Depth of Prism given Shear Stress and Saturated Unit Weight Calculator

Depth of Prism Formula:

\[ z = \frac{\zeta_{soil}}{\gamma_{saturated} \times \cos\left(\frac{i \times \pi}{180}\right) \times \sin\left(\frac{i \times \pi}{180}\right)} \]

Shear Stress in Soil Mechanics:

Saturated Unit Weight of Soil:

Angle of Inclination to Horizontal in Soil:

Depth of Prism (m):

Definition: This calculator determines the depth of a soil prism based on shear stress, saturated unit weight, and inclination angle.

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

The calculator uses the formula:

\[ z = \frac{\zeta_{soil}}{\gamma_{saturated} \times \cos(i) \times \sin(i)} \]

Where:

Explanation: The formula relates the depth of a soil prism to the shear stress and material properties under given slope conditions.

Details: Accurate depth calculation is crucial for slope stability analysis, retaining wall design, and foundation engineering.

Tips: Enter shear stress (%), saturated unit weight (%), and inclination angle (%). All values must be > 0.

Q1: What is the typical range for saturated unit weight?
A: For most soils, it ranges between 18-22 kN/m³ (18000-22000 N/m³).

Q2: How does inclination angle affect the depth?
A: As the angle increases, the required depth decreases for the same shear stress conditions.

Q3: What units should I use for input?
A: The calculator expects percentage values for all inputs.

Q4: Can this be used for unsaturated soils?
A: No, this formula specifically applies to saturated soil conditions.

Q5: What's the practical application of this calculation?
A: It's used in slope stability analysis to determine critical failure depths.