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Highway Engineering: WEEK 10 - Solutions

This document contains solutions to 6 exercises related to highway engineering. Exercise 1 calculates the volume of a trench excavation given the trench dimensions. Exercise 2 defines the economic limit of haul as the distance where hauling excavated material is more economical than wasting and borrowing. Exercise 3 calculates cut and fill volumes between stations and accounts for material shrinkage. Exercise 4 determines the economic limit of haul using costs of excavation and overhaul. Exercise 5 involves drawing a mass haul diagram to identify areas requiring money to haul. Exercise 6 calculates the free haul volume using total haul distance, free haul distance, and total free haul volume.

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Caio Da Silva Cespedes
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285 views14 pages

Highway Engineering: WEEK 10 - Solutions

This document contains solutions to 6 exercises related to highway engineering. Exercise 1 calculates the volume of a trench excavation given the trench dimensions. Exercise 2 defines the economic limit of haul as the distance where hauling excavated material is more economical than wasting and borrowing. Exercise 3 calculates cut and fill volumes between stations and accounts for material shrinkage. Exercise 4 determines the economic limit of haul using costs of excavation and overhaul. Exercise 5 involves drawing a mass haul diagram to identify areas requiring money to haul. Exercise 6 calculates the free haul volume using total haul distance, free haul distance, and total free haul volume.

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Caio Da Silva Cespedes
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HIGHWAY ENGINEERING

WEEK 10 – Solutions
EXERCISE 1:
Trench Excavations
• Volume = Cross Sectional Area x Length of Trench
• EXAMPLE: Find the volume (bank measure) of excavation
required for a trench 0.92m (3 ft) wide, 1.8m (6 ft) deep, and
152m (500 ft) long. Assume that the trench sides will be
approximately vertical
EXERCISE 1
SOLUTION: Trench Excavations
• Volume = Cross Sectional Area x Length of Trench
• EXAMPLE: Find the volume (bank measure) of excavation
required for a trench 0.92m (3 ft) wide, 1.8m (6 ft) deep, and
152m (500 ft) long. Assume that the trench sides will be
approximately vertical.

• Solution:
• X-section area: 0.92x1.8 = 1.656 = 1.656m2
• Volume: 1.656x152 = 251.72m3
EXERCISE 2: The Economical Limit of Haul

• The economical limit of haul is defined as the distance through


which it is more economical to haul excavated material than to
waste and borrow. The following formula is presented as a guide to
assist the designer in determining the economic limit of haul:
EXERCISE 3:
Given the end areas below, calculate the volumes of cut and fill between
stations 3+000 and 3+150. If the material shrinks 12 percent, how much
excess cut or fill is there?

Station End Areas, m2


Cut Fill
3+000 57.93
3+050 52.28
3+075 0 23.58
3+100 8.4 3.73
3+114 13.8 0
3+150 33.34
EXERCISE 3
SOLUTION:
EXERCISE 4:
A mass haul diagram shows a free-haul distance of 1,100 m., cos of
excavation of $1.91 per cubic meter and a price of overhaul of
$0.01/cubic meter. The limit of economical haul is most nearly.

a) 1000 m
b) 1103 m
c) 1291 m
d) 1155 m
EXERCISE 4
SOLUTION:
𝐿𝑒𝑛𝑔ℎ𝑡 𝑜𝑓 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐𝑎𝑙 ℎ𝑎𝑢𝑙 = ℎ + 𝐹𝑟𝑒𝑒 ℎ𝑎𝑢𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
ℎ = 𝑒/𝑜
ℎ = ($1.91Τ𝑐𝑢 − 𝑚)/($0.01Τ𝑐𝑢 − 𝑚 − 𝑚 = 191𝑚
𝐿𝑒𝑛𝑔ℎ𝑡 𝑜𝑓 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐𝑎𝑙 ℎ𝑎𝑢𝑙 = 191𝑚 + 1100𝑚 = 1291𝑚
EXERCISE 5:
The free-haul distance for a cut and fill project 100 ft. Draw the Mass
Diagram and shade in the areas that will cost money to haul

• Station 0+00 to 1+00: 450 cu-m cut


• Station 1+00 to 1+60: 450 cu-m fill
• Station 1+60 to 2+00: 250 cu-m fill
• Station 2+00 to 2+50: 350 cu-m cut
EXERCISE 5
SOLUTION:
EXERCISE 6:
Given the following requirements for a site balancing project:
• The total haul distance Station 9 + 630.00 and 15+210.00
• Free haul distance is between Station 10+390.00 and 14+560.00
• Free haul is approximately 642,186 cu-m-m
The free haul volume is most nearly:
a) 658.0 cu-m
b) 115.0 cu-m
c) 154.0 cu-m
d) 455.45 cu-m SOLUTION:
Total haul distance = 15+210 – 9+630 = 15210-9630 =5.580 stations = 5580 m
Free-haul distance = 14+560 – 10+390 = 14560-10390 = 4.170 stations = 4170 m
Overhaul distance = Total Haul distance – Free-haul distance
= 5580 – 4170 m = 1410 m (1.41 stations)
Free-haul volume = Overhaul volume = Overhaul/Overhaul distance
= 642186 cu-m-m/1410 m = 455.45 cu-m.

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