Inclined Length of Prism given Saturated Unit Weight Calculator

Inclined Length Formula:

\[ b = \frac{W_{prism}}{γ_{saturated} \times z \times \cos(i)} \]

Weight of Prism:

Saturated Unit Weight:

N/m³

Depth of Prism:

Inclination Angle:

Tolerance:

Inclined Length (m):

Length Range (±5%):

1. What is Inclined Length of Prism?

Definition: The inclined length of a prism in soil mechanics is the length of the prism along the slope direction.

Purpose: This calculation is essential for slope stability analysis and earth pressure calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{W_{prism}}{γ_{saturated} \times z \times \cos(i)} \]

Where:

\( b \) — Inclined length of prism (meters)
\( W_{prism} \) — Weight of soil prism (Newtons)
\( γ_{saturated} \) — Saturated unit weight of soil (N/m³)
\( z \) — Depth of prism (meters)
\( i \) — Angle of inclination (degrees)

Explanation: The weight is divided by the product of unit weight, depth, and cosine of the inclination angle to get the inclined length.

3. Importance of Inclined Length Calculation

Details: Accurate calculation of inclined length is crucial for proper slope stability analysis and design of retaining structures.

4. Using the Calculator

Tips: Enter the prism weight in Newtons, saturated unit weight (default 11890 N/m³), depth (default 3 m), inclination angle (default 64°), and tolerance percentage (default 5%). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical saturated unit weight for soil?
A: Common values range from 18-22 kN/m³ (18000-22000 N/m³) for saturated soils.

Q2: Why is the cosine of the angle used?
A: The cosine accounts for the component of weight acting perpendicular to the slope.

Q3: What does the tolerance percentage represent?
A: It shows the acceptable range (±value) around the calculated length for practical applications.

Q4: How do I determine the weight of the prism?
A: The weight can be calculated from the volume and unit weight of the soil mass.

Q5: What's the significance of the inclination angle?
A: The angle affects how much of the weight contributes to the normal force on the potential failure plane.