Cohesion Of Soil Given Loading Intensity By Terzaghi's Analysis Calculator

Formula Used:

\[ Cohesion = \frac{Load\ Intensity - \left(\frac{2 \times Passive\ Earth\ Pressure}{Width\ of\ Footing} - \frac{Unit\ Weight\ of\ Soil \times Width\ of\ Footing \times \tan\left(\frac{Angle\ of\ Shearing\ Resistance \times \pi}{180}\right)}{4}\right)}{\tan\left(\frac{Angle\ of\ Shearing\ Resistance \times \pi}{180}\right)} \]

\[ C = \frac{q - \left(\frac{2 \times Pp}{B} - \frac{\gamma \times B \times \tan\left(\frac{\phi \times \pi}{180}\right)}{4}\right)}{\tan\left(\frac{\phi \times \pi}{180}\right)} \]

Load Intensity (q):

Pascal

Passive Earth Pressure (Pp):

Pascal

Width of Footing (B):

Meter

Unit Weight of Soil (γ):

N/m³

Angle of Shearing Resistance (φ):

Degrees

Cohesion (C):

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1. What is Terzaghi's Analysis?

Terzaghi's analysis is a fundamental theory in soil mechanics that provides a method for calculating the bearing capacity of shallow foundations. It considers factors such as soil cohesion, unit weight, and angle of shearing resistance to determine the maximum load a soil can support.

2. How Does the Calculator Work?

The calculator uses Terzaghi's formula:

\[ C = \frac{q - \left(\frac{2 \times Pp}{B} - \frac{\gamma \times B \times \tan\left(\frac{\phi \times \pi}{180}\right)}{4}\right)}{\tan\left(\frac{\phi \times \pi}{180}\right)} \]

Where:

\( C \) — Cohesion of soil (Pascal)
\( q \) — Load Intensity (Pascal)
\( Pp \) — Passive Earth Pressure (Pascal)
\( B \) — Width of Footing (Meter)
\( \gamma \) — Unit Weight of Soil (N/m³)
\( \phi \) — Angle of Shearing Resistance (Degrees)
\( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: This formula calculates soil cohesion based on Terzaghi's bearing capacity theory, accounting for various soil properties and loading conditions.

3. Importance of Cohesion Calculation

Details: Accurate cohesion calculation is crucial for foundation design, slope stability analysis, and determining the shear strength of cohesive soils in geotechnical engineering.

4. Using the Calculator

Tips: Enter all values in the specified units. Load intensity and passive earth pressure should be in Pascal, width in meters, unit weight in N/m³, and angle of shearing resistance in degrees. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is soil cohesion?
A: Cohesion is the ability of like particles within soil to hold onto each other. It represents the shear strength or force that binds together soil particles.

Q2: When is Terzaghi's analysis typically used?
A: Terzaghi's analysis is primarily used for calculating the bearing capacity of shallow foundations in various soil conditions.

Q3: What are typical cohesion values for different soil types?
A: Cohesion values vary significantly: clay soils typically have higher cohesion (10-100 kPa), while sandy soils have little to no cohesion (0-10 kPa).

Q4: How does angle of shearing resistance affect cohesion calculation?
A: The angle of shearing resistance (friction angle) significantly influences the calculation as it appears in the trigonometric functions of the formula.

Q5: Are there limitations to Terzaghi's formula?
A: Yes, the formula assumes homogeneous soil conditions and may not account for all real-world complexities such as soil layering or unusual loading conditions.