Scour at a bend by Lacey’s recommendation: If D is the normal regime scour depth in a straight reach, what is the design scour depth in a right-angled river bend?

Introduction / Context:
River training and hydraulic structure foundations must consider aggravated scour at bends. Lacey provided multipliers over the normal regime scour depth D to account for curvature effects. Designers use these to determine founding levels or protection depths at bends.

Given Data / Assumptions:

• D is the regime (straight-reach) scour depth.
• Right-angled bend indicates strong curvature.
• Applicability: alluvial rivers in regime conditions.

Concept / Approach:

Bends increase secondary currents and attack on the outer bank, deepening the scour hole beyond straight-reach values. Empirical multipliers convert D to a conservative design scour at bends.

Step-by-Step Solution:

Verification / Alternative check:

Where data allow, compare with observed thalweg depths during high flows or use numerical modeling. The empirical factor is typically conservative.

Why Other Options Are Wrong:

1.25 D and 1.10 D underestimate scour at a sharp bend; 1.75 D and 2.00 D are excessive for a right-angled bend in common practice without special aggravating factors.

Common Pitfalls:

Ignoring local contraction or pier effects which can further increase scour; using bend multipliers without verifying river planform dynamics.

Final Answer:

1.50 D