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Retaining Wall Design Calculator
Calculate stability of cantilever and gravity retaining walls including Rankine earth pressures, overturning, sliding, bearing pressure, and stem design.
Structural / Geotechnical Geotechnical engineers, structural engineers, civil engineering students Commercial Intent: HIGH
Engineering Formulas
Active Earth Pressure Coefficient (Rankine)
Ka = (1 − sin φ) / (1 + sin φ)
Where:
φ = backfill friction angle (degrees)
Ka: Active earth pressure coefficient
φ: Backfill friction angle (degrees)
Passive Earth Pressure Coefficient (Rankine)
Kp = (1 + sin φ) / (1 − sin φ)
Where:
φ = backfill friction angle (degrees)
Kp: Passive earth pressure coefficient
φ: Backfill friction angle (degrees)
Active Earth Thrust
Pa = ½ · γ · H² · Ka
action at H/3 from base
Horizontal: Pah = Pa · cos β
Vertical: Pav = Pa · sin β
γ: Backfill unit weight (kN/m³)
H: Total wall height (m)
Ka: Active earth pressure coefficient
β: Backfill slope angle (degrees)
Overturning Check
FSoverturning = MR / MOT ≥ 1.5
MOT = Pah · H/3 + Ps · H/2
MR = Σ (Wi · xi)
M_R: Resisting moment about toe (kN-m/m)
M_OT: Overturning moment about toe (kN-m/m)
Sliding Check
FSsliding = (V · μ + Pp) / (Pah + Ps) ≥ 1.5
V = total vertical force
μ = friction coefficient
Pp = passive thrust
V: Total vertical force (kN/m)
μ: Friction coefficient
P_p: Passive thrust (kN/m)
Bearing Pressure
e = B/2 − (MR − MOT) / V
If |e| ≤ B/6:
qmax = V/B · (1 + 6e/B)
qmin = V/B · (1 − 6e/B)
If |e| > B/6:
qmax = 2V / [3(B/2 − |e|)]
qmin = 0 (tension)
e: Eccentricity (m)
B: Base width (m)
q_max: Maximum bearing pressure (kPa)
q_min: Minimum bearing pressure (kPa)
Worked Example
Cantilever Wall — Height 4 m
wallType: cantileverH: 4stemTop: 0.3stemBottom: 0.5baseWidth: 3baseThickness: 0.4toeProjection: 0.6heelProjection: 1.9gamma: 18phi: 30surcharge: 10frictionCoeff: 0.45concreteUnitWeight: 24backfillSlope: 0
Ka
(1 − sin 30°) / (1 + sin 30°) = 0.3333
Active thrust
Pa = 0.5 × 18 × 4.4² × 0.333 = 58.1 kN/m
Overturning Moment
M_OT = 58.1 × 4.4/3 + 10 × 0.333 × 4.4²/2 = 117.4 kN-m/m
Resisting Moment
M_R = 165.9 kN-m/m (stem + base + backfill + surcharge)
FS Overturning
165.9 / 117.4 = 1.41 — below 1.5, enlarge base
Result: FS_overturning = 1.41, FS_sliding = 1.72, q_max = 112.5 kPa
Engineering Notes
Minimum FS_overturning = 1.5, minimum FS_sliding = 1.5 (typical code requirements).
If eccentricity > B/6, the base must be widened or a shear key added.
For cantilever walls, the stem is designed as a cantilever from the base slab.
Drainage behind the wall is critical — hydrostatic pressure doubles the lateral force.
Always verify allowable bearing capacity exceeds q_max.
Assumptions
• Backfill is dry, cohesionless soil
• Rankine theory assumes planar failure surface
• No wall friction (conservative)
• No water table within the failure zone
• Rigid wall and foundation (no soil-structure interaction)
• Uniform surcharge across entire backfill surface
Common Mistakes
✕ Neglecting surcharge effects on lateral pressure
✕ Using wrong height for stem design vs overturning
✕ Forgetting vertical component of active thrust on sloping backfill
✕ Not checking bearing pressure eccentricity
✕ Using φ in degrees in trig functions without conversion to radians
Frequently Asked Questions
What is the difference between a cantilever and gravity retaining wall?
A cantilever wall uses a stem and base slab, relying on the weight of backfill on the heel for stability. A gravity wall relies entirely on its own weight (mass concrete or masonry) to resist overturning and sliding.
What is the minimum factor of safety for overturning?
Most codes require FS ≥ 1.5 for overturning. Some codes require FS ≥ 2.0 for cohesive soils or seismic conditions.
Why does eccentricity matter?
When the resultant force falls outside the middle third (|e| > B/6), tension develops at the heel, which is usually unacceptable for soil foundations. The base must be enlarged or the wall geometry adjusted.
What is the Rankine active pressure coefficient?
Ka = (1 − sin φ) / (1 + sin φ). It assumes a planar failure surface and no wall friction. It is conservative for most retaining wall designs.
References & Standards
IS 456:2000BS 8002AASHTO
IS 456:2000
Plain and Reinforced Concrete — Code of Practice
BS 8002
Code of Practice for Earth Retaining Structures
AASHTO LRFD
Bridge Design Specifications — Section 11: Abutments and Retaining Walls
Bowles, J.E.
Foundation Analysis and Design — retaining wall theory and design examples