Factor of Safety given Angle of Mobilized Friction Calculator

Factor of Safety Formula:

\[ F_s = \frac{\tan\left(\frac{\Phi_i \cdot \pi}{180}\right)}{\tan\left(\frac{\phi_m \cdot \pi}{180}\right)} \]

Factor of Safety:

Definition: The Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Purpose: It helps geotechnical engineers assess the stability of slopes and foundations.

The calculator uses the formula:

\[ F_s = \frac{\tan\left(\frac{\Phi_i \cdot \pi}{180}\right)}{\tan\left(\frac{\phi_m \cdot \pi}{180}\right)} \]

Where:

Explanation: The ratio of the tangent of internal friction angle to the tangent of mobilized friction angle.

Details: Proper calculation ensures structural stability and prevents slope failures in geotechnical projects.

Tips: Enter both angles in degrees (±5% accuracy). Typical values range from 25°-45° for internal friction and 10°-30° for mobilized friction.

Q1: What is a typical Factor of Safety value?
A: For slopes, typically 1.3-1.5; for foundations, 2.0-3.0 depending on regulations.

Q2: Why use tangent functions in the formula?
A: The tangent represents the ratio of shear strength to normal stress in soil mechanics.

Q3: What does mobilized friction angle represent?
A: It's the friction angle at which the soil is actually resisting shear stress.

Q4: How accurate is this calculation?
A: It provides a theoretical value (±5% accuracy) but field conditions may vary.

Q5: When would the Factor of Safety be 1.0?
A: When the slope is at the verge of failure (mobilized friction equals internal friction).