Effective Surcharge for Rectangular Footing given Shape Factor Calculator

Effective Surcharge Formula:

\[ \sigma_s = \frac{q_{fc} - \left( (C \cdot N_c) \cdot (1 + 0.3 \cdot \frac{B}{L}) + (0.5 \cdot \gamma \cdot B \cdot N_\gamma) \cdot (1 - 0.2 \cdot \frac{B}{L}) \right)}{N_q} \]

Ultimate Bearing Capacity (kPa):

kPa

Cohesion in Soil (kPa):

kPa

Bearing Capacity Factor (Cohesion):

Width of Footing (m):

Length of Footing (m):

Unit Weight of Soil (kN/m³):

kN/m³

Bearing Capacity Factor (Unit Weight):

Bearing Capacity Factor (Surcharge):

Effective Surcharge (kPa):

1. What is Effective Surcharge for Rectangular Footing?

Definition: Effective surcharge refers to the vertical pressure or load acting over the ground surface in addition to basic earth pressure, considering shape factors for rectangular footings.

Purpose: This calculation helps geotechnical engineers determine the additional load capacity a soil can support when designing rectangular foundations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_s = \frac{q_{fc} - \left( (C \cdot N_c) \cdot (1 + 0.3 \cdot \frac{B}{L}) + (0.5 \cdot \gamma \cdot B \cdot N_\gamma) \cdot (1 - 0.2 \cdot \frac{B}{L}) \right)}{N_q} \]

Where:

\( \sigma_s \) — Effective surcharge (kPa)
\( q_{fc} \) — Ultimate bearing capacity (kPa)
\( C \) — Cohesion in soil (kPa)
\( N_c \) — Bearing capacity factor for cohesion (±5%)
\( B \) — Width of footing (m)
\( L \) — Length of footing (m)
\( \gamma \) — Unit weight of soil (kN/m³)
\( N_\gamma \) — Bearing capacity factor for unit weight (±5%)
\( N_q \) — Bearing capacity factor for surcharge (±5%)

3. Importance of Effective Surcharge Calculation

Details: Proper calculation ensures foundation stability, prevents excessive settlement, and optimizes foundation design for rectangular footings.

4. Using the Calculator

Tips: Enter all required parameters. The bearing capacity factors include a ±5% tolerance. Ensure all values are positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why are shape factors important?
A: Shape factors account for the rectangular footing's dimensions (B/L ratio) affecting the bearing capacity.

Q2: What are typical values for bearing capacity factors?
A: Common defaults are Nc=9, Nγ=1.6, Nq=2.01, but these vary with soil type and friction angle.

Q3: How does footing shape affect the calculation?
A: Rectangular footings have higher capacity than strip footings due to 3D confinement effects.

Q4: What if my soil has no cohesion (C=0)?
A: The calculator works for both cohesive and cohesionless soils. Just enter C=0 for cohesionless soils.

Q5: Why the ±5% tolerance on capacity factors?
A: These factors are empirically derived and have inherent variability in real-world conditions.