theory of seepage

Bligh’S CREEP THEORY
LIMITATIONS OF BLIGH’S THEORY
LANE’S WEIGHTED CREEP THEORY
KHOSLA’S THEORY AND CONCEPT OF FLOW NETS
COMPARISON OF BLIGH’S THEORY AND KHOSLA’S THEORY

1. z
PREPARED
BY
ER. SANJEEV SINGH
[email protected]

2. z
CONTENT
Bligh’S CREEP THEORY
LIMITATIONS OF BLIGH’S THEORY
LANE’S WEIGHTED CREEP THEORY
KHOSLA’S THEORY AND CONCEPT OF
FLOW NETS
COMPARISON OF BLIGH’S THEORY AND
KHOSLA’S THEORY

3. z
Bligh’S CREEP THEORY
Blighassumedthatthewaterwhichpercolatesintothefoundationcreepsthroughthejoint
betweentheprofileofthebaseofweirandthesubsoil.Ofcoursewateralsopercolatesintothe
subsoil.Hethenstatedthatthispercolatingwaterlosesitsheaden-route.Theseepingwater
finallycomesoutatthedownstreamend.AccordingtoBlighwatertravelsalongvertical,
horizontalorinclinedpathwithoutmakinganydistinction.
Thetotallengthcoveredbythepercolatingwatertillitemergesoutatthedownstreamendis
calledacreeplength.Itisclearfromtheknowledgeofhydraulicsthattheheadofwaterlostin
thepathofpercolationisthedifferenceofwaterlevelsontheupstreamandthedownstream
ends.Also,animaginarylinewhichjoinsthewaterlevelsontheupstreamandthe
downstreamendiscalledahydraulicgradientline.Figure19.3(a,b)givesthelullexplanation
ofBligh’stheory.

4. z
In Fig. 19.3 (a) arrows show the path followed by the creeping water.
B = L = total creep length and h/L is the head lost in creeping.
Loss of head per unit creep length will be h/L and it is hydraulic gradient.
To increase the path of percolation vertical cutoffs or sheet piles can be provided.
Fig. 19.3 (b).

5. zBligh took vertical and horizontal path of percolation in the same sense. So now
Calculation of Total Creep Length
When the water follows a vertical path the loss takes place in a vertical plane at same
section. This loss is proportional to the length of the vertical path. For example, for
cutoff d1, loss will be h/L x2d1 and it takes place in its plane. Loss of head at other
cutoffs may be calculated in the same way.

6. z
Bligh gave the criteria for the safety of a weir against piping and uplift separately and
is as follows:
The structure is safe against piping when the percolating water retains negligible
upward pressure when it emerges out at the downstream end of the weir. Obviously
the path of percolation should be sufficiently long to provide safe hydraulic gradient.
It depends on the soil type.
This condition is provided by equation
L= CH
where Lis creep length or path of percolation;
Cis Bligh’s creep co-efficient for soil; and
His head of water against the weir.

7. z
TABLE 19.1 GIVES VALUES OF
C FOR VARIOUS SOIL TYPES

8. zLIMITATIONS OF BLIGH’S
THEORY
In his theory Bligh made no distinction between horizontal and vertical creep
lengths.
The idea of exit gradient has not been considered.
The effect of varying lengths of sheet piles not considered.
No distinction is made between inner or outer faces of the sheet piles.
Loss of head is considered proportional to the creep length which in actual is not so.
The uplift pressure distribution is not linear as assumed but in fact it follows a sine
curve.
Necessity of providing end sheet pile not appreciated.

9. zLANE’S WEIGHTED CREEP
THEORY
Bligh,inhistheory,hadcalculatedthelengthofthecreep,bysimplyaddingthe
horizontalcreeplengthandtheverticalcreeplength,therebymakingnodistinction
betweenthetwocreeps.
However,Lane,onthebasisofhisanalysiscarriedoutonabout200damsallover
theworld,stipulatedthatthehorizontal
creepislesseffectiveinreducinguplift(orincausinglossofhead)thanthevertical
creep.
He,therefore,suggestedaweightagefactorof1/3forthehorizontalcreep,asagainst
1.0fortheverticalcreep.

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11. zThe total Lane’s creep length (Ll) is given by
Ll= (d1+ d1) + (1/3) L1+ (d2+ d2) + (1/3) L2+ (d3+ d3)
= (1/3) (L1+ L2) + 2(d1+ d2+ d3)
= (1/3) b+ 2(d1+ d2+ d3)
To ensure safety against piping, according to this theory, the
creep length Llmust no be less than C1HL,
where HLis the head causing flow, and C1is Lane’s creep
coefficient given in table –2

12. z
Table –2: Values of Lane’s Safe
Hydraulic Gradient for different
types of Soils

13. z KHOSLA’S THEORY AND
CONCEPT OF FLOW NETS
Manyoftheimportanthydraulicstructures,suchasweirsand
barrage,weredesignedonthebasisofBligh’stheorybetweenthe
periods1910to1925.In1926–27,theupperChenabcanalsiphons,
designedonBligh’stheory,startedposingunderminingtroubles.
Investigationsstarted,whichultimatelyleadtoKhosla’stheory.
Themainprinciplesofthistheoryaresummarizedbelow:
(a)Theseepagewaterdoesnotcreepalongthebottomcontourof
puccafloodasstartedbyBligh,butontheotherhand,thiswater
movesalongasetofstream-lines.Thissteadyseepageinavertical
planeforahomogeneoussoilcanbeexpressedbyLaplacianequation:

14. z
Where, φ= Flow potential = Kh; K = the co-efficient of permeability of
soilas defined by Darcy’s law, and h is the residual head at any point
within the soil. The above equation represents two sets of curves
intersecting each other orthogonally. The resultant flow diagram
showing both of the curves is called a Flow Net.

15. z STREAM LINES
Thestreamlinesrepresentthepathsalongwhichthewaterflows
throughthesub-soil.
Everyparticleenteringthesoilatagivenpointupstreamofthework,
willtraceoutitsownpathandwillrepresentastreamline.Thefirst
streamlinefollowsthebottomcontouroftheworksandisthesameas.
Bligh’spathofcreep.Theremainingstreamlinesfollowssmooth
curvestransitingslowlyfromtheoutlineofthefoundationtoasemi-
ellipse,asshownbelow.

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17. z EQUIPOTENTIAL LINES
(a)Treatingthedownstreambedasdatumandassumingnowateronthedownstreamside,it
canbeeasilystartedthateverystreamlinepossessesaheadequaltoh1whileenteringthe
soil;andwhenitemergesatthedown-streamendintotheatmosphere,itsheadiszero.Thus,
theheadh1isentirelylostduringthepassageofwateralongthestreamlines.
Further,ateveryintermediatepointinitspath,thereiscertainresidualhead(h)stilltobe
dissipatedintheremaininglengthtobetraversedtothedownstreamend.Thisfactis
applicabletoeverystreamline,andhence,therewillbepointsondifferentstreamlineshaving
thesamevalueofresidualheadh.Ifsuchpointsarejoinedtogether,thecurveobtainedis
calledanequipotentialline.
EverywaterparticleonlineABishavingaresidualheadh=h1,andonCDishavinga
residualheadh=0,andhence,ABandCDareequipotentiallines.
Sinceanequipotentiallinerepresentthejoiningofpointsofequalresidualhead,henceif
piezometerswereinstalledonanequipotentialline,thewaterwillriseinallofthemuptothe
samelevelasshowninfigurebelow.

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19. z
(b)Theseepagewaterexertsaforceateachpointinthedirectionofflowand
tangentialtothestreamlinesasshowninfigureabove.Thisforce(F)hasan
upwardcomponentfromthepointwherethestreamlinesturnsupward.Forsoil
grainstoremainstable,theupwardcomponentofthisforceshouldbe
counterbalancedbythesubmergedweightofthesoilgrain.Thisforcehasthe
maximumdisturbingtendencyattheexitend,becausethedirectionofthisforce
attheexitpointisverticallyupward,andhencefullforceactsasitsupward
component.Forthesoilgraintoremainstable,thesubmergedweightofsoil
grainshouldbemorethanthisupwarddisturbingforce.Thedisturbingforceat
anypointisproportionaltothegradientofpressureofwateratthatpoint(i.e.
dp/dt).Thisgradientofpressureofwaterattheexitendiscalledtheexit
gradient.Inorderthatthesoilparticlesatexitremainstable,theupward
pressureatexitshouldbesafe.Inotherwords,theexitgradientshouldbesafe.

20. zCRITICAL EXIT GRADIENT
This exit gradient is said to be critical, when the upward disturbing force on the grain is just equal to the
submerged weight of the grain at the exit. When a factor of safety equal to 4 to 5 is used, the exit gradient
can then be taken as safe. In other words, an exit gradient equal to ¼ to 1/5 of the critical exit gradient is
ensured, so as to keep the structure safe against piping.
The submerged weight (Ws) of a unit volume of soil is given as:
 γw(1 –n) (Ss –1)
 Where, w = unit weight of water.
 Ss = Specific gravity of soil particles
 n= Porosity of the soil material
For critical conditions to occur at the exit point
 F= Ws
 Where Fis the upward disturbing force on the grain
 ForceF = pressure gradient at that point = dp/dl = γw ×dh/dl

21. zCOMPARISON OF BLIGH’S
THEORY AND KHOSLA’S
THEORY
Comparison # Bligh’s Theory:
1. Loss of head of seeping water is linear.
2. Seeping water follows the path along the surface, in contact with the underside of
the impervious floor profile.
3. Bligh did not give any significance to the cut-off at D/Send of the floor of the weir.
4. In order to prevent undermining, reduction of hydraulic gradient was considered
adequate measure.
5. This theory is very simple and requires very simple calculation work

22. z
Comparison#Khosla’sTheory:
1.Lossofheadofseepingwaterdependsuponprofileofweirfloor,cut-offs,slope
etc.Lossofheadisdefinitelynotlinear.
2.Seepingwaterfollowsparabolicorellipticalstreamlinepath.
3.Khoslaconsideredprovisionofcut-offatD/Sendoftheweirfloorasamust.
4.Khoslareliedupontheexitgradientforpreventingundermining.Hesaidthat
valueofexitgradientattheD/Sendofthefloorshouldbelessthanthecriticalvalue
forthesoil.
5.Itisaverysimplecomplextheoryenvolvinglotofcalculations.Khoslacurveshave
howeverreducedthiswork,butstillthistheoryisdifficulttounderstand.