Design and Analysis of a Cantilever Retaining Wall

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Dr Lalit Johari · Accepted Answer

To design the cantilever retaining wall as per the given data, we'll follow the steps corresponding to the objectives provided earlier: 1. Geometry and Stability Analysis Base Width (B), Heel Width (H), Toe Width (T), and Stem Height (h): The height of the wall is given as 5 meters. We'll assume a base width of approximately 0.5 to 0.7 times the height of the wall (H ≈ 0.5h to 0.7h). Let's assume B = 3.0 meters initially. The toe width is usually around 0.3 to 0.4 times the base width, and the heel width would be the remaining portion. Assuming: Base width  B = 3.0 m B = 3.0 \, 	ext{m} B = 3.0 m Heel width  H = 2.0 m H = 2.0 \, 	ext{m} H = 2.0 m Toe width  T = 1.0 m T = 1.0 \, 	ext{m} T = 1.0 m Stem height  h = 5 m h = 5 \, 	ext{m} h = 5 m Stability Analysis: Sliding Stability : Check if the resisting force against sliding is greater than the driving force. Overturning Stability : Check the overturning moment against the restoring moment. Bearing Capacity : Ensure that the soil bearing pressure under the footing does not exceed the allowable bearing capacity. 2. Soil Pressure Calculations Active Earth Pressure (Pa) using Rankine's Theory: K a = 1 − sin ⁡ ϕ 1 + sin ⁡ ϕ K_a = \frac{1 - \sin \phi}{1 + \sin \phi} K a ​ = 1 + s i n ϕ 1 − s i n ϕ ​ For  ϕ = 3 0 ∘ \phi = 30^\circ ϕ = 3 0 ∘ ,  K a ≈ 0.333 K_a \approx 0.333 K a ​ ≈ 0.333 Active earth pressure,  P a = 0.5 × γ × h 2 × K a P_a = 0.5 	imes \gamma 	imes h^2 	imes K_a P a ​ = 0.5 × γ × h 2 × K a ​ P a = 0.5 × 18 × 5 2 × 0.333 ≈ 37.46 kN/m P_a = 0.5 	imes 18 	imes 5^2 	imes 0.333 \approx 37.46 \, 	ext{kN/m} P a ​ = 0.5 × 18 × 5 2 × 0.333 ≈ 37.46 kN/m Passive Earth Pressure: This is typically calculated for the toe section, where the resisting pressure helps stabilize the wall. 3. Structural Design Reinforcement Design: Consider the bending moment at the base of the stem, heel, and toe sections to determine the required reinforcement. Reinforcement bars are placed based on the moment and shear forces calculated. The distribution of reinforcement would consider the load from the backfill and the wall's self-weight. 4. Drainage and Safety Considerations Drainage Design: A drainage system must be included to prevent water buildup behind the wall, which could otherwise increase the lateral earth pressure. Perforated pipes or weep holes at the base of the wall are typical solutions. Factor of Safety: Ensure a minimum factor of safety against sliding, overturning, and bearing capacity failure is maintained. Factor of safety against sliding and overturning is typically set to be at least 1.5.

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Dr Lalit Johari

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