A 10 m x 6 m mat foundation is placed at 2.0 m depth in sand where the average value of N60 is 23. Determine the allowable net pressure that would limit the settlement to 75 mm, using the following equations. ### Bearing Capacity of FoundationsThe following equation is used to determine the net bearing capacity (\(q_{net}\)) of a foundation:\[q_{net}(kN/m^2) = \frac{N_{60}}{0.08} \left( \frac{B + 0.3}{B} \right)^2 F_d \left( \frac{S_e}{25} \right) \quad \text{(for \(B > 1.22 \, m\))}\]#### Where:- **\(F_d\)** : Depth factor = \(1 + 0.33 \left( \frac{D_f}{B} \right)\)- **\(B\)** : Foundation width, in meters- **\(S_e\)** : Settlement, in mmAdditional Definitions:- **\(N_{60}\)** : Standard penetration resistance- **\(D_f\)** : Depth of foundation#### Approximation for Large WidthsWhen the width **\(B\)** is large, the equation can be simplified as follows:\[q_{net}(kN/m^2) \approx \frac{N_{60}}{0.08} F_d \left( \frac{S_e}{25} \right)\]\[= \frac{N_{60}}{0.08} \left( 1 + 0.33 \left( \frac{D_f}{B} \right) \right) \left[ \frac{S_e(mm)}{25} \right]\]\[\leq 16.63 N_{60} \left[ \frac{S_e(mm)}{25} \right]\]The approximation highlights how the bearing capacity scales with increasing width and settlement conditions of the foundation, allowing for simplification when certain parameters like width become significant.

Given data: Length (L) = 10 m Width (B) = 6 m Foundation Depth (Df) = 2 m N60 = 23 Settlement (Se) =…

Answered: A 10 m x 6 m mat foundation is placed…

A 10 m x 6 m mat foundation is placed at 2.0 m depth in sand where the average value of N60 is 23. Determine the allowable net pressure that would limit the settlement to 75 mm,

Principles of Foundation Engineering (MindTap Course List)

8th Edition

ISBN:9781305081550

Author:Braja M. Das

Publisher:Braja M. Das

Chapter14: Sheet-pile Walls

Section: Chapter Questions

Problem 14.11P

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Question

A 10 m x 6 m mat foundation is placed at 2.0 m depth in sand where the average value of N₆₀ is 23. Determine the allowable net pressure that would limit the settlement to 75 mm, using the following equations.

### Bearing Capacity of Foundations

The following equation is used to determine the net bearing capacity (\(q_{net}\)) of a foundation:

\[
q_{net}(kN/m^2) = \frac{N_{60}}{0.08} \left( \frac{B + 0.3}{B} \right)^2 F_d \left( \frac{S_e}{25} \right) \quad \text{(for \(B > 1.22 \, m\))}
\]

#### Where:
- **\(F_d\)** : Depth factor = \(1 + 0.33 \left( \frac{D_f}{B} \right)\)
- **\(B\)** : Foundation width, in meters
- **\(S_e\)** : Settlement, in mm

Additional Definitions:
- **\(N_{60}\)** : Standard penetration resistance
- **\(D_f\)** : Depth of foundation

#### Approximation for Large Widths

When the width **\(B\)** is large, the equation can be simplified as follows:

\[
q_{net}(kN/m^2) \approx \frac{N_{60}}{0.08} F_d \left( \frac{S_e}{25} \right)
\]

\[
= \frac{N_{60}}{0.08} \left( 1 + 0.33 \left( \frac{D_f}{B} \right) \right) \left[ \frac{S_e(mm)}{25} \right]
\]

\[
\leq 16.63 N_{60} \left[ \frac{S_e(mm)}{25} \right]
\]

The approximation highlights how the bearing capacity scales with increasing width and settlement conditions of the foundation, allowing for simplification when certain parameters like width become significant.

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