EARTHWORKS
It involves reshaping a site's terrain by digging deep
and moving large quantities of earth or rock. The
purpose is to create an ideal base for various types
of construction, including: houses, decks, pools,
driveways; and large-scale projects like roads,
highways, dams and buildings.
AREAS OF CROSS SECTION
• Level Cross Section (Equivalent level Or Trapezoidal Section) :
B = base/width
C = center height
s = side slope
AL = BC + S𝐂 𝟐
AREAS OF CROSS SECTION
• Three-level Cross Section :
𝟏
𝑩
𝑨𝟑𝑳 = [𝑪 𝒅𝑳 + 𝒅𝑹 +
𝒉𝑳 + 𝒉𝑹 ]
𝟐
𝟐
AREAS OF CROSS SECTION
• Five-level Cross Section :
𝟏
𝑨𝟓𝑳 = (𝑩𝑪 + 𝒇𝑹𝒅𝑹 + 𝒇𝑳𝒅𝑳)
𝟐
PROBLEM NO. 1
Compute the side slope and the base of the given cross-section that has an area
of 31.7 m2.
Cross section notes:
PROBLEM NO. 2
Find the value of x if the width of the roadway for cut is 6m and 4.8m in fill. Side
slope is 1:1 Also, compute the area of cut and fill.
Cross section notes:
VOLUMES OF EARTHWORK
• Volume by End Area Method (Average End Area) - it is assumed that the volume
between successive cross sections is the average of their areas multiplied by the
distance between them.
𝑽=
𝑳
𝟐
𝑨𝟏 + 𝑨𝟐
Note: It is only valid when A1 = A2 and
approximate if A1 ≠ A2.
VOLUMES OF EARTHWORK
• Prismoidal Formula
𝑽=
𝑳
𝟔
𝑨𝟏 + 𝟒𝑨𝒎 + 𝑨𝟐
Note: Am is determined by averaging the corresponding linear dimensions of the end
sections and NOT by averaging the end areas A1 and A2.
• Prismoidal Correction
𝑳
𝑽=
𝒄𝟏 − 𝒄𝟐 (𝒅𝟏 − 𝒅𝟐)
𝟏𝟐
PROBLEM NO. 1
The following data are cross-section notes of the ground which will be excavated
for a roadway.
The base road is 10 m and the sideslopes are 1.5:1
a. Find the volume of excavation by end area method.
b. Compute the volume by prismoidal formula.
c. Determine the prismoidal correction
Cut and Fill Example 1 :
Given the following cross sections
Base for cut = 9m
Sideslope = 1:1
Base for fill = 8m
Sideslope = 1.5:1
a. Compute the volume of cut using end area method.
b. Find the volume of fill using end area method.
Cut and Fill Example 2 :
From Station 0+200 with center height of 1.4 m in fill, the ground line makes a uniform slope
of +5% to station 0+260 whose center height is 2.8 m in cut. Assuming both sections to be
trapezoidal with a roadway of 10m and sideslope of 2:1
a. Compute the grade of the finished roadway.
b. How far from station 0+200 will the filling extend?
c. What is the area of the section at station 0+250?