Angle of Inclination given Shear Strength and Submerged Unit Weight Calculator

Angle of Inclination Formula:

\[ i = \arctan\left(\frac{\gamma' \cdot \tan(\phi)}{\gamma_{sat} \cdot \left(\frac{T_f}{\zeta_{soil}}\right)}\right) \]

Submerged Unit Weight (γ'):

N/m³

Angle of Internal Friction (φ):

rad

Saturated Unit Weight (γ_sat):

N/m³

Shear Strength (T_f):

Shear Stress (ζ_soil):

Angle of Inclination (i):

1. What is Angle of Inclination Calculator?

Definition: This calculator determines the angle of inclination to horizontal in soil based on shear strength, submerged unit weight, and other soil parameters.

Purpose: It helps geotechnical engineers analyze slope stability and soil mechanics problems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ i = \arctan\left(\frac{\gamma' \cdot \tan(\phi)}{\gamma_{sat} \cdot \left(\frac{T_f}{\zeta_{soil}}\right)}\right) \]

Where:

\( i \) — Angle of inclination to horizontal (radians)
\( \gamma' \) — Submerged unit weight (N/m³)
\( \phi \) — Angle of internal friction (radians)
\( \gamma_{sat} \) — Saturated unit weight (N/m³)
\( T_f \) — Shear strength of soil (Pa)
\( \zeta_{soil} \) — Shear stress in soil (Pa)

Explanation: The formula calculates the angle at which soil would naturally incline based on the balance between shear strength and shear stress.

3. Importance of Angle of Inclination Calculation

Details: Proper calculation helps in designing stable slopes, preventing landslides, and ensuring structural safety in geotechnical projects.

4. Using the Calculator

Tips: Enter all required soil parameters. The calculator accounts for ±5% variation in input values. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is submerged unit weight?
A: It's the effective unit weight of soil when submerged in water, accounting for buoyancy.

Q2: How is angle of internal friction determined?
A: Typically measured through triaxial or direct shear tests in a geotechnical laboratory.

Q3: What's a typical value for saturated unit weight?
A: For most soils, it ranges between 18-22 kN/m³ (18000-22000 N/m³).

Q4: Why is shear strength important?
A: It determines the soil's resistance to sliding along internal surfaces.

Q5: Can I use degrees instead of radians?
A: The calculator uses radians, but you can convert degrees to radians (1° = π/180 radians).