Exit gradient in seepage and piping checks: The seepage exit gradient i_exit at a downstream toe or exit point is defined as which ratio?

Introduction / Context:
The exit gradient is critical for evaluating piping and heave at the downstream toe of hydraulic structures such as sheet-pile cutoffs, weirs, and earth dams. An excessive gradient can initiate particle movement and undermine stability.

Given Data / Assumptions:

• Steady seepage through a permeable medium.
• Hydraulic gradient i = dh/dl, where dh is head loss and dl is distance along the flow path.
• Exit gradient refers specifically to conditions near the downstream emergence point.

Concept / Approach:
The hydraulic gradient quantifies the driving force for flow per unit length of path. At exits, the gradient is highest and must be compared with critical gradients that cause boiling or piping. Filters and drainage blankets are used to reduce gradients and prevent particle migration.

Step-by-Step Solution:

Verification / Alternative check:
Flow-net construction shows steep equipotential spacing at exits, confirming larger i values there.

Why Other Options Are Wrong:

• A: Uses total head rather than head loss.
• B: Not a hydraulic definition; geometric only.
• C: Ratio of heads is dimensionless and not the gradient definition.
• E: Incorrect since a correct definition exists (option D).

Common Pitfalls:
Confusing geometric slope with hydraulic gradient; neglecting local path length near the exit when estimating i_exit.

Final Answer:
Head loss divided by the length of the seepage path