed over impervious baseConsidering cde

Rate of seepage at the section bf

33

FiltersUsed for: facilitating drainage preventing fines from being washed away

Used in:

earth dams

retaining walls

Filter Materials:

granular soils

geotextiles

34

Granular Filter DesignTwo major criteria:

(a) Retention Criteria

(b) Permeability Criteria

- to prevent washing out of fines

- to facilitate drainage and thus avoid build-up of pore pressures

Filter grains must not be too coarse

Filter grains must not be too fine

granular filter

35

Granular Filter DesignRetention criteria:D15, filter < 5 D85,soil

- after Terzaghi & Peck (1967)

Permeability criteria:D15, filter > 4 D15,soil

average filter pore size

D15, filter < 20 D15, soil

D50, filter < 25 D50, soil- after US Navy (1971)

GSD Curves for the soil and filter must be parallel

Example

From the left figure Nf =3 Nd = 6

Head loss for each drop = h/Nd = 10/6 = 1.667

Potensial drop at a = 1x 1.667 ftWater in the piezometerAt a = 15-1.667=13.333 ft above ground surface

(ags)At b = 15-2x1.667= 11.67 ft agsAt c = 15-5x1.667= 8.67 ft agsAt d = 15-5x1.667= 8.67 ft ags

kx= kz =k = 5x 10-3 cm/sec= 1.64 x 10-4 ft/sec

q = (1.64 x 10-4) x 1.667= 2.73x10-4

ft3/sec/ft

Impermeable layer

Lecture 4Slide Number 2Laplace equationsLaplace equations of continuityLaplace equations of continuitySimple flow Simple flow Simple flow Simple flow Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Flow netsSeepage TerminologySeepage TerminologyFlownetSlide Number 23Slide Number 24Seepage calculation from flow netSeepage calculation from flow net contSeepage calculation from flow net cont Flow nets in anisotropic soilQuantity of Seepage (Q)Heads at a Point XUplift pressure under hydraulic structuresSeepage through an earth dam on impervious baseSlide Number 33Granular Filter DesignSlide Number 35Example

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Flownet Seepage