Question & 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 
    $B = 3.0 \, \text{m}$
  • Heel width 
    $H = 2.0 \, \text{m}$
  • Toe width 
    $T = 1.0 \, \text{m}$
  • Stem height 
    $h = 5 \, \text{m}$

• 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:

  • $K_a = \frac{1 - \sin \phi}{1 + \sin \phi}$
  • For 
    $\phi = 30^\circ$$K_a \approx 0.333$
  • Active earth pressure, 
    $P_a = 0.5 \times \gamma \times h^2 \times K_a$
  • $P_a = 0.5 \times 18 \times 5^2 \times 0.333 \approx 37.46 \, \text{kN/m}$

• 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.