Question

Two rows of sheet piles are driven to a depth of 4.4 m below the bed of a river to form a coffer dam. Excavation is then carried out within the coffer dam up to a depth of 3.3 m below the water level by keeping the area free from water by pumping. The river bed is sand with k = 3 x 10-3 cm/s and is underlain by an impermeable stratum at a depth of 6.0 m below the river bed. What is the quantity of flow into the coffer dam per hour per meter length of the sheet pile walls? Is there any danger of quick condition developing at the bottom of the excavation?

Answer 1

Answer:

Explanation:

Given Two rows of sheet piles are driven to a depth of 4.4 m below the bed of a river to form a coffer dam. Excavation is then carried out within the coffer dam up to a depth of 3.3 m below the water level by keeping the area free from water by pumping. The river bed is sand with k = 3 x 10-3 cm/s and is underlain by an impermeable stratum at a depth of 6.0 m below the river bed. What is the quantity of flow into the coffer dam per hour per meter length of the sheet pile walls? Is there any danger of quick condition developing at the bottom of the excavation?

We have section and flow net. The flow net is symmetrical about the line. The flow on either side remains on that side.

So for flow net Nf  = 6 and Nd = 11, total head loss = 3.3 m

Now q = k h Nf / Nd

          = 3 x 10^-3 x 10^-2 x 3.3 x 6 / 11 cu m / s / m

         = 5.4 x 10^-5 cu m / s / m

Now q = 5.4 x 3600 x 10^-5

 So q = 19,440 x 10^-5

         = 0.19 cu m / hr / m

So to keep excavation free from water pumping is done at this rate.

We know that Δh = 3.3 / 11 = 0.3 m and l = 0.65 m the field below base of excavation.

Now hydraulic gradient is i = Δh / l

                               So i = 0.3 / 0.65

                      Or i = 0.46

So there is no danger for quick development of the condition, but a safety of at least 4 to 5 will be preferred.

Answer 2

Answer:

i=0.46 will be the correct answer hope it helps you