Typical flow net for the flow beneath the dam with heel cutoff wall [Lambe & R.V. Whitman (1979)]

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1 Typical flow net for the flow beneath the dam with heel cutoff wall [Lambe & R.V. Whitman (1979)] Typical flow net for the flow beneath the dam with toe cutoff wall [Lambe & R.V. Whitman (1979)] Exit gradient Hydraulic Gradient: The potential drop between two adjacent equipotential lines divided by distance between them is known as hydraulic gradient. Thus, the hydraulic gradient across any square in the flow net involves measuring the average dimension of the square. The maximum value of hydraulic gradient which results in maximum seepage velocity occurs across smallest square (flow grid). Exit Gradient: The exit gradient is the hydraulic gradient at the downstream end of the flow line where percolating water leaves the soil mass and emerges into the free water at the downstream

2 i exit Maximum Exit Gradient: dams and sheet pile walls The maximum exit gradient for the cases of both dams and sheet pile walls can be determined from the flow net. The maximum exit gradient is given by h l Where, h is the head lost between the last two equipotential lines, and the l length of the flow element Computation of maximum exit gradient Computation of maximum exit gradient for sheet pile wall

3 Maximum Exit Gradient: Sheet pile walls Maximum exit gradient Sheet pile walls can be computed alternatively as explained below. A theoretical solution for the determination of the maximum exit gradient for a single row of sheet pile structures is available and is of the form (Refer to Figure 4.7) 1 J Maximum hydraulic head ] 1 J H i 1 H 2 ] exit [ depth of penetration of sheet pile ] [ l d ] Critical Hydraulic Gradient Consider a case of water flowing under a hydraulic head x through a soil column of height H as shown in the Figure Computation of critical hydraulic gradient at point O. The state of stress at point O situated at a depth of h2 from the top of soil column may be computed as follows, Vertical stress at O is, vo h 1 w h 2 sat If w is the unit weight of water then pore pressure u O at O is, u o (h 1 h 2 x) w

4 ` O ' If sat and saturated and submerged unit weights of the soil column respectively, Then effective stress at O is, ' v u o (h 1 w h 2 ) (h sat 1 h 2 x) w ' h ( ) x h ' x 2 sat w w 2 w For quick sand condition(sand boiling) the effective stress tends to zero; that is, ' 0 We get critical hydraulic gradient i critical as, ' h 2 ' x 0; x ' w (G 1) 1 G 1 i w critical h 2 w 1 e w 1 e Where G is the specific gravity of the soil particles and e is the void ratio of the soil mass. Therefore critical hydraulic gradient corresponds to hydraulic gradient which tends to a state of zero effective stress. Hence critical hydraulic gradient is given by i critical G 1 1 e Piping Effects Soils can be eroded by flowing water. Erosion can occur underground, beneath the hydraulic structures, if there are cavities, cracks in rock, or high exit gradient induced instability at toe of the dam, such that soil particles can be washed into them and transported away by high velocity seeping water. This type of underground erosion progresses and creates an open path for flow of water; it is called piping. Preventing piping is a prime consideration in the design of safe dams. Briefly the processes associated with initiation of piping in dams are as follows, 1. Upward seepage at the toe of the dam on the downstream side causes local instability of soil in that region leading erosion. 2. A process of gradual erosion and undermining of the dam may begin, this type of failure known as piping, has been a common cause for the total failure of earth dams 3. The initiation of piping starts when exit hydraulic gradient of upward flow is close to critical hydraulic gradient Factor of safety against piping is defined as, FS i critical I exit Where iexit is the maximum exit gradient and icritical is the critical hydraulic gradient. The maximum exit gradient can be determined from the flow net. A factor of safety of 3 to 4 is considered adequate for the safe performance of the structure against piping failure.

5 ` esign of Filters In order to avoid failures of hydraulic structures due to piping effects, many remedial measures are available. Some of these remedial measures that are usually adopted in practice are shown in Figure. They include providing impervious blanket on the upstream and gravel filter at the toe as shown for the case of an earth dam. Main objectives of these measures are preventing buildup of high seepage pressure and migration of eroded soil particles. Remedial measures against piping When seepage water flows from a soil with relatively fine grains into a coarser material there is a danger that the fine soil particles may wash away into the coarse material. Over a period of time, this process may clog the void spaces in the coarser material. Such a situation can be prevented by the use of a protective filter between the two soils. Conditions for the proper selection of the filter material are, 1. The size of the voids in the filter material should be small enough to hold the larger particles of the protected material in place. 2. The filter material should have a high permeability to prevent buildup of large seepage forces and hydrostatic pressures in the filters. The experimental investigation of protective filters provided the following criteria which are to be followed to satisfy the above conditions: Creteria-1 Creteria-2 4 to To satisfy condition 1 4 to To satisfy condition 2 Where, 15 (F) = diameter through which 15% of filter material will pass 15(S) = diameter through which 15% of soil to be protected will pass 85(S) = diameter through which 85% of soil to be protected will pass