The rock specimen obtained from the overlying strata in a coal mine were tested in uni-axial compression and the following results were obtained at 50% of average compressive strength Longitudinal strain = 0.06 and Lateral strain = 0.012 The ratio of vertical to horizontal stress in the mine is

From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.

A

P, Q

B

Q, R

C

Q, S

D

R, S

During uniaxial compressive testing of a rock specimen of diameter 54 mm and length 120 mm, the axial strain was found to be 6.5 × 10^-4 mm/mm. If the Poisson's ratio of the rock is 0.3, the volumetric strain of the rock specimen in mm/mm is

A

1.95 ∗ 10-4

B

2.60 ∗ 10-4

C

2.34 ∗ 0-2

D

3.12 ∗ 10-2

A rock specimen of 120 mm length and 54 mm diameter is subjected to uniaxial compressive loading. Two strain gauges, one axially and other radially, are attached to the specimen. At the breaking load, if these two gauges read 0.0082 m/m and 0.0023 m/m respectively, the Poisson's ratio of the specimen is

A

3.56

B

0.25

C

0.28

D

0.32

The ratio of uniaxial compressive strength to uniaxial tensile strength of a sandstone specimen is 8 : 1. The theoretical, value of angle of internal friction of the specimen in degree is

A

51

B

41

C

32

D

7

The uniaxial compressive strength of a limestone sample is 80 MPa. The sample is confined at a pressure of 20 MPa in a triaxial compressive strength test. Based on Hoek-Brown failure criteria the maximum principal stress at failure in MPa is
(Consider rock constants as m = 7.88, s = 1.0 and a = 0.5)

A

117.9

B

132.3

C

137.9

D

157.9

Tresca or maximum-shear stress criteria assumes that yielding occurs when the maximum shear stress reaches a value of the shear stress in the uniaxial tension test. Assume the principal stress being σ1, σ2, σ3 where σ1 is largest, and σ3 is the smallest principal stresses. Find the value of minimum shear stress to cause yielding, given that yield stress in tension is equal to σo?

A

τ = σo

B

τ = σo/2

C

τ = σo/3

D

τ = σo/4

Four mines A, B, C and D are located along a road as shown with production in Mt per year 1, 2, 1 and 3 respectively. In order to handle total coal produced. the ideal distance of a coal washery along the road from the mine A in Km is

A

4.01

B

3.91

C

3.81

D

3.71

An O.C. mine requires 16 blocks of overburden of 3000 te each to mine 4 blocks of coal of 2000 te each. The mining cost of both overburden and coal is Rs. 50 per tonne. The cost of transportation of overburden to dump areas is Rs. 50 per tonne. Coal transportation cost to the selling point is Rs. 75 per tonne. The price of coal is Rs. 800 per tonne, If the royalty and tax to the state is Rs. 50 per tonne, the nominal profit in rupees is

A

2,00,000

B

20,00,000

C

30,00,000

D

50,00,000

A metallic sheet 1 m wide and 10 mm thick is to be rolled under a front tension force of 100 KN. A specimen from the sheet, tested under tension, shows a yield stress of 100 MPa. Assume plain strain condition during rolling and ignore the friction. If yielding is assumed to start at a roll pressure of σ3 MPa, then the stress in the width direction (where strain is zero) is

A

$$2 + \frac{{\sigma 3}}{2}$$

B

$$4 + \frac{{\sigma 3}}{5}$$

C

$$5 + \frac{{\sigma 3}}{2}$$

D

$$5 + \frac{{\sigma 3}}{3}$$

The following characteristic curves (P, Q, R, S) pertain to rotary drilling in rock.

Title of the curve
I : Torque versus RPM
II: Rate of penetration versus uniaxial compressive strength of rock
III : Rate of penetration versus weight on bit
IV : Specific energy versus weight on bit
Match the curves with their titles

A

P-III, Q-IV, R-II, S-I

B

P-II, Q-IV, R-I, S-III

C

P-IV, Q-III. R-II, S-I

D

P-I, Q-III, R-II, S-IV