Submerged-Backfill Earth Pressure (Buoyant + Hydrostatic)
The push of a backfill below the water table, where the dry Rankine tile no longer applies: the soil skeleton pushes with its buoyant weight (gamma_sat - 62.4) at the Ka reduction, but the water pushes with the full hydrostatic pressure at no reduction. Pa' = 0.5 x Ka x gamma_buoy x H^2, Pw = 0.5 x 62.4 x H^2, plus the Ka q H surcharge. A 10 ft phi = 30, 125 pcf sand pushes 2,083 lb/ft dry but 4,163 lb/ft submerged -- almost exactly 2x, and three-quarters of it is water, which is why a working drain is the cheapest structural element on the wall. Fully-submerged active case. A design aid, not a substitute for a geotechnical engineer's report.
Formula and source
Ka = (1 - sin phi)/(1 + sin phi); Pa' = 0.5 Ka (gamma_sat - 62.4) H^2 at H/3; Pw = 0.5 x 62.4 x H^2 at H/3; surcharge Ka q H at H/2; total and resultant height, with the dry-case thrust for contrast.
Rankine active pressure with effective-stress (buoyant) unit weight, as compiled in Das, Principles of Foundation Engineering, and NAVFAC DM-7.02 (Foundations and Earth Structures), by name.
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