Active Pressure Coefficient Calculator

Active Pressure Coefficient Formula:

\[ K_a = \tan^2(45 - \frac{\phi}{2}) \]

Active Pressure Coefficient (K_a):

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1. What is the Active Pressure Coefficient?

The Active Pressure Coefficient (K_a) is a dimensionless parameter used in geotechnical engineering to calculate the lateral earth pressure exerted by soil on a retaining wall when the wall moves away from the soil mass.

2. How Does the Calculator Work?

The calculator uses the Rankine's active earth pressure coefficient formula:

\[ K_a = \tan^2(45 - \frac{\phi}{2}) \]

Where:

\( K_a \) — Active earth pressure coefficient
\( \phi \) — Angle of internal friction of soil (degrees)

Explanation: The formula calculates the ratio of horizontal to vertical stress when soil is in an active state (wall moving away from soil).

3. Importance of K_a Calculation

Details: Accurate calculation of K_a is essential for designing retaining walls, sheet piles, and other earth-retaining structures to ensure stability and safety.

4. Using the Calculator

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.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of K_a values?
A: For common soils (φ=25°-45°), K_a ranges from about 0.41 to 0.17.

Q2: How does K_a relate to passive pressure coefficient?
A: The passive coefficient K_p is calculated similarly but with a positive sign inside the tangent function.

Q3: What assumptions does Rankine's theory make?
A: It assumes a frictionless wall, homogeneous isotropic soil, and a planar failure surface.

Q4: When is Coulomb's theory used instead?
A: When wall friction and non-vertical walls need to be considered.

Q5: How does water pressure affect the calculation?
A: Water pressure must be considered separately and added to the effective earth pressure.