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Coulomb Cantilever Retaining Wall Active Earth Pressure Calculator

Coulomb wedge theory determines lateral active earth pressure acting on earth retaining structures, accounting for wall batter, soil backfill slope, and wall-soil interface friction.

Effective internal friction angle of backfill soil.

Inclination angle of backfill ground surface above horizontal.

Inclination of wall back face from vertical (0° = vertical).

Friction angle between soil backfill and wall interface (typically 1/2 to 2/3 of φ).

Moist bulk unit weight of the backfill soil.

Total height of retaining wall stem supporting backfill.

Calculated Result
0.3307

Coulomb Active Coefficient (K_a)

Total Active Thrust (P_a)

110.12 kN/m

Horizontal Driving Thrust (P_ah)

99.8 kN/m

Vertical Stabilizing Thrust (P_av)

46.54 kN/m

Rankine Baseline K_a

0.2827

Calculation Breakdown

  1. Coulomb Wedge Active Earth Pressure Coefficient (Ka)Ka(Coulomb) = 0.3307 vs Rankine Ka = 0.2827 (factors wall batter θ = 5° and friction δ = 20°)
  2. Total Active Lateral Earth ThrustP_a = 0.5 · γ · H² · K_a = 0.5 · 18.5 · 6² · 0.3307 = 110.12 kN/m
  3. Directional Vector Thrust ComponentsP_ah = P_a · cos(θ + δ) = 99.8 kN/m (driving); P_av = P_a · sin(θ + δ) = 46.54 kN/m (stabilizing)

Coulomb Thrust Components

Interactive visualization based on your current inputs

kN/m
0.025507499Ka (x100)Total Pa (kN/m)Horizontal Pah (kN/m)Vertical Pav (kN/m)Force ComponentkN/m

What Is the Coulomb Cantilever Retaining Wall Active Earth Pressure Calculator?

Coulomb wedge theory determines lateral active earth pressure acting on earth retaining structures, accounting for wall batter, soil backfill slope, and wall-soil interface friction.

Unlike Rankine idealized smooth vertical wall theory, Coulomb provides realistic lateral loading when friction angle δ develops along the back face of the retaining wall.

This calculator determines Ka, total active thrust Pa, horizontal overturning thrust Pah, and vertical stabilizing thrust Pav.

How Does the Coulomb Cantilever Retaining Wall Active Earth Pressure Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Coulomb Cantilever Retaining Wall Active Earth Pressure Calculator Formula & Variables

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

Ka = cos²(φ - θ) / [ cos²θ · cos(θ + δ) · (1 + √[ sin(φ + δ)·sin(φ - β) / (cos(θ + δ)·cos(θ - β)) ])² ]

Coulomb active earth pressure coefficient accounts for friction between backfill and the wall face, providing more accurate thrust than Rankine for inclined walls.

How to Use the Coulomb Cantilever Retaining Wall Active Earth Pressure Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

6m Cantilever Wall (φ = 34°, δ = 20°, β = 10°)

Input Values:

internalFrictionAnglePhiDeg:34
wallBackfillSlopeBetaDeg:10
wallBackFaceAngleThetaDeg:5
wallSoilFrictionDeltaDeg:20
soilUnitWeightKNPerM3:18.5
retainingWallHeightM:6
Worked Steps: Computes Ka = 0.298, total thrust Pa = 99.2 kN/m, Pah = 89.9 kN/m, Pav = 41.9 kN/m.

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • The vertical thrust Pav acts downward on the wall heel, providing a stabilizing moment against overturning.
  • Backfill slope angle β must not exceed soil friction angle φ for physical slope stability.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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