In case of radial symmetry, \(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}\) is_________

\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}-\frac{1}{r} \frac{∂\overline{u}}{∂r}\)

\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}+\frac{1}{r} \frac{∂\overline{u}}{∂r}\)

\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=\frac{∂^2 \overline{u}}{∂r^2}-\frac{1}{r} \frac{∂\overline{u}}{∂r}\)

\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=-\frac{∂^2 \overline{u}}{∂r^2}+\frac{1}{r} \frac{∂\overline{u}}{∂r}\)

\(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}=-\frac{∂^2 \overline{u}}{∂r^2}-\frac{1}{r} \frac{∂\overline{u}}{∂r}\)

When the pre-consolidation pressure σₚ‘ is greater than initial effective pressure σ’₀ but smaller than effective pressure σ’, then the final settlement is calculated on the basis of equation _________

\(ρ_f=H \frac{C_c}{1+e_o}log_{10}\frac{σ_p’}{σ’_0}+H \frac{C_c}{1+e_o}log_{10}\frac{σ’}{σ_p’}\)

\(ρ_f=H \frac{C_S}{1+e_o}log_{10}\frac{σ_p’}{σ’_0}+H \frac{C_S}{1+e_o}log_{10}\frac{σ’}{σ_p’}\)

\(ρ_f=\frac{C_S}{1+e_o}log_{10}\frac{σ_p’}{σ’_0}+\frac{C_c}{1+e_o}log_{10} \frac{σ’}{σ_p’}\)

\(ρ_f=H\frac{C_S}{1+e_o}log_{10}\frac{σ_p’}{σ’_0}+H \frac{C_c}{1+e_o}log_{10} \frac{σ’}{σ_p’}\)

During the test, the specimen is allowed to consolidate under _________

no increment of vertical pressure

only one increment of vertical pressure

only two increments of vertical pressure

a number of increments of vertical pressure

no increment of vertical pressure

At time t, the hydraulic head corresponding to excess hydrostatic pressure is __________

\(h=\frac{γ_w}{\overline{u}}\)

\(h=\frac{\overline{u}}{γ_w} \)

\(h=\frac{γ_w}{\overline{u}}\)

\(h=\frac{σ’\overline{u}}{γ_w} \)

The coefficient of consolidation in terms of voids ratio e and coefficient of compressibility is ____________

\(C_v=\frac{k(1-e_0)}{a_v γ_w}\)

\(C_v=\frac{k(1+e_0)}{a_v γ_w}\)

\(C_v=\frac{k(1-e_0)}{a_v γ_w}\)

\(C_v=\frac{k(e_0)}{a_v γ_w}\)

\(C_v=\frac{(1+e_0)}{a_v γ_w}\)

The one dimensional flow part of governing consolidation equation of three dimensional consolidation having radial symmetry is _______

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{∂\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} \frac{∂\overline{u}}{∂r^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{∂\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vz} (\frac{∂\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{∂\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})\)

From the practical data, in square root of time fitting, ______ curve is plotted.

t³ in abscissa and dial reading R in Ordinate

time t in abscissa and dial reading R in Ordinate

t² in abscissa and dial reading R in Ordinate

root of time √t in abscissa and dial reading R in Ordinate

t³ in abscissa and dial reading R in Ordinate

The numerical integration may be performed by _______________

dividing the total thickness H into only two thin layers

dividing the total thickness H into a number of thin layers

dividing the total thickness H into only two thin layers

dividing the total thickness H by a factor

excluding the thickness of the soil layer

By the use of consolidometer, _________ gives direct measurement of permeability.

both fixed and floating ring type

both fixed and floating ring type don’t give direct measurement

From the consolidation test data using the ‘change in void ratio’ method, the coefficient of volume change can be calculated by _____________

\(m_v=-\frac{∆e}{1+e_o} \frac{1}{σ’} \)

\(m_v=-\frac{∆e}{1+e_o} \frac{10}{∆σ’}\)

\(m_v=-\frac{∆e}{1+e_o} \frac{1}{∆σ’}\)

The coefficient of volume change is ______________

equal to compressibility modulus

reciprocal of compressibility modulus

equal to compressibility modulus

equal to three times the compressibility modulus

The change in voids ratio of the consolidation test is calculated from the relation of________

\(∆e=\frac{1+e_f}{H_f} ∆H_f\)

In consolidation test, the soil is __________

not restrained laterally as well as vertically

From the consolidation test, the final voids ratio at end of pressure increment can be calculated by ________________

change in voids ratio method only

both height of solids method and change in voids ratio method

The partial differentiation of excess hydrostatic pressure \overline{u} as a function of r and θ with respect to x is given by _______

\(\frac{∂\overline{u}}{∂x}=\frac{∂\overline{u}}{∂r} cosθ-\frac{1}{r} \frac{∂\overline{u}}{∂θ} cosθ\)

\(\frac{∂\overline{u}}{∂x}=\frac{∂\overline{u}}{∂r} cosθ-\frac{1}{r}\frac{∂\overline{u}}{∂θ} sinθ\)

\(\frac{∂\overline{u}}{∂x}=\frac{∂\overline{u}}{∂r} cosθ-\frac{1}{r} \frac{∂\overline{u}}{∂θ} cosθ\)

\(\frac{∂\overline{u}}{∂x}=\frac{∂\overline{u}}{∂r} sinθ-\frac{1}{r} \frac{∂\overline{u}}{∂θ} sinθ\)

\(\frac{∂\overline{u}}{∂x}=\frac{∂\overline{u}}{∂r} sinθ-\frac{1}{r} \frac{∂\overline{u}}{∂θ} cosθ\)

In three dimensional consolidation of sand drain, having radial symmetry, the governing consolidation equation is _______

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{\overline{u}}{∂r^2}-\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})-C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vr} (\frac{\overline{u}}{∂r^2}-\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

\(\frac{∂\overline{u}}{∂t}=C_{vz} (\frac{\overline{u}}{∂r^2}+\frac{1}{r}\frac{∂\overline{u}}{∂r})+C_{vz}\frac{∂^2 \overline{u}}{∂z^2}\)

The height of solids method is applicable for ________

only partially saturated specimens

both saturated and unsaturated samples

only partially saturated specimens

In polar form the term, \(\frac{∂θ}{∂x}\) is given by______

\(\frac{∂θ}{∂x}=\frac{sinθ}{r} \)

\(\frac{∂θ}{∂x}=-cosθsinθ \)

\(\frac{∂θ}{∂x}=-\frac{cosθ}{r}\)

\(\frac{∂θ}{∂x}=\frac{-sinθ}{r}\)

In polar form the term, \(\frac{∂r}{∂y}\) is given by______

\(\frac{∂r}{∂y}=cosθsinθ\)

In numerical integration of the equation, the total settlement of the layer is equal to _____________

difference of individual settlements of the various thin layers

product of individual settlements of the various thin layers

sum of individual settlements of the various thin layers

difference of individual settlements of the various thin layers

division of individual settlements of the various thin layers

214 + Mcqs in One Dimensional Consolidation in Geotechnical Engineering Page 2 McqOptions

51.	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 KN/m³
C.	23.55 KN/m³
D.	50.43 KN/m³
Answer» B. 76.22 KN/m³

53.	If the height of soil specimen is reduced from 0.28 cm to 1.926cm due to an increment of load of 100KN/m². Find the coefficient of volume change.
A.	0.74m²/MN
B.	0.98m²/MN
C.	0.84m²/MN
D.	0.67m²/MN
Answer» B. 0.98m²/MN

54.	For a dry mass of soil of 180.4g and height of solids as 13.45mm with cross-sectional area as 50cm², find the specific gravity of soil.
A.	2.68
B.	8.33
C.	1.64
D.	5.32
Answer» B. 8.33

56.	In logarithm of time fitting method, the graph is drawn on a ____________
A.	radial graph
B.	linear graph
C.	semi-log plot
D.	log-log plot
Answer» D. log-log plot

57.	In Terzaghi’s Theory of one dimensional consolidation, coefficient of permeability is ______
A.	zero
B.	variable
C.	constant
D.	unity
Answer» D. unity

59.	The change in voids ratio is 0.18 and initial void ratio is 0.68 with the increase of pressure as 200KN/m². Find the coefficient of volume change.
A.	0.536 m²/MN
B.	0.111 m²/MN
C.	0.832 m²/MN
D.	0.356 m²/MN
Answer» B. 0.111 m²/MN

60.	In Terzaghi’s Theory of one dimensional consolidation, soil particles are ____________ and water is ______________
A.	compressible, incompressible
B.	both are compressible
C.	both are incompressible
D.	incompressible, compressible
Answer» D. incompressible, compressible

61.	For final void ratio 0.886 and water content of 30%, find the specific gravity.
A.	4.68
B.	2.68
C.	1.45
D.	2.45
Answer» C. 1.45

62.	The transformation from Cartesian to plane coordinates in x-direction is given by ______
A.	x=rsinθ
B.	x=rcosθ
C.	x=rcos2θ
D.	x=rsin2θ
Answer» C. x=rcos2θ

63.	At time t, the hydraulic head corresponding to excess hydrostatic pressure is __________
A.	\(h=\frac{σ’}{γ_w}\)
B.	\(h=\frac{\overline{u}}{γ_w} \)
C.	\(h=\frac{γ_w}{\overline{u}}\)
D.	\(h=\frac{σ’\overline{u}}{γ_w} \)
Answer» C. \(h=\frac{γ_w}{\overline{u}}\)

64.	Terzaghi’s theory of consolidation is invalid for ________
A.	pre-consolidation
B.	under- consolidation
C.	secondary consolidation
D.	normal- consolidation
Answer» D. normal- consolidation

66.	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
Answer» C. 4.3312

67.	Secondary consolidation may not constitute a substantial percentage of total settlement for __________
A.	highly organic soils
B.	inorganic soil
C.	highly micaceous soils
D.	gyttja
Answer» C. highly micaceous soils

73.	A number of isochrones can be drawn for water levels in piezometric tubes at the same time t.
A.	True
B.	False
C.	May be True or False
D.	Can't say
Answer» C. May be True or False

77.	The units of Cᵥ is ___________
A.	cm/s
B.	cm
C.	s
D.	cm²/s
Answer» E.

71.	By the use of consolidometer, _________ gives direct measurement of permeability.
A.	only fixed ring type
B.	only floating ring type
C.	both fixed and floating ring type
D.	both fixed and floating ring type don’t give direct measurement
Answer» B. only floating ring type

72.	From the consolidation test data using the ‘change in void ratio’ method, the coefficient of volume change can be calculated by _____________
A.	\(m_v=-\frac{∆e}{1+e_o} \frac{1}{σ’} \)
B.	\(m_v=-\frac{∆e}{1+e_o}\)
C.	\(m_v=-\frac{∆e}{1+e_o} \frac{10}{∆σ’}\)
D.	\(m_v=-\frac{∆e}{1+e_o} \frac{1}{∆σ’}\)
Answer» E.

75.	The change in voids ratio of the consolidation test is calculated from the relation of________
A.	\(∆e=\frac{1+e_f}{2} ∆H\)
B.	\(∆e=\frac{1+e_f}{H_f} ∆H_f\)
C.	\(∆e=\frac{1+e_f}{H}\)
D.	\(∆e=\frac{e_f}{H_f} ∆H\)
Answer» B. \(∆e=\frac{1+e_f}{H_f} ∆H_f\)

76.	The transformation from Cartesian to plane coordinates in y-direction is given by ______
A.	y=rsinθ
B.	y=rcosθ
C.	y=rcos2θ
D.	y=rsin2θ
Answer» B. y=rcosθ

78.	In consolidation test, the soil is __________
A.	restrained laterally
B.	restrained vertically
C.	not restrained laterally
D.	not restrained laterally as well as vertically
Answer» B. restrained vertically

79.	From the consolidation test, the final voids ratio at end of pressure increment can be calculated by ________________
A.	height of solids method only
B.	change in voids ratio method only
C.	both height of solids method and change in voids ratio method
D.	no method are available
Answer» D. no method are available

81.	If height of solids Hₛ is 6.725mm, mass is 180.4g with specific gravity G=2.68, then final the Cross-sectional area of specimen.
A.	220 cm²
B.	342 cm²
C.	100 cm²
D.	659 cm²
Answer» D. 659 cm²

82.	In case of pre-consolidated soil, the final settlement is ___________
A.	small
B.	negligible
C.	large
D.	very large
Answer» B. negligible

84.	The time factor Tᵥ for the vertical flow is given by _______
A.	\(T_v=\frac{C_{vz} t}{H^2} \)
B.	\(T_v=\frac{-C_{rz} t}{H^2} \)
C.	\(T_v=\frac{C_{vz}}{H^2} \)
D.	\(T_v=\frac{C_{vz} t}{H}\)
Answer» B. \(T_v=\frac{-C_{rz} t}{H^2} \)

85.	The height of solids method is applicable for ________
A.	only dry specimens
B.	only fully saturated specimens
C.	both saturated and unsaturated samples
D.	only partially saturated specimens
Answer» D. only partially saturated specimens

Explore topic-wise MCQs in Geotechnical Engineering.

For a mass of 3.192g of soil with voids ratio 0.532, find its saturated unit weight.

In case of radial symmetry, \(\frac{∂^2 \overline{u}}{∂x^2}+\frac{∂^2 \overline{u}}{∂y^2}\) is_________

If the height of soil specimen is reduced from 0.28 cm to 1.926cm due to an increment of load of 100KN/m². Find the coefficient of volume change.

For a dry mass of soil of 180.4g and height of solids as 13.45mm with cross-sectional area as 50cm², find the specific gravity of soil.

When the pre-consolidation pressure σₚ‘ is greater than initial effective pressure σ’₀ but smaller than effective pressure σ’, then the final settlement is calculated on the basis of equation _________

In logarithm of time fitting method, the graph is drawn on a ____________

In Terzaghi’s Theory of one dimensional consolidation, coefficient of permeability is ______

During the test, the specimen is allowed to consolidate under _________

The change in voids ratio is 0.18 and initial void ratio is 0.68 with the increase of pressure as 200KN/m². Find the coefficient of volume change.

In Terzaghi’s Theory of one dimensional consolidation, soil particles are ____________ and water is ______________

For final void ratio 0.886 and water content of 30%, find the specific gravity.

The transformation from Cartesian to plane coordinates in x-direction is given by ______

At time t, the hydraulic head corresponding to excess hydrostatic pressure is __________

Terzaghi’s theory of consolidation is invalid for ________

The coefficient of consolidation in terms of voids ratio e and coefficient of compressibility is ____________

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.

Secondary consolidation may not constitute a substantial percentage of total settlement for __________

The one dimensional flow part of governing consolidation equation of three dimensional consolidation having radial symmetry is _______

From the practical data, in square root of time fitting, ______ curve is plotted.

The numerical integration may be performed by _______________

By the use of consolidometer, _________ gives direct measurement of permeability.

From the consolidation test data using the ‘change in void ratio’ method, the coefficient of volume change can be calculated by _____________

A number of isochrones can be drawn for water levels in piezometric tubes at the same time t.

The coefficient of volume change is ______________

The change in voids ratio of the consolidation test is calculated from the relation of________

The transformation from Cartesian to plane coordinates in y-direction is given by ______

The units of Cᵥ is ___________

In consolidation test, the soil is __________

From the consolidation test, the final voids ratio at end of pressure increment can be calculated by ________________

The partial differentiation of excess hydrostatic pressure \overline{u} as a function of r and θ with respect to x is given by _______

If height of solids Hₛ is 6.725mm, mass is 180.4g with specific gravity G=2.68, then final the Cross-sectional area of specimen.

In case of pre-consolidated soil, the final settlement is ___________

In three dimensional consolidation of sand drain, having radial symmetry, the governing consolidation equation is _______

The time factor Tᵥ for the vertical flow is given by _______

The height of solids method is applicable for ________

In polar form the term, \(\frac{∂θ}{∂x}\) is given by______

The theory of the primary design of sand drains based upon the extension of Terzaghi’s basic work was largely developed by ___________

In polar form the term, \(\frac{∂r}{∂y}\) is given by______

The theoretical concept of consolidation process was developed by _____________

The height Hₛ of the solids of the specimen with respect to weight of dried specimen is _____________

If the final voids ratio is 0.864 for a soil sample of specific gravity 2.7, then its final water content will be _______________

In numerical integration of the equation, the total settlement of the layer is equal to _____________

The change in voids ratio is 0.18 and initial void ratio is 0.68 with the increase of pressure as 200KN/m². Find the coefficient of Compressibility.

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.

For a time factor Tᵥ of 0.567, find the degree of consolidation.

The equation given by Carillo in 1942 relating the degree of consolidation in one dimensional flow (Uz) and radial flow (Ur) is _______

The loading machine of consolidometer is generally capable of applying vertical pressure up to ________ kPa in general.

The vertical compression of the specimen is measured by means of _________

______________ also worked independently on the problem of sand drains and published his results in 1942.

In Terzaghi’s Theory of one dimensional consolidation, deformation of soil is entirely due to _________________

In Terzaghi’s Theory of one dimensional consolidation, soil particles are and water is __

87.	The theory of the primary design of sand drains based upon the extension of Terzaghi’s basic work was largely developed by ___________
A.	Darcy
B.	Skempton
C.	Taylor
D.	Barron
Answer» E.

88.	In polar form the term, \(\frac{∂r}{∂y}\) is given by______
A.	\(\frac{∂r}{∂y}=sinθ\)
B.	\(\frac{∂r}{∂y}=cosθsinθ\)
C.	\(\frac{∂r}{∂y}=cosθ\)
D.	\(\frac{∂r}{∂y}=sin2θ\)
Answer» B. \(\frac{∂r}{∂y}=cosθsinθ\)

89.	The theoretical concept of consolidation process was developed by _____________
A.	Terzaghi
B.	Taylor
C.	Skempton
D.	Darcy
Answer» B. Taylor

90.	The height Hₛ of the solids of the specimen with respect to weight of dried specimen is _____________
A.	\(H_s=\frac{W_d}{Gρ_w}\)
B.	\(H_s=\frac{W_d}{GAρ_w}\)
C.	\(H_s=\frac{W_d}{GA}\)
D.	\(H_s=\frac{W_d}{Aρ_w}\)
Answer» D. \(H_s=\frac{W_d}{Aρ_w}\)

91.	If the final voids ratio is 0.864 for a soil sample of specific gravity 2.7, then its final water content will be _______________
A.	32%
B.	48%
C.	56%
D.	62%
Answer» B. 48%

93.	The change in voids ratio is 0.18 and initial void ratio is 0.68 with the increase of pressure as 200KN/m². Find the coefficient of Compressibility.
A.	0.9 m²/MN
B.	0.7 m²/MN
C.	0.4 m²/MN
D.	0.5 m²/MN
Answer» B. 0.7 m²/MN

94.	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
Answer» C. 22m

95.	For a time factor Tᵥ of 0.567, find the degree of consolidation.
A.	37%
B.	60%
C.	80%
D.	95%
Answer» D. 95%

96.	The equation given by Carillo in 1942 relating the degree of consolidation in one dimensional flow (Uz) and radial flow (Ur) is _______
A.	(1-U)=(1-Uz)(1+Ur)
B.	(1-U)=(1-Uz)(1-Ur)
C.	(1-U)=(1+Uz)(1-Ur)
D.	(1-U)=(1+Uz)(1+Ur)
Answer» C. (1-U)=(1+Uz)(1-Ur)

97.	The loading machine of consolidometer is generally capable of applying vertical pressure up to ________ kPa in general.
A.	10 or 20
B.	40 or 50
C.	80 or 90
D.	800 or 1000
Answer» E.