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Q. 1

A discontinuity is found fully developed from the toe to the bench surface on a 15 m high slope, slope angle 65°. The discontinuity (frictional angle 32° and cohesion 20 kN/m2) is planar and its strike is parallel to the slope face with a dip 45°. Determine the factor of safety in case of a planar slope failure. Unit weight of the rock is 27 kN/m3. You are required to use RocPlane software to evaluate the stability of the slope. If the factor of safety is less than 1.3, then you need to design slope reinforcement system to raise the factor safety to 1.3.

Q. 2
The following table shows data obtained from a single-stage triaxial compression test on a cylindrical rock sample, conducted with closed-loop servo-control, at a confining stress of 10.0 MPa, and at zero pore pressure.

 Total Axial Load (KN) Sample Height (mm) Sample Diameter (mm) 0.00 100.84 50.20 19.89 100.80 50.20 39.60 100.77 50.20 63.40 100.74 50.20 88.67 100.71 50.21 116.18 100.68 50.21 144.68 100.65 50.22 162.38 100.63 50.22 185.23 100.58 50.24 190.62 100.56 50.25 191.99 100.54 50.25 180.22 100.52 50.26 137.56 100.49 50.26 115.79 100.46 50.27 101.93 100.43 50.28 97.97 100.40 50.28 96.98 100.37 50.28

Draw the complete stress-strain curve and determine values for the following:
1. Peak strength,
2. Residual strength,
3. Tangent Young's modulus at 50% peak axial stress; and
4. Poisson's ratio at 50% peak axial stress.

Q. 3
A series of shear tests were performed on a weak rock. Each test was carried out until the sample sheared, and the principal stresses for each test were:

 S. No. σ3 (KN/m2) σ1 (KN/m2) 1 200 570 2 300 875 3 400 1162

Plot the Mohr's stress circle and hence determine the angle of internal friction and cohesion of the rock from Mohr's envelope. If the confining pressure was 600 KN/m2, extrapolate the failure stresses of the rock sample.

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