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Rankine earth pressure, overturning and sliding checks to IS 456, base pressure, shear key, and stem, heel and toe reinforcement.

Tools · RCC design

Retaining wall:Guided step by step: Rankine earth pressure, stability against overturning and sliding as per IS 456, base pressures, then the stem, heel and toe designed by limit state with bar spacing.

Guided · step 1 of 11

The wall and Rankine’s active pressure

A cantilever retaining wall is a vertical stem fixed to a base slab. The base is split into the toe (in front) and the heel (under the retained soil, whose weight helps hold the wall down). Rankine’s theory gives the active pressure coefficient for a smooth vertical back and level backfill.

Ka = 1 − sin φ1 + sin φ

Wall and soil

Proportions (blank = rule of thumb)

Section through the wall

B = 2.4 m (toe 0.8, stem 0.35, heel 1.25)H = 4Df 1
FOS overturning
3.07
≥ 1.55 ✓
FOS sliding
1.34
key 0.3 m → 1.72
p max / min
75.9 / 31kN/m²
SBC 150 ✓
Stem steel
12 @ 150mm
Full solution, all steps at once
  1. The wall and Rankine’s active pressureKa = 1 − sin φ1 + sin φ

    H = 4 m, γ = 18 kN/m³, φ = 30°, SBC = 150 kN/m², μ = 0.5

    Ka = 1 − 0.51 + 0.5 = 0.3333

  2. Minimum depth of foundationDf = (SBCγ)·Ka²

    Df = (15018) × 0.3333² = 0.926 m; adopted 1 m below front ground

  3. Trial proportions

    Base width B = 2.4 m (0.6H = 2.4)

    Toe = 0.8 m, stem bottom ts = 0.35 m, heel = 1.25 m

    Base thickness tb = 0.35 m; stem height h = H − tb = 3.65 m

  4. Earth pressure on the wallPa = KaγH²2

    Pa = 0.3333 × 18 × 4²2 = 48 kN/m at 1.333 m

    Overturning moment about the toe MO = 64 kN·m/m

  5. Weights and restoring momentΣW = W₁ + W₂ + …MR = ΣW·x

    Stem (rectangle): 18.25 kN × 1.05 m = 19.16 kN·m

    Stem (triangle): 6.84 kN × 0.9 m = 6.16 kN·m

    Base slab: 21 kN × 1.2 m = 25.2 kN·m

    Soil on heel: 82.13 kN × 1.775 m = 145.77 kN·m

    ΣW = 128.22 kN/m; MR = 196.29 kN·m/m

  6. Check against overturningFOS = MRMO ≥ 1.55

    FOS = 196.2964 = 3.07 ✓

  7. Check against slidingFOS = μΣWP ≥ 1.55Pp = Kpγ[(Df + a)² − Df²]2

    FOS = 0.5 × 128.2248 = 1.34 ✗

    Short by 1.55 × 48 − 64.11 = 10.29 kN/m; Kp = 1/Ka = 3

    Shear key depth a = 0.175 m → provide 0.3 m deep key (Pp = 18.63 kN/m, FOS = 1.72 ✓)

  8. Pressure under the basex̄ = MR − MOΣWe = B2 − x̄p = ΣWB·(1 ± 6eB)

    x̄ = 196.29 − 64128.22 = 1.032 m

    e = 1.2 − 1.032 = 0.168 m ≤ B6 = 0.4 ✓

    pmax = 75.89 kN/m² ≤ 150 ✓; pmin = 30.96 kN/m² ✓

  9. Stem designM = Kaγh³6Mu = 1.5·M

    M = 0.3333 × 18 × 3.65³6 = 48.63 kN·m; Mu = 72.94 kN·m/m

    d = 350 − 50 − 122 = 294 mm; dreq = 162.6 mm ✓

    Ast = 725 mm²/m → 12 mm @ 150 c/c on the earth face

    Distribution and front-face steel: 8 mm @ 150 c/c; shear τv = 0.204 ≤ τc = 0.363 ✓

  10. Heel slabw = γh + 25tbM = ∫(w − p)·x dx

    Downward w = 18 × 3.65 + 25 × 0.35 = 74.45 kN/m²; upward p from 30.96 (heel end) rising towards the toe

    M = 27.88 kN·m/m (service), Mu = 41.83

    Ast = 420 mm²/m → 12 mm @ 260 c/c at the top; τv = 0.203 ≤ 0.28 ✓

  11. Toe slabM = ∫(p − 25tb)·(toe − x) dx

    p at toe = 75.89, at stem face = 60.91 kN/m²

    M = 19.89 kN·m/m, Mu = 29.83

    Ast = 420 mm²/m → 12 mm @ 260 c/c at the bottom (extend the stem bars into the toe)