Slope Angle given Shear Strength along Slip Plane Calculator

Slope Angle Formula:

\[ \theta_{slope} = \cos^{-1}\left(\frac{\zeta_{soil} - (C_s \times L)}{W_{wedge} \times \tan\left(\frac{\phi \times \pi}{180}\right)}\right) \]

Shear Strength of Soil (ζ_soil):

Cohesion of Soil (C_s):

Length of Slip Plane (L):

Weight of Wedge (W_wedge):

Angle of Internal Friction (φ):

Tolerance:

Slope Angle (θ_slope):

1. What is Slope Angle given Shear Strength along Slip Plane?

Definition: This calculator determines the slope angle at which failure might occur based on soil shear strength parameters.

Purpose: It helps geotechnical engineers assess slope stability and potential failure planes in soil mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta_{slope} = \cos^{-1}\left(\frac{\zeta_{soil} - (C_s \times L)}{W_{wedge} \times \tan(\phi)}\right) \]

Where:

\( \theta_{slope} \) — Slope angle (degrees)
\( \zeta_{soil} \) — Shear strength of soil (Pa)
\( C_s \) — Cohesion of soil (Pa)
\( L \) — Length of slip plane (m)
\( W_{wedge} \) — Weight of soil wedge (N)
\( \phi \) — Angle of internal friction (degrees)

Explanation: The formula calculates the critical slope angle where driving forces equal resisting forces.

3. Importance of Slope Angle Calculation

Details: Proper slope angle determination prevents landslides, ensures stable embankments, and informs construction safety measures.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. The tolerance field (±%) allows for safety factor consideration.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical angle of internal friction for soils?
A: It varies: 25-30° for loose sand, 30-35° for dense sand, 15-25° for silt, and 0° for pure clay.

Q2: How does cohesion affect slope stability?
A: Higher cohesion increases stability, allowing steeper slopes. Cohesionless soils (sand) have lower stable slope angles.

Q3: What does the tolerance percentage represent?
A: It accounts for measurement uncertainties and provides a safety margin in the calculation.

Q4: When would this calculation be invalid?
A: When the numerator exceeds denominator magnitude (resulting in non-real acos value), indicating impossible conditions.

Q5: How is the weight of the wedge determined?
A: It's the product of soil unit weight and wedge volume (area × unit thickness × unit weight).