Engineering Questions with Answers - Multiple Choice Questions

# Consolidation Problems – 3

1 - Question

For a mass of 3.192g of soil with voids ratio 0.532, find its saturated unit weight.
a) 20.44 KN/m3
b) 76.22
c) 23.55
d) 50.43

Explanation:
ρsat=M1+e=3.1921+0.532=2.084 g/cm3
γsat = 9.81ρsat = 9.81×2.084 = 20.44 kN/m3.

2 - Question

For a remolded sample of clay with liquid limit of 45%, find its compression index.
a) 0.753
b) 0.561
c) 0.493
d) 0.245

Explanation: Given,
WL= 45%, for remolded sample of clay
Cc=0.007(WL-10%)
=0.245.

3 - Question

For an ordinary clay of medium sensitivity, the value of compression index is _____ if liquid limit is 50%.
a) 0.36
b) 0.45
c) 0.12
d) 0.64

Explanation: WL=50%
For ordinary sample of clay
Cc=0.009(WL -10)
=0.36.

4 - Question

If change in voids ratio is 0.18 and change in effective pressure is 100KN/m2, then the coefficient of compressibility is ______
a) 2.5×10-3 m2/kN
b) 2×10-3 m2/kN
c) 9×10-3 m2/kN
d) 9.5×10-3 m2/kN

Explanation: Given,
∆e=0.18
∆σ’=100 kN/m3
aw=ΔeΔσ=0.18100=2×10-3 m2/kN.

5 - Question

Two clay layer of A and B of thickness 2cm and 3 cm is load with pressure of 200KN/m2. If the time taken by soil A to reach 50% consolidation is 1/4th of that required by soil B to reach 50% consolidation, then find the ratio of coefficients of consolidation.
a) 2.4432
b) 1.7778
c) 4.3312
d) 5.3489

Explanation: Given,
dA=2/2 = 1cm
dB=3/2= 1.5 cm
tBtA=41
The ratio of coefficient of consolidation is, (Cv)A(Cv)B
(Cv)A(Cv)B=(dA)2(dB)2×tBtA=(2/2)2(3/2)2×41=1.7778.

6 - Question

Two clay layer of A and B of thickness 2cm and 3 cm is load with pressure of 200KN/m2. If the time taken by soil A to reach 50% consolidation is 1/4th of that required by soil B to reach 50% consolidation, then find the ratio of coefficients of Permeability. Given that ratio of coefficient of volume change is 1.751.
a) 5.234
b) 2.456
c) 3.114
d) 4.233

Explanation: Given,
(mv)A(mv)B=1.751
KBKA=(Cv)A(Cv)B×(mv)A(mv)B=1.7778×1.751
KBKA=3.114.

7 - Question

A clay sample 24mm thick takes 20 minutes to consolidate 50% with double drainage. The field clay layer from which sample was obtained takes 386 days to consolidate 50% with double drainage. Find the depth of the clay layer in the field.
a) 4m
b) 7m
c) 3m
d) 2m

Explanation: Given,
t1= 20 min
t2= 386 days
d1= 2.4/2 = 1.2 cm
since, t2t1=(d2d1)2
therefore d2=d1t2t1−−√=1.2386×60×2420−−−−−−−√=200cm=2m
since double drainage is allowed, the depth is 4m.

8 - Question

A clay sample 24mm thick takes 20 minutes to consolidate 50% with double drainage. The field clay layer from which sample was obtained takes 386 days to consolidate 50% with single drainage. Find the depth of the clay layer in the field.
a) 5m
b) 2m
c) 22m
d) 16m

Explanation: Given, the sample has double drainage while the field layer has single drainage.
t1= 20 min
t2= 386 days
d1= 2.4/2 = 1.2 cm
since, t2t1=(d2d1)2
therefore d2=d1t2t1−−√=1.2386×60×2420−−−−−−−√=200cm=2m.

9 - Question

A clay sample 24mm thick takes 20 minutes to consolidate 50% with single drainage. The field clay layer from which sample was obtained takes 386 days to consolidate 50% with single drainage. Find the depth of the clay layer in the field.
a) 200cm
b) 367cm
c) 400cm
d) 569cm

Explanation: Given, both the sample and the field layer has single drainage,
t1= 20 min
t2= 386 days
d1= 2.4cm
since, t2t1=(d2d1)2
therefore d2=d1t2t1−−√=2.4386×60×2420−−−−−−−√=400cm=4m.

10 - Question

A clay sample 24mm thick takes 20 minutes to consolidate 50% with single drainage. The field clay layer from which sample was obtained takes 386 days to consolidate 50% with double drainage. Find the depth of the clay layer in the field.
a) 800cm
b) 500cm
c) 600cm
d) 480cm

Explanation: Given, the sample has single drainage while the field layer has double drainage.
t1= 20 min
t2= 386 days
d1= 2.4 cm
since, t2t1=(d2d1)2
therefore d2=d1t2t1−−√=2.4386×60×2420−−−−−−−√=400cm=4m.
Since double drainage is allowed in field, the depth is 400×2= 800 cm.

11 - Question

For a foundation, find the elapsed time in which 10% of ultimate settlement will occur. The coefficient of consolidation is 4*10-4cm2/s. The average drainage path is 50cm.
a) 19.9 hours
b) 15.5 hours
c) 13.9 hours
d) 17.5 hours

Explanation: Given,
d=50 cm
Cv=4×10-4 cm2/s
For consolidation of 10%, U<60%
Tv=π4(v100)2=π4(10100)2=0.008
Therefore time elapsed t10=(Tv)10d2Cv=0.008×(50)24×104s=13.9hours.

12 - Question

For a foundation, find the elapsed time in which 90% of ultimate settlement will occur. The coefficient of consolidation is 4*10-4cm2/s. The average drainage path is 50cm.
a) 56.38 days
b) 43.78 days
c) 61.34 days
d) 78.23 days

Explanation: Given,
d=50 cm
Cv=4×10-4 cm2/s
For consolidation of 90%, U>60%
Therefore Tv= 1.7813 – 0.9332 log10 (100-U)
Tv= 1.7813 – 0.9332 log10 (100-90)
Tv= 0.848
G0=(Tv)90d2Cv=0.848×(50)24×104s
G0= 61.34 days.

13 - Question

If initial voids ratio is 1.08, then find the compression index.
a) 0.524
b) 0.243
c) 0.728
d) 0.871

Explanation: Given,
From Hough equation,
Cc=0.3(e0-0.27)
Cc=0.3(1.08-0.27)
Cc= 0.243.

14 - Question

If excess hydraulic pressure is 19.62 KN/m2 then find the hydraulic head.
a) 2m
b) 4m
c) 8m
d) 16m

Explanation: Given,
u=19.62 kN/m2
Therefore h=u¯¯¯γω=19.629.81=2m
h = 2m.

15 - Question

Find the hydrostatic pressure of water at depth 10m.
a) 98.1KN/m2
b) 54. 1KN/m2
c) 32. 1KN/m2
d) 43. 1KN/m2