17...Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Typical flow net for an...

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

17


Permeability and Seepage -6


Flow net construction for an earth dam

H1

H2

A

B

CD

E

AE – Flow line; AB – Eqp. Line with head H1;

DE -Eqp. Line with head H2; BC – flow line ( or phreatic surface);

CD – neither a flow line nor an eqp. line (component of flow normal to CD ad water flows freely down the surface of the slope).


Embankment with permeable filter

H

A

a

0.3∆

d

∆H

pp∆

a′Basic parabola

β = 180; ∆l/(l+∆l) = 0

EQP. Line with zero head


Seepage through homogeneous sand beneath base of concrete dams


seepage through homogeneous dam ~consisting of very fine, clean sand.


Filter designWhen seepage water flows from a soil with relativelyfine grains into a coarser material, there is a dangerthat the fine soil particles may wash away into thecoarse material.

Such a situation can be prevented by the use of afilter or protective filter between the two soils.


Typical flow net for an earthdam with rock toe filterWithout filter at the toe, the seepage water would wash the finesoil grains into the toe and undermine the structure.

For FOS


Typical flow net for an earth dam withchimney drain


Filter design

1) The size of the voids in the filter material should besmall enough to hold the larger particles of theprotected material in place.

2) The filter material should have a high permeabilityto prevent buildup of large seepage forces andhydrostatic pressure in the filters.

For the proper selection of the filter material,

54)

)(85

(15 −≤S

F

dd

54)

)(15

(15 −≥S

F

dd

d15(F) = Dia. Through which 15% of filter materialwill pass

d85(S) = Dia. Through which 85% of soil to be protectedwill pass

d15(S) = Dia. Through which 15% of soil to beprotected will pass


Earthen dam section without any drainage (or with clogged drain)

6 m

30g


Numerical simulation of Earthen dam section without any drainage

(or with clogged drain)


Transient seepage analysis duration-30 days (SEEP/W)


Earthen dam section with horizontal sand drain of 0.6 m thickness

6 m

30g


Transient seepage analysis duration-30 days (SEEP/W)


Numerical simulation of Earthen dam section with horizontal sand drain of

0.6 m thickness


For a single row of sheet pile structure, draw a flownet diagram, given that:

a) the soil is isotropic, with permeability of 0.001m/sec.b) the soil is anisotropic with ratio of permeabilitiesas kx=6kz

Example Problem:


FEM mesh of the sheet pile section


Case a: Isotropicsection. Note that theflow and equipotentiallines are orthogonal inthis case.


Case b: Anisotropicsection. Note that theflow and equipotentiallines are not orthogonalin this case.


Construct a flow net for the dam section resting ona two layered soil deposit with k1= 5 x 10-2

mm/sec and k2 = 1 x 10-2 mm/sec. Hencecomment on the results obtained.

Example problem:


k1= 5 x 10-2 mm/sec

k2= 1 x 10-2 mm/sec

FEM mesh

of the dam section15 m


Note: Since k1/k2 =5,the length-to-widthratio of the flowelements in layer 2with respective tolayer 1 is 1/5.

l2/b2 = 1/5 with b1/l1 = 1


Drop in pressure head along the length of thedam due to seepage losses


Construct the flow nets for the dam sections shown,given that:

a) the soil is isotropic, with permeability of 5 x 10-5

m/sec

b) the dam is zoned with k2 = 5k1

Example problem:


Case a: Homogeneous dam; k = 5 x 10-5 m/sec


Solution for Case a:

fd

NNhkq =

Nf = 2.5; Nd = 10


Case b) Zoned dam


Flow net for seepage through a zoned earth dam

The soil for the upstream half of the dam has apermeability k1, and the soil for the downstream halfof the dam has a permeability k2 = 5 k1.

Square elementsl1 = b1

k1

k2

α1

α2

k1 < k2

b2/l2 <1

Using

For k1/k2 = 5 b2/l2 = 1/5b2

l2


Solution for Case b:

k1

k2 = 5 k1

Nf1 = Number of full flow channels in soil 1 with k1 = 2 +2/3

11

2/3

1/51/5

2/15

Nf2 = Number of full flow channels in soil 2 with k2 = 8/15

Nd = 10

2211 fd

fd

NNhkN

Nhkq ==


Failure due to piping for single row of sheet-pile wall structure (Terzaghi, 1922)By considering a soil prismon the downstream side ofunit thickness and ofsection D x D/2Using the flow net the hydraulic uplift pressure can be determined as:

mwDhU γ21

=2

BAm

hhh += hA

hBhm = Avg. hydraulic head at the base of the soil prism

2

21 DW γ ′=′


Failure due to piping for single row of sheet-pile wall structureFOS against heave(or piping) is wm

mwhD

Dh

D

UWFOS

γγ

γ

γ ′=

′=′

=

2121 2

m

c

iiFOS =

eGi s

wc +

−=

′=

11

γγ∴≈ 4

Dhi m

m =To find hm – Find the total head within D/2 zone horizontally


For structures other than a single row of sheet pile walls

Terzaghi (1943) recommendedthat D/2 x D′X1

0 < D′ ≤ D


Safety of hydraulic structures against piping

According to Harza (1935)

exit

c

iiFOS =

iexit = maximum hydraulic gradient

lhiexit

∆= From flow net

=

DHiexit π

1 According to Harr (1962)H = Maximum hydraulic head;

D = Depth of penetration of sheet pile wall


Safety of hydraulic structures against piping

maximum hydraulic gradient


Example problem

A stiff clay layer underlies a 12 m thick silty sanddeposit. A sheet pile is driven into the sand to a depthof 7 m. k of silty sand is 8 x 10-6 m/s. The stiff clay canbe assumed to be impervious. e of silty sand is 0.72and Gs = 2.65

a) Draw the flow net and estimate Q

b) What is the PWP at the tip of the sheet pile wall

c) FOS against piping failure?


3 m

2 m

7 m

5 m

Silty sand

Stiff clay

Example problem


Example problem

2 m8

65

3

0


Example problem

a) From flow net; Nf = 3; Nd = 8; hL = 3 m;

d

fL N

Nhkq )(= = 0.836 m3/day per metre

b) PWP at the tip of the sheet pile wall

TH = 1.5 m

EH = -9 m

PH = 10.5 m ; PWP = 105 kN/m2


Example problem

c) Head loss per EQP drop ∆h = 3/8 = 0.375 m

Max. exit hydraulic gradient = 0.375/2.6 = 0.144

ic = (2.65-1)/(1 + 0.72) = 0.96

exit

c

iiFOS = = 0.96/0.144 = 6.7 > 5

The arrangement is quite safe with respect to piping failure

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17...Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Typical flow net for an...

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