Exit gradient at downstream of a weir or barrage floor as per Khosla’s theory: On which non-dimensional parameter does the exit gradient primarily depend?

Introduction / Context:
Exit gradient governs piping safety at the downstream edge of hydraulic structures such as barrages and weirs. Khosla’s theory of independent variables provides a rational framework to compute uplift pressures and gradients beneath floors with cutoffs.

Given Data / Assumptions:

• Pervious foundation; floor with upstream and downstream sheet piles (cutoffs).
• Focus on exit gradient at the downstream end.
• Steady seepage conditions.

Concept / Approach:
Khosla’s method shows that uplift and gradients depend on geometric ratios rather than absolute sizes. A key parameter is b/d, where b is the floor length and d is the depth of the downstream cutoff. Larger b and deeper d reduce the exit gradient, improving safety against piping and heave.

Step-by-Step Solution:
1) Identify controlling geometric variables in potential flow beneath floors.2) Normalize dimensions to build b/d ratio.3) Recognize exit gradient g_exit decreases as b/d increases.4) Conclude dependence primarily on b/d, consistent with Khosla’s curves/tables.

Verification / Alternative check:
Design charts derived from Khosla’s theory tabulate pressure and gradient coefficients for various b/d values, confirming sensitivity to this ratio. Field experience also correlates safer performance with deeper downstream cutoffs or longer floors (higher b/d).

Why Other Options Are Wrong:

• Independent of b/d: contradicts the very basis of Khosla’s independent variable approach.
• Independent of cutoff depth: not true; d appears in b/d.
• Only on upstream head: head influences magnitude but geometric ratio b/d controls gradient distribution shape.

Common Pitfalls:

• Using absolute dimensions without non-dimensionalizing; leads to inconsistent conclusions.
• Neglecting downstream cutoff depth under the assumption that upstream cutoff dominates.

Final Answer:
The ratio of floor length to depth of downstream cutoff (b/d).