Quick condition and piping – critical hydraulic gradient: Under what conditions can the critical hydraulic gradient (quick condition) occur in soils subjected to seepage?

Introduction / Context:
Boiling, quicksand, or piping occurs when seepage forces counteract the submerged weight of soil grains, reducing effective stress to zero. Recognizing the conditions that lead to the critical hydraulic gradient is essential near excavations, sheet piles, and hydraulic structures.

Given Data / Assumptions:

• Steady seepage governed by Darcy’s law.
• Effective stress principle: sigma′ = sigma − u.
• Upward gradients are especially dangerous beneath floors or at downstream toes.

Concept / Approach:
The critical gradient icr is reached when the upward seepage force equals the submerged unit weight of the soil skeleton, driving sigma′ → 0. Typically icr ≈ (Gs − 1) / (1 + e). When upward flow raises pore pressure, effective stress diminishes; at zero, particles can become mobile, causing boils and piping channels.

Step-by-Step Solution:

Verification / Alternative check:
Field indicator: boiling at the base of an excavation with upward gradients; preventive measures include relief wells, cutoffs, or lowering the water table to keep i < icr.

Why Other Options Are Wrong:

• Each alone is a partial description. The complete understanding requires acknowledging all three simultaneously.

Common Pitfalls:
Ignoring that even moderate upward gradients can be critical in loose silts; overlooking factor of safety against piping defined as icr / i.

Final Answer:
All of the above