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
View Answer
Answer: b
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+∂v∂zdz)dxdy
d) (v+∂v∂zdz)dxdz
View Answer
Answer: c
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+∂v∂zdz). Therefore, the quantity of water leaving the element is (v+∂v∂zdz)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=∂v∂zvdzdy
d) Δq=∂v∂zdxdydz
View Answer
Answer: d
Explanation: The net quantity of water squeezed out of the element per unit time is given by,
Δq=qout−qin=(v+∂v∂zdz)dxdy−vdxdy
∴ Δq=∂v∂zdxdydz.
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
View Answer
Answer: a
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’
View Answer
Answer: d
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) ∂ΔV∂z=−V0Δσ′
b) ∂ΔV∂z=−avV0Δσ′
c) ∂ΔV∂z=−mv∂Δσ′∂t
d) ∂ΔV∂z=−mvdxdydz∂Δσ′∂t
View Answer
Answer: d
Explanation: Since the decrease in volume is given by the equation,
∆v=-mv V0 ∆σ’ where V0=dxdydz,
differentiating the equation, we get,
∂ΔV∂z=−mvdxdydz∂Δσ′∂t where, mv is the coefficient of volume change.
Explanation: Since the decrease in volume is given by the equation,
∆v=-mv V0 ∆σ’ where V0=dxdydz,
differentiating the equation, we get,
∂ΔV∂z=−mvdxdydz∂Δσ′∂t 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) ∂v∂z=mv∂2u¯¯¯∂t2
b) ∂v∂z=mvu¯¯¯∂t2
c) ∂v∂z=∂2u¯¯¯∂t2
d) ∂v∂z=mv∂u¯¯¯∂t
View Answer
Answer: d
Explanation: From the volume of water squeezed out, ∆q=∂v∂z dxdydz and change of volume per unit time, ∂ΔV∂z=−mvdxdydz∂Δσ′∂t
we get, ∂v∂z=−mv∂Δσ′∂t —————–(1)
since, ∆σ=∆σ’+u, partally differentiating it with respect to time t,
∂Δσ′∂t=−∂u¯¯¯∂t ————————(2)
∴ from (1) and (2),
∂v∂z=mv∂u¯¯¯∂t.
8 - Question
The term ∂u¯¯¯∂t in terms of coefficient of volume change and coefficient of permeability is given by ____________
a) ∂u¯¯¯∂t=kmvγw∂u¯¯¯∂z
b) ∂u¯¯¯∂t=kmvγw∂u¯¯¯∂z
c) ∂u¯¯¯∂t=kmvγw∂2u¯¯¯∂z2
d) ∂u¯¯¯∂t=kmvγw∂u¯¯¯∂z
View Answer
Answer: c
Explanation: The decrease in volume is given by,
∆v=-mv V0 ∆σ’—————–(1)
also ∂v∂z=mv∂u¯¯¯∂t ——————————-(2)
∴ from (1) and (2), we get,
∂u¯¯¯∂t=kmvγw∂2u¯¯¯∂z2.
9 - Question
The coefficient of consolidation is given by ___________
a) Cv=qmvγw
b) Cv=1mvγw
c) Cv=kmv
d) Cv=kmvγw
View Answer
Answer: d
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(1−e0)avγw
c) Cv=k(e0)avγw
d) Cv=(1+e0)avγw
View Answer
Answer: a
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
View Answer
Answer: b
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
View Answer
Answer: d
Explanation: The coefficient of consolidation Cv is given by,
Cv=kmvγw
where, k is in cm/s
mv in cm2/kN
and γw in kN/cm3.
combining the units of these in the formula,
The units of Cv is cm2/s.