Question

Bishop's simplified method of slices satisfies

• A. only the moments equilibrium
• B. only the vertical forces equilibrium
• C. all the statics equations, except the horizontal forces equilibrium
• D. only the horizontal forces equilibrium

Hint:

Slope stability analysis methods often involve assumptions regarding interslice forces to simplify the complex indeterminate problem. Bishop's simplified method is popular due to its improved accuracy over the Fellenius method, while still being relatively simple to apply. However, its limitation is the non-satisfaction of horizontal force equilibrium. More rigorous methods, like Janbu's generalized method or Morgenstern-Price method, satisfy all three equilibrium conditions.

Answer 1

The Correct Option is C

The Bishop's simplified method of slices, commonly used in geotechnical engineering to analyze the stability of slopes, satisfies most of the statics equilibrium conditions with specific limitations. This method accounts for:

1. Vertical Forces Equilibrium: Bishop's method considers the balance of vertical forces acting on each slice. This is crucial for determining the normal and shear forces acting on the potential sliding surface.
2. Moment Equilibrium: The method ensures the moments around a point (commonly the base of the slice) are balanced. This helps in assessing the rotational stability of the slice around its center of gravity.

However, Bishop's method does not explicitly satisfy:

• Horizontal Forces Equilibrium: The assumption is made that the inter-slice forces are predominantly vertical, and therefore, the horizontal equilibrium is not directly considered. This simplifies calculations but is a noted limitation of the method.

In conclusion, Bishop's simplified method satisfies all the static equilibrium equations except for the horizontal forces equilibrium. It is a practical approach for stability analysis with reasonable accuracy under typical conditions.

Correct answer: all the statics equations, except the horizontal forces equilibrium