Triaxial Angle of Shearing Resistance by Meyerhof's Analysis Calculator

Meyerhof's Analysis Formula:

\[ \phi = \frac{\Phi_p}{1.1 - 0.1 \times \left(\frac{B}{L}\right)} \]

Angle of Internal Friction For Plain Strain (Φp):

radians

Width of Footing (B):

meters

Length of Footing (L):

meters

Angle of Internal Friction (φ):

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1. What is Meyerhof's Analysis?

Meyerhof's Analysis provides a method to determine the triaxial angle of shearing resistance based on plain strain conditions and footing dimensions. It accounts for the effect of footing shape on the angle of internal friction.

2. How Does the Calculator Work?

The calculator uses Meyerhof's formula:

\[ \phi = \frac{\Phi_p}{1.1 - 0.1 \times \left(\frac{B}{L}\right)} \]

Where:

\( \phi \) — Angle of Internal Friction (radians)
\( \Phi_p \) — Angle of Internal Friction For Plain Strain (radians)
\( B \) — Width of Footing (meters)
\( L \) — Length of Footing (meters)

Explanation: The formula adjusts the plain strain angle of internal friction based on the aspect ratio (B/L) of the footing to obtain the triaxial angle of shearing resistance.

3. Importance of Angle of Shearing Resistance

Details: The angle of shearing resistance is a critical parameter in soil mechanics that determines the shear strength of soil. It is essential for foundation design, slope stability analysis, and earth pressure calculations.

4. Using the Calculator

Tips: Enter the plain strain angle of internal friction in radians, footing width and length in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between plain strain and triaxial conditions?
A: Plain strain conditions occur when strain in one direction is zero, while triaxial conditions involve stress application in three principal directions.

Q2: How does footing shape affect the angle of shearing resistance?
A: The aspect ratio (B/L) of the footing influences the stress distribution and consequently affects the mobilized angle of shearing resistance.

Q3: What are typical values for angle of internal friction?
A: Values range from 25° to 45° for sandy soils and 0° to 25° for cohesive soils, depending on soil type and density.

Q4: When is Meyerhof's analysis particularly useful?
A: This analysis is particularly valuable for rectangular footings where the length-to-width ratio significantly affects bearing capacity.

Q5: Are there limitations to this formula?
A: The formula provides an approximation and may need adjustment for very large or very small aspect ratios, or for soils with significant cohesion.