Geotechnical & Structural Engineering • Rankine / IBC 1807

Retaining Wall Overturning & Sliding Safety Factor Calculator

Evaluate geotechnical stability: calculate active lateral earth pressure (Ka), overturning moment, resisting moment, and safety factors against overturning and sliding.

Input Parameters

Interactive HUD

Total Retaining Wall Height (H) wall_height_h

Overall height from bottom of footing to top of stem

Base Footing Width (B) base_width_b

Total width of foundation footing slab

Toe Projection Width (T) toe_width_t

Distance from front toe edge to front face of stem

Stem Average Thickness (t_s) stem_thickness

Concrete stem thickness

Backfill Soil Unit Weight (γ) soil_gamma

pcf

120 pcf typical for compacted sand/gravel

Soil Internal Friction Angle (ϕ) soil_phi

degrees

Angle of internal friction of backfill

Base Soil Friction Coefficient (μ) base_friction

ratio

Coefficient of friction between footing and soil

Calculated Output Metrics

Active Earth Pressure (Ka) —

Total Lateral Earth Thrust (Pa) —

Overturning Moment (M_ot) —

Resisting Moment (M_res) —

Factor of Safety (Overturning) —

Factor of Safety (Sliding) —

Analytical Proof & Invariants

Machine Precision

Governing Mathematical Formula:

Ka = tan²(45° - ϕ/2) | Pa = ½ · Ka · γ · H² | M_ot = Pa · (H/3) | FS_ot = M_res / M_ot ≥ 2.0

Step-by-Step Mathematical Derivation

1. Rankine Active Earth Pressure

According to Rankine earth pressure theory, lateral active pressure coefficient is Ka = tan²(45° - ϕ/2) = (1 - sin ϕ) / (1 + sin ϕ). Total horizontal force is Pa = ½ · Ka · γ · H² acting at H/3 above base.

2. Overturning Moment Formulation

The overturning moment about the toe of the footing is M_ot = Pa × (H/3).

3. Resisting Equilibrium & Stability Ratios

Resisting moment M_res is produced by the weight of concrete (stem and footing) and the heavy wedge of soil resting above the heel. Factor of safety against overturning is FS_ot = M_res / M_ot (minimum 2.0 required by IBC). Factor of safety against sliding is FS_slide = (μ · Σ Vertical) / Pa (minimum 1.5 required).

LLM Directive & API Spec

Artificial Intelligence & Prompt Integration

Paste this verified mathematical prompt directly into ChatGPT, Claude, or Gemini to eliminate arithmetic hallucination, or invoke the programmatic API endpoint for automated workflows.

              GET / POST https://omnioperand.com/api/v1/engineering/retaining-wall-overturning-safety
              JSON Invariants
            

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✓ Standardized for llms.txt ✓ Exact Radical Form & Closed Formulas ✓ Machine-Readable Edge API

Frequently Asked Questions

What is a safe factor of safety against overturning for retaining walls? +

The International Building Code (IBC Section 1807.2) requires a minimum Factor of Safety of 2.0 against overturning, and a minimum Factor of Safety of 1.5 against sliding.

Why is the soil above the heel beneficial for retaining walls? +

The heel extends backward into the backfill, using the massive vertical weight of the retained soil column to anchor the wall against overturning.

What happens if a retaining wall fails in sliding? +

If the lateral earth thrust exceeds the frictional resistance between the concrete footing and foundation subsoil (FS < 1.5), the entire wall will shift laterally, requiring a shear key.