Seepage safety by Khosla’s theory: What is the critical exit gradient for stability against piping under a hydraulic structure?

Introduction / Context:

Hydraulic structures on permeable foundations are designed to avoid piping and heave at the downstream exit. Khosla’s theory of independent variables provides a framework to estimate exit gradients and plan under-seepage control (aprons, cutoffs, filters).

Given Data / Assumptions:

• Typical sandy foundations with conventional gradation.
• Critical gradient is the threshold beyond which upward seepage forces mobilize soil particles, initiating piping.
• Conservative handbook value used for preliminary design checks.

Concept / Approach:

The critical gradient ic is commonly taken around 0.5 for design safety in sands, representing the ratio at which effective stresses at the exit are sufficiently reduced to risk particle movement. While a more exact ic may be determined from submerged unit weights and gradation, 0.5 is widely adopted as a safe benchmark.

Step-by-Step Solution:

Verification / Alternative check:

Design guides stipulate that exit gradient ≤ (critical gradient / adopted factor of safety). Using ic ≈ 0.5 provides a clear pass/fail criterion.

Why Other Options Are Wrong:

• 0 or 1: Non-physical extremes for typical soils in this context.
• 0.25 or 0.75: Do not represent the standard conservative design value for ic in sands.

Common Pitfalls:

• Ignoring local grading or filter criteria at the exit, even when global gradient checks pass.

Final Answer:

0.50