Force Exerted By Silt In Addition To External Water Pressure Represented By Rankine's Formula Calculator

Rankine's Formula:

\[ P_{silt} = \frac{1}{2} \times \Gamma_s \times h^2 \times K_a \]

Force Exerted by Silt in Water Pressure (Psilt):

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1. What is Rankine's Formula for Silt Force?

Rankine's formula calculates the force exerted by silt in addition to external water pressure on structures like dams and retaining walls. It accounts for the submerged unit weight of silt materials, height of silt deposition, and the coefficient of active earth pressure.

2. How Does the Calculator Work?

The calculator uses Rankine's formula:

\[ P_{silt} = \frac{1}{2} \times \Gamma_s \times h^2 \times K_a \]

Where:

\( P_{silt} \) — Force exerted by silt in water pressure (Pa)
\( \Gamma_s \) — Sub merged unit weight of silt materials (N/m³)
\( h \) — Height of silt deposited (m)
\( K_a \) — Coefficient of active earth pressure of silt

Explanation: The formula calculates the lateral pressure exerted by submerged silt on structures, considering the buoyant weight of silt and its active earth pressure characteristics.

3. Importance of Silt Force Calculation

Details: Accurate calculation of silt force is crucial for designing and analyzing hydraulic structures like dams, retaining walls, and sheet piles to ensure structural stability and safety against silt pressure.

4. Using the Calculator

Tips: Enter submerged unit weight in N/m³, height of silt in meters, and coefficient of active earth pressure. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is submerged unit weight of silt?
A: Submerged unit weight is the effective weight of silt particles when submerged under water, accounting for buoyancy effects.

Q2: How is coefficient of active earth pressure determined?
A: Ka is typically determined through soil testing and can be calculated as Ka = (1 - sinφ)/(1 + sinφ) where φ is the angle of internal friction.

Q3: When is this calculation most important?
A: This calculation is critical for structures in silt-laden waters like reservoirs, rivers, and coastal areas where silt accumulation occurs.

Q4: Are there limitations to Rankine's formula?
A: The formula assumes homogeneous silt, level ground surface, and may not account for all complex soil-structure interaction effects.

Q5: How does silt force differ from water pressure?
A: Silt force includes both the weight of submerged silt particles and their earth pressure characteristics, while water pressure is purely hydrostatic.