5 Seepage Theories

7/21/2019 5 Seepage Theories

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Seepage Theories


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Blighs Creep Theory :

The design of the impervious floor, or the apron is directlydependent on the possibilities of percolation in the porous soil on

which the apron is built.

Bligh assumes as an approximation that the hydraulic slope orgradient is constant throughout the impervious length of the apron.

He further assumed the percolating water to creep along the

contact of the base profile of the apron with the sub-soil, losinghead enroute, proportional to the length of its travel.

He designated the length of the travel as the creep length, which

is the sum of horiontal as well as vertical length of creep.


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Bligh asserted that no amount of sheet piling or another cut-off

could ever stop the percolation unless the cut-off extends upto the

impermeable sub-soil strata.


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Thus, according to Blighs theory, the total creep length ! from fig "a# is

$or the case of fig "b# is, the total creep length is

This means that in calculating the length of creep, the depth of every

cutoff "i.e. %ertical creep# is multiplied by the coefficient &.

'f H is the total loss of head, the loss of head per unit length of the

creep would be

He called the loss of head per unit length of creep as percolation

coefficient.


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The reciprocal "!(H# is called the coefficient of creep ")# and

Bligh assigned its safe values for different soils in the table

below *

Type of soil Value of C

+. !ight sand and mud&. $ine micaceous sand. )oarse grained sand. Boulders or shingle, gravels sand

mixed

+/+0+&

0 to 1


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Design Criteria : Bligh gave two criteria for design

1. Safety against piping: The length of should be sufficient toprovide a safe hydraulic gradient according to the type of soil.

Thus, the safe creep length is given by *

L = CH

where C 2 coefficient of creep 2 +(c.


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2. Safety against uplift pressure: !et hbe uplift pressure head at any pointof the apron.

The uplift pressure 2 wh

'f t 2 thic3ness of the floor at the point

& = specific gravity of the floor material

4 2 unit weight of water

Then, downward force "resisting force# per unit area 2

e5uating the two, we get

4here h 2 ordinate of the hydraulic gradient line measured above the top of

the floor.


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Limitations of Blighs Theory :

+. Bligh made no distinction between horiontal and vertical creep.

&. Blighs method holds good so long as the horiontal distance

between the pile lines is greater than twice their depth.

. Bligh did not explain the idea of exit gradient. The safety againstundermining cannot simply be obtained by considering a flataverage gradient but by 3eeping this gradient well below critical.


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. Bligh ma3es no distinction between outer and inner faces of sheetpiles or the intermediate sheet pile, whereas according toinvestigations, the outer faces of the end sheet piles are much moreeffective than inner ones. 6lso, intermediate sheet piles of shorterlength than the outer ones are ineffective except for localredistribution of pressure.

0. !oss of head does not ta3e place in the same proportion as creeplength. 6lso, the uplift pressure distribution is not linear butfollows a sine curve.

7. Bligh does not specify the absolute necessity of providing a sheetpile at d(s end whereas it is absolutely essential to have a deepvertical cut off at d(s end to prevent undermining.


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LANES !E"#$TED C%EE& T$E'%( :

Based on statistical investigations of as many as &8/ dams, weirs

and barrages all over the world, !ane observed that vertical creep is

more effective than the horiontal creep.

He therefore modified Blighs creep theory by evolving !anes

weighted creep theory.

6ccording to this theory, the weighted creep length "!w# is given by

4here 2 the sum of all horiontal contacts and all the sloping contacts

having slope less than 5

%2 sum of all the vertical contacts and all the sloping contacts

steeper than 5


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To ensure safety against piping, lane suggested that the weighted

creep length must not be less than the following *

where Lw2 weighted creep length

Cw2 !ane9s creep coefficient, the value of which depends on

the type of soil.


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)hoslas Theory :

Provisional conclusions led by Khosla are :

+. The outer faces of the end sheet piles were much more effective than

the inner ones and the horiontal length of the floor.

&. The intermediate piles if smaller in length than the outer ones were

ineffective except for the local redistribution of pressure.

. :ndermining of the floor started from the tail end. 'f the hydraulic

gradient at exit was more than the critical gradient for the particularsoil, the particles would move with the flow of water, thus causing

progressive degradation of the sub-soil, resulting in cavities and

ultimate failure.

. 't was absolutely essential to have a reasonably deep vertical cutoff atthe downstream end to prevent undermining.

;hosla and his associates too3 into account the flow pattern

below the impermeable base of hydraulic structures, to calculate

the uplift pressure and exit gradient


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Spe*ifi* Cases :

+.


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Case 1 : &ile at some interme+iate point

These cases were analysed by ;hosla and his associates

with the help of


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For Pile at intermediate point :

The uplift pressures, =>, =?, =)at the three 3ey points >, ? and ) are

given by the following e5uations *


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)hoslas *ur,e for interme+iate sheet pile


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Case 2 : &ile at +o-nstream en+

The uplift pressure at the 3ey points >, ? and ) aregiven by the following e5uations *


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)hoslas *ur,e for *utoff at +s en+


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Case / : &ile at upstream en+

'f the pile is provided at the upstream end, the pressure at the3ey points >+, ?+and )+are given by the following e5uations *


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)hoslas *ur,e for e0it gra+ient


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E0it #ra+ient :

$or the case of horiontal impervious floor with cutoff

at the down stream end, the exit gradient "@># is given

by the following expression *


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Depresse+ loor :

6 depressed floor is a straight horiontal apron or floor of

finite thic3ness "or depression# d penetrating into the

foundation. ;hosla also solved this case empirically and gave

uplift for at point ?.

where are the corresponding values for an

e5uivalent horiontal apron of negligible thic3ness of length

b with d(s cutoff of depth d.


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&ermissile E0it #ra+ient :

$or alluvial soils, the critical hydraulic gradient may be approximately e5ual

to +.

The permissible hydraulic gradient can be found by adopting a suitable factor

of safety of 0 to 8.

The permissible exit gradient for three soils are given below *


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)hoslas metho+ of in+epen+ent ,ariales

To 3now that how the seepage below the foundation of a hydraulic

structure is ta3ing place, it is necessary to plot flownet. This can beaccomplished by-

A athematical solution of the !aplacian e5uations

A >lectrical analogy method

A @raphical method

These methods are complicated and are time consuming.

Therefore, for designing hydraulic structures such as weirs or

barrages on pervious foundations, ;hosla has evolved a simple, 5uic3

and an accurate approach, called ethod of 'ndependent %ariables.

This method consists of brea3ing up a complex profile into a numberof simple profiles, each of which is independently amenable to

mathematical treatment, and then applying corrections due to the

mutual interference of pile and due to the thic3ness and slope of the

floor


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The *omple0 profile *an e ro3en up into the follo-ing simple

profile an+ pressures at 3ey points *an e otaine+ -

+. 6 straight horiontal floor of negligible thic3ness with a sheet pileline on the u/s end and d(s end

&. 6 straight horiontal floor depressed below the bed but without any

vertical cut-offs

. 6 straight horiontal floor of negligible thic3ness with a sheet pileline at some intermediate point

. The pressure otaine+ at the 3ey points y *onsi+ering the

simple profile are then *orre*te+ for the follo-ing4+. )orrection for thic3ness of the floor

&. )orrection for mutual interference of the piles

. )orrection due to the sloping floor


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1. Corre*tion for thi*3ness of the floor

@raphs + and & give pressure at 3ey points assuming thic3ness of

the floor to be negligibly small. Thus the pressure at 3ey points >

and ) pertain to the level at the top of the floor ,while actually the

Cunction of the pile is at the bottom "points >+ )+# of the floor.

The pressure at actual points >+ )+ are computed by

considering linear variation of pressure between point ? and the

hypothetical points > and ).


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4hen the pile is at u(s end-

$or the intermediate pile-

4hen the pile is at the d(s end- where t2

d2


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2. Corre*tion for the mutual interferen*e of piles4

The correction ")# is given by D

The correction is positive for points in the rear or bac3 water and subtractive for points forward in

the direction of flow.


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/. Corre*tion for slope

6 correction is applied for a sloping floor and is ta3en as Eve for

the down slopes, and -ve for the up slopes following the directionof flow.

The correction factor given above is to be multiplied by the

horiontal length of the slope and divided by the distance between

the two pile lines between which the sloping floor is located.

This correction is applicable only to the 3ey points of the pile line

fixed at the start or end of the slope.

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5 Seepage Theories