Angle of internal friction for rice grain is 27°, bulk density of rice at 14% moisture content is 833 kg m⁻³ and coefficient of friction between rice and concrete wall is 0.5. For a silo of 5 m diameter and 20 m height, the ratio between the lateral pressures at the bottom of the silo obtained by Rankine and Janssen formulae is
Options:
(A) 1.63
(B) 3.16
(C) 6.13
(D) 9.47
Official Answer Key:
B
Step-by-Step Solution & Explanation
Rankine active earth-pressure coefficient: K_a = (1−sinφ)/(1+sinφ) = (1−sin27°)/(1+sin27°) = 0.3755. Rankine lateral pressure (full overburden, no wall-friction relief): P_R = K_a·ρ·g·H = 0.3755×833×9.81×20 = 61,374 Pa. Janssen (accounting for wall friction reducing pressure with depth), hydraulic radius R=D/4=1.25 m: vertical pressure σ_v = (ρgR/μK_a)[1−exp(−μK_aH/R)]; lateral P_J = K_a·σ_v = 19,416 Pa. Ratio P_R/P_J = 61,374/19,416 = ≈3.16. (Rankine overpredicts silo wall pressure at depth because it ignores the load-relieving effect of wall friction that Janssen's formula captures.)
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