Introduction:
When a footing fails due to insufficient bearing capacity, distinct failure patterns are developed. These patterns depend upon the failure mechanism rather than plastic equilibrium or shear strength.

Explanation:
The bearing capacity of a footing refers to its ability to safely support the applied loads without excessive settlement or failure. When the bearing capacity is insufficient, the footing may fail, resulting in different failure patterns. These failure patterns are primarily determined by the failure mechanism.

Failure Mechanism:
The failure mechanism refers to the process by which the footing fails when subjected to excessive loads. It involves the redistribution of stress and strain within the soil mass underlying the footing. The failure mechanism can be classified into three main types:

1. General Shear Failure:
In this type of failure, the soil beneath the footing fails in a shear mode, similar to a sliding block. The failure surface is usually inclined and extends from the base of the footing to a certain depth within the soil mass. It occurs when the ultimate bearing capacity of the soil is exceeded.

2. Local Shear Failure:
Local shear failure is characterized by the development of shear cracks or shear bands within the soil mass. These cracks or bands are localized and occur near the edges of the footing. This failure mechanism is typically observed in cohesive soils.

3. Punching Shear Failure:
Punching shear failure occurs when the applied loads cause the soil directly beneath the footing to undergo excessive vertical deformation. This results in the formation of a localized failure cone or bulb beneath the footing. It is commonly observed in loose or granular soils.

Conclusion:
In summary, when a footing fails due to insufficient bearing capacity, the distinct failure patterns are primarily determined by the failure mechanism. The failure mechanism can be classified into general shear failure, local shear failure, and punching shear failure. Understanding these failure patterns is crucial for designing safe and stable footings to ensure adequate bearing capacity.