Passive Earth Pressure Coefficient given Bearing Capacity Factor Calculator

Passive Earth Pressure Coefficient Formula:

\[ K_p = \left(\frac{N_γ}{\tan(\frac{φ}{2})} + 1\right) \times \cos^2(φ) \]

Passive Earth Pressure Coefficient (K_p):

1. What is Passive Earth Pressure Coefficient?

Definition: The passive earth pressure coefficient (K_p) is the ratio of horizontal to vertical stress when soil is in a passive state (being pushed against).

Purpose: It's used in geotechnical engineering to calculate lateral earth pressure on retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ K_p = \left(\frac{N_γ}{\tan(\frac{φ}{2})} + 1\right) \times \cos^2(φ) \]

Where:

\( K_p \) — Passive earth pressure coefficient
\( N_γ \) — Bearing capacity factor dependent on unit weight
\( φ \) — Angle of shearing resistance (degrees)

Explanation: The formula relates bearing capacity factor and soil friction angle to determine passive pressure conditions.

3. Importance of Passive Earth Pressure Calculation

Details: Accurate K_p calculation ensures proper design of retaining walls, sheet piles, and other earth-retaining structures.

4. Using the Calculator

Tips: Enter the bearing capacity factor (Nγ) and angle of shearing resistance (φ) in degrees. The angle must be between 0° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for K_p?
A: K_p typically ranges from 1.5 to 10, depending on soil properties.

Q2: Why is the angle of shearing resistance important?
A: Higher angles indicate more frictional resistance, significantly increasing passive pressure.

Q3: What does the ±5% tolerance mean?
A: It indicates the inherent variability in soil properties and measurement accuracy.

Q4: How is Nγ determined?
A: Nγ is calculated from soil properties or obtained from geotechnical tables based on soil type.

Q5: Can this be used for cohesive soils?
A: This formula is primarily for granular soils. Cohesive soils require additional cohesion terms.