Angle Of Shearing Resistance Given Passive Earth Pressure Calculator

Formula Used:

\[ \phi_d = \tan^{-1}\left(\frac{q \times B - (2 \times P_p)}{B \times C - \left(\frac{\gamma \times B^2}{4}\right)}\right) \]

Intensity of Loading in Kilopascal (q):

kPa

Width of Footing in Soil Mechanics (B):

Passive Earth Pressure in kilopascal (Pp):

kPa

Cohesion in Soil as Kilopascal (C):

kPa

Unit Weight of Soil (γ):

N/m³

Angle of Shearing Resistance (φd):

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1. What is Angle of Shearing Resistance?

The angle of shearing resistance in soil mechanics is a fundamental parameter that represents the frictional component of soil shear strength. It is the angle (φ) at which soil fails under shear stress and is a critical factor in determining the bearing capacity of foundations and slope stability.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \phi_d = \tan^{-1}\left(\frac{q \times B - (2 \times P_p)}{B \times C - \left(\frac{\gamma \times B^2}{4}\right)}\right) \]

Where:

\( \phi_d \) — Angle of shearing resistance (degrees)
\( q \) — Intensity of loading (kPa)
\( B \) — Width of footing (m)
\( P_p \) — Passive earth pressure (kPa)
\( C \) — Cohesion in soil (kPa)
\( \gamma \) — Unit weight of soil (N/m³)

Explanation: This formula calculates the angle of shearing resistance by considering the balance between applied loads, passive earth pressure, soil cohesion, and the unit weight of soil.

3. Importance of Angle of Shearing Resistance

Details: The angle of shearing resistance is crucial for designing stable foundations, retaining walls, and slopes. It helps engineers determine the soil's ability to resist shear forces and prevent structural failures.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure intensity of loading, width of footing, and unit weight of soil are positive values. Cohesion and passive earth pressure can be zero for cohesionless soils.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for angle of shearing resistance?
A: For most soils, φ ranges from 0° (pure clay) to 45° (dense gravel). Sandy soils typically range from 28° to 45°.

Q2: How does soil density affect the angle of shearing resistance?
A: Denser soils generally have higher angles of shearing resistance due to increased interparticle friction and better particle interlocking.

Q3: What is the difference between effective and total stress parameters?
A: Effective stress parameters (φ') consider pore water pressure effects, while total stress parameters (φ) are used for undrained conditions in cohesive soils.

Q4: Can this calculator be used for all soil types?
A: This formula is particularly useful for soils with both cohesive and frictional components. For purely cohesive soils, cohesion is the dominant factor.

Q5: How does moisture content affect the angle of shearing resistance?
A: Increased moisture content typically reduces the angle of shearing resistance in granular soils due to reduced interparticle friction, while in cohesive soils it affects both cohesion and friction angles.