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Retaining Wall Active & Passive Earth Pressure Calculator (Rankine)

William Rankine developed classical lateral earth pressure theory in 1857, assuming plastic equilibrium in a cohesionless backfill soil mass.

Total exposed vertical stem height of the retaining wall in meters.

Moist bulk soil unit weight (typical backfill sand/gravel ≈ 17 - 20 kN/m³).

Internal friction angle in degrees (compacted granular backfill ≈ 30° - 36°).

Uniform vehicular or pavement surcharge pressure acting on backfill surface.

Calculated Result
61.33 kN/m

Total Active Lateral Thrust

Total Active Lateral Thrust (Pa)

61.33 kN/m

Active Pressure Coeff (Ka)

0.3333

Passive Pressure Coeff (Kp)

3

Overturning Moment (M_ot)

90.67 kN·m/m

Resultant Thrust Location

1.48 m above base

Thrust Breakdown

Soil: 48 kN/m | Surcharge: 13.33 kN/m

Calculation Breakdown

  1. 1. Rankine Earth Pressure CoefficientsKa = (1 - sin(30°)) / (1 + sin(30°)) = (1 - 0.5) / (1 + 0.5) = 0.3333; Kp = 1 / Ka = 3
  2. 2. Soil Self-Weight Lateral ThrustPa(soil) = 0.5 · Ka · γ · H² = 0.5 · 0.3333 · 18 · 4² = 48 kN/m acting at H/3 = 1.33 m
  3. 3. Surcharge Lateral Thrust & Total ResultantPa(surcharge) = Ka · q · H = 0.3333 · 10 · 4 = 13.33 kN/m acting at H/2 = 2.00 m. Total Pa = 61.33 kN/m

Lateral Soil Pressure vs Depth (4m Wall)

Interactive visualization based on your current inputs

Stress (kPa)
0.06.81420270 m (Surface)1 m2 m3 m4 m (Base)Depth (m)Lateral Stress (kPa)

What Is the Retaining Wall Active & Passive Earth Pressure Calculator (Rankine)?

Rankine earth pressure theory predicts the lateral horizontal forces exerted by soil backfill against retaining walls and basement structures.

How Does the Retaining Wall Active & Passive Earth Pressure Calculator (Rankine) Work?

It models Mohr-Coulomb failure criteria for plane strain slip surfaces forming at angles of 45° + φ/2 behind the retaining stem.

Retaining Wall Active & Passive Earth Pressure Calculator (Rankine) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

K_a = \frac{1 - \sin\phi}{1 + \sin\phi}, \quad P_a = \frac{1}{2} K_a \gamma H^2 + K_a q H, \quad M_{ot} = \frac{1}{6} K_a \gamma H^3 + \frac{1}{2} K_a q H^2

Active earth pressure coefficient Ka multiplies triangular soil weight pressure and rectangular surcharge pressure, yielding lateral thrust and base overturning moment.

How to Use the Retaining Wall Active & Passive Earth Pressure Calculator (Rankine)

  1. Enter wall height in meters.
  2. Provide backfill moist unit weight (kN/m³) and internal friction angle (degrees).
  3. Optionally supply roadway or building surcharge load in kPa.

Step-by-Step Example Calculation

4m Granular Backfill Wall with 10 kPa Traffic Surcharge

Input Values:

wallHeightMeters:4.0
soilUnitWeightKNm3:18.0
frictionAngleDeg:30.0
surchargeKPa:10.0
Worked Steps: With φ = 30° (Ka = 0.3333), the wall sustains 61.33 kN/m lateral thrust producing 90.67 kN·m/m overturning moment.

Understanding Your Result

Total Lateral Thrust (Pa): Horizontal driving force in kN per linear meter of wall.

Active Coefficient (Ka): Lateral-to-vertical effective stress ratio.

Overturning Moment (M_ot): Rotational moment about the wall toe (kN·m/m).

Thrust Centroid: Height above wall base where resultant force acts.

Factors That Affect the Result

  • Higher friction angle drastically lowers active pressure; wall height increases thrust with the square (H²).

When Should You Use This Calculator?

  • Highway bridge abutments, basement diaphragm walls, cantilever gravity wall design, and soil mechanics education.

Assumptions & Limitations

  • Assumes vertical frictionless wall backface, horizontal backfill surface, and dry cohesionless granular soil.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard classical Rankine limit-equilibrium geotechnical formulation.

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