Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Soil loss estimation
Question Statement:
The slope length of an area having land slope of 6% is reduced to half while other conditions are kept unchanged. The reduction in annual soil loss from the area, in %, is __________. (Rounded off to 2 decimal places)
Official Answer Key:
29.00 to 29.50
Step-by-Step Solution & Explanation
In the Universal Soil Loss Equation (USLE), A = R·K·L·S·C·P, the slope-length factor is:
L ∝ λ^m
where λ is the slope length and m depends on the land slope. For slopes of 5 % and steeper, m = 0.5. Here the slope is 6 %, so m = 0.5.
Step 1 — ratio of new to original soil loss (all other factors unchanged):
A₂/A₁ = (λ₂/λ₁)^0.5 = (0.5)^0.5 = 0.7071
Step 2 — reduction:
Reduction = (1 − 0.7071) × 100 = 29.29 %
(Had the slope been below 5 %, m would be 0.4 or 0.3, giving a smaller reduction — so identifying the correct exponent from the 6 % slope is the crux of this question.)
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