Question

3. The flow net shown below illustrates flow conditions beneath a concrete dam featuring an upstream "clay blanket" (an impermeable clay layer) and a downstream "cutoff wall", both of which serve to lengthen the flow path. The coefficient of permeability, k, of the permeable strata is 8 x 10 cm/s. a. Calculate the flow rate, q, per day beneath the dam (per m of dam out-of-plane). b. Calculate the total head, elevation head, pressure head, and pore water pressure at points A, B and C. c. Calculate the FS against uplift failure for this dam. concrete CUTOFF WALL 5m CLAY datum il 4.5 m 5m 5m 8 5m 5m IMPERViOUS

Answer 1

a, The flow rate is given by q = k x H x N_f / N_d

k = 8 x 10^-4 cm/sec

H = 5-1= 4 m

Nf = 4

Nd = 14

q = 8 x 10^-4 x 10^-3 x 4 x 4/14 = 9.143 x 10^-7 m²/sec per metre of dam out of plane

= 9.143 x 10^-7 x 3600 x 24 = 0.0789942 m2/day per metre out of dam out of plane

b.

Nf = 14

Head drop = 16/14 = 1.143m per equipotential drop;

Head at point A = 16- 3x1.143 = 12.571

Head at point B=16- 5x1.143 = 10.258

Head at point C= 16-9x1.143= 5.713

c.

FS against uplift faillure for this dam= i_critical/i_{actual ;}

i_{critical =} (G-1)/(1+e) = (2.7-1)/(1+0.85) = 0.865

i_{actual =}  4/(11x1) = 0.3636

FS against uplift failure = 0.865/0.3636 = 2.379