Introduction:
Black cotton soil, also known as expansive soil, is a type of clayey soil that exhibits large swelling and shrinkage behavior. This behavior is primarily caused by the presence of certain clay minerals. Among the given options, montmorillonite is the clay mineral responsible for the significant swelling and shrinkage of black cotton soil.

Explanation:
1. Montmorillonite:
- Montmorillonite is a type of clay mineral that belongs to the smectite group.
- It is characterized by its high cation exchange capacity and ability to hold water molecules.
- Montmorillonite has a layered structure with negatively charged layers and exchangeable cations in between.
- The layers can easily expand and contract depending on the amount of water present in the soil.
- When water is absorbed by the montmorillonite, the layers swell and the soil volume increases.
- On the other hand, when the soil dries out, the layers shrink, leading to a decrease in soil volume.

2. Swelling and Shrinkage of Black Cotton Soil:
- Black cotton soil is highly expansive due to the presence of montmorillonite.
- When the soil absorbs water, the montmorillonite mineral expands, causing the soil to swell.
- This swelling can exert significant pressure on structures built on black cotton soil, leading to damage and instability.
- Conversely, during dry periods or when the soil loses moisture, the montmorillonite mineral contracts, causing the soil to shrink.
- This shrinkage can result in cracks and fissures in the soil, leading to foundation failure and structural damage.

Conclusion:
Among the given options, montmorillonite is the clay mineral responsible for the large swelling and shrinkage behavior exhibited by black cotton soil. Its ability to absorb and hold water, along with its expandable layered structure, contributes to the expansive nature of this type of soil. Understanding the presence and behavior of montmorillonite is crucial for engineers and geotechnical experts when dealing with construction projects on black cotton soil.