Earth pressure is the sideways push of soil against walls; retaining walls must resist sliding, overturning, and bearing failure.

Scope (earth pressure)

This page covers lateral earth pressure for retaining walls, basement walls, and trenches: at-rest, active, and passive states; Rankine and Coulomb concepts; and stability (sliding, overturning, bearing) checks. In South Africa, characteristic actions and geotechnical design are framed in SANS 10160-5; wall structural design follows concrete or masonry standards as applicable. Drainage and surcharge loading must match the site model.

Active thrust (concept)

  1. Define effective soil strength (φ′, c′) and unit weight γ for the retained soil; check groundwater and drainage.
  2. Choose a pressure theory (Rankine/Coulomb) and wall friction δ; compute Ka or use charts from your code.
  3. Integrate lateral stress over height H to get thrust Pa; add surcharge and seismic coefficients if required.
  4. Use the calculator below for a level Rankine active case; use software for layered profiles and wall stability.

Geotechnical Engineering — Earth Pressure & Retaining Walls

Lateral earth pressures (at-rest, active, passive) for retaining wall and basement design.

Introduction

Soil exerts horizontal stress on vertical faces. If the wall moves away from the soil, the active limit can develop (lower lateral pressure). If the wall pushes into the soil, passive resistance increases. At-rest pressure applies when movement is negligible.

Retaining walls (gravity, cantilever, cantilever with heel, anchored) must resist lateral loads and satisfy global stability (sliding, overturning, bearing) and drainage.

Types of retaining wall structures including gravity and cantilever
Examples of retaining wall types (schematic). See licence on Wikimedia Commons
Cross-section of a gravity retaining wall
Gravity (mass) retaining wall section. See licence on Wikimedia Commons

What earth-pressure analysis produces

  • Design thrust and line of action for structural design of the stem and footing.
  • Passive pressure in front of the toe for sliding checks (where mobilized).
  • Water pressures and seepage effects when the water table is present.
  • Inputs to global stability (overturning, sliding, bearing) and detailing (drainage, weep holes).

Standards (South Africa)

Actions and geotechnical design basis: SANS 10160 (including Part 5). Soil strength and testing: SANS 3001. Structural concrete or masonry for the wall follows the relevant SANS material standards. Always align with the geotechnical investigation and drainage design.

Rankine (level backfill, no wall friction):   Ka = tan²(45° − φ/2) ;   Pa = ½ Ka γ H²   per unit wall width.

Notation (common)

  • Ka, Kp, K0 — active, passive, at-rest pressure coefficients.
  • γ — soil unit weight (kN/m³); clarify saturated vs buoyant below water table.
  • H — retained height for pressure integration.
  • δ — wall–soil friction angle (often taken as β·φ′).

Examples in practice

  • Basement wall: at-rest to active range depending on stiffness and movement tolerance.
  • Highway cut slope: gravity or cantilever wall with drainage blanket and surcharge from traffic.
  • Sheet pile in sand: embedment for passive resistance and water flow.
  • Braced excavation: strut loads from apparent earth pressure envelopes.

Calculator — Rankine active pressure

Level cohesionless backfill; horizontal effective stress field; wall friction neglected. φ in degrees; γ in kN/m³; H in m. Result Pa in kN per metre run of wall.

Ka = tan²(45° − φ/2) ;   Pa = ½ Ka γ H²

Active thrust (no surcharge)

Rankine total active thrust Pa = ½ KaγH² for level cohesionless backfill.

Key terms

Active state
Soil wedge moves enough to mobilize minimum lateral pressure on the wall.
Coefficient Ka
Ratio of lateral to vertical effective stress at active limit.

Software and retaining-wall design

Layered soils, water, surcharges, and seismic coefficients are usually analysed with geotechnical or structural–geotechnical tools. Examples (official sites):

  • PLAXIS — 2D/3D geotechnical analysis including walls.
  • GeoStudio — Slope/W and finite-element options for earth structures.
  • Rocscience — RS2, Settle3, and related tools.
  • Autodesk Civil 3D — site modelling and civil design.
  • gINT — logs and parameters for design.

No product endorsement—wall design must include drainage, durability, and structural checks. This Rankine calculator does not include cohesion, surcharge, or wall friction.

Diagram sources

Educational schematics. Files in Images/earth-pressure-retaining-walls/ were downloaded from Wikimedia Commons into this repo (not copied from other topic folders). Confirm licence on each Commons file page before reuse.