Question

In the schematic cross-section of a hill, a planar discontinuity intersects a planar slope face. Using kinematic analysis, which of the following conditions favor(s) plane failure to occur?

• A. The dip of the discontinuity surface is less than that of the slope face.
• B. Friction angle on the discontinuity surface is more than the dip of the slope face.
• C. Friction angle on the discontinuity surface is less than the dip of the discontinuity.
• D. The dip direction of the discontinuity surface is same as that of the slope face.

Hint:

For plane failure: the discontinuity dip should be less than the slope face dip but greater than the friction angle, and the dip direction must coincide with the slope face. Always check both geometric and mechanical conditions.

Answer 1

The Correct Option is C, D

Step 1: Concept of plane failure in slopes.
Plane failure occurs when a planar discontinuity (e.g., bedding plane, joint, fault surface) becomes unstable and slides along the slope. For this to happen, two main conditions must be satisfied: 1. Geometric condition: The discontinuity plane should have the same dip direction as the slope face, and its dip angle should be less than that of the slope face but greater than the angle of internal friction. 2. Kinematic condition: The shear resistance is overcome when the dip of the discontinuity exceeds the friction angle.

Step 2: Examine each option.
- (A) Dip of discontinuity less than slope face: This is necessary but not sufficient. If too low, failure cannot occur. Alone, it does not guarantee plane failure.
- (B) Friction angle more than slope face dip: This makes the surface stable, not unstable. So this prevents failure.
- (C) Friction angle less than dip of discontinuity: This is the critical condition for sliding. If discontinuity dip exceeds friction angle, shear resistance is overcome → Correct.
- (D) Dip direction of discontinuity same as slope face: Without the same dip direction, sliding cannot occur in that slope → Correct.

Step 3: Combine conditions.
Thus, plane failure is possible when (C) and (D) are satisfied together.

Final Answer: \[ \boxed{\text{(C) and (D)}} \]