Calculate Active Earth Pressure Coefficient

Active Earth Pressure Coefficient Formula:

\[ K_a = \frac{1 - \sin \phi}{1 + \sin \phi} \]

Active Earth Pressure Coefficient (K_a):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Active Earth Pressure Coefficient?

The active earth pressure coefficient (K_a) 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. It's used to calculate lateral earth pressures on retaining structures.

2. How Does the Calculator Work?

The calculator uses the Rankine's earth pressure theory formula:

\[ K_a = \frac{1 - \sin \phi}{1 + \sin \phi} \]

Where:

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

Explanation: This formula assumes a cohesionless soil, horizontal backfill, and a frictionless wall. The coefficient represents the minimum lateral pressure that soil can exert on a retaining structure.

3. Importance of K_a Calculation

Details: Accurate calculation of active earth pressure coefficient is crucial for designing retaining walls, sheet piles, and other earth-retaining structures. It helps determine the lateral forces that soil will exert, ensuring structural stability and safety.

4. Using the Calculator

Tips: Enter the angle of internal friction in degrees (typically between 25°-45° for most 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 with φ between 25°-45°, K_a typically ranges from 0.41 to 0.17.

Q2: How does K_a differ from K_p?
A: K_a is for active pressure (soil moving away from wall), while K_p is for passive pressure (soil moving toward wall). K_p = (1 + sinφ)/(1 - sinφ).

Q3: What factors affect the angle of internal friction?
A: Soil type, density, moisture content, and particle shape all influence φ values. Dense, angular soils have higher φ values.

Q4: When is this formula not applicable?
A: For cohesive soils (clays), sloping backfill, or when wall friction is significant. More complex methods like Coulomb's theory may be needed.

Q5: How is K_a used in design?
A: It's multiplied by the vertical stress to calculate lateral earth pressure, which is then used to determine bending moments and shear forces in retaining structures.