Lateral Earth Pressure and Thrust (Rankine)
The push of retained soil: the Rankine active coefficient Ka = tan^2(45 - phi/2) and passive Kp = 1/Ka, the triangular active thrust Pa = 0.5 x Ka x gamma x H^2 at H/3, the rectangular surcharge term Ka x q x H at H/2, the combined resultant and its height, and the passive resistance. A 10 ft wall of phi = 30 sand carries exactly 2,000 lb/ft active against 18,000 lb/ft passive -- the 9:1 ratio that is why passive is never counted on lightly; a 250 psf parking surcharge grows the thrust 42% and lifts its arm. Cohesionless, vertical, frictionless, dry Rankine case only. A design aid, not a substitute for a geotechnical engineer's report.
Formula and source
Ka = tan^2(45 - phi/2) = (1 - sin phi) / (1 + sin phi); Kp = 1/Ka; Pa = 0.5 Ka gamma H^2 at H/3, plus surcharge Ka q H at H/2; Pp = 0.5 Kp gamma H^2.
Rankine (1857) lateral earth pressure, as compiled in Das, Principles of Foundation Engineering, and NAVFAC DM-7.02 (Foundations and Earth Structures), by name.
Audience
This tile is built for trades and the adjacent professions in the Carpentry and Construction group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.