Stability of Slopes MCQ with answer and solution

Concept

Morgenstern-Price Method

Formula

X = λ × f(x) × E

Step-by-step solution

1. Identify the requirement: find the slope stability method that satisfies both force and moment equilibrium. 2. Recognize that the Morgenstern-Price method relates interslice forces using X = λ · f(x) · E to achieve full force and moment equilibrium. 3. Select option C.

Explanation

The Morgenstern-Price method is a rigorous slope stability analysis method that satisfies both force equilibrium (horizontal and vertical) and moment equilibrium for each slice.

Shortcut

Remember: "MP" stands for "Morgenstern-Price" and "More Precise" - it satisfies BOTH Force and Moment equilibrium (Full Equilibrium). Quick summary to eliminate options: - Ordinary Method: Moment equilibrium only - Bishop's Simplified: Moment and Vertical Force equilibrium only - Morgenstern-Price & Spencer: Both Force and Moment equilibrium

Common mistake

A common mistake is selecting Bishop’s simplified method, assuming it satisfies full static equilibrium, whereas it only satisfies overall moment equilibrium and vertical force equilibrium (ignoring interslice shear forces).