Railway permanent way (India): For 13 m rails with sleeper density specified as M + 7, what is the minimum thickness of ballast cushion provided beneath wooden sleepers of size 25 cm × 13 cm?

Introduction / Context:
Ballast provides load distribution, drainage, and resilience for railway track. For Indian Broad Gauge practice, standard sleeper densities (e.g., M + 7 for 13 m rails) are associated with typical ballast cushions under sleepers to balance performance and economy.

Given Data / Assumptions:

• Sleeper density: M + 7 for 13 m rails (i.e., 20 sleepers per 13 m rail length).
• Wooden (timber) sleepers of size 25 cm × 13 cm.
• We seek the minimum ballast thickness under sleeper (crown to formation top).

Concept / Approach:
Minimum ballast cushion must ensure adequate load spread and drainage. For timber sleepers on BG with sleeper density M + 7, Indian practice generally prescribes a 20 cm minimum under sleeper to prevent punching of sleepers, enable cross drainage, and allow for tamping without formation contamination.

Step-by-Step Solution:
Relate sleeper density to track stiffness and maintenance regime.Adopt the standard minimum cushion recommended for timber sleepers on BG under this density class.Select 20 cm as the minimum that meets drainage and support criteria.

Verification / Alternative check:
Heavier densities or concrete sleepers often use larger cushions (e.g., 25–30 cm). However, the minimum for timber sleepers with M + 7 commonly remains 20 cm.

Why Other Options Are Wrong:

• 15 cm: Too thin; inadequate drainage and load distribution.
• 25 cm and 30 cm: Possible for heavier duty or concrete sleepers, but not the minimum stipulated here.
• 36 cm: Excessive for the case; used in special conditions only.

Common Pitfalls:
Confusing shoulder ballast depth with under-sleeper cushion; assuming concrete-sleeper standards for timber track.

Final Answer:
20 cm