Passive Earth Pressure Given Loading Intensity Calculator

Passive Earth Pressure Formula:

\[ P_p = \left(q - \left(C \cdot \tan\left(\frac{\phi \cdot \pi}{180}\right) - \frac{\gamma \cdot B \cdot \tan\left(\frac{\phi \cdot \pi}{180}\right)}{4}\right)\right) \cdot \frac{B}{2} \]

Intensity of Loading (q):

kPa

Cohesion in Soil (C):

kPa

Angle of Shearing Resistance (φ):

degrees

Unit Weight of Soil (γ):

N/m³

Width of Footing (B):

Passive Earth Pressure (P_p):

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1. What is Passive Earth Pressure?

Passive Earth Pressure is the maximum resistance that soil can offer when a structure (like a retaining wall) moves towards the soil mass. It represents the soil's capacity to resist compression and shear forces when subjected to external loading.

2. How Does the Calculator Work?

The calculator uses the passive earth pressure formula:

\[ P_p = \left(q - \left(C \cdot \tan\left(\frac{\phi \cdot \pi}{180}\right) - \frac{\gamma \cdot B \cdot \tan\left(\frac{\phi \cdot \pi}{180}\right)}{4}\right)\right) \cdot \frac{B}{2} \]

Where:

\( P_p \) — Passive Earth Pressure (kPa)
\( q \) — Intensity of Loading (kPa)
\( C \) — Cohesion in Soil (kPa)
\( \phi \) — Angle of Shearing Resistance (degrees)
\( \gamma \) — Unit Weight of Soil (N/m³)
\( B \) — Width of Footing (m)
\( \pi \) — Mathematical constant (3.14159)

Explanation: The formula accounts for soil cohesion, internal friction angle, unit weight, and footing dimensions to determine the passive resistance capacity of the soil.

3. Importance of Passive Earth Pressure Calculation

Details: Accurate calculation of passive earth pressure is crucial for designing retaining structures, foundation systems, and slope stability analysis. It ensures structural safety and prevents soil failure under loading conditions.

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. Ensure angle of shearing resistance is between 0-90 degrees, and all other values are positive. The calculator provides results in kilopascals (kPa).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between active and passive earth pressure?
A: Active pressure occurs when soil moves away from a structure, while passive pressure occurs when soil is compressed against a structure. Passive pressure is typically much higher than active pressure.

Q2: How does cohesion affect passive earth pressure?
A: Higher cohesion values generally increase passive earth pressure capacity as cohesive soils offer greater resistance to shear failure.

Q3: What is the significance of the angle of shearing resistance?
A: This angle represents the soil's internal friction. Higher angles indicate greater shear strength and consequently higher passive resistance.

Q4: When is this calculation most applicable?
A: This calculation is particularly important for designing retaining walls, basement walls, anchor systems, and other structures where soil compression resistance is critical.

Q5: Are there limitations to this formula?
A: The formula assumes homogeneous soil conditions and may need modification for layered soils, unusual loading conditions, or complex geometries.