Boiling/Quicksand Safety – Factors that Increase Critical Exit Gradient (i_c) The critical exit gradient for seepage-induced boiling in soils (i_c) changes with soil properties. Which combination increases i_c (thereby improving safety against piping)?

Introduction / Context:
Boiling or quick conditions arise where upward seepage causes effective stress to vanish. The critical gradient i_c indicates the threshold at which seepage force equals submerged unit weight. Designers aim for low exit gradients relative to i_c to prevent piping and heave at downstream toes or excavation bottoms.

Given Data / Assumptions:

• Critical gradient formula: i_c ≈ (Gs − 1) / (1 + e).
• Homogeneous, saturated cohesionless soil near an exit boundary.
• Steady, upward seepage.

Concept / Approach:

From i_c = (Gs − 1) / (1 + e), increasing Gs raises the numerator and decreasing void ratio e lowers the denominator, both leading to a larger i_c and thus greater resistance to boiling. Conversely, lowering Gs or increasing e reduces i_c, making piping more likely for a given hydraulic gradient.

Step-by-Step Solution:

Verification / Alternative check:

Back-analyses of field failures show low Gs loose sands with high e are most vulnerable; densification (lower e) or using heavier mineral backfills (higher Gs) improves safety margins.

Why Other Options Are Wrong:

(b) lowers i_c; (e) contradicts the governing formula; (a) or (c) alone is incomplete but directionally correct—(d) captures both.

Common Pitfalls:

Confusing porosity n with void ratio e; forgetting to compare exit gradients against i_c rather than against unity.

Final Answer:

Both (a) and (c)