Shear strength of sands — effect of particle shape and density: For which soil is the angle of internal friction (φ) typically the smallest?

Introduction / Context:
In granular soils, shear strength arises mainly from interlocking and dilation. Particle shape (angular vs rounded) and relative density (dense vs loose) strongly influence the friction angle φ measured in drained shear tests.

Given Data / Assumptions:

• Clean sands with varying particle shape and density.
• Effective-stress, drained behavior governs φ.
• No significant cementation or cohesion.

Concept / Approach:
Angular particles interlock and resist sliding better than rounded ones, yielding a higher φ. Dense packs dilate upon shearing, further increasing peak φ compared with loose packs. Hence the smallest φ occurs when both interlocking and dilation are minimal: rounded particles in a loose state.

Step-by-Step Solution:

Verification / Alternative check:
Typical peak φ values may be 40–45° for angular dense sands, 35–40° for rounded dense sands, 30–34° for angular loose sands, and as low as high-20s to low-30s for rounded loose sands (ranges indicative).

Why Other Options Are Wrong:

• Angular dense or angular loose: angularity increases φ via interlock.
• Round dense: density raises φ via dilation.
• Silty sand with fines may reduce φ, but not as consistently minimal as round loose sands under clean conditions.

Common Pitfalls:
Comparing clays to sands; φ in clays is a different mechanism and often treated via effective-stress parameters with possible apparent cohesion.

Final Answer:
Round-grained loose sand