Question

Water is flowing at a rate of 0.04 m^3/s in a soil sample of 12m thick and cross section of 50m^2. The coefficient of permeability is 1.6*10^-3m/s. The submerged unit weight γ’=9.59 kN/m^3. Calculate the effective pressure if flow is in upward direction.

(a) 50.76 kN/m^2

(b) 52.34 kN/m^2

(c) 55.34 kN/m^2

(d) 56.22 kN/m^2

The question was posed to me in class test.

This interesting question is from Seepage Pressure and Upward Flow in chapter Seepage Analysis of Geotechnical Engineering I

Answer 1

Correct answer is (d) 56.22 kN/m^2

To elaborate: Given,

Discharge q=0.04 m^3/s

z=12m

Area A=50 m^2

coefficient of permeability k=1.6*10^-3m/s

the hydraulic gradient i is given by,

i=q/(kA)

i=0.04/(50*1.6*10^-3)

i=0.5

∴ The effective pressure is given by

σ’=zγ’-izγw

σ’=12*9.59-0.5*12*9.81

σ’=56.22 kN/m^2.