Unprotected Side Slopes Shear Stress Required To Move Single Grain Calculator

Critical Shear Stress on Horizontal Bed Formula:

\[ \zeta_c' = \zeta_c \times \sqrt{1 - \frac{\sin(\theta)^2}{\sin(\Phi)^2}} \]

Resisting Shear against Movement of Particle (ζc):

Pascal

Side Slope (θ):

Radian

Angle of Repose of Soil (Φ):

Radian

Critical Shear Stress on Horizontal Bed (ζc'):

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1. What is Critical Shear Stress on Horizontal Bed?

Critical Shear Stress on Horizontal Bed is the magnitude of shear stress required to move a given particle on an unprotected side slope. It accounts for the effects of side slope angle and soil properties on particle movement.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \zeta_c' = \zeta_c \times \sqrt{1 - \frac{\sin(\theta)^2}{\sin(\Phi)^2}} \]

Where:

\( \zeta_c' \) — Critical shear stress on horizontal bed (Pascal)
\( \zeta_c \) — Resisting shear against movement of particle (Pascal)
\( \theta \) — Side slope angle (Radian)
\( \Phi \) — Angle of repose of soil (Radian)

Explanation: The formula calculates the critical shear stress required to initiate particle movement on side slopes, considering the geometric relationships between slope angle and soil's angle of repose.

3. Importance of Critical Shear Stress Calculation

Details: Accurate calculation of critical shear stress is essential for designing stable slopes, preventing soil erosion, and ensuring the stability of earth structures in geotechnical engineering.

4. Using the Calculator

Tips: Enter resisting shear in Pascal, side slope angle in radians, and angle of repose in radians. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of angle of repose?
A: The angle of repose represents the steepest angle at which a soil material can be piled without slumping, indicating its internal friction and stability characteristics.

Q2: How does side slope affect critical shear stress?
A: Steeper side slopes generally require lower critical shear stress to initiate particle movement due to gravitational forces acting parallel to the slope.

Q3: What units should be used for input values?
A: All stress values should be in Pascal, and all angles should be in radians for consistent calculations.

Q4: When is this calculation particularly important?
A: This calculation is crucial for designing erosion control measures, assessing slope stability, and designing protective measures for unprotected side slopes.

Q5: Are there limitations to this formula?
A: The formula assumes homogeneous soil properties and may need adjustment for layered soils or soils with significant cohesion components.