Calculator for RCC Retaining Tentative Non seismic design

RCC Retaining Wall Calculator

Preliminary Non-Seismic Design as per IS 456 & IS 14458

Important Note: Preliminary estimation tool only. Field implementations require structural checks for shear, water table heads, and surcharge loads.

Total Wall Height H (m):

Stem Top Width (m):

Stem Bottom Width (m):

Toe Length (m):

Heel Length (m):

Base Slab Thickness (m):

Soil Unit Wt γ (kN/m³):

Soil Friction Angle ϕ (°):

Safe Bearing Capacity SBC (kN/m²):

Base Friction Coefficient (μ):

Concrete Grade fck (N/mm²):

Steel Grade fy (N/mm²):

Stem Bar Dia (mm):

Base Slab Bar Dia (mm):

RCC Cantilever Retaining Wall Design

Step-by-Step Solved Numerical Example (IS 456 & IS 14458)

1. Design Parameters & Trial Geometry

Design a cantilever retaining wall to retain an earth embankment 4.0 m high above ground level.

Parameter	Value
Overall Height of Wall (H)	4.0 m
Unit Weight of Soil (γ)	18 kN/m³
Angle of Internal Friction (ϕ)	30°
Safe Bearing Capacity (SBC)	150 kN/m²
Coefficient of Friction (μ)	0.5
Concrete Grade (M25)	fck = 25 N/mm²
Steel Grade (Fe500)	fy = 500 N/mm²
Base Width (B)	3.5 m (Toe: 1.0m, Stem Bottom: 0.5m, Heel: 2.0m)
Base Slab Thickness (D)	0.5 m
Stem Height (h)	3.5 m (4.0m - 0.5m)

2. Active Earth Pressure & Overturning Moment

Coefficient of active earth pressure (K_a):

K_a = (1 - sin 30°) / (1 + sin 30°) = 0.333

Total active earth pressure per meter length (P_a):

P_a = 0.5 × K_a × γ × H²
P_a = 0.5 × 0.333 × 18 × (4.0)² = 48.0 kN/m

Overturning moment about toe (M_ot):

M_ot = P_a × (H / 3) = 48.0 × (4.0 / 3) = 64.0 kNm/m

3. Vertical Loads & Resisting Moments

Calculation of loads and moments acting about the toe point:

Item / Component	Load Calculation (kN/m)	Magnitude	Lever Arm (m)	Moment (kNm/m)
1. Rectangular Stem Portion	0.3 × 3.5 × 25	26.25	1.35	35.44
2. Triangular Stem Portion	0.5 × 0.2 × 3.5 × 25	8.75	1.133	9.91
3. Base Slab	3.5 × 0.5 × 25	43.75	1.75	76.56
4. Soil Load over Heel	2.0 × 3.5 × 18	126.00	2.50	315.00
Total Sum		ΣV = 204.75	—	Mr = 436.91

4. Stability Checks

A. Factor of Safety against Overturning:

FoS_overturning = M_r / M_ot = 436.91 / 64.0 = 6.83 ≥ 1.5 SAFE

B. Factor of Safety against Sliding:

FoS_sliding = (μ × ΣV) / P_a = (0.5 × 204.75) / 48.0 = 2.13 ≥ 1.5 SAFE

C. Eccentricity Check:

x̅ = (M_r - M_ot) / ΣV = (436.91 - 64.0) / 204.75 = 1.821 m
e = (B / 2) - x̅ = (3.5 / 2) - 1.821 = -0.071 m
|e| ≤ B / 6 = 0.583 m SAFE

D. Maximum Soil Pressure Check:

q_max = (ΣV / B) × (1 + 6|e| / B)
q_max = (204.75 / 3.5) × (1 + (6 × 0.071 / 3.5)) = 65.62 kN/m² ≤ 150 kN/m² SAFE

5. Stem Reinforcement Design

Factored Bending Moment at the base of the stem:

P_a,stem = 0.5 × 0.333 × 18 × (3.5)² = 36.75 kN/m
M_u = 1.5 × [36.75 × (3.5 / 3)] = 64.31 kNm/m

Effective Depth (d): 500 mm - 50 mm (clear cover) = 450 mm

Required Tension Steel Area (A_st):

A_st = (0.5 f_ck / f_y) × [1 - √(1 - (4.6 M_u) / (f_ck b d²))] × b × d
A_st = 340.5 mm²/m

Checking minimum steel percentage requirement (0.12% per IS 456):

A_st,min = 0.0012 × 1000 × 500 = 600 mm²/m

Since A_st < A_st,min, provide minimum steel of 600 mm²/m.

Final Rebar Detail: Provide 12 mm dia bars @ 180 mm c/c (A_st,provided = 628 mm²/m).

Yogendra Gopal Borse

Civil Engineer | Assistant Engineer Grade-I, Maharashtra PWD

B.Tech (Civil) from VJTI Mumbai. Experienced in bridge design, road works, estimation, project monitoring and digital engineering tools. Creator of YogiPWD – practical technical resources for civil engineers.

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