By the end of this chapter, you will be able to:
Mastering these skills will help you create safe, efficient, and well-planned roads that serve communities and support development.
Compiled by: Michael Githaiga
Resource mobilization and OGL analysis are critical steps in road geometric design, ensuring that projects are properly planned, resourced, and optimized for safety and efficiency. In Kenya, where infrastructure development is a key driver of economic growth, understanding how to mobilize resources effectively and analyze the Outstanding Geometric Line (OGL) is essential for civil engineers. These processes influence project timelines, cost control, and compliance with design standards. This chapter addresses the mathematical principles and practical calculations involved in these areas.
Resource mobilization in road geometric design involves quantifying and allocating the necessary materials, equipment, labor, and finances to execute design plans effectively. Accurate mobilization ensures that projects proceed without delays or budget overruns, which is particularly important in Kenyan county government projects where funding and timelines are tightly controlled.
Calculating the volume of earthworks is vital for resource planning, including excavation and embankment materials. The volume depends on the cross-sectional area of the cut or fill and the length of the road section.
The general formula for volume \(V\) of earthworks is:
$$ V = A \times L $$
where
\(A\) = cross-sectional area (m\(^2\))
\(L\) = length of the road section (m)
Example 1: Calculate the volume of earthworks for a road section 100 m long with a cross-sectional area of 15 m\(^2\).
Given:
\(A = 15 \, m^2\), \(L = 100 \, m\)
$$ V = A \times L $$$$ V = 15 \times 100 $$$$ V = 1500 \, m^3 $$
Answer: 1500 m\(^3\)
Example 2: A road embankment has a trapezoidal cross-section with a top width of 6 m, bottom width of 10 m, and height 2 m. Calculate the volume over a length of 250 m.
Calculate \(A\) first:
$$ A = \frac{(b_1 + b_2)}{2} \times h $$$$ A = \frac{(6 + 10)}{2} \times 2 $$$$ A = 8 \times 2 $$$$ A = 16 \, m^2 $$
Then volume:
$$ V = A \times L $$$$ V = 16 \times 250 $$$$ V = 4000 \, m^3 $$
Answer: 4000 m\(^3\)
Example 3: For a road cut section shaped as a triangle with base 8 m and height 3 m, calculate the volume over 150 m length.
Calculate \(A\):
$$ A = \frac{1}{2} \times base \times height $$$$ A = \frac{1}{2} \times 8 \times 3 $$$$ A = 12 \, m^2 $$
Then volume:
$$ V = A \times L $$$$ V = 12 \times 150 $$$$ V = 1800 \, m^3 $$
Answer: 1800 m\(^3\)
Example 4: A road section has variable cross-sectional areas: 20 m\(^2\) for the first 100 m, 25 m\(^2\) for the next 150 m. Calculate total volume.
Calculate volumes separately and sum:
$$ V_1 = 20 \times 100 = 2000 \, m^3 $$$$ V_2 = 25 \times 150 = 3750 \, m^3 $$$$ V_{total} = 2000 + 3750 = 5750 \, m^3 $$
Answer: 5750 m\(^3\)
Example 5: A road embankment has a cross-sectional area that changes linearly from 10 m\(^2\) at start to 18 m\(^2\) at end over 200 m. Calculate volume using average area.
Calculate average area:
$$ A_{avg} = \frac{10 + 18}{2} = 14 \, m^2 $$
Volume:
$$ V = A_{avg} \times L = 14 \times 200 = 2800 \, m^3 $$
Answer: 2800 m\(^3\)
For example, in a project managed by the Kenya National Highways Authority (KeNHA), accurate earthwork volume calculations are essential for budgeting and resource allocation. The formulae and methods above are applied in real projects such as the Nairobi-Mombasa Highway expansion, where precise material quantities are required for tendering and construction.
Estimating equipment needs involves calculating machine productivity based on volume and machine capacity to ensure timely completion.
The formula for required machine hours \(H\) is:
$$ H = \frac{V}{P} $$
where
\(V\) = volume of work (m\(^3\))
\(P\) = productivity of equipment (m\(^3\)/hour)
Example 1: How many hours will a bulldozer with productivity 100 m\(^3\)/hour take to excavate 1500 m\(^3\)?
$$ H = \frac{1500}{100} $$$$ H = 15 \, hours $$
Answer: 15 hours
Example 2: A grader has productivity 120 m\(^3\)/hour and must level 2400 m\(^3\). Calculate required hours.
$$ H = \frac{2400}{120} = 20 \, hours $$
Answer: 20 hours
Example 3: For a project with 4000 m\(^3\) earthwork, two excavators each with 150 m\(^3\)/hour productivity work simultaneously. Calculate total hours.
Combined productivity:
$$ P_{total} = 2 \times 150 = 300 \, m^3/hour $$
Hours:
$$ H = \frac{4000}{300} = 13.33 \, hours $$
Answer: 13.33 hours
Example 4: If the available work time per day is 8 hours, how many days will the above project take?
$$ Days = \frac{13.33}{8} = 1.67 \, days $$
Answer: 1.67 days
Example 5: A roller has productivity 500 m\(^3\)/hour compacting embankment. For 2800 m\(^3\), find required hours.
$$ H = \frac{2800}{500} = 5.6 \, hours $$
Answer: 5.6 hours
Equipment requirement calculations are routinely performed in projects by contractors such as H-Young & Co. Ltd and the Kenya Urban Roads Authority (KURA), ensuring that machinery like bulldozers and graders are scheduled efficiently for projects such as the Kisumu city bypass.
Budgeting involves calculating total cost based on quantities and unit prices.
The formula for total cost \(C\) is:
$$ C = Q \times U $$
where
\(Q\) = quantity (e.g., volume in m\(^3\))
\(U\) = unit cost (Ksh per m\(^3\))
Example 1: Calculate cost for 1500 m\(^3\) of earthworks at Ksh 350 per m\(^3\).
$$ C = 1500 \times 350 = 525000 \, Ksh $$
Answer: Ksh 525,000
Example 2: For 4000 m\(^3\) of gravel at Ksh 480 per m\(^3\), find total cost.
$$ C = 4000 \times 480 = 1,920,000 \, Ksh $$
Answer: Ksh 1,920,000
Example 3: A project requires 2800 m\(^3\) of embankment material costing Ksh 420 per m\(^3\). Calculate cost.
$$ C = 2800 \times 420 = 1,176,000 \, Ksh $$
Answer: Ksh 1,176,000
Example 4: If unit cost increases by 10% from Ksh 350 to Ksh 385, calculate new cost for 1500 m\(^3\).
$$ C = 1500 \times 385 = 577,500 \, Ksh $$
Answer: Ksh 577,500
Example 5: Estimate total material cost for 5750 m\(^3\) at Ksh 400 per m\(^3\).
$$ C = 5750 \times 400 = 2,300,000 \, Ksh $$
Answer: Ksh 2,300,000
Budgeting for material costs is a critical step in road projects funded by the Kenya Roads Board (KRB). For instance, the budgeting process for the Thika Superhighway involved detailed calculations of earthwork and gravel costs to ensure compliance with government procurement regulations.
Effective scheduling ensures that labor resources match project demands over time, avoiding idle time or shortages.
Calculate required workforce \(W\):
$$ W = \frac{H}{D \times h} $$
where
\(H\) = total machine hours or man-hours
\(D\) = number of working days
\(h\) = working hours per day per worker
Example 1: For 15 machine hours and 5 working days with 8 hours/day, calculate workforce.
$$ W = \frac{15}{5 \times 8} = \frac{15}{40} = 0.375 $$
Since partial workers aren't possible, round up:
Answer: 1 worker
Example 2: A project requires 80 man-hours. If 4 workers work 6 hours daily, find days needed.
Calculate total daily man-hours:
$$ 4 \times 6 = 24 \, man-hours/day $$
Days:
$$ D = \frac{80}{24} = 3.33 \, days $$
Answer: 3.33 days
Example 3: To complete 120 hours of work in 4 days with 8-hour shifts, calculate needed workers.
$$ W = \frac{120}{4 \times 8} = \frac{120}{32} = 3.75 $$
Round up:
Answer: 4 workers
Example 4: If 3 workers can complete a task in 6 days working 7 hours daily, calculate total man-hours.
$$ H = 3 \times 6 \times 7 = 126 \, man-hours $$
Answer: 126 man-hours
Example 5: For a task requiring 200 man-hours to be completed in 5 days with 8-hour shifts, find workforce.
$$ W = \frac{200}{5 \times 8} = \frac{200}{40} = 5 $$
Answer: 5 workers
Workforce allocation calculations are used in projects by county governments, such as the Machakos County road improvement program, to ensure labor resources are matched to project timelines and avoid delays.
Create a free account to open more of this chapter.
Free: practical guides, quick cards, workplace scenarios and more.
Create a free accountThis chapter covers the essential steps involved in carrying out road geometric design, starting with resource mobilization which ensures all necessary materials, equipment, and personnel are available for the project. It then addresses OGL analysis, a critical evaluation of the original ground levels to inform design decisions. The chapter progresses to the design of horizontal and vertical alignments, focusing on optimizing the road path for safety and efficiency. Various types of road intersections are examined in detail, including Y-junctions, T-junctions, under-passes, roundabouts, overpasses, cross junctions, and interchanges, each with their specific design considerations. The production of detailed drawings follows, providing clear visual guidance for construction. Finally, the chapter emphasizes the importance of comprehensive report preparation to document the design process and facilitate project communication. Together, these topics provide a complete framework for effective road geometric design.
Calculate the total volume of earthworks required to construct a road embankment 500 m long, 8 m wide, and an average height of 2.5 m. (2 marks)
A road alignment has a horizontal curve with a radius of 150 m. Determine the length of the curve if the central angle is 40°. (2 marks)
At the start of this chapter we promised you would be able to:
Tick each one you can genuinely do.
So, are you there yet?
You're competent when you can confidently do 50% or more of what this chapter promised.
Sign in to record how you're doing.