The document discusses various aspects of vertical alignment in transportation infrastructure design and construction. It covers key components like gradient and ruling, the effects of gradient on vehicle resistance, and the design of vertical curves including summit and valley curves. Design parameters discussed include sight distance, centrifugal force, and length determination based on these factors. Equations are provided for calculating curve length and heights. The document also includes examples of previous questions asked on these topics in civil engineering examinations.

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Vertical Alignment

2. Mainly 2 components
Gradient
Ruling
Exceptional
Limiting
Vertical Curves
Summit Curves
Valley Curves

3. Effects of Gradient
 Resistance to the vehicles
 Grade resistance
 Grade Compensation
 According to IRC
(30+R)/R %
Maximum Compensation = 75/R %
Not required on flat gradients i.e., <
4%

4. Vertical Curves – Summit Curve

5. Shape of Summit Curve
 Circular
 Equal Sight distance at all points
 Most Ideal
 Parabola
 Good riding comfort
 Calculation of ordinates
 Laying out on ground
 Most preferred
 For small deviation angles above shapes doesn’t
make substantial difference

6. Design Parameters for Length
 Sight Distance
Stopping Sight Distance
Overtaking Sight Distance
 Centrifugal Force
Acts Upwards
Counteracted by weight of vehicle

7. Summit Curve – S < L

8.  Y = ax
 a = N/2L
 h1 = aS12
 h2 = aS22
 S1 = √h1/a
 S1 = √h2/a
 S = h1+h2
 L = NS2/2(√h1+√h2)2

9. Summit Curve = S > L

10. Valley Curves
 Convexity Downwards
 Different types like summit curves

11. Valley curves - types

12. Design Parameters
 Daytime – No Problem
 SD reduces at night
 SSD under head lights
 CF acts downwards
 W acts downwards
 From the above
 Impact free movement of vehicles
 Availability of SSD
 Transition curves – for safely introducing C.F (P)
 Cubic Parabola shape is preferred

13. Length
 2 transition curves of equal length
 Y = bX3
 b= 2N/3L2
 Allowable rate of change of acceleration =
0.6m/s2
 Adequate sight distance

14. Length - Based on C.F
Acceleration
 C = ((v2 /R) – 0) /t
 t = Ls/v
 From the above
 Ls = v3 / cR
 But for Cubic Parabola,
 R = Ls/N
 Hence, Ls = √(Nv3 /c)
 Required L = 2Ls
 N – deviation angle in radian, c = c.f acceleration,
v = m/s

15. Based on SD = SD <L

16. Length – SD < L
 Available SD is minimum at Lowest Point
 Also it is start of transition curve
 In the above Formula,
 h1 = height of headlight beam (0.75m)
 α = head beam inclination in degrees (approx 1 degree)
 S = Sight dist


17. Length - SD > L

18. Length - SD > L
 Beginning and Ending Points of the curve
 SD Varies in both Cases
 SD calculated assuming vehicle is at beginning of
the curve.

19. GATE 2015 Questions
 A vehicle is moving in a circular curve and it has a
super elevation of e when it does not slide
inwards. When friction factor is f (A) e f ≤ (B) e f ≥
(C) e f = (D) Cannot be determined
 Which of these statements is false?
(1) Plumb line is along direction of gravity
(2) Mean Sea Level in reference surface for
establishing horizontal control
(3) Mean Sea Level is simplification of geoid
(4) Geoid is an equi potential surface of gravity

20.  For a portion of highway descending gradient 1 in 25
meets an ascending gradient 1 in 20. A valley curve
needs to be designed at a velocity of 90 kmph based
on (i) Head light sight distance equal to stopping sight
distance of a level terrain. Consider length of curve >
SSD (ii) Comfort condition if rate of change of
acceleration is 3 0.5 m / s Reaction time = 2.5 sec,
coefficient of longitudinal friction µ = 0.35. Height of
head light = 0.75 m, and beam angle o = 1 48.
 What is the length of valley curve as per headlight
sight distance?
 What is the length of valley curve (in meter) based on
comfort condition?
 Ans: 308, 106

21.  While designing a hill road with a ruling gradient
of 6%, if a sharp horizontal curve of 50m radius is
encountered, the compensated gradient at the
curve as per the Indian Roads Congress
specifications should be (A) 4.4% (B) 4.75% (C)
5.0% (D) 5.25%
 A road is provided with a horizontal circular curve
having deflection angle 550 and centre line radius
of 250m. A transition curve is to be provided at
each end of the circular curve of such a length
that the rate of gain of radial acceleration is
0.3m/s3 at a curve required at each of the ends is
(A) 2.57m (B) 33.33m (C) 35.73m (D) 1666.67m

22.  A horizontal circular curve with a centre line
radius of 200m is provided on a 2-lane, 2- way
SH section. The width of the 2-lane road is 7.0m.
Design speed for this section is 80 km per hour.
The brake reaction time is 2.4s, and the
coefficients of friction in longitudinal and lateral
directions are 0.355 and 0.15, respectively.
 The safe stopping sight distance on the section is
(A) 221m (B) 195m (C) 125m (D) 65m
 The set-back distance from the centre line of the
inner lane is (A) 7.93m (B) 8.10m (C) 9.60m (D)
9.77m

23. GATE PREVIOUS QUESTIONS
 A rest vertical curve joins two gradients of +3%
and -2% for a design speed of 80km/h and the
corresponding stopping sight distance of 120m.
The height of driver’s eye and the object above
the road surface are 1.20m and 0.15m
respectively. The curve length (which is less than
stopping sight distance) to be provided is
 (A) 120m (B) 152m (C) 163m (D) 240m

24.  The length of Summit Curve on a two lane two
way highway depends upon (A) Allowable rate of
change of centrifugal acceleration (B) Coefficient
of lateral friction (C) Required Stopping Sight
Distance (D) Required Overtaking Sight Distance

25.  1. A valley curve is formed by descending gradient
n1= 1 in 25 and ascending gradient n2= 1 in 30.
Design the length of the valley curve for V =80kmph.
(Hint: c=0.6 m/cm3)
 2. A vertical summit curve is formed by n1 = +3.0%
and n2 = −5.0%. Design the length of the summit
curve for V=80 kmph.
 3. n1 = +1/50 and n2 = −1/80, SSD=180m,
OSD=640m. Due to site constraints, L is limited to
500m. Calculate the length of summit curve to meet
SSD, ISD and OSD. Discuss results.
 1. c=0.6 m/cm3 , SSD=127.3m), L=max(73.1,199.5)
 2. SSD=128m), L = 298m
 3. L for SSD=240m, okay, L for OSD=1387m, > 500m
not ok, L for ISD=439m ok

26. Pavement Materials
 Objectives
 Understanding Different types of materials for
different types of pavements
 Different parameters for selecting the material
 Properties of Soil used for pavement design
 Testing and Evaluation of Pavement materials

27. Pavement Vertical Cross-Section
 Embankment
 Subgrade
 Subbase
 Base
 Wearing Course + Shoulders

28. Pavement Materials
 Variety of materials
 Soil
 Aggregates
 Bitumen
 Concrete
 Binders
 Geotextiles
 Etc
 Materials, Properties and Interaction b/w them
decides properties of pavement.
 Durability and Stability are affected

29. Pavement materials
 Soil
 Deposit of earth material formed by disintegration of
rocks etc.
 Used in Embankment, Subgrade
 Aggregates used in sub base and base
 Binders
 Bituminous mixes – aggregates+ Bitumen +
binders
 In concrete pavements – Cement + reinforcement
etc
 Recycled materials

30. Why Study?
 Understand the behaviour individually and in
combination
 Characterize
 Classify/Grade
 For design purpose
 Study the condition of existing pavement
 Quality control
 Tests are conducted to ensure quality during pre and post
construction phases.
 Lab tests on representative samples
 Field tests
 Estimation

31. Parameters considered for
characterization
 Loads
 Stationary/ Moving
 Heavy/Light
 Application mode
 Climatic conditions
 Temperature, Rainfall, Moisture
 Weathering Action
 Behaviour under cyclic nature
 Wetting/Drying, Chemical Action, Freezing etc

32. Soil
 Used in Embankment, Subgrade, Shoulders
 Natural form or stabilized form
 Classified based on the particle size distribution
and index properties
 IS Soil Classification
 Course Grained 50% > 0.075mm sieve
 Fine Grained - Viceversa
 Gravel – 80 to 4.75 mm
 Sand – 4.75 to 0.075mm
 Silt and Clay < 0.075mm

33. ThankYou