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2. GEOMETRIC DESIGN OF ROAD
2.1 Introduction to road alignment
2.2 Road cross sectional elements
2.3 Sight distance
2.4 Horizontal and vertical alignments
2.5. Road intersections
Road Surveys and Location
Selecting the location of a proposed road is an
important initial step in its design. The decision
to select a particular location is usually based on
topography, soil characteristics, environmental
factors such as noise and air pollution,
and economic factors
Principles of road location
The road location process involves four phases:
Office study of existing information
Reconnaissance survey
Preliminary location survey
Final location survey
Office Study of Existing Information
The first phase in any road location study is the
examination of all available data of the area in
which the road is to be constructed .
The type and amount of data collected and
examined depend on the type of road being
considered, but in general, data should be
obtained on the following characteristics of the
area.
• Engineering, including topography, geology, climate,
and traffic volumes
• Social and demographic, including land use and zoning
patterns
• Environmental, including types of wildlife; location of
recreational, historic, and
archeological sites; and the possible effects of air, noise,
and water pollution
• Economic, including unit costs for construction and the
trend of agricultural, commercial, and industrial
activities
At the completion of this phase of the study, the engineer
will be able to select general areas through which the
road can traverse
Reconnaissance Survey
The object of this phase of the study is to identify several feasible routes, each
within a band of a limited width. Feasible routes are identified by a
stereoscopic examination of the aerial photographs, taking into consideration
factors such as:
• Terrain and soil conditions
•Serviceability of route to industrial and population areas
• Crossing of other transportation facilities, such as rivers, railroads, and roads
• Directness of route
Control points between the two endpoints are determined for each feasible
route. For example, a unique bridge site with no alternative may be taken as a
primary control point. The feasible routes identified are then plotted on
photographic base maps.
3 Preliminary Location Survey
During this phase of the study, the positions of
the feasible routes are set as closely as
possible by establishing all the control points
and determining preliminary vertical
and horizontal alignments for each. Preliminary
alignments are used to evaluate the
economic and environmental feasibility of the
alternative routes.
Economic Evaluation
Economic evaluation of each alternative route is carried
out to determine the future
effect of investing the resources necessary to construct
the road
Factors usually taken into consideration include road
user costs, construction
costs, maintenance costs, road user benefits, and any
disbenefits, which may include
adverse impacts due to dislocation of families,
businesses, and so forth
For example, these results will provide
information on the economic
resources that will be gained or lost if
a particular location is selected.
This information is also used to aid the
policy maker in determining whether
the road should be built, and if so,
what type of road it should be.
Environmental Evaluation
A road is therefore an integral part of the local environment
and must be considered as such.
This environment includes plant, animal, and human
communities and encompasses social, physical, natural,
and man-made variables.
The construction of a road at a given location may result in
significant changes in one or more variables, which in turn
may offset the equilibrium and result in significant adverse
effects on the environment
The environmental impact statements should
include:
• A detailed description of alternatives
• The probable environmental impact, including the
assessment of positive and negative effects
• An analysis of short-term impact as differentiated
from long-term impact
• Any secondary effects, which may be in the form
of changes in the patterns of social and economic
activities
• Probable adverse environmental effects that cannot
be avoided if the project is constructed
• Any irreversible and irretrievable resources that
have been committed
In cases where an environmental impact study is
required, it is conducted at this stage to
determine the environmental impact of each
alternative route. Such a study will determine the
negative and/or positive effects the road facility
will have on the environment
For example, the construction of a freeway at
grade through an urban area may result in an
unacceptable noise level for the residents of the
area (negative impact), or the road facility may
be located so that it provides better access to jobs
and recreation centers (positive impact)
Preliminary Location Survey
Environmental Evaluation
Public hearings are also held at this stage to
provide an opportunity for constituents to give their
views on the positive and negative impacts of the
proposed alternatives.
The best alternative, based on all the factors
considered, is then selected as the
preliminary alignment of the road
Final Location Survey
The final location survey is a detailed layout of the
selected route.
The horizontal and vertical alignments are
determined, and the positions of structures and
drainage channels are located.
Detailed design of the vertical and horizontal
alignments is then carried out to obtain both the
deflection angles for horizontal curves and the cuts
or fills for vertical curves and straight sections of
the road.
ROAD SURVEY METHODS
Surveying techniques can be grouped into three general
categories:
• Ground surveys
• Remote sensing
• Computer graphics
Ground surveys are the basic location technique for roads.
The total station is used for measuring angles in both
vertical and horizontal planes, distances, and changes in
elevation through the use of trigonometric levels; the level
is used for measuring changes in elevation only .
Remote sensing
Remote sensing is the measurement of distances and
elevations by using devices located above the earth,
such as airplanes or orbiting satellites using Global
Positioning Satellite systems (GPS).
The most commonly used remote-sensing method is
photogrammetry, which utilizes aerial photography
Computer Graphics
Computer graphics, when used for road
location, is usually the combination of
photogrammetry and computer techniques.
With the use of mapping software, line styles,
and feature tables, objects and photographic
features can be recorded digitally and stored in
a computer file. This file can then either be
plotted out in map form or sent on to the
design unit.
Factors controlling alignment
• Obligatory points
• Traffic
• Geometric design
• Economy
• Other consideration (Drainage, political,
monotony)
Geometric Design of road Facilities
Geometric design deals with the
dimensioning of the elements of
roads, such as vertical and
horizontal curves, cross sections,
truck climbing lanes, bicycle paths,
and parking facilities.
FACTORS INFLUENCING road DESIGN
Road design is based on specified design standards and
controls which depend on the following roadway system
factors:
• Functional classification
• Design hourly traffic volume and vehicle mix
• Design speed
• Design vehicle
• Cross section of the road, such as lanes, shoulders, and
medians
• Presence of heavy vehicles on steep grades
• Topography of the area that the road traverses
• Level of service
• Available funds
• Safety
• Social and environmental factors
ROAD CROSS SECTION ELEMENTS
Cross slope or Camber
Cross slope or camber is the slope provided to the road
surface in the transverse direction to drain off the rain
water from the road surface.
The cross slope is provided because of the following
reasons:
• To prevent the entry of water into the bituminous
pavement layers
• To prevent the entry of surface water into the subgrade
soil through pavement.
• To remove the rain water from the pavement surface as
quickly as possible and to allow the pavement to get dry
soon after the rain
Cross slope or Camber
The required camber of pavement depends on;
The type of pavement surface
The amount of rainfall
Recommended rates of cross slopes are 1.5 to 2.5 percent
for high-type pavements and 2 to 6 percent for low-type
pavements.
High-type pavements have wearing surfaces that can
adequately support the expected traffic load without visible
distress due to fatigue and are not susceptible to weather
conditions.
Low-type pavements are used mainly for low-cost roads
and have wearing surfaces ranging from untreated loose
material to surface-treated earth.
.
Width of pavement or carriageway
The width of carriageway for various classes of roads standardized by
IRC (Indian Roads Congress) are given in the table below
Class of road Width of
carriageway
1 Single lane 3.75m
2 Two lanes without raised kerbs 7.0m
3 Two lanes with raised kerbs 7.5m
4 Intermediate carriageway 5.5m
5 Multi-lane pavement 3.5/lane
Curbs (Am: Kerbs)
• Curb indicates the boundary between the pavement
and shoulder or sometimes islands; foot path or
parking space.
Curbs may be mainly divided into 3 groups based on
their functions
• Low or mountable curb which encourage traffic to
remain in the through traffic lanes.
The height of this type of shoulder curbs is about 10cm
above the pavement edge with a slope (or batter) to
help vehicles climb the curb easily
Curbs (Am: Kerbs) ctd
• ii. Semi barrier provided on the roadway where the
pedestrian traffic is high. This type of curbs has a
height of about 15cm above the pavement edge with
a batter of 1:1 on the top 7.5cm
• iii. Barrier kerb is provided in built up area adjacent
to foot path with considerable pedestrian traffic. The
height of stone is about 20cm above the pavement
edge with a steep batter of 1 vertical 0.25 horizontal.
Sight distance
• Sight distance is the roadway ahead that is visible to the
driver. Various sight distance criteria exist in road geometric
design to provide drivers with sufficient warning of potential
obstacle or conflict ahead.
• Stopping Sight Distance
• Decision Sight Distance
• Passing Sight Distance on Two-Lane Road
Criteria for Measuring Sight Distance
The Sight Distance is dependent on the height of the driver’s eye
above the road surface, the object height (or size) above the
road surface, and the height and lateral position of sight
obstructions within the driver’s line of sight. These have effect
on the design of horizontal and vertical curve
Stopping Sight Distance
Where:
SSD = Stopping sight distance (m)
BRD = Brake Reaction Distance (m) = vt
BD = Braking Distance (m) = v2/2gf
V = Design speed
t = time
f = Coefficient of friction
g = Gravity acceleration
Stopping Sight Distance When we have an
ascending or a descending grade
SSD = vt + v2/2g(f+n%)
Where:
V = Design speed
t = time
f = Coefficient of friction
g = Gravity acceleration
n = is the grade (negative when descending, positive when ascending)
Decision Sight Distance
3. While descending a -7% grade at a speed of 90
km/h, George notices a large object in the roadway
ahead of him. Without thinking about any alternatives,
George stabs his brakes and begins to slow
down. Assuming that George is so paralyzed with fear
that he won't engage in an avoidance maneuver,
calculate the minimum distance at which George must
have seen the object in order to avoid colliding with it
. You can assume that the roadway surface is concrete
and that the surface is wet so that the coefficient of
friction was 0.29 . You can also assume that George
has a brake reaction time of 0.9 seconds because he is
always alert on this stretch of the road.
Solution
First, we need to calculate the distance that George
traveled during his brake reaction time. This is
done using the equation D = VT from
physics. Since George's brake reaction time was 0.9
seconds and his velocity was 25 m/sec (90 km/h),
the distance he traveled during his brake reaction
time was 22.5 meters. Second, we need to
calculate the distance George will travel while
braking. This is done using the equation shown
below.
d = V2/(2g(f + G))
Where:
V = George's Velocity, 25 m/sec (90 km/h)
g = Acceleration due to gravity, 9.81 m/sec2
f = Coefficient of friction, 0.29 ( we'll use the value for
96 km/h (60 mph) just to be conservative)
G = The grade of the road, -0.07 (-7%)
Solving the equation yields a distance of 145
meters. Summing the distance traveled while braking
and the distance traveled during the brake reaction time
yields a total stopping sight distance of 168
meters. George needed to be about 168 meters away
from the object at the instant he first saw it in order to
avoid a collision
Design of horizontal alignment
• The horizontal alignment includes the straight (tangent)
sections of the roadway and the circular curves that connect
their change in direction.
• The plan view gives the horizontal alignment of a road. The
length of the road is measured along the plan view, on a
horizontal plane.
• The objectives of horizontal alignment design is to provide a
smooth transition between two straight road sections that
also provide proper cross sectional drainage, ensure
vehicle/driver safety while traveling at a design speed
Various design factors to be considered in the horizontal
alignment are: Design speed; Radius of circular curves, types
and length of transition curves, superelevation and widening of
pavement on curves
Design speed (is the speed selected to be used in the design
calculations )
The design speed of roads depends upon
• Class of the road
• Terrain
Terrain classification (IRC) Cross slope of country per cent
Plain 0-10
Rolling 10-25
Mountainous 25-60
Steep Greater than 60
Terrain classification according to
overseas road note 6
• Level (0-10 five metre ground contours per kilometre). Level or
gently rolling terrain with largely unrestricted horizontal and vertical
alignment. Minimum values of alignment will rarely be necessary.
Roads will, for the most part, follow the ground contours and
amounts of cut and fill will be very small.
• Rolling (11-25 five metre ground contours per kilometre). Rolling
terrain with low hills introducing moderate levels of rise and fall
with some restrictions on vertical alignment. Whilst low standard
roads will be able to follow the ground contours with small amounts
of cut and fill, the higher standards will require more substantial
amounts.
• Mountainous (Greater than 25 five metre ground contours per
kilometre). Rugged, hilly and mountainous with substantial
restrictions in both horizontal and vertical alignment. Higher
standard roads will generally require large amounts of cut and fill
ROAD TYPE TERRAIN
DESIGN SPEED
(Km/h)
Primary road
(National,
Expressway)
1.Flat area 80-110
2. Hilly 55-80
3.Mountainous 40-55
Secondary road
(State, district roads )
1.Flat area 60-80
2. Hilly 50-60
3.Mountainous 35-50
Tertiary roads
(Village, others )
1.Flat area 50-60
2. Hilly 35-50
3.Mountainous 25-35
Horizontal curve
Circular curve
SUPER ELEVATION
Super elevation. Super elevation is the amount
of cross slope or "bank" provided on a horizontal
curve to help counterbalance the outward pull
of a vehicle traversing the curve.
The maximum rate of super elevation (emax)
depends on several factors including climatic
conditions, terrain conditions and type of area
(rural or urban).
• 1.Super elevation Transition Length/ development Length.
The super elevation transition length is the distance required
to transition the roadway from a normal crown section to the
full super elevation needed. Super elevation transition length
is the sum of the tangent run out and super elevation runoff.
• 2. Tangent Run out/runoff. AASHTO defines tangent run out
as the change from a normal crown section to a point where
the adverse cross slope of the outside lane or lanes is
removed (i.e., the outside lane(s) is level).
• 3. Super elevation Runoff. AASHTO defines super elevation
runoff as the change in cross slope from the end of tangent
run out (adverse crown removed) to a section that is fully
super elevated.
• 4.Axis of Rotation. The super elevation axis of rotation is the
line about which the pavement is revolved to super elevate
the roadway. This line will maintain the normal road profile
throughout the curve, and it is known as the construction
centreline or control edge.
• 5. Super elevation Rollover. Super elevation "rollover" is the
algebraic difference between the travel lane cross slope and
shoulder cross slope on the outside of a horizontal curve.
• 6. Normal Crown (NC): The typical cross section on a tangent
section (i.e., no super elevation).
• 7. Remove Crown (RC): A super elevated cross section which
is sloped across the entire travelled way in the same direction
and at a rate equal to the typical cross slope on a tangent
section (e.g., 2.0%)
Super elevation attainment
• The available options for rotating travelled ways to attain
super elevation are graphically shown in Figures A to D below.
These are:
1. Revolving a travelled way with normal cross slopes about the
centreline profile.
2. Revolving a travelled way with normal cross slope about the
inside-edge profile.
3. Revolving a travelled way with normal cross slopes about the
outside-edge profile.
4. Revolving a straight cross-slope travelled way around the
inside edge profile lines
SIGHT DISTANCE ON HORIZONTAL
CURVE
When a driver travels along a horizontal curve, his sight
distance is limited by a physical obstruction, such as
sidewall, slope or building, at the inside of the curve.
Figure below illustrates this point, where M is the offset
from the centre line of the inside lane to the
obstruction.
For design purpose, the stopping sight distance is the
length of curve along the centre line of the inside lane,
where the vehicle will be traveling or braking (with the
vehicle in full control).
SIGHT DISTANCE ON HORIZONTAL CURVE
SIGHT DISTANCE ON HORIZONTAL CURVE
SIGHT DISTANCE ON HORIZONTAL
CURVE
SIGHT DISTANCE ON HORIZONTAL CURVE
Example: A sound wall is to be constructed at
the edge of shoulder, along the inside of a
horizontal curve of an urban freeway. The inside
lane is 3.8 m wide, with a shoulder of 1.20 m.
The radius of the curve, measured up to the
outer edge of the shoulder is 45 m. Determine
the sight distance of this section of the curve
with the sound wall.
SIGHT DISTANCE ON HORIZONTAL CURVE
RADIUS OF HORIZONTAL CURVE
RADIUS OF HORIZONTAL CURVE
RADIUS OF HORIZONTAL CURVE
Example
HORIZONTAL TRANSITION CURVE
A transition curve differs from a circular curve in
that its radius is always changing.
Purpose of Transition Curves
• They Provide path for vehicle to move from
straight to a circular curve
• They Improve appearance of curve to driver
• They allow introduction of super elevation and
pavement widening
Example of horizontal alignments with and without
transition curves
Example of horizontal alignments with and without
transition curves(ctd)
Characteristics of Transition Curve
The transition curve must satisfy the following
characteristics:
• Should have constant rate of change of radius
of curvature
• Transition should be equal to zero at start of
straight and equal to radius of curvature at
circular curve
• Allows passengers to adjust to change in rate
of curvature
Functions of transition curve
• It provides a convenient length of road over which super
elevation and/or widening is applied,
• It can improve the appearance of a road, particularly on a
bridge where a rigid handrail follows the exact road
alignment,
• It can improve the appearance of the road where a curve is
visible in plan at the end of a long straight.
• It provides a length of road over which steering adjustment
can be made, particularly in reverse curve situations
• It provides a length of road over which speed adjustments
may be made between curves of different radii.
Forms of Transition Curves
• Clothoid – the one that we will examine in
more detail, most commonly used
• Lemniscate – used for large deflection angles
on high speed roads
• Cubic Parabola –unsuitable for large deflection
angles
Forms of Transition Curves
Calculation of Transition Length (Lp
or L)
Transition curves are normally of spiral
(clothoid) form
The length of plan transition (Lp or L) is
determined by
• The rate of change of radial acceleration.
• Rate of change of rotation of pavement
Radial Acceleration Method
• The length of a Transition Curve Required to
Minimise Passenger Discomfort is given by
Radial Acceleration Method
The value Radial acceleration C will vary with
design speed and design authority. Typical
values for C lie between (0.6 -0.3 m/sec3) for V
from 40-140km/hr respectively
• C = 0.6m/sec3 for V= 40km/hr to 70 km/hr
• C = 0.45m/sec3 for V= 80km/hr to 120 km/hr
• C = 0.3m/sec3 for V >120 km/hr
Radial Acceleration Method
A value above 0.6 can result in instability in the
vehicle while values less than 0.3 will lead to
excessively long transition curves leading to
general geometric difficulties. The design
process usually commences with an initial value
of 0.3 being utilised, with this value being
increased gradually if necessary towards its
upper ceiling.
Radial Acceleration Method
Radial Acceleration Method
Radial Acceleration Method
If a series of angles and chord lengths are used,
the spiral is the preferred form. If, as is the case
here, x and y co-ordinates are being used, then
any point on the transition curve can be
estimated using the following equation of the
curve which takes the form of a cubic parabola
(Figure below)
Generation of offset values for plotting a
transition curve
Solution
Table: Offsets at 10m intervals
Y X
10 0.0038
20 0.0304
30 0.1026
40 0.2431
50 0.4748
60 0.8205
70 1.303
80 1.945
Rate of change of rotation of pavement
Rate of change of rotation of
pavement
Minimum Lp or L = Le – 0.4V
Note: (e in %) and (V in km/h)
CURVE WIDENING(EXTRAWIDENING)
Extra widening refers to the additional width of
carriageway that is required on a curved section
of a road over and above that required on a
straight alignment.
Factors of extra widening
• Vehicles travelling on a curve occupy a greater
width of pavement than they do on a straight.
At low speeds the rear wheels track inside the
front wheels and at high speeds the rear
wheels track outside the front wheels.
• Vehicles tend to deviate more from the
centreline of the traffic lane on a curve than
on a straight.
Factors of extra widening
and Types of widening
• To maintain clearances between vehicles to
those on straight sections of road.
• Other factors, such as overhang of the front of
the vehicle, wheelbase and track width, also
contribute to the need for curve widening.
Types of widening
• Mechanical widening
• Psychological widening
Mechanical widening
The reasons for the mechanical widening are: When a
vehicle negotiates a horizontal curve, the rear wheels
follow a path of shorter radius than the front wheels as
shown in figure below. This phenomenon is called off-
tracking, and has the effect of increasing the effective
width of a road space required by the vehicle.
Therefore, to provide the same clearance between
vehicles traveling in opposite direction on curved roads
as is provided on straight sections, there must be extra
width of carriageway available.
Mechanical widening
Let R1 is the radius of the outer track line of the
rear wheel, R2 is the radius of the outer track
line of the front wheel l is the distance between
the front and rear wheel, n is the number of
lanes, then the mechanical widening Wm (refer
figure below) is derive below.
Therefore the widening needed for a single lane
road is:
If the road has n lanes, the extra widening
should be provided on each lane. Therefore, the
extra widening of a road with n lanes is given by
Please note that for large radius, R2 = R, which is
the mean radius of the curve, and then Wm is
given by:
Psychological widening
• Widening of pavements has to be done for
some psychological reasons also. There is a
tendency for the drivers to drive close to the
edges of the pavement on curves. Some extra
space is to be provided for more clearance for
the crossing and overtaking operations on
curves. An empirical relation for the
psychological widening at horizontal curves is
Wps
Total widening
Therefore, the total widening
needed at a horizontal curve is
Design of super-elevation
Design of super-elevation
EXERCISE:
A national road passing through a rolling terrain
has two horizontal curves of radius 450 m and
150 m. Design the required superelevation for
the curves if the ruling design speed is 80 kmph.
The coefficient of lateral friction f=0.15.
DESIGN OF VERTICAL ALIGNMENT
The purpose of vertical alignment design is to
determine the elevation of selected points along
the roadway, to ensure proper drainage, safety,
and ride comfort.
A vertical alignment is the elevation or profile of
the centre line of the road; it consists of grades,
and vertical curve
DESIGN OF VERTICAL ALIGNMENT ctd
Gradient and Vertical curves
Gradient
The gradient is the rate of rise or fall along the length of
the road with respect to the horizontal. It is expressed
as a ratio of 1 in x (1 vertical unit to x horizontal units)
sometimes the gradient is also expressed as a
percentage, n i.e n in 100.
Note that an uphill is expressed in a positive gradient
while a downhill is expressed in a negative gradient
A vertical curve provides a smooth transition between
two tangent grades. There are two types of vertical
curves: crest vertical curves and sag vertical curves
Vertical curves
A vertical curve starts at the point of vertical
curvature (PVC) and ends at the point of vertical
tangent (PVT). The length of road between PVC
and PVT is L: The initial and final grades are
denoted by G1 and G2; respectively, expressed in
%. Based on the equation of a parabolic curve,
the vertical offset y at any distance x from the
projected initial gradient is
Vertical curves
Vertical curves
Vertical curves
Example
A road must traverse a 6% followed by a -2%
grade. The length of the crest vertical curve is
2040 m. calculate the elevation for the first 600
m of the vertical curve at 100 m intervals, and
the highest point of the curve.
x
(m)
100 20
0
300 400 500
600
y
(m)
-
0.196
-
0.784
-
1.764
5
- 3.1375 -
4.902
-
7.0585
Criteria to be considered in calculate
minimum lengths of vertical curves
To calculate minimum lengths of vertical curves
one of the following will govern
• Sight distance
• Appearance criterion
• Comfort criterion:
Sight distance criterion on
Crest Vertical Curve
Example:
Which violates the assumption of L < S:
Therefore we should use L = 3214.29 m.
In vertical curve, for stopping sight distance, the
height of object is normally taken to be 0.150 m.
For passing sight distance, the height of object
used by AASHTO is 1.300 m. Height of eye is
assumed to be 1.070 m
SSD, Sag Vertical Curve
Figure below shows the driver’s sight limitation
when approaching a sag vertical curve. The
problem is more obvious during the night time
when the sight of the driver is restricted by the
area projected by the headlight beams of
his/her vehicle. Hence, the angle of the beam
from the horizontal plane is also important. This
design control criteria is known as headlight
sight distance.
Sag Vertical Curve, ctd
Comfort criterion
The curve length to satisfy this criterion is
usually about half the length that is needed to
meet the stopping sight distance criteria.
Appearance criterion:
• Minimum vertical curve standards for roads
may also be based on appearance.
• This problem arises because short vertical
curves tend to look like kinks when viewed
from a distance. Appearance standards vary
from agency to agency. Current California
standards, for instance, require a minimum
vertical curve length of 60 m where grade
breaks are less than 2 per cent or design
speeds are less than 60 km/h.
Where the grade break is greater than 2 per
cent and the design speed is greater than 60
km/h, the minimum vertical curve is given by L =
2V, where L in the vertical curve length in
meters and V is the design speed in km/h.
Sight Distance at under crossings
• Sight distance on the roadway that is the
lower tier of a grade separated intersection
should also consider obstruction of the sight
pose by the structure. Most of the roadways
at the lower tier of an interchange are
designed as sag vertical curves. Figure: below
illustrates a typical design situation.
• The general equation for a sag vertical curve length at an
undercrossing is
• Where C is the vertical clearance from the road surface to the
bottom of the obstructing structure.
• The above equations have several applications. In deciding the
length of the vertical curve for a given A; the design may select
the sight distance S to cater for, with appropriate h1 and h2 to
calculate L: The designed curve length should be at least L: On
other hand, given a designed curve length L; A and C; the
designer may check whether S satisfies the sight distance criteria
(with corresponding h1 and h2).
• Also, given L; A; S; h1 and h2; the designer may use these
equations to decide the minimum clearance C
Exercise:
• Determine the minimum length of curve required to connect a
descending 4% grade to an ascending 3% grade. The vertical
clearance should be 5.1 m and the required sight distance is 300
m. The height of eye for a commercial vehicle is 1.83 m and the
hazardous object is 0.46 m above the pavement surface.
• Solution: Given h1 =1.83 m, h2= 0.46 m, S=300 m, C= 5.1 m, G1 =
-4%; G2 = +3%
K Values for Vertical Curves
road INTERSECTIONS
Introduction
A road intersection is required to control conflicting
and merging streams of traffic so that delay is
minimized. This is achieved through choice of geo-
metric parameters that control and regulate the
vehicle paths through the intersection. These
determine priority so that all movements take place
with safety.
The three main types of junction dealt with in this
part are:
• Priority intersections
• Signalized intersections
• Roundabouts.
Major/minor priority intersections
A priority intersection occurs between two
roads; one termed the ‘major’ road and the
other the ‘minor’ road. The major road is the
one assigned a permanent priority of traffic
movement over that of the minor road. The
minor road must give priority to the major road
with traffic from it only entering the major road
when appropriate gaps appear. The principal
advantage of this type of junction is that the
traffic on the major route is not delayed.
Priority intersections can be in the form of simple T-junctions, staggered junctions or
crossroads, though the last form should be avoided where possible as drivers exiting
the minor road can misunderstand the traffic priorities. This may lead to increased
accidents
Simple junctions: A T-junction or staggered junction without any ghost or
physical islands in the major road and without channelling islands in the
minor road approach.
Ghost island junctions: Usually a T-junction or staggered junction within
which an area is marked on the carriageway, shaped and located so as to
direct traffic movement
Single lane dualling: Usually a T-junction or staggered junction within which
central reservation islands are shaped and located so as to direct traffic
movement
Mini-roundabout
Mini-roundabouts can be extremely successful in improving
existing urban junctions where side road delay and safety are a
concern
Mini-roundabouts consist of a 1-way circulatory carriageway
around a reflectorised, flush/slightly raised circular island less
than 4 m in diameter which can be overrun with ease by the
wheels of heavy vehicles. Mini- roundabouts are used
predominantly in urban areas with speed limits not exceeding
48 km/h (50 mph).
Normal roundabout
A normal roundabout is defined as a roundabout having a 1-
way circulatory carriageway around a kerbed central island at
least 4 m in diameter, with an inscribed circle diameter (ICD) of
at least 28 m and with flared approaches to allow for multiple
vehicle entry. The number of recommended entry arms is
either three or four. If the number is above four, the
roundabout becomes larger with the probability that higher
circulatory speeds will be generated. In such situations double
roundabouts may provide a solution
Double roundabout
A double roundabout can be defined as an individual junction
with two normal/mini-roundabouts either contiguous or
connected by a central link road or kerbed island.
• Other forms
Other roundabout
configurations include two-
bridge roundabouts, dumbbell
roundabouts, ring junctions and
signalised roundabouts.
End of Geometric Design

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Road Geometric Design-The alignment is the route of the road, defined as a series of horizontal tangents and curves.

  • 1. 2. GEOMETRIC DESIGN OF ROAD 2.1 Introduction to road alignment 2.2 Road cross sectional elements 2.3 Sight distance 2.4 Horizontal and vertical alignments 2.5. Road intersections
  • 2. Road Surveys and Location Selecting the location of a proposed road is an important initial step in its design. The decision to select a particular location is usually based on topography, soil characteristics, environmental factors such as noise and air pollution, and economic factors
  • 3. Principles of road location The road location process involves four phases: Office study of existing information Reconnaissance survey Preliminary location survey Final location survey
  • 4. Office Study of Existing Information The first phase in any road location study is the examination of all available data of the area in which the road is to be constructed . The type and amount of data collected and examined depend on the type of road being considered, but in general, data should be obtained on the following characteristics of the area.
  • 5. • Engineering, including topography, geology, climate, and traffic volumes • Social and demographic, including land use and zoning patterns • Environmental, including types of wildlife; location of recreational, historic, and archeological sites; and the possible effects of air, noise, and water pollution • Economic, including unit costs for construction and the trend of agricultural, commercial, and industrial activities At the completion of this phase of the study, the engineer will be able to select general areas through which the road can traverse
  • 6. Reconnaissance Survey The object of this phase of the study is to identify several feasible routes, each within a band of a limited width. Feasible routes are identified by a stereoscopic examination of the aerial photographs, taking into consideration factors such as: • Terrain and soil conditions •Serviceability of route to industrial and population areas • Crossing of other transportation facilities, such as rivers, railroads, and roads • Directness of route Control points between the two endpoints are determined for each feasible route. For example, a unique bridge site with no alternative may be taken as a primary control point. The feasible routes identified are then plotted on photographic base maps.
  • 7. 3 Preliminary Location Survey During this phase of the study, the positions of the feasible routes are set as closely as possible by establishing all the control points and determining preliminary vertical and horizontal alignments for each. Preliminary alignments are used to evaluate the economic and environmental feasibility of the alternative routes.
  • 8. Economic Evaluation Economic evaluation of each alternative route is carried out to determine the future effect of investing the resources necessary to construct the road Factors usually taken into consideration include road user costs, construction costs, maintenance costs, road user benefits, and any disbenefits, which may include adverse impacts due to dislocation of families, businesses, and so forth
  • 9. For example, these results will provide information on the economic resources that will be gained or lost if a particular location is selected. This information is also used to aid the policy maker in determining whether the road should be built, and if so, what type of road it should be.
  • 10. Environmental Evaluation A road is therefore an integral part of the local environment and must be considered as such. This environment includes plant, animal, and human communities and encompasses social, physical, natural, and man-made variables. The construction of a road at a given location may result in significant changes in one or more variables, which in turn may offset the equilibrium and result in significant adverse effects on the environment
  • 11. The environmental impact statements should include: • A detailed description of alternatives • The probable environmental impact, including the assessment of positive and negative effects • An analysis of short-term impact as differentiated from long-term impact • Any secondary effects, which may be in the form of changes in the patterns of social and economic activities • Probable adverse environmental effects that cannot be avoided if the project is constructed • Any irreversible and irretrievable resources that have been committed
  • 12. In cases where an environmental impact study is required, it is conducted at this stage to determine the environmental impact of each alternative route. Such a study will determine the negative and/or positive effects the road facility will have on the environment For example, the construction of a freeway at grade through an urban area may result in an unacceptable noise level for the residents of the area (negative impact), or the road facility may be located so that it provides better access to jobs and recreation centers (positive impact)
  • 13. Preliminary Location Survey Environmental Evaluation Public hearings are also held at this stage to provide an opportunity for constituents to give their views on the positive and negative impacts of the proposed alternatives. The best alternative, based on all the factors considered, is then selected as the preliminary alignment of the road
  • 14. Final Location Survey The final location survey is a detailed layout of the selected route. The horizontal and vertical alignments are determined, and the positions of structures and drainage channels are located. Detailed design of the vertical and horizontal alignments is then carried out to obtain both the deflection angles for horizontal curves and the cuts or fills for vertical curves and straight sections of the road.
  • 15. ROAD SURVEY METHODS Surveying techniques can be grouped into three general categories: • Ground surveys • Remote sensing • Computer graphics Ground surveys are the basic location technique for roads. The total station is used for measuring angles in both vertical and horizontal planes, distances, and changes in elevation through the use of trigonometric levels; the level is used for measuring changes in elevation only .
  • 16. Remote sensing Remote sensing is the measurement of distances and elevations by using devices located above the earth, such as airplanes or orbiting satellites using Global Positioning Satellite systems (GPS). The most commonly used remote-sensing method is photogrammetry, which utilizes aerial photography
  • 17. Computer Graphics Computer graphics, when used for road location, is usually the combination of photogrammetry and computer techniques. With the use of mapping software, line styles, and feature tables, objects and photographic features can be recorded digitally and stored in a computer file. This file can then either be plotted out in map form or sent on to the design unit.
  • 18. Factors controlling alignment • Obligatory points • Traffic • Geometric design • Economy • Other consideration (Drainage, political, monotony)
  • 19. Geometric Design of road Facilities Geometric design deals with the dimensioning of the elements of roads, such as vertical and horizontal curves, cross sections, truck climbing lanes, bicycle paths, and parking facilities.
  • 20. FACTORS INFLUENCING road DESIGN Road design is based on specified design standards and controls which depend on the following roadway system factors: • Functional classification • Design hourly traffic volume and vehicle mix • Design speed • Design vehicle • Cross section of the road, such as lanes, shoulders, and medians • Presence of heavy vehicles on steep grades • Topography of the area that the road traverses • Level of service • Available funds • Safety • Social and environmental factors
  • 21. ROAD CROSS SECTION ELEMENTS
  • 22. Cross slope or Camber Cross slope or camber is the slope provided to the road surface in the transverse direction to drain off the rain water from the road surface. The cross slope is provided because of the following reasons: • To prevent the entry of water into the bituminous pavement layers • To prevent the entry of surface water into the subgrade soil through pavement. • To remove the rain water from the pavement surface as quickly as possible and to allow the pavement to get dry soon after the rain
  • 23. Cross slope or Camber The required camber of pavement depends on; The type of pavement surface The amount of rainfall Recommended rates of cross slopes are 1.5 to 2.5 percent for high-type pavements and 2 to 6 percent for low-type pavements. High-type pavements have wearing surfaces that can adequately support the expected traffic load without visible distress due to fatigue and are not susceptible to weather conditions. Low-type pavements are used mainly for low-cost roads and have wearing surfaces ranging from untreated loose material to surface-treated earth. .
  • 24. Width of pavement or carriageway The width of carriageway for various classes of roads standardized by IRC (Indian Roads Congress) are given in the table below Class of road Width of carriageway 1 Single lane 3.75m 2 Two lanes without raised kerbs 7.0m 3 Two lanes with raised kerbs 7.5m 4 Intermediate carriageway 5.5m 5 Multi-lane pavement 3.5/lane
  • 25. Curbs (Am: Kerbs) • Curb indicates the boundary between the pavement and shoulder or sometimes islands; foot path or parking space. Curbs may be mainly divided into 3 groups based on their functions • Low or mountable curb which encourage traffic to remain in the through traffic lanes. The height of this type of shoulder curbs is about 10cm above the pavement edge with a slope (or batter) to help vehicles climb the curb easily
  • 26. Curbs (Am: Kerbs) ctd • ii. Semi barrier provided on the roadway where the pedestrian traffic is high. This type of curbs has a height of about 15cm above the pavement edge with a batter of 1:1 on the top 7.5cm • iii. Barrier kerb is provided in built up area adjacent to foot path with considerable pedestrian traffic. The height of stone is about 20cm above the pavement edge with a steep batter of 1 vertical 0.25 horizontal.
  • 27. Sight distance • Sight distance is the roadway ahead that is visible to the driver. Various sight distance criteria exist in road geometric design to provide drivers with sufficient warning of potential obstacle or conflict ahead. • Stopping Sight Distance • Decision Sight Distance • Passing Sight Distance on Two-Lane Road Criteria for Measuring Sight Distance The Sight Distance is dependent on the height of the driver’s eye above the road surface, the object height (or size) above the road surface, and the height and lateral position of sight obstructions within the driver’s line of sight. These have effect on the design of horizontal and vertical curve
  • 28. Stopping Sight Distance Where: SSD = Stopping sight distance (m) BRD = Brake Reaction Distance (m) = vt BD = Braking Distance (m) = v2/2gf V = Design speed t = time f = Coefficient of friction g = Gravity acceleration
  • 29. Stopping Sight Distance When we have an ascending or a descending grade SSD = vt + v2/2g(f+n%) Where: V = Design speed t = time f = Coefficient of friction g = Gravity acceleration n = is the grade (negative when descending, positive when ascending)
  • 31.
  • 32. 3. While descending a -7% grade at a speed of 90 km/h, George notices a large object in the roadway ahead of him. Without thinking about any alternatives, George stabs his brakes and begins to slow down. Assuming that George is so paralyzed with fear that he won't engage in an avoidance maneuver, calculate the minimum distance at which George must have seen the object in order to avoid colliding with it . You can assume that the roadway surface is concrete and that the surface is wet so that the coefficient of friction was 0.29 . You can also assume that George has a brake reaction time of 0.9 seconds because he is always alert on this stretch of the road.
  • 33. Solution First, we need to calculate the distance that George traveled during his brake reaction time. This is done using the equation D = VT from physics. Since George's brake reaction time was 0.9 seconds and his velocity was 25 m/sec (90 km/h), the distance he traveled during his brake reaction time was 22.5 meters. Second, we need to calculate the distance George will travel while braking. This is done using the equation shown below. d = V2/(2g(f + G))
  • 34. Where: V = George's Velocity, 25 m/sec (90 km/h) g = Acceleration due to gravity, 9.81 m/sec2 f = Coefficient of friction, 0.29 ( we'll use the value for 96 km/h (60 mph) just to be conservative) G = The grade of the road, -0.07 (-7%) Solving the equation yields a distance of 145 meters. Summing the distance traveled while braking and the distance traveled during the brake reaction time yields a total stopping sight distance of 168 meters. George needed to be about 168 meters away from the object at the instant he first saw it in order to avoid a collision
  • 35. Design of horizontal alignment • The horizontal alignment includes the straight (tangent) sections of the roadway and the circular curves that connect their change in direction. • The plan view gives the horizontal alignment of a road. The length of the road is measured along the plan view, on a horizontal plane. • The objectives of horizontal alignment design is to provide a smooth transition between two straight road sections that also provide proper cross sectional drainage, ensure vehicle/driver safety while traveling at a design speed
  • 36. Various design factors to be considered in the horizontal alignment are: Design speed; Radius of circular curves, types and length of transition curves, superelevation and widening of pavement on curves Design speed (is the speed selected to be used in the design calculations ) The design speed of roads depends upon • Class of the road • Terrain Terrain classification (IRC) Cross slope of country per cent Plain 0-10 Rolling 10-25 Mountainous 25-60 Steep Greater than 60
  • 37. Terrain classification according to overseas road note 6 • Level (0-10 five metre ground contours per kilometre). Level or gently rolling terrain with largely unrestricted horizontal and vertical alignment. Minimum values of alignment will rarely be necessary. Roads will, for the most part, follow the ground contours and amounts of cut and fill will be very small. • Rolling (11-25 five metre ground contours per kilometre). Rolling terrain with low hills introducing moderate levels of rise and fall with some restrictions on vertical alignment. Whilst low standard roads will be able to follow the ground contours with small amounts of cut and fill, the higher standards will require more substantial amounts. • Mountainous (Greater than 25 five metre ground contours per kilometre). Rugged, hilly and mountainous with substantial restrictions in both horizontal and vertical alignment. Higher standard roads will generally require large amounts of cut and fill
  • 38. ROAD TYPE TERRAIN DESIGN SPEED (Km/h) Primary road (National, Expressway) 1.Flat area 80-110 2. Hilly 55-80 3.Mountainous 40-55 Secondary road (State, district roads ) 1.Flat area 60-80 2. Hilly 50-60 3.Mountainous 35-50 Tertiary roads (Village, others ) 1.Flat area 50-60 2. Hilly 35-50 3.Mountainous 25-35
  • 40.
  • 41.
  • 42. SUPER ELEVATION Super elevation. Super elevation is the amount of cross slope or "bank" provided on a horizontal curve to help counterbalance the outward pull of a vehicle traversing the curve. The maximum rate of super elevation (emax) depends on several factors including climatic conditions, terrain conditions and type of area (rural or urban).
  • 43.
  • 44. • 1.Super elevation Transition Length/ development Length. The super elevation transition length is the distance required to transition the roadway from a normal crown section to the full super elevation needed. Super elevation transition length is the sum of the tangent run out and super elevation runoff. • 2. Tangent Run out/runoff. AASHTO defines tangent run out as the change from a normal crown section to a point where the adverse cross slope of the outside lane or lanes is removed (i.e., the outside lane(s) is level). • 3. Super elevation Runoff. AASHTO defines super elevation runoff as the change in cross slope from the end of tangent run out (adverse crown removed) to a section that is fully super elevated.
  • 45. • 4.Axis of Rotation. The super elevation axis of rotation is the line about which the pavement is revolved to super elevate the roadway. This line will maintain the normal road profile throughout the curve, and it is known as the construction centreline or control edge. • 5. Super elevation Rollover. Super elevation "rollover" is the algebraic difference between the travel lane cross slope and shoulder cross slope on the outside of a horizontal curve. • 6. Normal Crown (NC): The typical cross section on a tangent section (i.e., no super elevation). • 7. Remove Crown (RC): A super elevated cross section which is sloped across the entire travelled way in the same direction and at a rate equal to the typical cross slope on a tangent section (e.g., 2.0%)
  • 46. Super elevation attainment • The available options for rotating travelled ways to attain super elevation are graphically shown in Figures A to D below. These are: 1. Revolving a travelled way with normal cross slopes about the centreline profile. 2. Revolving a travelled way with normal cross slope about the inside-edge profile. 3. Revolving a travelled way with normal cross slopes about the outside-edge profile. 4. Revolving a straight cross-slope travelled way around the inside edge profile lines
  • 47.
  • 48. SIGHT DISTANCE ON HORIZONTAL CURVE When a driver travels along a horizontal curve, his sight distance is limited by a physical obstruction, such as sidewall, slope or building, at the inside of the curve. Figure below illustrates this point, where M is the offset from the centre line of the inside lane to the obstruction. For design purpose, the stopping sight distance is the length of curve along the centre line of the inside lane, where the vehicle will be traveling or braking (with the vehicle in full control).
  • 49. SIGHT DISTANCE ON HORIZONTAL CURVE
  • 50. SIGHT DISTANCE ON HORIZONTAL CURVE
  • 51. SIGHT DISTANCE ON HORIZONTAL CURVE
  • 52. SIGHT DISTANCE ON HORIZONTAL CURVE Example: A sound wall is to be constructed at the edge of shoulder, along the inside of a horizontal curve of an urban freeway. The inside lane is 3.8 m wide, with a shoulder of 1.20 m. The radius of the curve, measured up to the outer edge of the shoulder is 45 m. Determine the sight distance of this section of the curve with the sound wall.
  • 53. SIGHT DISTANCE ON HORIZONTAL CURVE
  • 58. HORIZONTAL TRANSITION CURVE A transition curve differs from a circular curve in that its radius is always changing. Purpose of Transition Curves • They Provide path for vehicle to move from straight to a circular curve • They Improve appearance of curve to driver • They allow introduction of super elevation and pavement widening
  • 59. Example of horizontal alignments with and without transition curves
  • 60. Example of horizontal alignments with and without transition curves(ctd)
  • 61. Characteristics of Transition Curve The transition curve must satisfy the following characteristics: • Should have constant rate of change of radius of curvature • Transition should be equal to zero at start of straight and equal to radius of curvature at circular curve • Allows passengers to adjust to change in rate of curvature
  • 62. Functions of transition curve • It provides a convenient length of road over which super elevation and/or widening is applied, • It can improve the appearance of a road, particularly on a bridge where a rigid handrail follows the exact road alignment, • It can improve the appearance of the road where a curve is visible in plan at the end of a long straight. • It provides a length of road over which steering adjustment can be made, particularly in reverse curve situations • It provides a length of road over which speed adjustments may be made between curves of different radii.
  • 63.
  • 64.
  • 65. Forms of Transition Curves • Clothoid – the one that we will examine in more detail, most commonly used • Lemniscate – used for large deflection angles on high speed roads • Cubic Parabola –unsuitable for large deflection angles
  • 67. Calculation of Transition Length (Lp or L) Transition curves are normally of spiral (clothoid) form The length of plan transition (Lp or L) is determined by • The rate of change of radial acceleration. • Rate of change of rotation of pavement
  • 68.
  • 69. Radial Acceleration Method • The length of a Transition Curve Required to Minimise Passenger Discomfort is given by
  • 70. Radial Acceleration Method The value Radial acceleration C will vary with design speed and design authority. Typical values for C lie between (0.6 -0.3 m/sec3) for V from 40-140km/hr respectively • C = 0.6m/sec3 for V= 40km/hr to 70 km/hr • C = 0.45m/sec3 for V= 80km/hr to 120 km/hr • C = 0.3m/sec3 for V >120 km/hr
  • 71. Radial Acceleration Method A value above 0.6 can result in instability in the vehicle while values less than 0.3 will lead to excessively long transition curves leading to general geometric difficulties. The design process usually commences with an initial value of 0.3 being utilised, with this value being increased gradually if necessary towards its upper ceiling.
  • 74. Radial Acceleration Method If a series of angles and chord lengths are used, the spiral is the preferred form. If, as is the case here, x and y co-ordinates are being used, then any point on the transition curve can be estimated using the following equation of the curve which takes the form of a cubic parabola (Figure below)
  • 75. Generation of offset values for plotting a transition curve
  • 76.
  • 77.
  • 78.
  • 80.
  • 81. Table: Offsets at 10m intervals Y X 10 0.0038 20 0.0304 30 0.1026 40 0.2431 50 0.4748 60 0.8205 70 1.303 80 1.945
  • 82. Rate of change of rotation of pavement
  • 83. Rate of change of rotation of pavement Minimum Lp or L = Le – 0.4V Note: (e in %) and (V in km/h)
  • 84. CURVE WIDENING(EXTRAWIDENING) Extra widening refers to the additional width of carriageway that is required on a curved section of a road over and above that required on a straight alignment.
  • 85. Factors of extra widening • Vehicles travelling on a curve occupy a greater width of pavement than they do on a straight. At low speeds the rear wheels track inside the front wheels and at high speeds the rear wheels track outside the front wheels. • Vehicles tend to deviate more from the centreline of the traffic lane on a curve than on a straight.
  • 86. Factors of extra widening and Types of widening • To maintain clearances between vehicles to those on straight sections of road. • Other factors, such as overhang of the front of the vehicle, wheelbase and track width, also contribute to the need for curve widening. Types of widening • Mechanical widening • Psychological widening
  • 87. Mechanical widening The reasons for the mechanical widening are: When a vehicle negotiates a horizontal curve, the rear wheels follow a path of shorter radius than the front wheels as shown in figure below. This phenomenon is called off- tracking, and has the effect of increasing the effective width of a road space required by the vehicle. Therefore, to provide the same clearance between vehicles traveling in opposite direction on curved roads as is provided on straight sections, there must be extra width of carriageway available.
  • 89. Let R1 is the radius of the outer track line of the rear wheel, R2 is the radius of the outer track line of the front wheel l is the distance between the front and rear wheel, n is the number of lanes, then the mechanical widening Wm (refer figure below) is derive below.
  • 90. Therefore the widening needed for a single lane road is: If the road has n lanes, the extra widening should be provided on each lane. Therefore, the extra widening of a road with n lanes is given by Please note that for large radius, R2 = R, which is the mean radius of the curve, and then Wm is given by:
  • 91. Psychological widening • Widening of pavements has to be done for some psychological reasons also. There is a tendency for the drivers to drive close to the edges of the pavement on curves. Some extra space is to be provided for more clearance for the crossing and overtaking operations on curves. An empirical relation for the psychological widening at horizontal curves is Wps
  • 92. Total widening Therefore, the total widening needed at a horizontal curve is
  • 94. Design of super-elevation EXERCISE: A national road passing through a rolling terrain has two horizontal curves of radius 450 m and 150 m. Design the required superelevation for the curves if the ruling design speed is 80 kmph. The coefficient of lateral friction f=0.15.
  • 95. DESIGN OF VERTICAL ALIGNMENT The purpose of vertical alignment design is to determine the elevation of selected points along the roadway, to ensure proper drainage, safety, and ride comfort. A vertical alignment is the elevation or profile of the centre line of the road; it consists of grades, and vertical curve
  • 96. DESIGN OF VERTICAL ALIGNMENT ctd
  • 97. Gradient and Vertical curves Gradient The gradient is the rate of rise or fall along the length of the road with respect to the horizontal. It is expressed as a ratio of 1 in x (1 vertical unit to x horizontal units) sometimes the gradient is also expressed as a percentage, n i.e n in 100. Note that an uphill is expressed in a positive gradient while a downhill is expressed in a negative gradient A vertical curve provides a smooth transition between two tangent grades. There are two types of vertical curves: crest vertical curves and sag vertical curves
  • 98.
  • 99. Vertical curves A vertical curve starts at the point of vertical curvature (PVC) and ends at the point of vertical tangent (PVT). The length of road between PVC and PVT is L: The initial and final grades are denoted by G1 and G2; respectively, expressed in %. Based on the equation of a parabolic curve, the vertical offset y at any distance x from the projected initial gradient is
  • 102. Vertical curves Example A road must traverse a 6% followed by a -2% grade. The length of the crest vertical curve is 2040 m. calculate the elevation for the first 600 m of the vertical curve at 100 m intervals, and the highest point of the curve.
  • 103. x (m) 100 20 0 300 400 500 600 y (m) - 0.196 - 0.784 - 1.764 5 - 3.1375 - 4.902 - 7.0585
  • 104.
  • 105. Criteria to be considered in calculate minimum lengths of vertical curves To calculate minimum lengths of vertical curves one of the following will govern • Sight distance • Appearance criterion • Comfort criterion:
  • 106. Sight distance criterion on Crest Vertical Curve
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  • 109.
  • 110. Which violates the assumption of L < S: Therefore we should use L = 3214.29 m. In vertical curve, for stopping sight distance, the height of object is normally taken to be 0.150 m. For passing sight distance, the height of object used by AASHTO is 1.300 m. Height of eye is assumed to be 1.070 m
  • 111. SSD, Sag Vertical Curve Figure below shows the driver’s sight limitation when approaching a sag vertical curve. The problem is more obvious during the night time when the sight of the driver is restricted by the area projected by the headlight beams of his/her vehicle. Hence, the angle of the beam from the horizontal plane is also important. This design control criteria is known as headlight sight distance.
  • 113.
  • 115.
  • 116. The curve length to satisfy this criterion is usually about half the length that is needed to meet the stopping sight distance criteria.
  • 117. Appearance criterion: • Minimum vertical curve standards for roads may also be based on appearance. • This problem arises because short vertical curves tend to look like kinks when viewed from a distance. Appearance standards vary from agency to agency. Current California standards, for instance, require a minimum vertical curve length of 60 m where grade breaks are less than 2 per cent or design speeds are less than 60 km/h.
  • 118. Where the grade break is greater than 2 per cent and the design speed is greater than 60 km/h, the minimum vertical curve is given by L = 2V, where L in the vertical curve length in meters and V is the design speed in km/h.
  • 119. Sight Distance at under crossings • Sight distance on the roadway that is the lower tier of a grade separated intersection should also consider obstruction of the sight pose by the structure. Most of the roadways at the lower tier of an interchange are designed as sag vertical curves. Figure: below illustrates a typical design situation.
  • 120. • The general equation for a sag vertical curve length at an undercrossing is • Where C is the vertical clearance from the road surface to the bottom of the obstructing structure. • The above equations have several applications. In deciding the length of the vertical curve for a given A; the design may select the sight distance S to cater for, with appropriate h1 and h2 to calculate L: The designed curve length should be at least L: On other hand, given a designed curve length L; A and C; the designer may check whether S satisfies the sight distance criteria (with corresponding h1 and h2). • Also, given L; A; S; h1 and h2; the designer may use these equations to decide the minimum clearance C
  • 121. Exercise: • Determine the minimum length of curve required to connect a descending 4% grade to an ascending 3% grade. The vertical clearance should be 5.1 m and the required sight distance is 300 m. The height of eye for a commercial vehicle is 1.83 m and the hazardous object is 0.46 m above the pavement surface. • Solution: Given h1 =1.83 m, h2= 0.46 m, S=300 m, C= 5.1 m, G1 = -4%; G2 = +3%
  • 122. K Values for Vertical Curves
  • 123. road INTERSECTIONS Introduction A road intersection is required to control conflicting and merging streams of traffic so that delay is minimized. This is achieved through choice of geo- metric parameters that control and regulate the vehicle paths through the intersection. These determine priority so that all movements take place with safety. The three main types of junction dealt with in this part are: • Priority intersections • Signalized intersections • Roundabouts.
  • 124. Major/minor priority intersections A priority intersection occurs between two roads; one termed the ‘major’ road and the other the ‘minor’ road. The major road is the one assigned a permanent priority of traffic movement over that of the minor road. The minor road must give priority to the major road with traffic from it only entering the major road when appropriate gaps appear. The principal advantage of this type of junction is that the traffic on the major route is not delayed.
  • 125. Priority intersections can be in the form of simple T-junctions, staggered junctions or crossroads, though the last form should be avoided where possible as drivers exiting the minor road can misunderstand the traffic priorities. This may lead to increased accidents
  • 126. Simple junctions: A T-junction or staggered junction without any ghost or physical islands in the major road and without channelling islands in the minor road approach.
  • 127. Ghost island junctions: Usually a T-junction or staggered junction within which an area is marked on the carriageway, shaped and located so as to direct traffic movement
  • 128. Single lane dualling: Usually a T-junction or staggered junction within which central reservation islands are shaped and located so as to direct traffic movement
  • 129. Mini-roundabout Mini-roundabouts can be extremely successful in improving existing urban junctions where side road delay and safety are a concern Mini-roundabouts consist of a 1-way circulatory carriageway around a reflectorised, flush/slightly raised circular island less than 4 m in diameter which can be overrun with ease by the wheels of heavy vehicles. Mini- roundabouts are used predominantly in urban areas with speed limits not exceeding 48 km/h (50 mph).
  • 130. Normal roundabout A normal roundabout is defined as a roundabout having a 1- way circulatory carriageway around a kerbed central island at least 4 m in diameter, with an inscribed circle diameter (ICD) of at least 28 m and with flared approaches to allow for multiple vehicle entry. The number of recommended entry arms is either three or four. If the number is above four, the roundabout becomes larger with the probability that higher circulatory speeds will be generated. In such situations double roundabouts may provide a solution
  • 131. Double roundabout A double roundabout can be defined as an individual junction with two normal/mini-roundabouts either contiguous or connected by a central link road or kerbed island.
  • 132. • Other forms Other roundabout configurations include two- bridge roundabouts, dumbbell roundabouts, ring junctions and signalised roundabouts.
  • 133. End of Geometric Design