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Rankine Coefficient Equation:
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The Active Earth Pressure Coefficient (Ka) is a fundamental parameter in geotechnical engineering that represents the ratio of horizontal to vertical stress in soil when it's in an active state (typically behind retaining walls). It's calculated using Rankine's theory for cohesionless soils.
The calculator uses the Rankine equation:
Where:
Explanation: The equation derives from the Mohr-Coulomb failure criterion and assumes a smooth vertical wall with horizontal backfill and no wall friction.
Details: Accurate calculation of Ka is crucial for designing retaining structures, calculating lateral earth pressures, ensuring slope stability, and preventing structural failures in geotechnical engineering projects.
Tips: Enter the angle of internal friction in degrees (typically between 25°-45° for common soils). The value must be between 0 and 90 degrees.
Q1: What is the typical range of Ka values?
A: For common soils with φ between 25°-45°, Ka typically ranges from 0.41 to 0.17, decreasing as friction angle increases.
Q2: When is the active state developed?
A: The active state occurs when a retaining wall moves away from the soil, allowing the soil to expand and mobilize its shear strength.
Q3: What are the limitations of Rankine's theory?
A: It assumes smooth vertical walls, horizontal backfill, no wall friction, and cohesionless soils. Different theories (Coulomb, etc.) may be needed for more complex conditions.
Q4: How does Ka relate to passive earth pressure?
A: Ka represents the minimum earth pressure coefficient, while passive pressure coefficient (Kp) represents the maximum, with Kp = 1/Ka.
Q5: Can this be used for cohesive soils?
A: No, Rankine's original equation is for cohesionless soils only. Modified equations exist for cohesive soils that include cohesion parameters.