cantilever retaining wall theory
The discussion of the design steps for a Cantilever Wall is set within Unit I: RETAINING WALLS.
In the context of Unit I, retaining walls are structural designs used primarily to maintain different elevations of ground level and often sustain lateral loads, retaining soil at two different levels. These structures must be steady under the impacts of horizontal earth pressure to prevent twisting, upsetting, or sliding caused by the sidelong weight of the retained material. Cantilevered Walls are specifically listed as a type of Reinforced Concrete Wall.
Cantilever Retaining Walls are RCC walls where the horizontal earth pressure is resisted by the structural members of the wall. The structural components—the vertical wall (known as the stem), the heel slab, and the toe slab—act as cantilevers, fixed at their connection points. The heel slab extends into the refill, and the refill material over it provides critical extra lateral stability. Cantilever walls typically use significantly less concrete than gravity walls but require more detailed design and careful construction.
The design process for a Cantilever Retaining Wall (Section 1.10) is presented in 12 distinct steps:
Design Steps: Cantilever Retaining Wall¶
Step 1: Depth of the Foundation
The design begins by determining the minimum Foundation depth using a formula incorporating the soil bearing capacity (\(q_a\)), the unit weight of the soil (\(\gamma_s\)), and the internal friction angle (\(\phi\)). The Overall depth of retaining wall (\(H\)) is then calculated by adding the foundation depth to the height of the soil retained by the wall.
Step 2: Selecting Preliminary Dimensions
Suitable proportioning of the wall is essential for an effective and optimal structure. Key preliminary dimensions include:
- The width of the footing (\(B\)), which should equal 0.5 to 0.7 times the retaining wall height (\(H\)).
- The width of the Heel slab, which is half the width of the footing.
- The thickness of the base slab, which is equal to \(H/12\).
- The thickness of the vertical stem at the top, which should not be less than \(200\text{ mm}\) to \(300\text{ mm}\).
- The thickness at the base of the vertical stem, which is 0.8 to 0.1 times the total wall height and not less than \(300\text{ mm}\). A shear key may also be included in the design elements.
Step 3: Calculating forces and moments per meter length of the wall
The forces and moments acting on the wall due to the vertical load are calculated.
Step 4: Calculating the Earth Pressure
This step involves calculating the Earth Pressure Coefficient (\(K_a\) and \(K_p\)) using formulas involving the internal friction angle (\(\phi\)). Subsequently, the Force due to active earth pressure (\(P_a\)) is calculated.
Step 5: Check for Stability (Overturning)
Stability against overturning is checked by calculating the Overturning moment (\(M_o\)) and the Stabilizing moment @ Toe (\(M_r\)). The Factor of Safety against Overturning must be ensured to be greater than 1.4.
Step 6: Calculation of soil pressure below the footing
The calculation ensures that the soil pressure below the footing does not exceed the Safe Bearing Capacity (SBC) and that no tension develops in the soil. If these conditions are not met, the base slab dimensions must be modified, and the calculations from Steps 2 and 4 must be repeated until satisfaction is achieved.
Step 7: Check for Stability against Sliding
The sliding force is compared against the factor of safety against sliding, which must be greater than 1.4. If this criterion is not met, a shear key must be provided.
Step 8: Design the Shear Key
If required, the shear key is designed, as its effect is to develop passive resistance over depth to counteract sliding.
Step 9: Design the Toe Slab
The loading acting on the toe slab is determined, and the shear force and bending force are calculated. Reinforcement is then designed based on the required area of steel.
Step 10: Design the Heel Slab
The load acting on the heel slab (due to self-weight and soil) is determined. Shear force and bending force are calculated, and reinforcement is designed based on the required steel area.
Step 11: Design the Stem
The load acting on the stem (due to self-weight and active earth pressure) is calculated. Shear force and bending force are determined, and reinforcement is designed. This step also involves checking for Shear at the base of the stem, Curtailment of Reinforcement, and Temperature and Shrinkage Reinforcement.
Step 12: Detailing of the Cantilever Retaining Wall
The final step involves producing the Reinforcement detailing, which is drawn based on the number of rebars and spacing obtained from the preceding steps, including rebar detailing of the stem, toe, and heel slab, sketched with dimensions.
These steps provide a comprehensive method for the structural design and stability checks necessary for a cantilever retaining wall.