Civil Engineering Design

By Author: Anthony W Bills
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Civil Engineering Design
Introduction
Designing a road involves the study of the texture and glade of the surface on which the road is to be constructed, calculating sight distance and radii of horizontal and vertical curves in relation to the recommended speed of vehicles. This project involves designing a section of a rural road that is to be re-aligned. The data that is available includes the map of the area, the contour information of the area and the topographic information of two potentially suitable points at which the stream may be crossed. The route taken by the road will involve acquisition of land because the section of the re-alignment is well away from the old road. The project will involve the design of a suitable horizontal and vertical alignment. The land on which the road is to be constructed is largely vacant, i.e. there are no human dwellings of other artificial constructions that will obstruct the route chosen. There are however portions of woods and a swampy area. In order to reduce the cost of the contract, it will be paramount to avoid the swamp and the woods. There is also a stream to be ...
... crossed and two suitable points at which the road can cross the stream have been identified (Jha and Schonfeld, 2006).
Horizontal Alignment
The route taken by the road in moving from point A to point B must involve crossing the stream. For the road to pass through either of the recommended stream crossing points, it will have to have curves. Since the construction of the road will involve the purchase of the land on which the road will pass, it is important that the road be designed to have the least length possible in order to minimize the cost of the contract. The best route which provides the shortest road distance is shown in fig. 1 below. Some of the points that have been put in consideration in plotting this road design are:
- The road should be straight where the land is sloppy.
- Curves should only appear at level or almost level parts.
- The road should be straight for at least 50m on either side of the stream crossing.
- Cutting and filling of the earth is costly and should be avoided as much as possible.
The diagram below shows the horizontal alignment of the section of the road drawn on the map of the area designated for the re-alignment. The radii of the curves on the new road are shown on fig. 2 and fig. 3 and the lengths of the curves are then calculated as shown.
Among the elements considered in this project are:
- Horizontal alignment
- Vertical alignment
- Curve length
- Grade
- Superelevation
The cost of realigning the road will be an important factor which will be considered in designing the realignment. At all costs, fill will be kept at a minimal level and the road will not be routed through swampy land.


Calculation of Length of Horizontal Curves
Curve IP1 – IP2
The length of the radius of the curve R1 = 850 m and the
Length of the chord IP1IP2 = 800 m

Fig. 1 Calculation of the length of curve
Sin P = 400/850
= 0.4706
P = 28.07o
The length of the curve of the road is represented by the length of the arc subtended by the chord IP1IP2 and is given by:
28.07/360 * Circumference of the circle of radius R1
= 2*28.07/360*2 πR1
= 2*28.07/360*2*3.14*850 where 3.14 is the value of π
= 832.4 m
Using the same argument, the lengths of the other curves are as calculated below:
Curve IP2 - IP3
R2 = 390 m
Length of the chord IP5B = 420 m
Angle subtending the arc = 65.16o
Length of the curve = 65.16/360*2*3.14*390
= 442 m
Curve IP5 – B
R3 = 800 m
Length of the chord IP2IP3 = 680 m
Angle subtending the arc = 50.3o
Length of curve = 50.3/360*2*3.14*800
= 702 m
Intersection Point A IP1 IP2 IP3 IP4 IP5 B
Distance (m) 0 1350 832.4 442 840 1050 702
Chainage 0 1350 2182.4 2624.4 3464.4 4514.4 5216.4

Calculation of Bearings of Intersection Points
Intersection Point A IP1 IP2 IP3 IP4 IP5 B
Northing
N 30,035N 29800 29800 29300 29100 28100 27,630N
Easting 66,340E 65000 64100 63100 63300 63000 62,500E
Bearing 276.3o 272 o 271.5 o 268 o 265.5 o 262.5 o 259.5o
Table 1 Bearing of Intersection Points
Coordinates of the Intersection Points (IP’s)
The co-ordinates of the intersection points are read directly from the map.
A 30035N, 66340E
IP1 29800N, 65000E
IP2 29800N, 64100E
IP3 29700N, 63700E
IP4 29100N, 63300E
IP5 28100N, 63000E
B 27630N, 62500E
Vertical Alignment
The construction of the road will involve cutting the earth at some parts and filling other parts in order to reduce the natural slope of the terrain. Since this process is costly, the route of the new road has been chosen in such a way that the cuts and fills are kept at a minimal level. In this project, the maximum magnitude of fill is plus or minus 3 meters.

Z

Fig. 4 Vertical alignment of the road
Calculation of Vertical Curves
a) Vertical Curve PQ
Angle subtended by the arc = 2*sin-1(18/48)
= 44o
Length of curve = 44/360*2*3.14
= 36 m
b) Vertical curve RS
Angle subtended by the arc = 2*sin-1(12.5/47)
= 30.8o
Length of curve = 30.8/360*2*3.14*47
= 25.25 m
c) Vertical Curve TU
Angle subtended by the arc = 2*sin-1(22/35)
= 77.9o
Length of curve = 77.9/360*2*3.14
= 47.5 m
d) Vertical Curve UV
Angle subtended by the arc = 2*sin-1(22/36)
= 78.3
Length of curve = 78.3/360*2*3.14*36
= 50 m
The table below shows the fill at every contour crossing of the re-aligned road. Positive value of fill means that a fill is added to the natural surface while a negative value implies that the natural surface is cut.
Contour 113
A 115 120 125 130 135 130 125 120
Cut (m) 0 0.6 0.5 0.2 -0.4 -0.3 -0.5 0 0.1

Contour 110 115 120 125 130 135 140 140 135
Cut (m) 0.2 0.4 0 -1 -1.5 -2 -1.5 -2 -2.2

Contour 130 125 125 130 135 140 145 147
B
Cut (m) 2.0 2.5 2.5 -0.1 1.2 -1.5 1 0
Table 2 Fill of the re-aligned road

Fig. 5 Complete map of road realignment
Conclusion
The design of the road realignment will involve cutting and filling of the natural surface in order to reduce the natural slope of the terrain. The vertical curves have been reduced in order to enhance visibility. The fill is within plus or minus 3 meters in order to reduce the cost. The road design also involves several horizontal curves in order to avoid steep slopes, woody land and the swamp and to reduce the cost of the construct by ensuring that the road passes through the stream crossing point that has already been identified. The design however has not taken into consideration the soil texture and drainage pattern of the area.

Reference
Schonfeld, P. and Jha, M. K., (2006). Intelligent Road Design. UK: WitPress.
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