PE-06-Seepage-Flownets

# PE-06-Seepage-Flownets - Solved Problems in: Seepage and...

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140 Solved Problems in: Seepage and Flow-nets *01: Correct flawed flow-nets. *02: Flow-net beneath a dam with a partial cutoff wall. *03: Velocity of the flow at any point under a dam. *04: Flow-net through an earth levee. *05: Finding the total, static and dynamic heads in a dam. *06: Hydraulic gradient profile within an earth levee. *07: Flow into a cofferdam and pump size. *08: Drainage of deep excavations. *09: Dewatering a construction site. *10: Dewatering in layered strata. **11: Flow through the clay core of an earth dam.

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141 These color contours permit the visualization of the flow and the 14 dynamic head drops.
142 *Flownets-01: Correcting flawed flow-nets. (Revision: Aug-08) Do you recognize something wrong with each of the following flow-nets? a) b) filter c) Well Solution: a) Incorrectly drawn mesh, because two equipotential lines intersect each other (equipotential lines and flowlines must intersect orthogonally to each other). b) Incorrectly drawn mesh, because two flow-lines intersect each other (same as above). c) The well should be at the center of the net (a sink or a source point). Equipotential Lines Flow Lines

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143 *Flow-nets-02: A flow-net beneath a dam with a partial cutoff wall. (Revision: Aug-08) The completed flow net for the dam shown below includes a steel sheet-pile cutoff wall located at the head-water side of the dam in order to reduce the seepage loss. The dam is half a kilometer in width (shore to shore) and the permeability of the silty sand stratum is 3.5 x 10 -4 cm/s. Find, (a) the total seepage loss under the dam in liters per year, and (b) would the dam be more stable if the cutoff wall was placed under its tail-water side? 15 m h = 6.0 m 2.0 m 10.0 m 17.0 m Solution: (a) Notice that h = 6.0 m, the number of flow channels N f = 3 and the equipotentials N eq = 10. Using Forcheimer’s equation, 4 6 2 3 3.5 10 (6.0 ) 6.3 10 /sec/ sec 100 10 f eq N cm m q k h m m per mof dam width N cm - - ± ± ± = Δ = × = × ² ³ ² ³ ² ³ ´ µ ´ µ ´ µ Since the dam is 500 meters wide (shore-to-shore) the total flow Q under the dam is, 3 6 3 6 3 10 sec 500 6.3 10 / 100 sec 31.5 10 1 liters Q Lq m m m year millionliters year - ± · = = × × = ² ³² ³ ¸ ¹ ´ µ ´ µ b) No. Placing the cutoff wall at the toe would allow higher uplift hydrostatic pressures to develop beneath the dam, thereby decreasing the dam’s stability against sliding toward the right (down-stream). ψ 1 ψ 2 ψ 3 IMPERVIOUS STRATUM (CLAY OR ROCK)
*Flow-nets-03: The velocity of the flow at any point under a dam. (Revision: 12 Oct.-08) Using the flow net shown below, (1) determine the seepage underneath the 1,000 foot wide concrete dam, and (2) the velocity at point “ a ” in feet/hour, where the height of the net’s square is 19 feet. The soil has a G S = 2.67, D 10 = 0.01 mm. Overestimate the flow by using Hazen’s coefficient C = 15 to determine the permeability k . a

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## This note was uploaded on 09/11/2011 for the course CEG 4011 taught by Professor Staff during the Summer '10 term at FIU.

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PE-06-Seepage-Flownets - Solved Problems in: Seepage and...

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