Bearing Capacity Factor Dependent on Cohesion for Case of Local Shear Failure Calculator

Formula Used:

\[ N_c = \frac{q_{nu} - \left( \sigma_s \times (N_q - 1) + 0.5 \times B \times \gamma \times N_\gamma \right)}{\frac{2}{3} \times C} \]

Net Ultimate BC (q_nu):

Effective Surcharge (σ_s):

Bearing Capacity Factor Dependent on Surcharge (N_q):

Width of Footing (B):

Unit Weight of Soil (γ):

N/m³

Bearing Capacity Factor Dependent on Unit Weight (N_γ):

Cohesion in Soil (C):

Bearing Capacity Factor Dependent on Cohesion (N_c):

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1. What is Bearing Capacity Factor Dependent on Cohesion?

The Bearing Capacity Factor Dependent on Cohesion (N_c) is a fundamental parameter in geotechnical engineering that quantifies the contribution of soil cohesion to the overall bearing capacity of foundations. It is particularly important in cases of local shear failure where soil exhibits partial mobilization of shear strength.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_c = \frac{q_{nu} - \left( \sigma_s \times (N_q - 1) + 0.5 \times B \times \gamma \times N_\gamma \right)}{\frac{2}{3} \times C} \]

Where:

\( N_c \) — Bearing Capacity Factor Dependent on Cohesion
\( q_{nu} \) — Net Ultimate Bearing Capacity (Pa)
\( \sigma_s \) — Effective Surcharge (Pa)
\( N_q \) — Bearing Capacity Factor Dependent on Surcharge
\( B \) — Width of Footing (m)
\( \gamma \) — Unit Weight of Soil (N/m³)
\( N_\gamma \) — Bearing Capacity Factor Dependent on Unit Weight
\( C \) — Cohesion in Soil (Pa)

Explanation: This formula calculates the bearing capacity factor that accounts for the cohesive strength of soil in foundation design, considering the reduced mobilization of shear strength in local failure conditions.

3. Importance of N_c Calculation

Details: Accurate calculation of N_c is crucial for safe foundation design, particularly in cohesive soils where the soil's internal bonding significantly contributes to bearing capacity. It helps prevent local shear failures and ensures structural stability.

4. Using the Calculator

Tips: Enter all required parameters in consistent units (Pa for pressures, m for length, N/m³ for unit weight). Ensure all values are positive numbers. The calculator automatically handles the computation and provides the N_c value.

5. Frequently Asked Questions (FAQ)

Q1: What is local shear failure?
A: Local shear failure occurs when the soil beneath a foundation fails gradually, with only partial mobilization of shear strength, typically in loose or soft soils.

Q2: How does N_c differ from general shear failure?
A: For local shear failure, the bearing capacity factors are typically reduced (by 2/3 for cohesion) compared to general shear failure due to partial mobilization of soil strength.

Q3: What are typical values for N_c?
A: N_c values typically range from 5 to 20 for most soils, but can vary significantly based on soil properties and failure conditions.

Q4: When should local shear failure be considered?
A: Local shear failure should be considered in loose sands, soft clays, or any soil condition where full mobilization of shear strength is not expected.

Q5: How does cohesion affect bearing capacity?
A: Cohesion significantly increases bearing capacity by providing additional shear resistance. Higher cohesion values generally lead to higher N_c values and greater bearing capacity.