Submerged Unit Weight for Steady Seepage along Slope Calculator

Formula:

\[ yS = \frac{(Fs \times γ_{saturated} \times z \times \cos(i) \times \sin(i)) - C}{z \times \tan(\Phi_i) \times (\cos(i))^2} \]

Factor of Safety (Fs):

Saturated Unit Weight (γ_saturated):

kN/m³

Depth of Prism (z):

Angle of Inclination (i):

Cohesion (C):

kPa

Angle of Internal Friction (Φ_i):

Submerged Unit Weight (yS): kN/m³

1. What is Submerged Unit Weight for Steady Seepage along Slope?

Definition: This calculator determines the submerged unit weight of soil under steady seepage conditions along a slope, considering factors like safety, soil properties, and geometry.

Purpose: It helps geotechnical engineers analyze slope stability under seepage conditions and design appropriate drainage systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ yS = \frac{(Fs \times γ_{saturated} \times z \times \cos(i) \times \sin(i)) - C}{z \times \tan(\Phi_i) \times (\cos(i))^2} \]

Where:

\( yS \) — Submerged unit weight (kN/m³)
\( Fs \) — Factor of safety
\( γ_{saturated} \) — Saturated unit weight of soil (kN/m³)
\( z \) — Depth of prism (m)
\( i \) — Angle of inclination to horizontal (°)
\( C \) — Cohesion in soil (kPa)
\( \Phi_i \) — Angle of internal friction of soil (°)

Explanation: The formula accounts for the balance between driving forces (weight and slope) and resisting forces (cohesion and friction) in submerged conditions.

3. Importance of Submerged Unit Weight Calculation

Details: Accurate calculation is crucial for slope stability analysis, retaining wall design, and foundation engineering in water-bearing soils.

4. Using the Calculator

Tips: Enter all required parameters. Angles should be in degrees (0-90°). The ±5% indicates typical measurement uncertainty.

5. Frequently Asked Questions (FAQ)

Q1: What is typical factor of safety for slopes?
A: Common Fs values range from 1.3 to 1.5 for temporary works and 1.5 to 2.0 for permanent structures.

Q2: How to determine saturated unit weight?
A: It can be measured in laboratory tests or estimated from soil type (typically 18-22 kN/m³ for saturated soils).

Q3: What if my soil has no cohesion?
A: For cohesionless soils (like sand), simply enter C = 0.

Q4: Why is angle of internal friction important?
A: It represents the soil's shear strength from particle interlocking, typically 25-45° for granular soils.

Q5: How does seepage affect slope stability?
A: Seepage reduces effective stress and can lead to slope failure by increasing pore water pressure.