Critical Hydraulic Gradient for Quicksand – Compute Using Gs and Porosity For a sand with specific gravity of soil solids Gs = 2.696 and porosity n = 44% (loose state), determine the critical hydraulic gradient i_c for the onset of quick (boiling) condition.

Introduction / Context:The critical hydraulic gradient i_c marks the threshold for boiling (quicksand) in cohesionless soils under upward seepage. Designers use i_c to check against piping at exits beneath hydraulic structures and to plan safe dewatering around excavations below the water table.

Given Data / Assumptions:

• Specific gravity of solids Gs = 2.696.
• Porosity n = 44% = 0.44.
• Water unit weight is reference; formula based on submerged weight balance.

Concept / Approach:

For upward seepage, the critical gradient is i_c = (Gs − 1) / (1 + e), where e is void ratio. Convert porosity to void ratio by e = n / (1 − n). If the applied gradient equals or exceeds i_c, the seepage force cancels the submerged unit weight, making σ′ → 0 (boiling condition).

Step-by-Step Solution:

Verification / Alternative check:

Check reasonableness: For typical sands with e around 0.7–0.9 and Gs near 2.65, i_c usually lies near 1.0; the computed value 0.95 fits expectations.

Why Other Options Are Wrong:

0.91–0.94 underestimate the ratio slightly given the stated porosity and Gs; 0.95 best matches the computed i_c.

Common Pitfalls:

Using n instead of e directly in the denominator; forgetting to convert percent to fraction; confusing Gs with unit weight ratio γ_s/γ_w (they are consistent here since γ_w is the reference).

Final Answer:

0.95