Ballast load dispersion assumption: For even distribution of load through the ballast, what angle to the vertical is commonly assumed for load dispersal?

Introduction / Context:
In railway track design, the load from wheel to rail, rail to sleeper, and sleeper to ballast is idealized using a dispersion angle. This aids quick estimation of contact pressures and formation design without complex numerical models.

Given Data / Assumptions:

• Engineering idealization of ballast pressure spread is required.
• Angle measured from the vertical to the sides of the load pyramid is used.
• We assume typical granular ballast behaviour under service compaction.

Concept / Approach:
A 45° to the vertical dispersion is a widely adopted rule-of-thumb. It implies that for every unit of vertical depth, the effective load-spread increases by one unit laterally, forming an isosceles right-angled load dispersion pyramid below the sleeper.

Step-by-Step Solution:
Recognize that ballast transmits load through interlock and friction.Adopt a conservative, symmetric spread: 45° on either side of the vertical.Use this to size ballast depth and predict formation pressure.

Verification / Alternative check:
Track design texts and empirical practice commonly use 1H:1V (i.e., 45°) dispersion beneath sleepers. More refined analyses may modify the angle for ballast condition but 45° is the standard preliminary assumption.

Why Other Options Are Wrong:

• 30°: Unrealistically steep; underestimates lateral spread, overestimates pressure below.
• 60°: Too shallow; overestimates spread and may underestimate formation pressure.
• None of these: Not correct because 45° is the established assumption.

Common Pitfalls:
Confusing 45° to the vertical with 45° to the horizontal; forgetting that fouled ballast or geogrid reinforcement may change effective spread in practice.

Final Answer:
45° to the vertical