Explanation:

In the context of soil mechanics, local shear failure refers to the failure that occurs within a small localized region of soil under shear stress. It is a type of failure that is typically observed in cohesive soils, which are soils that contain a significant amount of cohesive forces between their particles.

Characteristics of cohesive soil:
- Cohesive soils are fine-grained soils such as clay or silt that have cohesive properties due to the presence of clay minerals.
- These soils have the ability to stick together and maintain their shape when dry or slightly moist.
- They have low permeability, which means they do not easily allow water to pass through.

Local shear failure in cohesive soil:
- Local shear failure occurs when the shear stress acting on a small region of cohesive soil exceeds the shear strength of that region. This results in the formation of shear planes or slip surfaces within the soil.
- Local shear failure is typically characterized by the formation of cracks or fissures within the soil mass.
- The failure occurs without any significant overall deformation of the soil mass.

Shear strength of cohesive soil:
- The shear strength of cohesive soil is determined by its cohesion (C) and the angle of internal friction (φ).
- Cohesion is the shear strength of the soil when it is under zero normal stress. It represents the cohesive forces between the soil particles.
- The angle of internal friction represents the resistance of the soil to shear deformation and is related to the frictional forces between the soil particles.

Condition for local shear failure:
- In purely cohesive soil, where there is no significant frictional resistance between the particles, local shear failure occurs when the shear stress exceeds the cohesion of the soil.
- Since cohesive soil has no significant angle of internal friction, the strength of the soil is mainly governed by its cohesion.
- Therefore, local shear failure may be assumed to occur in cohesive soil when the soil is soft to medium in consistency.
- This means that the soil is neither too hard nor too soft, but has sufficient cohesion to resist shear stresses up to a certain limit.

Conclusion:
In summary, for purely cohesive soil, local shear failure may be assumed to occur when the soil is soft to medium in consistency. This is because cohesive soil primarily derives its shear strength from its cohesion, and local shear failure occurs when the shear stress exceeds the cohesion of the soil.