Coulomb Active Earth Pressure Coefficient

Definition

The Coulomb active earth pressure coefficient is a measure used in soil mechanics to determine the lateral pressure exerted by soil against a retaining structure when the soil is allowed to deform and mobilize its shear strength. This coefficient helps engineers calculate the forces acting on walls, slopes, and other structures due to soil weight, considering factors like wall friction and soil cohesion.

5 Must Know Facts For Your Next Test

1. The Coulomb active earth pressure coefficient ($$K_a$$) is calculated using the formula: $$K_a = \frac{\sigma_{h}}{\sigma_{v}}$$ where $$\sigma_{h}$$ is the horizontal stress and $$\sigma_{v}$$ is the vertical stress.
2. This coefficient is influenced by several factors, including wall friction, soil cohesion, and the angle of internal friction of the soil.
3. In the case of cohesionless soils, $$K_a$$ can be simplified to depend primarily on the angle of internal friction with the formula: $$K_a = \tan^2(45° - \frac{\phi}{2})$$ where $$\phi$$ is the angle of internal friction.
4. When considering cohesive soils, the equation becomes more complex as it includes terms for both cohesion and internal friction.
5. Coulomb's theory assumes a plane failure surface and does not account for three-dimensional effects, making it more suitable for simple geometries.

Review Questions

• How does the Coulomb active earth pressure coefficient help in determining the design of retaining walls?
  • The Coulomb active earth pressure coefficient is essential for calculating the lateral forces acting on retaining walls. By providing a measure of the soil pressure when it expands, engineers can ensure that walls are designed to withstand these forces without failure. The coefficient takes into account various factors such as wall friction and soil cohesion, which helps in optimizing wall thickness and material use.
• Discuss how changes in soil properties affect the Coulomb active earth pressure coefficient and its application in engineering designs.
  • Changes in soil properties, such as variations in cohesion or internal friction angle, can significantly affect the Coulomb active earth pressure coefficient. For instance, an increase in cohesion may reduce lateral pressures against a retaining wall, allowing for thinner walls or less reinforcement. Conversely, if internal friction decreases due to saturation or other factors, lateral pressures could increase, necessitating redesigns or additional support to ensure stability.
• Evaluate the limitations of using Coulomb's theory for calculating active earth pressures in complex engineering scenarios.
  • While Coulomb's theory provides a foundational approach to calculating active earth pressures, its limitations become apparent in more complex scenarios. It assumes a two-dimensional plane failure surface and does not address three-dimensional stress states or potential failure mechanisms that may occur in layered soils. Additionally, it may oversimplify conditions such as wall rotation or variable loading scenarios. Engineers must often supplement this theory with more advanced methods or numerical modeling to accurately predict behaviors in complex applications.

Related terms

Active Earth Pressure: The pressure exerted by soil on a structure when the structure is moving away from the soil, allowing for maximum expansion of the soil.

Retaining Wall: A structural wall that holds back soil and prevents it from collapsing into a different elevation or area.

Soil Shear Strength: The maximum resistance of soil to shear stress, which determines how well it can support loads without sliding.