Khosla's theory improved upon Bligh's theory of seepage under hydraulic structures in several ways. Khosla recognized that seepage follows elliptical streamlines rather than the bottom contour as Bligh assumed. Khosla also introduced the important concept of exit gradient and specified that the exit gradient must be less than the critical value to prevent soil particles from being dislodged. While more complex, Khosla's theory provides a more accurate representation of seepage flow compared to Bligh's assumption of linear head loss.

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PREPARED
BY
ER. SANJEEV SINGH
SNJV432@GMAIL.COM

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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

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Bligh’S CREEP THEORY
 Bligh assumed that the water which percolates into the foundation creeps through the joint
between the profile of the base of weir and the subsoil. Of course water also percolates into the
subsoil. He then stated that this percolating water loses its head en-route. The seeping water
finally comes out at the downstream end. According to Bligh water travels along vertical,
horizontal or inclined path without making any distinction.
 The total length covered by the percolating water till it emerges out at the downstream end is
called a creep length. It is clear from the knowledge of hydraulics that the head of water lost in
the path of percolation is the difference of water levels on the upstream and the downstream
ends. Also, an imaginary line which joins the water levels on the upstream and the
downstream end is called a hydraulic gradient line. Figure 19.3 (a, b) gives the lull explanation
of Bligh’s theory.

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 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.

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 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 L is creep length or path of percolation;
 C is Bligh’s creep co-efficient for soil; and
 H is head of water against the weir.

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TABLE 19.1 GIVES VALUES OF
C FOR VARIOUS SOIL TYPES

8. z LIMITATIONS 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. z LANE’S WEIGHTED CREEP
THEORY
 Bligh, in his theory, had calculated the length of the creep, by simply adding the
horizontal creep length and the vertical creep length, thereby making no distinction
between the two creeps.
 However, Lane, on the basis of his analysis carried out on about 200 dams all over
the world, stipulated that the horizontal
 creep is less effective in reducing uplift (or in causing loss of head) than the vertical
creep.
 He, therefore, suggested a weightage factor of 1/3 for the horizontal creep, as against
1.0 for the vertical creep.

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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 Ll must no be less than C1HL,
 where HL is the head causing flow, and C1 is Lane’s creep
coefficient given in table –2

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

13. z KHOSLA’S THEORY AND
CONCEPT OF FLOW NETS
 Many of the important hydraulic structures, such as weirs and
barrage, were designed on the basis of Bligh’s theory between the
periods 1910 to 1925. In 1926 – 27, the upper Chenab canal siphons,
designed on Bligh’s theory, started posing undermining troubles.
Investigations started, which ultimately lead to Khosla’s theory.
 The main principles of this theory are summarized below:
 (a) The seepage water does not creep along the bottom contour of
pucca flood as started by Bligh, but on the other hand, this water
moves along a set of stream-lines. This steady seepage in a vertical
plane for a homogeneous soil can be expressed by Laplacian equation:

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 Where, φ = Flow potential = Kh; K = the co-efficient of permeability of
soil as 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
 The streamlines represent the paths along which the water flows
through the sub-soil.
 Every particle entering the soil at a given point upstream of the work,
will trace out its own path and will represent a streamline. The first
streamline follows the bottom contour of the works and is the same as.
 Bligh’s path of creep. The remaining streamlines follows smooth
curves transiting slowly from the outline of the foundation to a semi-
ellipse, as shown below.

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17. z EQUIPOTENTIAL LINES
 (a) Treating the downstream bed as datum and assuming no water on the downstream side, it
can be easily started that every streamline possesses a head equal to h1 while entering the
soil; and when it emerges at the down-stream end into the atmosphere, its head is zero. Thus,
the head h1 is entirely lost during the passage of water along the streamlines.
 Further, at every intermediate point in its path, there is certain residual head (h) still to be
dissipated in the remaining length to be traversed to the downstream end. This fact is
applicable to every streamline, and hence, there will be points on different streamlines having
the same value of residual head h. If such points are joined together, the curve obtained is
called an equipotential line.
 Every water particle on line AB is having a residual head h = h1, and on CD is having a
residual head h = 0, and hence, AB and CD are equipotential lines.
 Since an equipotential line represent the joining of points of equal residual head, hence if
piezometers were installed on an equipotential line, the water will rise in all of them up to the
same level as shown in figure below.

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 (b) The seepage water exerts a force at each point in the direction of flow and
tangential to the streamlines as shown in figure above. This force (F) has an
upward component from the point where the streamlines turns upward. For soil
grains to remain stable, the upward component of this force should be
counterbalanced by the submerged weight of the soil grain. This force has the
maximum disturbing tendency at the exit end, because the direction of this force
at the exit point is vertically upward, and hence full force acts as its upward
component. For the soil grain to remain stable, the submerged weight of soil
grain should be more than this upward disturbing force. The disturbing force at
any point is proportional to the gradient of pressure of water at that point (i.e.
dp/dt). This gradient of pressure of water at the exit end is called the exit
gradient. In order that the soil particles at exit remain stable, the upward
pressure at exit should be safe. In other words, the exit gradient should be safe.

20. z CRITICAL 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 F is the upward disturbing force on the grain
 Force F = pressure gradient at that point = dp/dl = γw ×dh/dl

21. z COMPARISON 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/S end 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

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 Comparison # Khosla’s Theory:
 1. Loss of head of seeping water depends upon profile of weir floor, cut-offs, slope
etc. Loss of head is definitely not linear.
 2. Seeping water follows parabolic or elliptical stream line path.
 3. Khosla considered provision of cut-off at D/S end of the weir floor as a must.
 4. Khosla relied upon the exit gradient for preventing undermining. He said that
value of exit gradient at the D/S end of the floor should be less than the critical value
for the soil.
 5. It is a very simple complex theory envolving lot of calculations. Khosla curves have
however reduced this work, but still this theory is difficult to understand.