Practice 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.

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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):
$$ V_{net}=8\ast(V_{ex}-V_{fill})\ast\frac{1\ yd^3}{27\ ft^3}\approx41\ yd^3 $$