Submerged-Backfill Earth Pressure (Buoyant + Hydrostatic)

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.

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.

NAVFAC DM-7.02 is a free public US Navy design manual; the effective-stress split of soil and water pressure is public and printed in every soil-mechanics text; gamma_w = 62.4 pcf fresh water.

Estimate. AHJ and licensed professional govern.

Field names used by the API: phi, gamma_sat, h_ft, pw, pa_tot, dry_ref, y_bar

• Effective stress below the water table the soil contributes its buoyant weight (gamma_sat - gamma_w) at the Ka reduction; the water contributes full hydrostatic pressure at no reductionDas / NAVFAC DM-7.02
• Fully submerged, drainage relieves it the water table stands at the top of the retained height (worst case); a working drain that unsaturates the backfill removes the hydrostatic termDas / NAVFAC DM-7.02