Angle of repose of soil: Which reference line is used to define the maximum angle that the natural slope (outer face) of a soil mass makes under its own weight without lateral support?

Introduction / Context:
The angle of repose is a fundamental geotechnical property indicating the steepest angle at which a loose granular material remains stable without lateral support. It controls natural slopes, embankments, storage piles, and influences earth pressure on retaining structures.

Given Data / Assumptions:

• Dry or near-dry granular soil considered for the classical definition.
• No cementation or apparent cohesion.
• Mass forms a self-supported slope under gravity alone.

Concept / Approach:
The angle of repose, typically denoted by phi_r (sometimes approximating the friction angle for dry, clean sands), is defined with respect to the horizontal plane. It is the maximum angle at which grains interlock and frictional resistance is sufficient to prevent sliding or rolling. Moisture, particle shape, and gradation alter this angle in practice.

Step-by-Step Solution:
Visualize a soil heap formed by pouring granular material.Measure the slope angle at which sliding begins; the greatest stable angle is the angle of repose.Reference is the horizontal plane because gravity acts vertically and slope stability is judged relative to level ground.

Verification / Alternative check:
Laboratory tilt box tests or simple pile tests give angles commonly ranging from about 28° to 40° for sands and gravels depending on particle shape and moisture content.

Why Other Options Are Wrong:

• “With the vertical” and “with a line perpendicular to the slope” are unconventional references and would confuse standard definitions.
• “None of these” is incorrect since the standard reference is clearly the horizontal.

Common Pitfalls:
Assuming angle of repose equals the friction angle for all soils; cohesive or wet materials can show different behavior (e.g., apparent cohesion raises temporary slopes above the dry angle of repose).

Final Answer:
With the horizontal.