GEO-16

Coulomb wedge (active, horizontal backfill)

Pa = ½ γ H² Ka with Ka from the critical wedge, φ and δ on the wall.

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Earth pressureCoulomb 1776

Governing equation

P_a=\tfrac12\gamma H^2 K_a

where

\gamma: Unit weight (kN/m³)
H: Height (m)
K_a: Ka (—)
P_a: Active thrust (kN/m)

Lecture brief

Historical brief

Soil mechanics became a quantitative laboratory after Karl von Terzaghi’s 1925–1943 work on effective stress, consolidation and bearing. These sheets still size shallow foundations, retaining walls, piles and drainage in SI. This sheet (GEO-16 — Coulomb wedge (active, horizontal backfill)) is the form associated with Coulomb 1776. Working symbols: $\gamma$ , $H$ , $K_a$ $\rightarrow$ $P_a$ . A planar trial wedge. Minimise/maximise the thrust versus the trial angle.

Purpose

Purpose: compute

P_a

from

\gamma

H

K_a

in Geotechnical engineering via

P_a=\tfrac12\gamma H^2 K_a

Pa = ½ γ H² Ka with Ka from the critical wedge, φ and δ on the wall. Use it when a real geotechnical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\gamma = 18.000\,\mathrm{kN/m^{3}}

H = 6.000\,\mathrm{m}

K_a = 0.330\,\mathrm{—}

, the governing relation

P_a=\tfrac12\gamma H^2 K_a

yields

P_a = 106.92\,\mathrm{kN/m}

. A wall, a sliding plane, a thrust arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Unit weight \gamma18 kN/m³Height H6 mKa K_a0.33 —

Outputs

Active thrust P_a106.92 kN/m

Reading speed

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Narration of this film

A wall, a sliding plane, a thrust arrow.

A planar trial wedge. Minimise/maximise the thrust versus the trial angle.

Reading speed

Watch on YouTube