Saturated Unit Weight given Vertical Stress on Prism Calculator

Saturated Unit Weight Formula:

\[ γ_{saturated} = \frac{σ_{z}}{z \times \cos\left(\frac{i \times \pi}{180}\right)} \]

Vertical Stress (σ_z):

kPa

Depth of Prism (z):

Inclination Angle (i):

Tolerance:

Saturated Unit Weight (γ_saturated): kN/m³

1. What is Saturated Unit Weight?

Definition: Saturated unit weight is the weight per unit volume of soil when all voids are filled with water.

Purpose: It's crucial in geotechnical engineering for analyzing soil stability, bearing capacity, and slope stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ γ_{saturated} = \frac{σ_{z}}{z \times \cos\left(\frac{i \times \pi}{180}\right)} \]

Where:

\( γ_{saturated} \) — Saturated unit weight (kN/m³)
\( σ_{z} \) — Vertical stress at a point (kPa)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (°)

Explanation: The vertical stress is divided by the depth multiplied by the cosine of the inclination angle to account for the slope effect.

3. Importance of Saturated Unit Weight

Details: Proper calculation ensures accurate analysis of soil behavior under saturated conditions, critical for foundation design and slope stability.

4. Using the Calculator

Tips: Enter vertical stress in kPa, depth in meters, inclination angle in degrees (0-90°), and tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is typical saturated unit weight range?
A: For most soils, it ranges between 18-22 kN/m³, but can vary based on soil type.

Q2: Why include angle of inclination?
A: The angle affects how vertical stress is distributed in sloping ground conditions.

Q3: What does the tolerance percentage mean?
A: It shows the acceptable variation range (±5% by default) for the calculated value.

Q4: How do I measure vertical stress?
A: It can be calculated from overburden pressure or measured with pressure sensors.

Q5: When would I adjust the tolerance?
A: For critical structures, you might reduce tolerance; for estimates, you might increase it.