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Bligh’s Creep Theory for Seepage Flow

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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. H L /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 H L 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 = d 1 + d 1 + L 1 + d 2 + d 2 + L 2 + d 3 + d 3 = (L 1 +...
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Lane’s Weighted Creep Theory

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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. Thus in Fig–1,  the total Lane’s creep length (L l ) is given by L l = (d 1 + d 1 ) + (1/3) L 1 + (d 2 + d 2 ) + (1/3) L 2 + (d 3 + d 3 ) = (1/3) (L 1 + L 2 ) + 2(d 1 + d 2 + d 3 ) = (1/3) b + 2(d 1 + d 2 + d 3 ) To ensure safety against piping, according to this theory, the creep length Ll must no be less than C1H L , where H L is the head causing flow, and C 1 is Lane’s creep coefficient given in table –2 Table – ...
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Khosla’s Method of independent variables for determination of pressures and exit gradient for seepage below a weir or a barrage

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In order to know as to how the seepage below the foundation of a hydraulic structure is taking place, it is necessary to plot the flow net. In other words, we must solve the Laplacian equations. This can be accomplished either by mathematical solution of the Laplacian equations, or by Electrical analogy method, or by graphical sketching by adjusting the streamlines and equipotential lines with respect to the boundary conditions. These are complicated methods and are time consuming. Therefore, for designing hydraulic structures such as weirs or barrage or pervious foundations, Khosla has evolved a simple, quick and an accurate approach, called Method of Independent Variables. In this method, a complex profile like that of a weir is broken into a number of simple profiles; each of which can be solved mathematically. Mathematical solutions of flow nets for these simple standard profiles have been presented in the form of equations given in Figure  and curves given in Plate...
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