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Engineering Mechanics(11)Geomechanics(33)Subsidence(9)

Engineering Mechanics

11 Questions

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q1

MCQ[1 Mark]

A simply supported beam is shown. The location at which the zero shear force is acting on the beam is

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q2

NAT[2 Marks]

A truss PQR carries vertical load of 10 kN at Q as shown. The force in member PR, in kN, is

Explanation

GATE→2026→Geomechanics and Ground Control→Engineering Mechanics

Q3

NAT[2 Marks]

Two blocks P and Q weighing 100 kN and 200 kN, respectively, are connected by a string passing through a frictionless pulley. Friction coefficient between P and Q is 0.4, and between Q and surface is 0.3. The minimum force, F, in kN, required to pull the block Q, is

Explanation

GATE→2025→Geomechanics and Ground Control→Engineering Mechanics

Q4

MCQ[1 Mark]

Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $m_{1}$ and $m_{2}$, in kg, respectively are

(A)

50, 100

(B)

50, 50

(C)

100, 50

(D)

50, 25

Explanation

GATE→2025→Geomechanics and Ground Control→Engineering Mechanics

Q5

NAT[2 Marks]

A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is (rounded off to 2 decimal places)

Explanation

GATE→2024→Geomechanics and Ground Control→Engineering Mechanics

Q6

NAT[2 Marks]

A mine worker weighing (W) 600 N lifts an object of 100 N as shown. The 50% body weight is applied downward through point A and a force $F_{E}$ is produced parallel to x axis by the contraction of erector spinae muscle during lifting. The lumber disc, L acts as a smooth hinge and keeps the upper body in static equilibrium. The magnitude of the resultant of the reaction forces, in N at the lumber disc, is

Explanation

GATE→2024→Geomechanics and Ground Control→Engineering Mechanics

Q7

NAT[2 Marks]

A solid ball of mass 10 kg is subjected to forces as shown. The magnitude of the acceleration in $\text{m/s}^{2}$, is

Explanation

GATE→2023→Geomechanics and Ground Control→Engineering Mechanics

Q8

MCQ[1 Mark]

A shear stress $\tau$ acts tangentially to the upper surface of a block and causes a small deformation $\Delta w$ as shown. The shear strain is calculated by

(A)

\frac{\Delta w}{w}

(B)

\frac{\Delta w}{h}

(C)

\frac{2\Delta w}{w}

(D)

\frac{2\Delta w}{h}

Explanation

GATE→2023→Geomechanics and Ground Control→Engineering Mechanics

Q9

NAT[2 Marks]

A dozer pushes up a 100 kg spool of cable along a $20^{\circ}$ incline road at a constant velocity as shown in the figure. The coefficient of static friction between the dozer bucket and the spool (Point B) is 0.45, and coefficient of kinetic friction between road and the spool (Point A) is 0.15. Consider the spool only slides up the incline. The maximum normal force in N acting at Point B, is [rounded off to 1 decimal place]

Explanation

GATE→2022→Geomechanics and Ground Control→Engineering Mechanics

Q10

MCQ[1 Mark]

In the truss shown in the figure, the force in the member BD, in kN is

(A)

7

(B)

5

(C)

2

(D)

0

Explanation

GATE→2022→Geomechanics and Ground Control→Engineering Mechanics

Q11

NAT[2 Marks]

Two weightless cables of equal length and cross sectional area are hanging from a ceiling as shown in the figure. They are connected by a horizontal light bar of length 1.0 m and pulled by a force, F. The modulus of elasticity of Cable-1 and Cable-2 are 50 GPa and 200 GPa, respectively. If the deformation in both the cables is equal, the distance x, in m is

Explanation

Geomechanics

33 Questions

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q12

MCQ[1 Mark]

In a Slake Durability Index (SDI) test, a rock sample of 500 g undergoes two standard cycles of wetting and drying. The mass of the sample retained after the test is 400 g. The SDI of the sample, in %, is

(A)

10

(B)

40

(C)

20

(D)

80

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q13

MCQ[1 Mark]

Results from the permeability test of rock samples, E, F, and G are shown. The correct order of hydraulic conductivity (k) of the rock samples is

(A)

k_E > k_F > k_G

(B)

k_E < k_F < k_G

(C)

k_E = k_F = k_G

(D)

k_F > k_G > k_E

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q14

MCQ[2 Marks]

The in-situ stresses are determined by Flat-jack method by making three slots (P, Q, and R) on the wall (ABCD) of a mine gallery as shown. If $\sigma_P > \sigma_Q$ and $\sigma_R = 0$, the shear stress on the wall is

(A)

\frac{\sigma_{P}+\sigma_{Q}}{2}

(B)

\frac{\sigma_{P}-\sigma_{Q}}{2}

(C)

-(\frac{\sigma_{P}+\sigma_{Q}}{2})

(D)

-(\frac{\sigma_{P}-\sigma_{Q}}{2})

Explanation

GATE→2026→Geomechanics and Ground Control→Geomechanics

Q15

NAT[2 Marks]

In a uniaxial compressive strength test, a $120\,\Omega$ strain gauge of gauge factor 2.0 is pasted on the rock sample as shown. At the end of the test, the change in resistance of the strain gauge is $0.5\,\Omega$. The longitudinal deformation of the sample, in mm, is

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q16

MCQ[1 Mark]

The major $(\sigma_{1})$ and minor $(\sigma_{3})$ principal stresses and the maximum shear stress $(\tau_{max})$ are related as $|\tau_{max}|=\sigma_{1}=-\sigma_{3}$. The magnitude of normal stress on the plane where $\tau_{max}$ acts is

(A)

0

(B)

\sigma_{1}

(C)

\sigma_{3}

(D)

(\sigma_{1} - \sigma_{3})/2

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q17

MCQ[1 Mark]

In a Brazilian test, the front view of a homogeneous rock sample is shown in the figure. The failure initiates at the point

(A)

M

(B)

N

(C)

O

(D)

P

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q18

NAT[1 Mark]

Hydraulic fracturing method is used to determine the major principal stress $(\sigma_{1})$ in an underground rock strata having tensile strength of 6 MPa. The minor principal stress $(\sigma_{3})$ in the strata is 8 MPa. If fluid pressure of 10 MPa is required to fracture the vertical borehole in that strata, the magnitude of $\sigma_{1}$, in MPa, is

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q19

NAT[1 Mark]

The unadjusted RMR of a tunnel roof is 64. A single joint set exists in the roof as shown in the figure... Using the abridged RMR table for adjustment orientation, the RMR is

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q20

NAT[1 Mark]

If the in-situ density of coal is $1320\text{ kg}/\text{m}^{3}$ and the density of blasted coal is $952\text{ kg}/\text{m}^{3}$, the swell factor is

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q21

MCQ[2 Marks]

A triaxial test on a sandstone sample is conducted at a confining pressure of 10 MPa. The elastic axial and volumetric strains at axial stress of 50 MPa are recorded to be $4.2\times10^{-3}$ and $2.0\times10^{-3}$ respectively. The modulus of elasticity, in GPa, and Poisson's ratio of the sample, respectively are closest to

(A)

5.11, 0.35

(B)

10.22, 0.35

(C)

5.11, 0.17

(D)

10.22, 0.17

Explanation

GATE→2025→Geomechanics and Ground Control→Geomechanics

Q22

MCQ[2 Marks]

A ground reaction curve (GRC) of a 3 m radius unlined circular tunnel is shown in the figure. The tunnel is supported by 300 mm thick shotcrete lining... If the lining is constructed after 5 mm radial deformation, the support reaction is best represented by the line

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2024→Geomechanics and Ground Control→Geomechanics

Q23

MCQ[1 Mark]

Principal stresses for a rock element have a relation $\sigma_3 = -\frac{1}{2}\sigma_1$. The maximum shear stress is expressed by

(A)

\frac{1}{3}\sigma_{1}

(B)

\frac{3}{4}\sigma_{1}

(C)

\frac{1}{2}\sigma_{1}

(D)

\frac{1}{4}\sigma_{1}

Explanation

GATE→2024→Geomechanics and Ground Control→Geomechanics

Q24

NAT[1 Mark]

The void ratio of an unconsolidated soil heap of volume $1000\text{ m}^{3}$ is 1.0. If the soil heap is consolidated to a volume of $800\text{ m}^{3}$, the corresponding void ratio is

Explanation

GATE→2024→Geomechanics and Ground Control→Geomechanics

Q25

NAT[1 Mark]

A scanline survey between points A and B of a rock mass is shown. Consider $RQD=100\times(0.1\lambda+1)\times exp(-0.1\lambda)$, where $\lambda$ is the frequency of discontinuity per m. The RQD of the rock mass is

Explanation

GATE→2024→Geomechanics and Ground Control→Geomechanics

Q26

NAT[2 Marks]

A Mohr-Coulomb envelop between shear stress, $\tau$ and normal stress, $\sigma_{n}$ of a sandstone rock is given as $\tau=7.5+0.84~\sigma_{n}$ (unit of stresses is MPa). A sandstone sample is tested in triaxial mode with confining pressure of 5.0 MPa. The value of the shear stress, $\tau$ in MPa at the failure, is

Explanation

GATE→2024→Geomechanics and Ground Control→Geomechanics

Q27

NAT[2 Marks]

A circular tunnel is constructed at a depth of 100 m. The average unit weight of overburden rock is $27.0\text{ kN/m}^{3}$. If the tangential stress measured at point A located at the horizontal boundary of the tunnel as shown, is 5.0 MPa, the tangential stress at point B in MPa, is

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q28

MCQ[1 Mark]

Axial stress versus axial strain curves for two test results of a porous rock from triaxial undrained compression tests are shown in the figure. The pore pressure for the curve B can be the best explained by

(A)

U < 0

(B)

U = 0

(C)

U > 10

(D)

0 < U < 10

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q29

NAT[1 Mark]

A slope stability radar shows that the position of a point P in a mine dump shifts from (200, 700, -60) m to (200.05, 700.1, -60.75) m over a time $\Delta t$. The net displacement in cm of the point P is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q30

NAT[1 Mark]

A Mohr-Coulomb failure envelop of a sandstone rock is given as $\sigma_{1}=30+3.5\sigma_{3}$ where $\sigma_{1}$ and $\sigma_{3}$, measured in MPa, are the major and minor principal stresses respectively. The angle ofキュリティ the failure plane with the $\sigma_{3}$ axis in degree is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q31

NAT[1 Mark]

A punch hole of diameter 10 mm is to be made in a 5 mm thick rock plate as shown. If the yield strength of rock plate is 25 MPa, the punch force P required in kN is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q32

MCQ[2 Marks]

A tunnel of diameter 8 m is to be driven in a rock mass having quality index, Q of 1.0. Assume the excavation support ratio (ESR) of the tunnel is 1.0. The support requirement of the tunnel wall using fibre reinforced shotcrete (based on the chart prepared by Grimstad and Barton, 1993) is

(A)

A

(B)

B

(C)

Shotcrete of thickness 9-12 cm, bolt length of 3.0-3.2 m

(D)

D

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q33

NAT[2 Marks]

A circular tunnel is developed in a biaxial in situ stress field as shown in the figure. If the ratio between tangential stress at the boundary point A and that at the boundary point B is 2.0, the value of k is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q34

NAT[2 Marks]

Stress waves are sent from the transmitter A to the receiver B through an isotropic and elastic cylindrical rock specimen as shown in the figure. The length of the specimen is 100 mm. The travel time of longitudinal and shear waves are 0.025 ms and 0.04 ms, respectively. The Poisson's ratio of the rock specimen is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q35

NAT[2 Marks]

A jointed rock sample is subjected to 20 MPa vertical stress as shown in the figure. The modulus of elasticity of the rock is 10 GPa and the normal stiffness of the joint surface is $5\text{ GPa/m}$. Assuming one-dimensional elastic behaviour of rock and joint, the displacement in mm of the loading surface AB is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q36

NAT[2 Marks]

An irregular shaped rock sample of mass 60 g displaces 27 g of brine when submerged in a filled jar. The specific gravity of brine is 1.05. The unit weight of the rock sample in $\text{kN/m}^{3}$ is [rounded off to 2 decimal places]

Explanation

GATE→2023→Geomechanics and Ground Control→Geomechanics

Q37

NAT[2 Marks]

A rock slope is intercepted by a joint plane at an angle $30^{\circ}$ as shown in figure... Unit weight of rock = $20\text{ kN/m}^{3}$, Cohesion of joint = 30 kPa, Friction angle of joint = $22^{\circ}$. The factor of safety of the rock slope to slide along the joint plane is [rounded off to 2 decimal places]

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q38

MCQ[1 Mark]

The correct vertical stress profile in the case of tributary area method for pillar design is

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q39

NAT[1 Mark]

Water flows through a vertical sand column of cross sectional area $4000\text{ mm}^2$ and length 300 mm. For a water head of 600 mm, quantity of seepage water is $100\text{ mm}^3/\text{min}$. The hydraulic conductivity of the sand column, in mm/min is

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q40

NAT[1 Mark]

The modified Lauffer diagram as shown in the figure relates to roof span, RMR and stand-up time. In a metal mine, roof span of a drive is 4 m. If the RMR of the rock mass changes from 40 to 60, then the stand-up time increases by a factor of

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q41

MCQ[2 Marks]

A 3-point borehole extensometer is installed to identify the location of a single discontinuity plane in a hanging wall rock by measuring deformations at three locations as shown in the figure. The absolute readings of deformations measured on two different dates are listed in the table. Based on the measured data the most likely inference is

(A)

Discontinuity between Anchor-1 and Anchor-2

(B)

Discontinuity between Anchor-2 and Anchor-3

(C)

Discontinuity between Anchor-3 and excavation boundary

(D)

No noticeable discontinuity

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q42

MCQ[2 Marks]

In a uniaxial compressive strength test, a rock sample of diameter 50 mm fails at an angle of $60^{\circ}$ as shown in the figure. If the peak load at failure is 120 kN, the normal and shear stresses on failure plane respectively, in MPa are

(A)

15.28 and 26.46

(B)

26.46 and 15.28

(C)

57.02 and -15.28

(D)

-15.28 and 15.28

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q43

NAT[2 Marks]

A circular tunnel of radius 3 m is constructed in a hydrostatic stress field of 15 MPa. The modulus of elasticity and Poisson's ratio of the rock are 5 GPa and 0.25, respectively. A uniform support pressure $p_{i}$ is applied at tunnel boundary to restrict the radial deformation at the tunnel boundary to 4 mm. The value of $p_{i}$ in MPa is

Explanation

GATE→2022→Geomechanics and Ground Control→Geomechanics

Q44

NAT[2 Marks]

The extraction ratio during development of a bord and pillar panel is 0.15 in a flat coal seam. The panel is further extracted by widening the galleries, and the extraction ratio changes to 0.25. The percentage change in pillar stress, considering tributary area method, is

Explanation

Subsidence

9 Questions

GATE→2026→Geomechanics and Ground Control→Subsidence

Q45

NAT[2 Marks]

A plug dam is to be constructed in a mine gallery of size $3.5\text{ m} \times 2.5$ m. The interfacial shear strength between surrounding rock and plug dam is 1.0 MPa. The minimum thickness of the dam, in m, to withstand a water pressure of 10.0 MPa is

Explanation

GATE→2026→Geomechanics and Ground Control→Subsidence

Q46

NAT[2 Marks]

In a bench blasting, 49 kg of explosive is put in each hole. The PPV at a distance of 100 m, in $\text{mm s}^{-1}$, is

Explanation

GATE→2025→Geomechanics and Ground Control→Subsidence

Q47

NAT[2 Marks]

A longwall panel is to be developed in a flat seam at a depth of H m. The surface subsidence profile (s) of the area with the horizontal distance x is estimated as $s=\frac{S_{max}}{2}[1.002-tanh(\frac{4.8x}{H})]$ where, $S_{max}$ is the maximum subsidence at the centre of the panel, x is measured from the inflection point. The ratio between the critical width of the panel and the depth is (rounded off to 2 decimal places)

Explanation

GATE→2025→Geomechanics and Ground Control→Subsidence

Q48

NAT[2 Marks]

In a bord and pillar panel, a square pillar of size $35\text{ m}\times35$ m (centre to centre) is extracted to form four equal square-shaped stooks as shown. The width of each gallery and crosscut is 5 m. The height of the working seam is 3 m. The reduction in safety factor after pillar splitting by using Bieniawski's pillar strength formula, in %, is (rounded off to 2 decimal places)

Explanation

GATE→2024→Geomechanics and Ground Control→Subsidence

Q49

MCQ[2 Marks]

The roof convergence data for 30 days at a monitoring station in a coal mine gallery is given. TARP is enforced if Premise 1 (rate exceeds 1.5 mm/day between consecutive measurements) and Premise 2 (cumulative rate exceeds 1.0 mm/day) occur simultaneously. Identify the day on which TARP is enforced.

(A)

10

(B)

16

(C)

22

(D)

30

Explanation

GATE→2024→Geomechanics and Ground Control→Subsidence

Q50

NAT[2 Marks]

A Bord and Pillar panel is developed at depth of 250 m in a flat coal seam. The vertical stress gradient is $0.027\text{ MPa/m}$. If the strength of a square pillar is 12.5 MPa, the extraction ratio of the pillar for a safety factor of 1.5, is

Explanation

GATE→2024→Geomechanics and Ground Control→Subsidence

Q51

NAT[2 Marks]

In an opencast coal mine, blast vibrations are measured at two locations, A and B simultaneously for a maximum charge per delay (Q) of 1200 kg as given. Location A: 100 m, 112.5 mm/s; Location B: 300 m, 20.3 mm/s. Assume $PPV=K[\frac{D}{\sqrt{Q}}]^{-\beta}$. The PPV in mm/s, at a distance of 200 m from the blast face, is

Explanation

GATE→2023→Geomechanics and Ground Control→Subsidence

Q52

NAT[1 Mark]

Critical subsidence has occurred on the surface due to mining of a flat longwall panel at a depth of 200 m. The width of the panel is 150 m. The maximum width of the panel in m that can be mined at a depth of 300 m, to reach critical subsidence is [rounded off to 1 decimal place]

Explanation

GATE→2023→Geomechanics and Ground Control→Subsidence

Q53

NAT[2 Marks]

Strength of a rectangular coal pillar in MPa is given by $S_{p}=S_{1}(0.64+0.54\frac{w}{h}-0.18\frac{w^{2}}{lh})$ where w, $l(\ge w)$ and h are width, length and height of the pillar, respectively. A 30 m square pillar is split into two halves as shown. The height of the pillar is 3 m. The ratio of safety factors between one half-pillar and the original square pillar is [rounded off to 2 decimal places]

Explanation