Abstract
The road sector around the world is undergoing a major evoloution.Through innovative and advanced technology, highways can be designed to go over s or around the slopes. Nevertheless, the two alignments serve the purpose of getting an individual or cargo from point A on one side to point B on the other.
There are two types of highway curves: horizontal and vertical curves. Horizontal curves are designed in the horizontal alignment while vertical curves are designed in the vertical alignment. The alignment considers the radius of curvature, the point of tangency, the point of intersection and the length of the circle among others. It is therefore an important design aspect for all civil and structural engineer. However, the design has to be according to the standards stipulated by the government or local authority.
As in this design report, the major concern is the proposed road connecting the villages Llanharry and Brynsalder.Therefore, the task therein is to investigate, determine and design the most feasible route of the three that will be proposed. The design will be based on the horizontal alignments but other aspects such as traffic forecasting, pavement design and drainage systems are considered.
Introduction
As with every road design manual, there are various factors that are highly considered. Some of the factors to consider in the design of vertical and horizontal curves is the design speed, radius of curvature, visibility among others. However, the manual used in this design case specifies the allowable limits to the road elements. Furthermore, as with any other civil engineering project, the design and actual construction of the road must be cost effective and must consider the environmental as well as the economic factors of the area.
The road is used both for commercial as well as public purposes and as such is a major asset to the development of this region.Therefore,one important issue to be considered in the design is the high design speed which takes into consideration all the commercial and public vehicles present. Moreover, some factors such as the curb height and the number of curves present must be properly established for appropriate.
There are primarily two reasons that call for the design of a new road and redesign of the existing road. To begin with, roads provide a means of economic growth by increasing the ease through which commodities can be transported and distributed to and from the specified locality. Furthermore, proper design of roads and curves may increase the capacity of roads decreasing congestion and at the same time reducing the travel time to and from the locality.
Horizontal Alignment
Introduction
Horizontal curves are defined as the curves that are used to connect two tangential planes in a route (Kim, 2006). However, unlike the vertical curves the alignment should be horizontal. Furthermore, the definitions may be based on the radius or the degree of curvature. To begin with, the degree refers to the angle that subtends a sector of the alignment which can be either an arc or a cord. Secondly, the radius of the curve refers to the distance from the midpoint of the circle to any point on the perimeter of the circle.
Horizontal curves are designed in order to go round obstacles such as hills, mountains and undesirable terrains. However, the design is based on the vertical orientation and therefore the approach view as well as the headlight distance should be considered in detail (Wong, 2009). As with the actual fields design, there are two methods that can be used by the surveyor in setting out the points of the curve: the angle of deflection methodology and the offset of the tangent methodology. Nevertheless, proper design and setting out using any of the two methods results into a safe and effective horizontal curve.
The circular curve
Circular curves have a large radius while the value of g is much smaller.
Total bendiness (B) = x_{1}+x_{2}+x_{3}+——————+x_{n} =
Distance AB
Setting out curves from the inside may depend very much on visibility inside the curve. Small curves are more easily set from inside. The chord distance x should preferably be 1/4 (or less of the value of the radius).
For very long curves of very large radii, it is not always possible to set out curves from the inside. In such cases, the equation y= x^{2}/2r seen earlier may also be used to set out curves from the outsides as shown above.
Transition curve –
Transition curves lies between straight line and circular curves having view to reducing order of lateral shock where tangent point is passed.
Length of Transition curves –
Design Speed (V) (km/h)
Radius of circular curve (R) (m)
Using the two parameters, we can calculate the rate at which a vehicle experiences a radial acceleration q along the transition curve (m/sec^{3})
L=V^{3}/ (46.7qR)
Super elevation
The super elevation is the forces acting on a vehicle on a straight section of the road ensuring that it is stable and does not skid offroad.
N= Mg
M= mass of vehicle
R = radius of curve
V= velocity of vehicle
N= normal reaction
P= frictional forces
Route selection
According to the features of the area that are shown by the aerial map below, there are a number of alignments that may be selected for the horizontal curves and the resultant highways as shown below.
First route
Second route
Third route
The selection of the most feasible route will be based on the economics as well as the impacts on the area. Therefore, the first two routes may be overlooked because they are likely to be more expensive in construction because of the number horizontal curves. Furthermore, the two routes are longer which makes the third route the most feasible. The route is as sketched below (in red) with the two points A and B indicating the length.
Drawing – route selection
Calculations
X coordinate  Y coordinate  
A  3.53  80.23 
IP_{1}  3.02  81.36 
IP_{2}  3.26  83.65 
IP_{3}  0.86  84.60 
B  0.36  84.74 
Scale – 1:100
Bearing tangent  The Angle in radians  The Angle in degrees  First quadrant  Second Quadrant  Third Quadrant  Fourth Quadrant  bearing  Quadrant number  
A  0.45  0.424  24.30  24.3  155.7  180.4  335.7  335.7  Q_{4} 
–  0.10  0.104  6.00  6.0  174.0  180.1  354.0  6.0  Q_{1} 
2.53  1.194  68.40  68.4  111.6  181.2  291.6  291.6  Q_{4}  
IP_{3 }– B  3.33  1.279  1.279  73.3  106.7  181.3  286.7  286.7  Q_{4} 
Bendiness (Degree) 
angle  Angle(deg) β ( θ/2) 
Angle β 
Tanβ  radius of the curve®  Point of tangency and intersection point (Distance) m  Distance cm 

IP_{1}  322.0  36.0  18.0  0.3  0.325  578  187.8  1.9 
IP_{2}  266.8  96.3  48.2  0.8  1.116  578  645.3  6.5 
IP_{3}  30.9  32.6  16.3  0.3  0.22  578  169  1.7 
Design speed –
The start point in determining the geometry of a highway is the design speed. The design speed is in term determined by the purpose of a road. Once established, the design speed thereafter determines the other road parameters.
Control access
Distance between junctions
Length of road with hard shoulder
Separation cross traffic
Prohibition of certain vehicle types .Depending on the radius of curvature, different horizontal curves have different design speeds. Some may be as high as 150 while others may be as low as 50.These design speeds prevent skidding because of the increase in centrifugal and centripetal force with increase in speed around a bend.. In the UK the maximum design speed used are 70 mph (120 km/h) for the dual carriage ways 60 mph (100 km/h) (Petit, Diakhate, & Millien, 2009)
Highway are typically of two categories –
Urban roads – design speed < 50 km/h
Rural roads – design speed > 50 km/h
One major design aspect is the percentile speed through which vehicles at a given section of the highway travel.
In UK, design speeds are normally the 85^{th} percentile speeds.
50^{th} percentile  85^{th} percentile  99^{th} % percentile 
100  120  145 
85  100  120 
70  85  100 
60  10  85 
For example
For 85^{th} percentile design speed is 100 km / h
Mathematical analysis
Arithmetic mean
x̅= _{j}
^{ }n
where xj_{ }= j^{th } spot speed
N = no of observation
Class interval
C _{l} = R/(9+3.22logn)
Where
C _{l} = class interval
R = range between the largest and smallest
n = no of observation
Standard deviation
S^{2}=
Vertical alignment
The vertical alignment of roads depend on the design speed , traffic mass , topography of area , safety classification of highway , typical section’s sight distance.
Vertical curves
Vertical curves are generally parabolic shaped. The length of the curve is fundamental in the design and is established alongside the design speed data.
The length is determined by the following formula:
L= k(pq)
Where,
P and q are gradients (expressed as %, with appropriate signs)
K is constant value
A minimum longitudinal gradient on a road is usually about 0.5% ( 1 in 200)
In order to determine the levels along the vertical curve formula used is
Y= [(qp)/2L] x^{2}
Where;
L = length of vertical curve
y = vertical offset measured downward from tangent to the curve
p & q are gradients
Vertical alignment design
Location  Chainage  Chainage in cm  Original ground level 
.5  50  95  
START  0  0  95 
0.8  190  95  
1.9  240  95  
2.4  280  100  
2.8  330  105  
3.3  390  110  
3.9  540  115  
IP_{1}  5.4  590  115 
5.9  620  115  
.3  680  110  
.9  750  105  
1.6  840  100  
2.5  1080  95  
4.9  1140  90  
5.5  1200  85  
6.1  1240  70  
6.5  1300  75  
7.1  1330  75  
7.4  1420  80  
IP_{2}  8.3  1520  90 
1  1890  90  
4.7  2130  90  
7.1  2220  85  
8  2360  80  
9.4  2380  75  
9.6  2450  70  
10.3  2530  65  
11.1  2530  60  
IP_{3}  11.6  2640  55 
0.6  2730  50  
1.5  2900  45  
3.2  2930  45  
3.5  3060  50  
4.8  3130  55  
END  5.5  3240  55 
6.6  4020  60 
Vertical ground profile –
Scale 1:100
Desirable
Curve index  P  q  K  Length of curve K(pq) 
Maxima or minima of curve  
X Lp/(pq) 
Y Lp^{2}/2(pq)/100 

1  4.2  5.2  100  940  420  8.8 
2  5.5  4.2  26  252.2  143  3.9 
3  4.3  0.72  100  358  430  9.2 
4  .65  5.3  100  602  72  0.3 
5  4.2  2.8  26  93.6  208  0.1 
Absolute
Curve index number  P  q  Value of K  Length of curve K(pq) 
Maxima or ,minima of the curve  
X Lp/(pq) 
Y Lp^{2}/2(pq)/100 

1  3.5  5.96  55  520.3  193  3.4 
2  5.8  4.3  26  262.6  151  4.4 
3  4.3  0.72  55  276.1  237  5.1 
4  0.65  5.6  55  343.75  36  0.1 
5  4.2  2.3  26  169  109  2.3 
Pavement design
The pavement is the major part of the road .However, it is an agglomerations of layers which are laid over each other with the wearing course at the top while the bottom layer made up of the subgrade. The layers in between the wearing course and the subgrade are designed to ensure the loads are distributed to the earth in an efficient manner without damaging the subgrade (Petit, Diakhate, & Millien, 2009).
Qualities present in good pavement
 Good riding surface.
 Good skid resistance.
 Good light reflecting qualities.
 Low noise pollution.
 Good stress reducing qualities.
Requirements of a pavement
A good pavement should have following characteristics:
 Sufficient thickness to distribute the wheel load to subgrade.
 Structurally strong to resist any type of stress imposed on it.
 smooth surface to increase the vehicle speeds
 It does not lead to noise pollution when in contact with the vehicle.
 Surface is dust proof.
Types of pavements
There are two types of pavement used in road as per performance
 Flexible pavement
 Rigid pavement
The pavement in this case will be flexible. Flexible pavements transfer the wheel loads to the subgrade through layers contact with the area under stress extending downwards in a pyramid fashion (papagiannakis, 2008)
CBR value
From given CBR value is = 5%
Soil specification = stabilized soil
Axle load – 80.05
Damage factor – 1
So the minimum thickness for sub base Is 80 mm (CBR <20%)
Traffic forecast
P = 0.9700.385 X 10^{4} F_{m}
F _{m} = F _{0 }(1+r) ^{0.5n}
F _{m }= 24 h average daily one way flow
F _{0 = }Primary one way daily flow
r = commercial vehicle growth rate
n = design life in years
T _{n} = 365 DF _{0 }[{(1+r) ^{n}1}/r]
N = T_{ n }D X 10^{ 6}
Given
Fm=1830
^{ }
Thickness of bearing course –85mm
Thickness of base course – 95 mm
Thickness of road base – 120 mm
Thickness of sub base – 150 mm
Drainage design
General Considerations
Roads have the effect of increasing the area of impermeable surfaces on the earth. Therefore, they affect the infiltration to the ground as well as the amount of surface runoff generated from a particular area (Martin, 2008). Therefore, drainage is a very important aspect in road design with the main purpose the protection of the subgrade. The design in this case is based on the open channel flow law and the flow due to gravity.
The presence of excess water or moisture may affect the road surface and may furthermore create a water logging problem in surrounding area. As with the road, water may cause cracks in pavement due to water logging. Therefore, water logging may weaken the subbase which will eventually lead to road failure (Kendrick, 2004).
Factors that lead to loss of pavement strength
In drainage design the Hydrological factors are considered following.
 Number of stream crossing
 Side sloe of channel
 The moisture regime
 How steep the slopes are
There are two types of drainage systems that are used to expel precipitation from the pavement layers: the perpendicular to the road drainage systems and the parallel drainage system (Smart, 2013). Culverts are the most dominant form of perpendicular drainage system while the vshaped drainage system form the basis of the latter. Culverts are used to collect water from a watershed and transfer it to the other side of the pavement without affecting the pavement while the latter transfers water to a disposal area.
Calculations
Q = 0.167(60/t) A. p .r
Q= discharge
t = time of concentration
P = proportion of total rainfall running off after allowing for soakage and evaporation
r = total rainfall
TRRL method –
Q = F _{A} .A. R _{B }/ 3.6 T Q in m^{3 }/ min
F _{A }= annual rainfall factor
F _{A }= 0.00127 R_{A }– 0.321
A = catchment area (km^{2})
R _{A }= Average rainfall
R _{B }= expected annual rainfall for time of concentration
T = time of concrete ration = (2.48(LN) ^{0.37})
Q = A .r
A = catchment area (m^{2})
R = average rainfall
For this road we have choose V shaped channel
Design of V shaped channel –
Using simplified manning formula
Q = A R ^{1/3}S ^{1/2}/ n
Slope S = ½
n = 0.024 for stabilized soil
V = 1.2 m/s
V = R^{2/3}S^{1/2}/n
R =0.00822 m
Appendix
Terms used in above report
 K is constant value
 P and q are gradients (expressed as %, with appropriate signs)
 A minimum longitudinal gradient on a road is usually applied typically about 0.5% (1 in 200)
 M= mass of vehicle
 R = radius of curve
 V= velocity of vehicle
 N= normal reaction
 P= frictional forces
 F _{A }= annual rainfall factor
 A = catchment area (km^{2})
 R _{A }= Average rainfall
 Q= discharge
 t= time of concentration
 P = proportion of total rainfall
 r = total rainfall in cm
References
Kendrick, p. (2004). Theory and Practice:Roadwork:UK.
Kim, Z. (2006). Realtime lane tracking of curved local road. Transportation systems conference,2006.
Martin, R. (2008). Highway engineering:UK.
papagiannakis, A. T. (2008). Hardcover:pavement design and materials.
Petit, C., Diakhate, M., & Millien, A. (2009). Pavement design for curved road sections:fatigue performance of interfaces and longitudinal top down cracking in multilayered pavements. Pavement design.
Smart, P. (2013). Paperback:drainage design UK.
Wong, J. Y. (2009). Terrainmechanics and off road vehicle engineering:terrain behaviour,off road vehicle performance and design.