# Soil Mechanics Questions and Answers – Seepage Pressure and Upward Flow – 2

This set of Soil Mechanics Problems focuses on “Seepage Pressure and Upward Flow – 2”.

1. The critical hydraulic gradient ic in terms of specific gravity G and voids ratio e is given by ______
a) Ge
b) G/e
c) $$\frac{G-1}{1+e}$$
d) $$\frac{G+1}{1-e}$$

Explanation: The critical hydraulic gradient ic is given by,
$$i_c= \frac{γ’}{γ_w}$$
$$γ’=\frac{G-1}{1+e} γ_w$$
∴ $$i_c=\frac{G-1}{1+e}.$$

2. The critical hydraulic gradient ic is unity when the specific gravity G=2.67 and voids ratio e is ______
a) 0.67
b) 0.33
c) 0.43
d) 0.80

Explanation: Given,
specific gravity G=2.67
The critical hydraulic gradient ic is given by,
$$i_c=\frac{G-1}{1+e}$$
$$1=\frac{2.67-1}{1+e}$$
∴ e=0.67.

3. A coarse-grained soil has a voids ratio of 0.66 and specific gravity G of 2.65. What will be its critical hydraulic gradient?
a) 0.99
b) 0.88
c) 0.77
d) 0.66

Explanation: The critical hydraulic gradient ic is given by,
$$i_c=\frac{G-1}{1+e}$$
$$i_c=\frac{2.65-1}{1+0.66}=0.99.$$

4. If a soil has a submerged unit weight of 10.69 kN/m3, what will be its critical hydraulic gradient?
a) 1.09
b) 0.88
c) 1.77
d) 1.66

Explanation: Given,
γ’=10.69 kN/m3
The critical hydraulic gradient ic is given by,
$$i_c= \frac{γ’}{γ_w}$$
$$i_c= \frac{10.69}{9.81}$$
∴ ic=1.09.

5. Calculate the height of water table rise in soil mass from a sand stratum of 12m deep from ground level, at which the effective pressure is zero. The water percolates through a soil mass of thickness 5m. The γsat=18.6 kN/m3 and γw=9.81 kN/m3.
a) 7.68m
b) 9.48m
c) 5.24m
d) 10m

Explanation: Given,
Thickness of soil mass=12m
water percolates through a soil mass of thickness 5m
γsat=18.6 kN/m3
γw=9.81 kN/m3
the effective pressure at sand stratum becomes aero,
σ’=zγsat-hwγw
∴hw= zγsatw
hw=5*18.6/9.81=9.48m.
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6. Water is flowing at a rate of 0.04 m3/s in a soil sample of 12m thick and cross section of 50m2. The coefficient of permeability is 1.6*10-3m/s. What will be the seepage pressure?
a) 50.76 kN/m2
b) 52.34 kN/m2
c) 55.34 kN/m2
d) 58.86 kN/m2

Explanation: Given,
Discharge q=0.04 m3/s
z=12m
Area A=50 m2
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
∴ ps =iγwz
ps =0.5*12*9.81
∴ ps =58.86 kN/m2.

7. Water is flowing at a rate of 0.04 m3/s in a soil sample of 12m thick and cross section of 50m2. The coefficient of permeability is 1.6*10-3m/s. What will be the seepage force?
a) 2943kN
b) 3453kN
c) 2454kN
d) 2443kN

Explanation: Given,
Discharge q=0.04 m3/s
z=12m
Area A=50 m2
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 seepage force J is given by,
J= iγwzA
J=0.5*12*9.81*50
∴ J=2943kN.

8. Water is flowing at a rate of 0.04 m3/s in a soil sample of 12m thick and cross section of 50m2. The coefficient of permeability is 1.6*10-3m/s. What will be the seepage force per unit volume?
a) 4.9 kN/m3
b) 3.9 kN/m3
c) 4.1 kN/m3
d) 3.2 kN/m3

Explanation: Given,
Discharge q=0.04 m3/s
z=12m
Area A=50 m2
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 seepage force per unit volume j is given by,
j=iγw
j=0.5*9.81
∴j=4.9 kN/m3.

9. Water is flowing at a rate of 0.04 m3/s in a soil sample of 12m thick and cross section of 50m2. The coefficient of permeability is 1.6*10-3m/s. The submerged unit weight γ’=9.59 kN/m3. Calculate the effective pressure if flow is in upward direction.
a) 50.76 kN/m2
b) 52.34 kN/m2
c) 55.34 kN/m2
d) 56.22 kN/m2

Explanation: Given,
Discharge q=0.04 m3/s
z=12m
Area A=50 m2
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/m2.

10. A soil has voids ratio of 0.78 and critical gradient at which quick sand condition occurs is 0.94. Calculate the specific gravity.
a) 2
b) 2.5
c) 2.67
d) 2.71

Explanation: Given,
Voids ratio e=0.78
$$i_c=\frac{G-1}{1+e}$$
$$0.94=\frac{G-1}{1+0.78}$$
∴ G=2.67.

11. If a soil has a voids ratio of 0.68 and water percolating through it has a discharge velocity of 1.35*10-2cm/s. Calculate its seepage velocity.
a) 1.35*10-2cm/s
b) 2.35*10-2cm/s
c) 3.34*10-2cm/s
d) 1.05*10-2cm/s

Explanation: Given,
Voids ratio e=0.68
discharge velocity of 1.35*10-2cm/s
seepage velocity $$v_p=\frac{(1+e)}{e}v$$
∴ vp=(1+0.68)/0.68 * 1.35*10-2
∴ vp=3.34*10-2cm/s.

12. If the discharge velocity is 1.35*10-2cm/s and seepage velocity is 3.95*10-2cm/s of water through a soil, then what will be its voids ratio?
a) 0.32
b) 0.43
c) 0.52
d) 0.66

Explanation: Given,
discharge velocity v=1.35*10-2cm/s
seepage velocity $$v_p=\frac{(1+e)}{e}v$$
∴ vp=(1+e)/ev
3.95*10-2=$$\frac{(1+e)}{e}1.35$$*10-2
2.6e=1.35
∴ e=0.52.

13. Water is flowing at a rate of 0.04 m3/s in a soil sample of 12m thick and cross section of 50m2. The coefficient of permeability is 1.6*10-3m/s. The submerged unit weight γ’=9.59 kN/m3. Calculate the effective pressure if flow is in downward direction.
a) 73.94 kN/m2
b) 152.34 kN/m2
c) 155.34 kN/m2
d) 173.94 kN/m2

Explanation: Given,
Discharge q=0.04 m3/s
z=12m
Area A=50 m2
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’=173.94 kN/m2.

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