Effective Angle of Internal Friction given Shear Strength Calculator

Effective Angle of Internal Friction Formula:

\[ \phi' = \tan^{-1}\left(\frac{\zeta_{soil} - c'}{\sigma_{nm} - u}\right) \]

Shear Strength of Soil (ζ_soil):

Effective Cohesion (c'):

Normal Stress (σ_nm):

MPa

Upward Force (u):

Tolerance:

Effective Angle of Internal Friction (φ'):

Tolerance Range (±5%):

1. What is Effective Angle of Internal Friction?

Definition: The effective angle of internal friction (φ') is a measure of the shear strength of soils due to friction between soil particles.

Purpose: It's a critical parameter in geotechnical engineering for analyzing soil stability and designing foundations, slopes, and retaining structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi' = \tan^{-1}\left(\frac{\zeta_{soil} - c'}{\sigma_{nm} - u}\right) \]

Where:

\( \phi' \) — Effective angle of internal friction (degrees)
\( \zeta_{soil} \) — Shear strength of soil (Pa)
\( c' \) — Effective cohesion (Pa)
\( \sigma_{nm} \) — Normal stress (MPa)
\( u \) — Upward force due to seepage water (Pa)

Explanation: The formula calculates the arctangent of the ratio between the difference of shear strength and cohesion to the difference of normal stress and upward force.

3. Importance of φ' Calculation

Details: Accurate determination of φ' is essential for predicting soil behavior under load, assessing slope stability, and designing earth structures.

4. Using the Calculator

Tips: Enter all required values in appropriate units. The tolerance field (default ±5%) allows you to specify an acceptable range for the calculated angle.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical φ' value for common soils?
A: Sand: 30-40°, Silt: 25-35°, Clay: 15-25°. These vary with density and moisture content.

Q2: Why include a tolerance percentage?
A: Soil properties are naturally variable. The tolerance accounts for this uncertainty in calculations.

Q3: How does effective cohesion affect φ'?
A: Higher cohesion generally reduces the apparent friction angle as it contributes to shear strength.

Q4: What if my normal stress is in kPa?
A: Convert to MPa (1 MPa = 1000 kPa) or modify the calculator to accept different units.

Q5: When would upward force be significant?
A: In situations with high water tables or significant seepage pressures, such as in dams or below groundwater level.