1 A 15 m high rock slope with an overall slope angle of 68° is intersected by a fully developed planar discontinuity extending from the toe to the crest. The discontinuity has a dip of 45° (strike parallel to the slope face), a friction angle of 32°, and a cohesion of 15 kN/m². The rock unit weight is 25 kN/m³, and the slope section can be assumed to have a unit thickness of 1 m. 1. Using a limit equilibrium approach, calculate the Factor of Safety (FoS) for the potential planar failure mode. Clearly justify any assumptions you make in your derivation and calculation. 2. Critically evaluate the calculated FoS with respect to acceptable design criteria. If the FoS is less than 1.3, propose and justify an appropriate reinforcement scheme (such as rock bolts, shotcrete, or anchors). Your design must include assumptions on reinforcement spacing, length, and capacity, and a discussion of how the reinforcement interacts with the slope geometry and discontinuity. 3. Using RocPlane (or equivalent slope stability software), verify your analytical calculation of the FoS before reinforcement. Provide screenshots of your input parameters and results. Discuss any discrepancies between the analytical and numerical outcomes. 4. Re-analyse the slope in RocPlane after incorporating your proposed reinforcement system. Compare the FoS obtained after reinforcement with your design target of 1.3, and critically assess whether your reinforcement design is both technically and economically justified.
