Bligh’s Creep Theory for Seepage Flow

According to Bligh’s Theory, the percolating water follows the outline of the base of the foundation of the hydraulic structure. In other words, water creeps along the bottom contour of the structure. The length of the path thus traversed by water is called the length of the creep. Further, it is assumed in this theory, that the loss of head is proportional to the length of the creep. If HL is the total head loss between the upstream and the downstream, and L is the length of creep, then the loss of head per unit of creep length (i.e. HL/L) is called the hydraulic gradient. Further, Bligh makes no distinction between horizontal and vertical creep.

Consider a section a shown in Fig above. Let HL be the difference of water levels between upstream and downstream ends. Water will seep along the bottom contour as shown by arrows. It starts percolating at A and emerges at B. The total length of creep is given by
L = d1 + d1 + L1 + d2 + d2 + L2 + d3 + d3
= (L1+ L2) + 2(d1 + d2 + d3)
= b + 2(d1 + d2 + d3)

(i) Safety against piping or undermining:-
                                                      According to Bligh, the safety against piping can be ensured by providing sufficient creep length, given  by
                         L = C.HL, 
                                where C is the Bligh’s Coefficient for the soil.
Different values of C for different types ofsoils are tabulated in Table –1 below:








Note: The hydraulic gradient i.e. HL/L is then equal to 1/C. Hence, it may be stated that the hydraulic
gradient must be kept under a safe limit in order to ensure safety against piping.

(ii) Safety against uplift pressure:-
                                                   The ordinates of the H.G line above the bottom of the floor represent the
residual uplift water head at each
point. Say for example, if at any point, the ordinate of H.G line above the bottom of the floor is 1 m, then 1
m head of water will act as uplift at that point. If h′ meters is this ordinate, then water pressure equal to h′
meters will act at this point, and has to be counterbalanced by the weight of the floor of thickness say t.

Uplift pressure = γw ×h′                           [where γw is the unit weight of water]
Downward pressure = (γw ×G).t              [Where G is the specific gravity of the floor material]

For equilibrium,
γw ×h′ = γw ×G. t
h′ = G × t
Subtracting t on both sides, we get

(h′ – t) = (G×t – t) = t (G – 1)


Where, h′ – t = h = Ordinate of the H.G line above the top of the floor
G – 1 = Submerged specific gravity of the floor material

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