Engineering Questions with Answers - Multiple Choice Questions

Terzaghi’s Theory of One Dimensional Consolidation – 3

1 - Question

If v is velocity at the entry of the soil element of size dx, dz and width dy as shown in the figure. The quantity of water entering the element is ___________

a) v
b) vdxdy
c) vdzdy
d) vdzdx

Explanation: Since the quantity of water q is equal to velocity of flow time the area of cross-section through which it flows,
∴ q=v*A. The area of element is dxdy.
∴ The quantity of water entering the element is vdxdy.

2 - Question

If v is velocity at the entry of the soil element of size dx, dz and width dy as shown in the figure. The quantity of water leaving the element is ___________

a) v
b) vdxdy
c) (v+vzdz)dxdy
d) (v+vzdz)dxdz

Explanation: Since the quantity of water q is equal to velocity of flow time the area of cross-section through which it flows,
∴ q=v*A. The area of element is dxdy. The velocity leaving the element is (v+vzdz). Therefore, the quantity of water leaving the element is (v+vzdz)dxdy.

3 - Question

If v is velocity at the entry of the soil element of size dx, dz and width dy as shown in the figure. The net quantity of water squeezed out of the element per unit time is ___________

a) ∆q=v
b) ∆q=vdxdy
c) Δq=vzvdzdy
d) Δq=vzdxdydz

Explanation: The net quantity of water squeezed out of the element per unit time is given by,
Δq=qoutqin=(v+vzdz)dxdyvdxdy
∴ Δq=vzdxdydz.

4 - Question

Decrease in the volume of the soil is equal to _________
a) volume of water squeeze out
b) volume of water entering the soil element
c) volume of water leaving the soil element
d) volume of soil in wet state

Explanation: Since the water occupies the voids between the soil particles and when the force is applied, the water is squeezed out and there is decrease in volume of soil. Therefore, decrease in the volume of the soil is equal to the volume of water squeeze out.

5 - Question

The decrease in volume is given by the equation ___________
a) ∆v=-V0 ∆σ’
b) ∆v=-av V0 ∆σ’
c) ∆v=-mv ∆σ’
d) ∆v=-mv V0 ∆σ’

Explanation: The decrease in the volume of the soil is equal to the volume of water squeeze out. Thus, the decrease in volume is given by the equation,
∆v=-mv V0 ∆σ’ where the negative sign indicates the decrease in volume.

6 - Question

The change of volume per unit time is __________
a) ΔVz=V0Δσ
b) ΔVz=avV0Δσ
c) ΔVz=mvΔσt
d) ΔVz=mvdxdydzΔσt

Explanation: Since the decrease in volume is given by the equation,
∆v=-mv V0 ∆σ’ where V0=dxdydz,
differentiating the equation, we get,
ΔVz=mvdxdydzΔσt where, mv is the coefficient of volume change.

7 - Question

The partial differentiation of velocity of water in soil element with respect to depth z in terms of coefficient of volume change is given by ____________
a) vz=mv2u¯¯¯t2
b) vz=mvu¯¯¯t2
c) vz=2u¯¯¯t2
d) vz=mvu¯¯¯t

Explanation: From the volume of water squeezed out, ∆q=vz dxdydz and change of volume per unit time, ΔVz=mvdxdydzΔσt
we get, vz=mvΔσt —————–(1)
since, ∆σ=∆σ’+u, partally differentiating it with respect to time t,
Δσt=u¯¯¯t ————————(2)
∴ from (1) and (2),
vz=mvu¯¯¯t.

8 - Question

The term u¯¯¯t in terms of coefficient of volume change and coefficient of permeability is given by ____________
a) u¯¯¯t=kmvγwu¯¯¯z
b) u¯¯¯t=kmvγwu¯¯¯z
c) u¯¯¯t=kmvγw2u¯¯¯z2
d) u¯¯¯t=kmvγwu¯¯¯z

Explanation: The decrease in volume is given by,
∆v=-mv V0 ∆σ’—————–(1)
also vz=mvu¯¯¯t ——————————-(2)
∴ from (1) and (2), we get,
u¯¯¯t=kmvγw2u¯¯¯z2.

9 - Question

The coefficient of consolidation is given by ___________
a) Cv=qmvγw
b) Cv=1mvγw
c) Cv=kmv
d) Cv=kmvγw

Explanation: The coefficient of consolidation is given by,
Cv=kmvγw
where, k=coefficient of permeability
mv=coefficient of volume change
γw=unit weight of water.

10 - Question

The coefficient of consolidation in terms of voids ratio e and coefficient of compressibility is ____________
a) Cv=k(1+e0)avγw
b) Cv=k(1e0)avγw
c) Cv=k(e0)avγw
d) Cv=(1+e0)avγw

Explanation: Since we know the coefficient of volume change mv=av1+e0
and the coefficient of consolidation is given by,
Cv=kmvγw. Therefore, combining the two equations, we get,
Cv=k(1+e0)avγw.

11 - Question

The term coefficient of consolidation Cv used in equation is adopted to indicate the effect of permeability only.
a) True
b) False

Explanation: The term coefficient of consolidation Cv used in equation is adopted to indicate the combined effects of the permeability and the compressibility of the soil on the rate of volume change.

12 - Question

The units of Cv is ___________
a) cm/s
b) cm
c) s
d) cm2/s