How to design for Retaining Wall: Stability and Reinforcement Calculations

Retaining Wall Design: Stability and Reinforcement Calculations

A retaining wall can be defined as a structural element that is used to hold up soils, especially in sloping areas. Its design would have to account for stability, and safety reasons, with regard to these forces. Here, we go through the calculations most relevant to designing a stable and reinforced retaining wall that would resist soil pressure and other loads.

In this article we explained below question tags related to retaining wall design

What Are the Types of Retaining Walls?

What Forces Act on a Retaining Wall?

What Are the Stability Calculations for Retaining Walls?

• How Is Sliding Stability Calculated?
• How Is Overturning Stability Assessed?
• What Is the Bearing Capacity Calculation?

How Is Earth Pressure Calculated?

How Are Reinforcement Calculations for Cantilever Walls Done?

• What Is the Moment Calculation?
• How Is the Steel Area Determined?

What Does an Example of Retaining Wall Design Look Like?

 

1. Types of Retaining Walls

There are lots of types of retaining walls, depending on the condition and type of retaining wall. Some of the common types are listed below:

• Gravity Walls: Based on its weight to counterbalance the earth pressure.
• Cantilever Walls: Use reinforced concrete. The backfilling is considered to give stability.
• Counterfort Walls: Similar to cantilever walls but have counterforts to reduce the bending moment.
• Anchored Walls: Supported by anchors that provide stability.

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2. Forces Acting on a Retaining Wall

Many forces push against a retaining wall, and the design must balance those forces to be stable:

• Active Earth Pressure (Pa): Gravity force of soil behind the wall.
• Water Pressure (Pw): Amount of water accumulated behind the wall that supports the load.
• Surcharge Load (Ps): Additional load from structures or traffic over the wall.
• Passive Earth Pressure (Pp): Resistance from the soil in front of the wall that stabilizes the wall.

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3. Stability Calculations

a. Sliding Stability
The wall has to resist sliding due to lateral forces. The factor of safety (FS) for sliding is calculated as:
FS_sliding = Resisting Force / Sliding Force

• Resisting Force: Given by friction between the soil and base of the wall and by passive pressure.
• Sliding Force: Consists of active earth pressure and any possible water pressure against the wall. A safety factor > 1.5 is usually recommended.

b. Overturning Stability
Lateral earth pressure must be resisted by the wall in overturning. Safety factor against overturning is calculated using the equation:
FS_overturning = Resisting Moment / Overturning Moment
This safety factor should be > 2.0 for safe design.

c. Bearing Capacity
The base of the wall will not exert too much pressure on the soil. The pressure under the base of the wall is calculated by:
Pressure = Weight of Wall and Backfill / Base Area of Wall
The pressure must not exceed the soil's allowable bearing capacity.

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4. Earth Pressure Calculation

The active earth pressure (Pa) exerted by the soil on the wall is calculated using Rankine's Theory for cohesionless soils:
Pa = (1/2) × γ × H² × Ka
Where:

• γ = Unit weight of the soil (kN/m³)
• H = Height of the retaining wall (m)
• Ka = Coefficient of active earth pressure, calculated as:
  Ka = (1 - sin(ϕ)) / (1 + sin(ϕ))
• ϕ = Soil internal friction angle (°)

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5. Calculations of Reinforcement of Cantilever Walls

Reinforcement of cantilever retaining wall works is required because of bending moments and shear forces.

a. Moment Calculation
The maximum moment (M) at the base of the wall according to lateral earth pressure:
M = (Pa × H) / 3
Where:

• Pa = Active earth pressure
• H = Wall height

b. Steel Area
Steel reinforcement is given in the wall to resist the moment. The area of steel (As) can be determined as follows:
As = M / (0.87 × fy × d)
Where:

• fy = Yield strength of steel (N/mm²)
• d = Effective depth of the wall section (mm)

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6. Example

Given Values:

• Height of the wall, H = 4m
• Unit weight of soil, γ = 18 kN/m³
• Angle of internal friction, ϕ = 30°
• Yield strength of steel, fy = 500 N/mm²
• Effective depth, d = 300mm

Step 1: Calculate Active Earth Pressure (Pa)
Using Rankine's Theory:
Ka = (1 - sin(30°)) / (1 + sin(30°)) = 0.33
Now, calculate Pa:
Pa = (1/2) × 18 × 4² × 0.33 = 47.52 kN/m²

Step 2: Calculate Moment (M)
The moment at the base of the wall:
M = 47.52 × 4 / 3 = 63.36 kNm/m

Step 3: Calculate Steel Reinforcement Area (As)
Calculate the required steel area:
As = 63.36 / (0.87 × 500 × 300) = 0.00048 m² = 480 mm²

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Conclusion

The designing of retaining walls requires complete calculation of forces acting on the wall for stability conditions, such as sliding, overturning, and bearing capacity. Proper amount of steel reinforcement is required in reinforced concrete cantilever walls to provide resistance to bending moments. This simplifies the approach that gives the necessary steps that will allow the construction engineer to design retaining walls effectively in many civil engineering projects.