Friction Circle Method - Resultant Reaction

The friction circle method is used in soil mechanics to analyze the stability of slopes. It involves constructing a friction circle to determine the equilibrium state of a soil mass on a slope. In this method, the resultant reaction is assumed to be parallel to the friction circle.

Friction Circle
- The friction circle represents the available shear strength of the soil mass on the slope.
- It is constructed by plotting the normal stress (σn) on the x-axis and the shear stress (τ) on the y-axis.
- The circle is centered at the origin of the graph, and its radius represents the maximum shear strength (τmax) of the soil.
- Any point within or on the circumference of the circle represents a stable equilibrium state of the soil.

Resultant Reaction
- The resultant reaction refers to the total force acting on the soil mass due to the weight of the soil and any external loads or forces.
- It can be decomposed into two components: the normal force (N) and the shear force (V).
- The normal force is perpendicular to the slope surface, while the shear force is parallel to the slope surface.
- The resultant reaction is the vector sum of these two components.

Assumption in Friction Circle Method
- In the friction circle method, it is assumed that the resultant reaction is parallel to the friction circle.
- This assumption simplifies the analysis by considering only the shear strength of the soil as the controlling factor in the stability of the slope.
- It neglects the effect of the normal force component of the resultant reaction on the slope stability.
- The assumption is valid for slopes where the normal force component is relatively small compared to the shear force component.

Justification of Assumption
- The assumption of parallel resultant reaction to the friction circle is justified based on the Coulomb's shear strength criterion.
- According to Coulomb's criterion, the shear stress (τ) is directly proportional to the normal stress (σn) multiplied by the coefficient of friction (μ).
- This relationship is represented by the equation: τ = μσn
- The friction circle represents the range of shear stresses (τ) that the soil can resist without failure, based on the available shear strength (τmax).
- As the resultant reaction is assumed to be parallel to the friction circle, it implies that the shear stress (τ) is proportional to the normal stress (σn).
- Therefore, the assumption of parallel resultant reaction to the friction circle is consistent with the Coulomb's shear strength criterion.

Hence, the correct answer is option 'C' - Parallel.