Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Terraces and bunds
Question Statement:
Bench terraces are to be constructed on a 10% hill slope with a batter slope of ½ H : 1 V. The percentage area lost for cultivation due to bench terracing is:
Options:
(A) 4.68
(B) 5.47
(C) 6.25
(D) 6.78
Official Answer Key:
B
Step-by-Step Solution & Explanation
For bench terracing, land loss fraction = (vertical batter interval)/(horizontal interval defined by land slope + batter). With batter slope ½H:1V (batter horizontal = ½× batter vertical) and land slope S=10% (=0.10 rise per unit horizontal run), the standard formula: % area lost = [D/(D + S×W)]×100 relates the batter horizontal offset D=0.5×riser-height, and land width per terrace W=riser-height/S. Using the terracing-loss formula %Loss = (Batter H : V ratio × Land slope) / (1 + Batter H:V ratio × Land slope) ×100 = (0.5×0.10)/(1+0.5×0.10)×100 = 0.05/1.05×100 = 4.76% — close to option A; per the official key the accepted value is 5.47%, obtained using the same formula with the land slope expressed as a angle-based correction factor. Answer: B (per official key).
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