Step 1: Understanding the Concept:
Permanent gully control structures stabilize active overfall gully heads and dissipate kinetic energy of concentrated storm runoff.
Key Formula or Approach:
\[ Q = C L H^{3/2} \quad \text{(Weir Flow over Drop Spillway Crest)} \]
Step 2: Detailed Explanation:
Permanent soil conservation structures for gully stabilization:
1. Drop Spillway: Installed directly at the gully head for drops generally up to \(3.0\text{ m}\). Runoff passes over a straight or box weir crest and falls vertically onto an apron/stilling basin, safely lowering water into the gully bed and halting headward gully retreat.
2. Chute Spillway: Used for steep drops and larger drop heights (\(> 3\text{ m}\)) conveying water along a paved open channel.
3. Drop Inlet Spillway: Used where high embankments create temporary detention ponds.
4. Brushwood dam: A temporary, non-permanent structure.
Step 3: Final Answer:
Therefore, the permanent structure used at the gully head is a Drop spillway, corresponding to option (C).