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MVS ACADEMY CIVIL ENGINEERING GATE – 2019

Syllabus as per GATE – 2019

Soil Mechanics:

45. Origin of soils, soil structure and fabric; Three-phase system and phase relationships,

index properties; Unified and Indian standard soil classification system;

46. Permeability - one dimensional flow, Darcy’s law; Seepage through soils - two-

dimensional flow, flow nets, uplift pressure, piping;

47. Principle of effective stress, capillarity, seepage force and quicksand condition;

48. Compaction in laboratory and field conditions; One-dimensional consolidation, time

rate of consolidation;

49. Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics

of clays and sand.

Foundation Engineering:

50. Sub-surface investigations - scope, drilling bore holes, sampling, plate load test,

standard penetration and cone penetration tests;

51. Earth pressure theories-Rankine and Coulomb;

52. Stability of slopes - finite and infinite slopes, method of slices and Bishop’s method;

53. Stress distribution in soils - Boussinesq’s and Westergaard’s theories, pressure bulbs;

54. Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity theories, effect of

water table; Combined footing and raft foundation; Contact pressure; Settlement

analysis in sands and clays;

55. Deep foundations - types of piles, dynamic and static formulae, load capacity of piles in

sands and clays, pile load test, negative skin friction.


Few Typical Questions with Solutions given module wise list for reference:

SOIL MECHANICS

MODULE -45

1) Match List-I (type of soil) with List-II (mode of transportation and deposition) and

select the correct answer using the codes given below the lists:

List – I

A) Lacustrine soils

B) Alluvial soils

C) Aeolian soils

D) Marine soils

List-II

1) Transportation by wind

2) Transportation by running water

3) Deposited at the bottom of lakes

4) Deposited in sea water

Codes:

A B C D

A) 1 2 3 4

B) 3 2 1 4

C) 3 2 4 1

D) 1 3 2 4

Ans: B

2) The water content of a saturated soil and the specific gravity of soil solids were found

to be 30% and 2.70, respectively. Assuming the unit weight of water to be 10 ,

the saturated unit weight and the void ratio of the soil are

A) 19.4, 0.81 B) 18.5, 0.30 C) 19.4, 0.45 D) 18.5, 0.45

Ans: A


Solution:

3) In a wet soil mass, air occupies one-sixth of its volume and water occupies one-third

of its volume. The void ratio of the soil is

A) 0.25 B) 0.5 C) 1.00 D) 1.50

Ans: C

Solution:

4) An earth embankment is to be compacted to a proctor density of 18 and a

water content of 15 %. Then situ bulk density and water content of the borrow pit are

17.5 and 8 % respectively. How much excavation should be carried out in the

borrow pit for 100 cu.m of embankment?

Ans: 96.6

Solution:

5) The liquid limit and plastic limit of samples are 65% and 29% respectively. The

percentage of clay fraction with grain size finer than 0.002 mm is 24. The activity

ratio of the soil sample is

A) 0.05 B) 1.00 C) 1.50 D) 2.00

Ans: C


Solution:

6) Data from a sieve analysis conducted on a given sample of soil showed that 67% of

the particles passed through 75 micron IS sieve. The liquid limit and plastic limit of

the finer fraction was found to be 45 and 33 percents respectively. The group symbol

of the given soil as per IS: 1498-1970 is

A) SC B) MI C) CH D) MH

Ans: B

Solution:

As more than 50 % of the total soil is finer than 75 the given soil is fine-grained

soil

on the A-line, =18.25

The soil is below A-line. So the soil is MI.

7) The correct sequence of plasticity of minerals in soil in an increasing order is

A) Silica, kaolinite, illite, montmorillonite

B) Silica, kaolinite, montmorillonite, illite

C) Kaolinite, silica, illite, montmorillonite

D) Kaolinite, silica, montmorillonite, illite

Ans: A


MODULE – 46

8) The soil profile below a lake with water level at elevation = 0 m and lake bottom at

elevation=-10 m is shown in the figure, where k is the permeability coefficient. A

piezometer (stand pipe) installed in the sand layer shows a reading of +10 m

elevation. Assume that the piezometric head is uniform in the sand layer. The quantity

of water (in ) flowing into the lake from the sand layer through the silt layer per

unit area of the lake bed is:

A) 1.5 x B) 2.0 x C) 1.0 x D) 0.5 x

Ans: D

Solution:

where Loss of head and L = Length of silt layer

=

0.5

9) In a falling head permeability test the time taken for the head to fall from 27cm to

3cm is 10min. If the test is repeated with same initial head i.e. 27 cm, what time (min)

would it take for the head to fall to 9cm.

Ans: 5

Solution:

(

)


(

)

(

)

(

)

(

)

10) In a falling head permeability test, the time interval noted for the head to fall from

to and from to have been found to be equal. Relation between ?

A) √ B) √ C) √ D) √

Ans: B

Solution:

(

) (

)

√

11) A bed of sand consists of three horizontal layers of equal thickness. The value of

Darcy’s ‘k’ for upper and lower layers is cm/sec and the middle layer is

cm/sec. The ratio of the permeability of the bed in the horizontal direction

to that in the vertical direction is

A) 10.0 to 1 B) 2.8 to 1 C) 2.0 to 1 D)1 to 10

Ans: B

Solution:

= 0.04

=


12) Find the ratio of average permeability in the horizontal direction to that in the vertical

direction for a soil deposit of three layers with thickness in the ratio 1: 2: 3. The

permeability of the second layer is twice that of the first and of the third is twice that

of the second.

Ans: 1.3

Solution:

13) The flow net around a sheet pile wall is shown in the sketch. The properties of the soil

are: permeability coefficient = 0.09 m/day (isotropic), specific gravity = 2.70 and void

ratio = 0.85. The sheet pile wall and the bottom of the soil are impermeable.

The seepage loss (in per day per unit length of the wall) of water is

A) 0.33 B) 0.38 C) 0.43 D) 0.54

Ans: B

Solution:

Q

0.09


14) A soil mass under seepage has a downward flow of water. Which of the following

statements are correct with regard to stresses at any point in the soil mass?

1. Effective stress is decreased by an amount equal to the seepage force

2. Effective stress is increased by an amount equal to the seepage force

3. Total stress will change

4. Total stress will be unaltered

Select the correct answer using the codes given below:

A) 1 and 3 B) 2 and 3 C) 1 and 4 D) 2 and 4

Ans: D

MODULE – 47

15) The specific gravity and in-situ void ratio of a soil deposit are 2.71 and 0.85

respectively. The value of the critical hydraulic gradient is

A) 0.82 B) 0.85 C) 0.92 D) 0.95

Ans: C

Solution:

16) A 10m thick clay layer is underlain by a sand layer of 20m depth (see figure below).

The water table is 5 m below the surface of clay layer. The soil above the water table

is capillary saturated. The value of is 19kN/m3. The unit weight of water is . If

now the water table rises to the surface, the effective stress at a point P on the

interface will


A) Increase by 5

B) Remain unchanged

C) Decrease by 5

D) Decrease by 10

Ans: C

Solution:

Before:

After:

17) Quick sand condition occurs when

A) The void ratio of the soil becomes 1.0

B) The upward seepage pressure in soil becomes zero

C) The upward seepage pressure in soil becomes equal to the saturated unit weight of

the soil

D) The upward seepage pressure in soil becomes equal to the submerged unit weight

of the soil

Ans: D

18) Compute the total, effective and pore water pressure at a depth of 20m below the

bottom of a lake 6m deep. The bottom of lake consists of soft clay with a thickness of

more than 20m. The average water content of the clay is 35% and specific gravity of

the soil may be assumed as 2.65.

A) 169.14 B) 234.5 C) 321.3 D) 123.4

Ans: A

Solution:

(

)

255.06


169.14

MODULE – 48

19) A compaction of an embankment is carried out in thick horizontal layers. The rammer

used for compaction has the foot of area 0.05 sq.m. The energy developed per drop of

the hammer is 40 kg-m. Assuming 50% more energy in each pass due to overlap,

calculate the number of passes required to develop compactive energy equivalent to

Indian standard (light compaction for each layer).

A) 16 B) 12 C) 8 D) 4

Ans: A

Solution:

Volume 0.3

Energy required 0.015

Energy per pass 40

No of passes

20) Match List-I (Equipment) with List-II (Purpose) and select the correct answer using

the codes given below the lists:

List-I

A. Sheep foot rollers

B. Frog hammer

C. Vibratory roller

List-II

1. To densify cohesion less soils to relatively larger depths

2. To compact lumpy cohesive soil fills

3. To compact soils at corners and places which bigger rollers cannot access

4. To compact cohesion less soils of shallow depth

Codes:

A B C

A) 4 1 2

B) 2 1 4

C) 4 3 2

D) 2 3 4

Ans: D


21) In a compaction test, G, W, S, and e represent the specific gravity, water content,

degree of saturation and void ratio of the soil sample respectively. If represents

unit weight of water and represents the dry unit weight of the soil, the equation for

zero-air voids line is

A)

B)

C) =

D)

Ans: B

Explanation:

Zero air void means, 100 % saturation state. In that state void ratio e becomes .

22) A normally consolidated clay layer settled by 20 mm when the effective stress was

increased from 25 KN/ to 50 KN/ . What will be the settlement when the

effective stress is increased from 50 KN/ to 100 KN/

A) 20 mm B) 30 mm C) 40 mm D) 50 mm

Ans: A

Solution:

23) Find the settlement in mm in over consolidated soil from the following data:

.

Ans: 30

Solution:


(

)

24) For a certain loading condition, a saturated clay layer undergoes 40% consolidation in

a period of 178 days. What would be the additional time required for further 20%

consolidation to occur?

A) 89 days B) 222.5 days C) 329.5 days D) 400.5 days

Ans: B

Solution:

=

=


MODULE – 49

25) The stresses on a failure plane in a drained test on a cohesion less soil are as follows:

Normal stress

Shear stress

Determine the angle of shearing resistance and the angle of failure plane makes with

the major principal plane. Also find major principal stress and minor principal stress?

Ans: 159, 73

Solution:

26) In a tri-axial test carried out on cohesion-less soil sample with a cell pressure of 20

kPa, the observed value of applied stress at the point of failure was 40 kPa. The angle

of internal friction of the soil is

A) 10° B) 15° C) 25° D) 30°

Ans: D

Solution:


27) A sample of saturated cohesion-less soil tested in a drained tri-axial compression test

showed an angle of internal friction of 30 . The deviatoric stress at failure for the

sample at a confining pressure of 200 kPa is equal to

A) 2000 kPa B) 400 kPa C) 600 kPa D) 800 kPa

Ans: B

Solution:

Deviator stress

28) In the consolidated drained test on a saturated soil sample, pore water pressure is zero

during

A) Consolidation stage only

B) Shearing stage only

C) Both consolidation and shearing stages

D) Loading stage

Ans: C

29) An unconfined compression test was conducted on an undisturbed sample of clay.

The sample had a diameter of 37.5 mm and was 80 mm long. The load at failure

measured by the proving ring was 28 N and the axial deformation of the sample at

failure was 13 mm. Determine of the clay.

Ans: 0.0106

Solution:


30) In a triaxial test, a soil sample was consolidated under a cell pressure of

and a back pressure of 350 . There after with drainage not allowed, the cell

pressure was raised to 800 resulting in the increased pore water pressure

reading of 445 . The axial load was then increased to give a deviator stress of

575 (while the cell pressure remained at 800 ) and a pore pressure

reading of 640 . Calculate the pore pressure coefficients B and A.

A) 0.95, 0.357 B) 0.92, 0.357 C) 0.95,0.33 D) 0.77, 0.271

Ans: A

Solution:

FOUNDATION ENGINEERING

MODULE – 50

31) In a plate load test on sandy soil, the test plate of 60cm 60cm undergoes a

settlement of 5mm at a pressure of 12 N/ . What will be the expected

settlement of 3m 3m footing under same pressure?

A) 25mm B) 20mm C) 15mm D) 9mm

Ans: D

Solution:

{

}

{

}


32) The number of blows observed in a Standard Penetration Test (SPT) for different

penetration depths are given as follows

Penetration of sampler Number of blows

0-150 mm 6

150-300 8

300-450 mm 10

The observed N value is

A) 8 B) 14 C) 18 D) 24

Ans: C

Solution:

SPT value = number of blows for last 30 cm

8 + 10 = 18

33) Match the items of List-I with List-II and select the correct answer.

List I

P. Modulus of subgrade reaction

Q. Relative density and strength

R. Skin friction and point bearing resistance

S. Elastic constants

List II

1) Cyclic pile load test

2) Pressure meter test

3) Plate load test

4) Standard penetration test

5) Dynamic cone penetration test

Codes:

P Q R S

A) 1 3 2 5

B) 1 2 4 3

C) 2 5 1 3

D) 3 4 1 2

Ans: D


Solution:

Plate load test : modules of sub grade reaction

SPT : Relative density and strength

Cyclic pile load test : Skin friction and point bearing resistance.

Pressure meter test : Elastic constants

MODULE – 51

34) Surcharge loading required to be placed on the horizontal backfill of a smooth

retaining vertical wall so as to completely eliminate tensile crack is:

A) B) C) √ D) √

Ans: D

Solution:

√

√

35) Consider the following statements:

1. The required yield of retaining wall reach equilibrium in the active case is less

than for the passive case.

2. The active pressure caused by a cohesionless backfill on a smooth vertical

retaining wall may be reduced by compacting the backfill.

3. Given a choice, one should prefer a cohesive soil for a backfill vis-à-vis a non-

cohesive soil.

Which of the above statements are correct?

A) 1, 2 and 3 only

B) 1 and 2 only

C) 1 and 3 only

D) 2 and 3 only

Ans: A


36) Assertion (A): The safe height (2Z0) to which an unsupported vertical cut in clay can

be made is 4c/ .

Reason (R): Active earth pressure of cohesive backfill shows that the negative

pressure (tension) is developed at top level. This tension decrease to zero at depth Z0

and total net pressure up to a depth 2Z0 is zero.

Codes:

A) Both A and R are true and R is the correct explanation of A

B) Both A and R are true but R in not a correct explanation of A

C) A is true nut r is false

D) A is false but R is true

Ans: A

37) The lateral earth pressure coefficient of a soil, ka for active state, kp for passive state

and k0 for at-rest condition, compare as

A) B) C) D)

Ans: B

38) In a cohesion-less soil deposit having a unit weight of 1.5 t/m2 and an angle of

internal friction of 300, the active and passive lateral earth pressure intensities (in

t/m2) at a depth of 10 m will, respectively, be

A) 15 and 5 B) 5 and 45 C)10 and 20 D)20 and 10

Ans: B

Solution:

= H 1/3 1.5 10 5

= H 3 1.5 10 45


MODULE – 52

39) A long slope is formed in a soil with shear strength parameters: and .

A firm stratum lies below the slope and it is assumed that the water table may

occasionally rise to the surface, with seepage taking place parallel to the slope. Use

and . The maximum slope angle (in degrees) to

ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the

slope, would be

A) B) C) D)

Ans: D

Solution:

40) The infinite sand slope shown in the figure is one the verge of sliding failure. The

ground water table coincides with the ground surface. Unit weight of water =

9.81 .

The value of the effective angle of internal friction (in degrees up to one decimal

place) of the sand is _________

Ans: 34.3

Solution:


41) Taylor’s stability number Sn is given by which one of the following expressions? (c is

cohesion, Fc is factor of safety, is density of soil and H, the height of the slope).

A)

B)

C)

D)

Ans: C

42) The factor of safety of an infinite soil slope shown in the figure having the properties

c = 0, φ , = 16 kN/ and = 20 is approximately equal to

A) 0.70 B) 0.80 C) 1.00 D) 1.20

Ans: A

Solution:

43) Find the factor of safety of an infinite slope constructed with a sandy soil having

. The soil is in dry state and the thickness of layer is 5m and

inclination is .

Ans: 2.716

Solution:


MODULE – 53

44) A 25 kN point load acts on the surface of an infinite elastic medium. The vertical

pressure intensity in kN/m2 at a point 6.0 m below and 4.0 m away from the load will

be

A) 132 B) 13.2 C) 1.32 D) 0.132

Ans: D

Solution:

[

(

) ]

⁄

[

(

) ]

⁄

45) Two columns A and B are situated 6m apart. Column A transfers a load of 500

and column B, a load of 250 . Determine the resultant vertical stress on a

horizontal plane 20m below the ground surface at points A and B

A) 59.8, 29.9 B) 29.9, 59.8 C) 79.8, 39.9 D) 39.9, 79.8

Ans: A

Solution:

a)

[

(

) ]

⁄

59.77

b)

[

(

) ]

⁄

46) Stresses obtained from Boussinesq’s theory are considered reasonably satisfactory in

foundation engineering because

A) They represent stress distribution in inhomogeneous soils below loaded area

B) They account for anisotropy of soil property

C) They give due regard to plastic behaviour of soils. Particularly for settlement

analysis

D) They consider elastic soil medium, and the intensity of allowable stresses below

foundations in most cases are quite small and justify elastic solutions.

Ans: D


47) A strip footing 2m wide is loaded on the ground surface with a pressure of 150

kN/ . A 4m thick soft clay layer exists at a depth of 10m below the foundation. Find

the average increase in vertical stress at the centre of clay layer below the centre line

and at the edge of footing.

A) 59.8, 29.9 B) 29.9, 59.8 C) 15.83, 15.59 D) 15.72, 15.83

Ans: C

Solution:

a) 2 (

) 0.166

15.83 kN/

b)

15.59 kN/

48) The figure given below represents the contact pressure distribution underneath a

A) Rigid footing on saturated clay

B) Rigid footing on sand

C) Flexible footing on saturated clay

D) Flexible footing on sand

Ans: A


MODULE – 54

49) A square footing of size 2.5 m m is resting on a soil at a depth of 2.0 m. The

value of c’ and of the soil are 15 kPa and 25 respectively. Assume general shear

failure. The bearing capacity coefficients for are 25.1, 12.7 and

9.7. Find ultimate bearing capacity of the soil? Given unit weight of soil is 18

Ans: 1121

Solution:

50) A circular footing of size 2.5 m is resting on a soil at a depth of 2.0 m. The



9.7. Find net ultimate bearing capacity of the soil? Given unit weight of soil is

18

Ans: 1042

Solution:

51) A rectangular footing of size 5 m m is resting on a soil at a depth of 2.0 m. The



9.7. Find gross safe bearing capacity of the soil? Given unit weight of soil is 18

and factor of safety is 2.5

A) 456 B) 546 C) 657 D) 765

Ans: A


Solution:

(

) (

)

(

) (

)

52) A strip footing of width 2.5 m is resting on a soil at a depth of 2.0 m. The value of c’

and of the soil are 15 kPa and 0 respectively. Assume general shear failure. Find

ultimate bearing capacity of the soil? Given unit weight of soil is 18

A) 111.5 B) 121.5 C) 131.1 D) 142.3

Ans: B

Solution:

53) A raft 10 m 20 m is placed at a depth of 3 m on a clay soil with the following

properties:

. Determine the factor of safety

available against shear failure if the raft, the structure and the live loads that it will

carry are expected to exert a pressure of 200 . There is a provision for a

basement floor. Use Skempton’s equation.

A) 2.6 B) 2.5 C) 2.4 D) 2.3

Ans: A

Solution:

(

) (

)

(

) (

)


,

MODULE -55

54) A precast concrete pile is driven with a 50kN hammer falling through a height of

1.0m with an efficiency of 0.6. The set value observed is 4mm per blow and the

combined temporary compression of the pile, cushion and the ground is 6mm. As per

Modified Hiley’s Formula, the ultimate resistance of the pile is

A) 3000kN B) 4285.7kN C) 8.333kN D) 11905kN

Ans: B

Solution:

⁄

55) A 500 mm diameter concrete pile is to be driven in a clayey soil. The design capacity

of the pile is 500 kN. The soil conditions are shown in figure. Determine the length

required for the pile for the above design capacity. (Assume (CS-2016-1)

Ans: 5.88


Solution:

56) For the soil profile shown in figure below, the minimum number of precast concrete

piles of 300 mm diameter required to safety carry the load for a given factor of safety

of 2.5 (assuming 100% efficiency for the pile group) is equal to

A) 10 B) 15 C) 20 D) 25

Ans: C

Solution:

Q =

No. of Piles =

57) A 3.3 m 2.2 m group consists of 9 m long piles. It carries a load of 1500 kN. The

piles penetrate a sand layer (bulk unit weight = 16 ), 1 m thick and rest in a

normally consolidated clay having a saturated unit weight of 19 , specific

gravity of 2.7 and liquid limit of 50. Clay extends to a depth of 12 m below the top of

the sand layer. Ground water is at a depth of 1 m below the ground surface. Bulk unit

weight of sand is . Compute the settlement in the clay, if the pile cap rests

on the top of sand. Use 2:1 stress distribution to estimate the average increase of stress

in the clay layer.

Ans: 200 mm


Solution:

58) Match List-I (type of foundation) with List-II ( type of soil) and select the correct

answer using the codes given below the lists:

List-I

A. Floating piles

B. Micro piles

C. Combined footing

D. Under-reamed piles

List-II

1. Closed spaced columns resting on compressible soil

2. Expansive soils

3. Deep soft clays

4. Loose sands

Codes:

A B C D

A) 2 1 4 3

B) 2 4 1 3

C) 3 1 4 2

D) 3 4 1 2

Ans: D

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