Retaining walls resist lateral soil pressure and prevent slope failure. They are encountered in highways, basements, bridge abutments, and terraced construction. Design involves calculating lateral earth pressure and checking structural stability and section adequacy.
Types of Retaining Walls
| Type | Height Range | Material | Principle |
|---|---|---|---|
| Gravity Wall | <3 m | PCC/Masonry | Self-weight resists overturning |
| Cantilever Wall | 3–7 m | RCC | Stem + footing cantilever action |
| Counterfort Wall | >7 m | RCC | Counterforts tie stem to base |
| Buttressed Wall | >7 m | RCC | Buttresses on fill side |
| Gabion Wall | <5 m | Stone + wire mesh | Flexible, permeable |
| Sheet Pile Wall | Any | Steel/Concrete | Driven into soil, braced or cantilevered |
Earth Pressure Theories
Rankine's Theory (1857)
Assumptions: Wall is smooth (no friction), soil is cohesionless, semi-infinite mass.
Active earth pressure coefficient:
Ka = tan²(45 − φ/2) = (1 − sinφ) / (1 + sinφ)
Passive earth pressure coefficient:
Kp = tan²(45 + φ/2) = (1 + sinφ) / (1 − sinφ)
Note: Ka × Kp = 1
Coulomb's Theory (1776)
Accounts for wall friction angle δ and backfill slope angle β:
Ka = sin²(α+φ) / [sin²α × sin(α−δ) × {1 + √(sin(φ+δ)sin(φ−β) / (sin(α−δ)sin(α+β)))}²]
where α = angle of wall back face with horizontal (90° for vertical wall).
Coulomb's Ka > Rankine's Ka when wall friction exists → more conservative for design.
Earth Pressure Values for Common Soils
| Soil Type | φ (degrees) | Ka | Kp |
|---|---|---|---|
| Loose sand | 30° | 0.333 | 3.00 |
| Medium dense sand | 35° | 0.271 | 3.69 |
| Dense sand/gravel | 40° | 0.217 | 4.60 |
| Stiff clay (drained) | 20° | 0.490 | 2.04 |
Earth Pressure Distribution
For cohesionless backfill, horizontal active pressure at depth z:
σh = Ka × γ × z
Total lateral force (per metre length) = ½ × Ka × γ × H²
Acting at H/3 from base.
For cohesive soil: σh = Ka × γ × z − 2c√Ka
Tension zone depth = 2c / (γ√Ka) — ignore tension in design (fill with cohesionless material).
Stability Checks for Retaining Walls
1. Overturning Check
Factor of Safety against overturning = Restoring moment / Overturning moment ≥ 1.5 (IS:456)
Restoring moment = W × x̄ (self-weight moments about toe)
Overturning moment = Pa × H/3
2. Sliding Check
FOS against sliding = (μ × ΣV + Pp) / Pa ≥ 1.5
where μ = tan δ ≈ 0.5–0.7 (concrete-soil friction), Pp = passive resistance at toe.
If FOS < 1.5, provide a shear key below the base.
3. Bearing Pressure Check
e = B/2 − x̄ (eccentricity of resultant from centre of base)
For e ≤ B/6: σ_max = ΣV/B × (1 + 6e/B) ≤ SBC (no tension)
For e > B/6: Meyerhof's effective area method applies.
Cantilever Retaining Wall — Worked Example
Problem Data
- Retained height H = 4.5 m, surcharge q = 10 kN/m²
- Backfill: φ = 30°, γ = 18 kN/m³, cohesionless
- SBC of foundation soil = 200 kN/m²
- μ = 0.5, fck = 25, fy = 415
Preliminary Dimensions
- Base width B ≈ 0.5–0.7H = 2.5–3.15 m → try B = 3.0 m
- Base slab thickness = H/12 = 375 mm → use 400 mm
- Stem thickness (bottom) = H/12 to H/10 = 375–450 mm → use 400 mm, taper to 200 mm at top
- Toe projection = B/3 = 1.0 m; Heel projection = 3.0 − 1.0 − 0.4/2 = 1.8 m
Active Earth Pressure
Ka = 0.333, H_total = 4.5 + 0.4 = 4.9 m (including base)
Pa = ½ × 0.333 × 18 × 4.9² = 71.8 kN/m (soil)
Ps = 0.333 × 10 × 4.9 = 16.3 kN/m (surcharge)
Total Pa = 71.8 + 16.3 = 88.1 kN/m
Stability Results
| Check | Calculated FOS | Required | Status |
|---|---|---|---|
| Overturning | 2.3 | 1.5 | OK |
| Sliding | 1.6 | 1.5 | OK |
| Bearing (σmax) | 172 kN/m² | <200 kN/m² | OK |
Structural Design of Stem
Design the stem as a cantilever fixed at base with:
Mu at base = 1.5 × (Pa × H/3 + Ps × H/2)
= 1.5 × (71.8 × 4.9/3 + 16.3 × 4.9/2) = 1.5 × (117.2 + 39.9) = 235.7 kN·m/m
Design for Mu to get Ast in vertical stem bars (earth face).
Distribution steel = 0.12% bD on non-earth face horizontally.
Drainage Behind Retaining Wall
Hydrostatic pressure from water accumulation can be catastrophic. Provide:
- Weep holes: 75–100 mm dia, at 1.5–3.0 m c/c (horizontal and vertical)
- Filter medium behind wall: coarse gravel or geotextile filter
- Subsoil drain at toe: perforated pipe in gravel bed
Undrained water pressure behind a 5 m wall = ½ × γw × H² = ½ × 9.81 × 5² = 122.6 kN/m — this alone can cause failure!
Frequently Asked Questions
What is the difference between active and passive earth pressure?
Active pressure develops when the wall moves away from the soil (wall yields, soil expands laterally). Passive pressure develops when the wall is pushed into the soil. Active pressure is much smaller than passive; typical ratio Ka/Kp = 1/9 for φ = 30°.
Why is Coulomb's theory preferred for retaining wall design over Rankine's?
Coulomb accounts for wall-soil friction, which reduces active pressure, and is more applicable to practical cases where the wall back face is inclined. However, Rankine is simpler and slightly conservative, making it common in preliminary design.
What is the safe eccentricity for a retaining wall base?
e ≤ B/6 ensures the entire base is in compression (no tension zone). This is the standard requirement for retaining wall foundations per IS 456.