The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: \(P\) as the reaction force between the wall and the soil, \(R\) as the reaction force on the failure plane, \(C\) as the cohesive force along the failure plane and \(W\) as the weight of the failure wedge. Assuming that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.
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In problems related to force polygons, always pay attention to the directions of forces and ensure that their relative magnitudes are depicted accurately in the polygon. This will help identify the correct choice.
The forces acting on the failure wedge are \(P\) (the reaction force between the wall and the soil), \(R\) (the reaction force on the failure plane), \(C\) (the cohesive force along the failure plane), and \(W\) (the weight of the failure wedge). These forces act on the failure plane and are interrelated geometrically. To form a force polygon for the wedge, we must consider the directions and the magnitudes of these forces in relation to each other.
- \(P\) acts horizontally at the wall.
- \(R\) is the reaction force on the failure plane.
- \(C\) is the cohesive force along the failure plane.
- \(W\) is the weight of the wedge.
The correct force polygon should represent these forces appropriately, and the most suitable option for the force polygon is shown in option (C). This polygon properly depicts the directions and relative magnitudes of the forces acting on the failure wedge. Thus, the correct answer is (C).
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