May 05 Daily Question: Net Excavation for a Foundation Plan

NCEES Civil PE Specification VIII.A.: Excavation and embankment

Problem

You are responsible for placement of 8 spread foundations required to support a new structure. Each foundation is composed of a square footing and pier as shown in the typical elevation. The project geotechnical report states that 3 feet of over-excavation and compaction is required below and around each footing. Based on typical footing dimensions shown, determine the total net excavation required for all foundations in cubic yards.

Select an Answer:

CORRECT 😃

INCORRECT 😟

Average:

18.2%

Solution

Answer: A) 41 cubic yards

Depth of Footing:
$$ d_f=5\ ft $$
Depth of Excavation:
$$ d_{ex}=d_f+3\ ft=8\ ft $$
Width of Footing:
$$ b_f=8\ ft $$
Width of Excavation:
$$ b_{ex}=b_f+2\ast3\ ft=14\ ft $$
Area of Excavation:
$$ A_{ex}=\left(b_{ex}\right)^2=196\ ft^2 $$
Volume of Excavation:
$$ V_{ex}=A_{ex}\ast\ d_{ex}=1568\ ft^3 $$
Area of Footing:
$$ A_f=\left(b_f\right)^2=64\ ft^2 $$
Thickness of Footing:
$$ t_f=2\ ft $$
Width of Pier:
$$ b_p=2\ ft $$
Area of Pier:
$$ A_p=\left(2\ ft\right)^2=4\ ft^2 $$
Height of Pier Below Grade:
$$ h_p=3\ ft $$
Volume of Foundation:
$$ V_f=A_f\ast\ t_f+A_p\ast\ h_p=140\ ft^3 $$
Volume of Fill per Foundation:
$$ V_{fill}=V_{ex}-V_f=1568\ ft^3-140\ ft^3=1428\ ft^3 $$
Total Net Excavation (cubic yards):
$$ V_{net}=8\ast(V_{ex}-V_{fill})\ast\frac{1\ yd^3}{27\ ft^3}\approx41\ yd^3 $$