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# Vertical alignment of highways

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summit curves and valley curves. design of vertical alignment. length of vertical curves. gate previous questions on vertical curves.

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### Vertical alignment of highways

1. 1. www.justbtech.com Vertical Alignment
2. 2. Mainly 2 components Gradient Ruling Exceptional Limiting Vertical Curves Summit Curves Valley Curves
3. 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. 4. Vertical Curves – Summit Curve
5. 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. 6. Design Parameters for Length  Sight Distance Stopping Sight Distance Overtaking Sight Distance  Centrifugal Force Acts Upwards Counteracted by weight of vehicle
7. 7. Summit Curve – S < L
8. 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. 9. Summit Curve = S > L
10. 10. Valley Curves  Convexity Downwards  Different types like summit curves
11. 11. Valley curves - types
12. 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. 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. 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. 15. Based on SD = SD <L
16. 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. 17. Length - SD > L
18. 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. 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. 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. 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. 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. 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. 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. 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. 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. 27. Pavement Vertical Cross-Section  Embankment  Subgrade  Subbase  Base  Wearing Course + Shoulders
28. 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. 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. 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. 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. 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. 33. ThankYou