Rankine's Theory

Definition

Rankine's Theory is a method used to calculate lateral earth pressures exerted by soil on retaining structures. It assumes that the soil is cohesionless and at rest, relying on basic geometric principles to determine the horizontal and vertical stress distributions acting on a wall or structure. This theory is foundational for understanding earth pressure concepts and serves as a basis for comparison with other earth pressure theories, such as Coulomb's.

5 Must Know Facts For Your Next Test

1. Rankine's Theory assumes that the soil is weightless and isotropic, meaning its properties are uniform in all directions.
2. The theory provides a simple analytical solution for determining active and passive earth pressures without needing complex calculations.
3. Rankine's active earth pressure coefficient is given by the formula $$K_a = an^2(45° - \frac{\phi}{2})$$, where \(\phi\) is the angle of internal friction.
4. The passive earth pressure coefficient can be calculated using the formula $$K_p = \tan^2(45° + \frac{\phi}{2})$$, which shows how resistance develops when soil is compressed against a wall.
5. Rankine's assumptions do not hold in layered soils or when significant wall movement occurs; these limitations often necessitate using more advanced theories like Coulomb's.

Review Questions

• How does Rankine's Theory simplify the calculation of earth pressures compared to more complex theories?
  • Rankine's Theory simplifies earth pressure calculations by making assumptions about soil behavior, such as neglecting cohesion and treating the soil as weightless and isotropic. This allows for straightforward equations to be used to derive active and passive pressure coefficients without needing extensive calculations or considerations of wall friction. In contrast, more complex theories like Coulomb’s require additional parameters and detailed analysis of soil interactions.
• Discuss the implications of using Rankine's Theory in real-world applications where layered soils are present.
  • Using Rankine's Theory in situations with layered soils can lead to inaccuracies because the theory does not account for variations in soil properties across different layers. In layered conditions, each layer may have distinct angles of internal friction and cohesiveness, affecting the overall lateral earth pressures acting on a retaining wall. As a result, applying Rankine’s simplified model could result in underestimating or overestimating pressures, highlighting the need for more complex approaches like Coulomb's Theory that can better address such scenarios.
• Evaluate how understanding Rankine's Theory contributes to effective design and safety in geotechnical engineering practices.
  • Understanding Rankine's Theory is crucial for geotechnical engineers as it lays the foundation for analyzing soil pressures on structures such as retaining walls. By grasping the basic principles behind lateral earth pressures, engineers can make informed decisions regarding material selection, structural design, and safety measures against potential failures. Moreover, this foundational knowledge allows engineers to recognize when to apply more complex models or adjustments based on site-specific conditions, ultimately enhancing safety and stability in engineering projects.

Related terms

Lateral Earth Pressure: The horizontal pressure exerted by soil on a retaining wall or structure, which can change based on factors like soil type, moisture content, and wall movement.

Coulomb's Earth Pressure Theory:

A method that considers both cohesion and friction in calculating earth pressures, providing a more complex model than Rankine's by accounting for wall friction and the angle of internal friction of the soil.

Active and Passive Pressure States: Conditions describing the lateral earth pressures when a wall is moving away from or towards the soil, respectively; these states are crucial for analyzing soil-structure interaction.