Vertical Alignment. Concepts of design & guidelines Computing elevations along vertical curves Designing vertical curves

Transcription

1 Vertical Alignment Concepts of design & guidelines Computing elevations along vertical curves Designing vertical curves

2 Flat terrain You can select smooth horizontal alignment and smooth vertical alignment

3 Rolling terrain It is relatively easy to find a good alignment in rolling terrain

4 Mountainous terrain Relatively difficult to find good alignment Loose material on cut side slope

5 Mountainous terrain Extremely difficult to find good alignment in hilly areas

6 Mountainous terrain Extremely difficult to find good alignment in hilly areas

7 Sand dune areas It is difficult to design an alignment in sand dune areas

8 Main topics Main concepts in selecting a vertical alignment or road profile Determining design elevations along the road profile Designing vertical curves along the vertical alignment General controls for vertical alignments

9 General definitions The grade line is a reference line by which the elevation of the pavement and other features of the highway are established All portions of the grade line must meet sight distance requirements for the design speed classification of the road. The grade line is controlled mainly by the topography, type of highway, horizontal alignment, performance of heavy vehicles, right of way costs, safety, sight distance, construction costs, cultural development, drainage, and pleasing appearance.

10 Road profile Grade line or design profile Fill Cut Original ground level (OGL)

11 Working in cut section in soft rock (normal cut)

12 Working in cut section in solid rock (blasting)

13 Finished cut side slope

14 Factors governing the road grade line 1. Earthwork quantities (cut & fill) 2. Control points (existing road, canal, water level, bridge, etc.) 3. Max & min grade 4. Critical length of the grade 5. Design speed & sight distance 6. General control of grade line 7. Coordination with horizontal alignment

15 Maximum grade Table 4.8 gives the max grade Upgrade: It limits the ability of vehicles to climb the upgrade (performance depends on the weight/horsepower ratio) Downgrade: It adds a driving force and speeding up, Downgrade: It adds a driving force and speeding up, pushes the vehicle outside the road, and/or causes a loss of control on the steering wheel.

16 Max grade

17 Example of steep gradient and sharp horizontal curves in mountainous terrain

18 Min grade is governed by the drainage conditions or requirements, especially in cut sections. Side ditch is required with cut section to drain water The minimum grade is used to facilitate draining the surface water in the longitudinal direction Minimum grade High qualify pavement: 0.35% Other types of pavements: 0.5% Avoid having sag curve with the lowest point in cut section

19 Critical length of grade It the maximum length of a given upgrade on which a loaded truck can operate without significant reduction in speed. Figure 4.15 gives the between the upgrade grade, length of grade, and the reduction of speed for 250 g/w truck. Figure 4.16 gives the relationship between the grade (up or down), length of grade, and the speed for 250 g/w truck.

20 Truck performance on upgrades Example: Truck starts moving on 4% with 60 km/h will reach, what is the critical length on this grade if maximum reduction in speed is 20 km/h?

21 Truck performance on downgrades

22 Climbing lanes When the reduction in speed is significant and road profile cannot be improved, a climbing lane should be used. It is not required in case of low traffic road. Function: to be used by slow trucks to facilitate the passing of light vehicles. Benefits: reduce accidents, reduce delay, improve section capacity and level of service. Length: should be determined based on the initial and final speed of truck. Transition length should be added at both ends of the climbing lane

23 Example of climbing lane 1. Truck starts to climb 5% grade at speed 60 km/h. This grade continues for about 400 m, and then followed by 1% grade for about 200 m and then by -1% for another 200 m. Determine the length of the climbing lane. 2. At the end of the 400 distance, the truck speed becomes about 25 km/h. After traveling 200 m on the 1% grade, truck speed reaches about 35 km/h. After traveling the 200 m on -1% grade, the truck speed reaches about 50 km/h 3. The climbing lane starts where the reduction in speed reaches 15 km/h (i.e., truck speed is 45 km/h) 4. This point is reached after the track travels ( ) or after traveling 160 m on the grade. 5. Use transition before this point 6. The climbing lane should end at a point where the truck re-gain at least its speed minus 15 km/h (i.e., truck speed reaches 45 km/h). 7. This sped is located on the -1% grade, after about 120 m on the grade. 8. Use a transition after this point 9. The length of the climbing lane is about = 560 m

24 g 2 g Types of vertical curves Crest (A=+ve) A= g 1 g 2 g 1 g Sag (A=- ve)

25 Difference in levels on grade 2 1 g g * X X E 2 = E 1 + g * X

26 Elements of vertical curves PC PI y + g x - g 2 1 L PT A= g 1 g 2 A is % or number K = e = Y L A A L A X = 200 L E x = E PC + g 1 * X - Y (Vertical curve parameter) A is number (External distance) A is number Vertical ordinate at distance (x) A is number Elevation on curve at distance (x) from PC Location of critical point on curve, measured from PC: Slope on curve at distance (X) from PC: Distance from PC where slope on curve equal (g ): Rate of change of gradient on vertical curve (r): X c 1 g x X = g ' g L = A = g g 1 1 m g A A X L r = 1/K = A/L ' L

27 Example 4% n -2% Given: L = 150 m, St PC = , Elev of PC = 20.5 m, St of n = , Req: a) Elev of n, b) Elev & Station of Highest point, c) station at g = 2%, d) slope at point n a) A= 6%, Y n = 6 * 30 2 /(200 * 150) = 0.18 m, Elev at n = *4/ = m b) X h = 4 * 150/ 6 = 100 m, Y h = 6* (100)2/ (200 * 150) = 2 m, Elev h = * 4/100 2 = = 22.5 (Also Elev h = = 22.5) c) X 2% = (4-2)/6 * 150 = 50 m, Y 2% = 6* (50) 2 / (200 * 150) = 0.5 m, Elev 2%= * 4/ = 22.5 m d) g = 4-6 * 30/150 = 2.8%

28 Sight distance on crest curve

29 Design of Crest curves for SSD h 2 h 1 S L General equations SSD Simplified equation S<L H1=1.05 m H2=0.15 m S>L

30 Design of Crest curves for PSD h 2 h 1 S L General equations PSD Simplified equation S<L H1=1.05 m H2=1.30 m S>L

31 Design of sag curves for SSD S H β L General equations SSD Simplified equation S<L H=0.6 m B =1 o m S>L

32 K Parameter of Vertical Curves

33 Example Given: 3%, -1% grades, Vd = 80 km/h A= 3% (-1%) = 4% S = 0.278*80* /(255*0.31)=136.6 m SSD = (calculated), 140 m (rounded) - (Table 4.1) PSD = 561 (calculated), 560 m (rounded) - (Table 4.4) Assume S<L L = A*S 2 /400 = 4*134 2 /400=179.6 m (L>S ok) For PSD: L = 4*560 2 /940 = m Note: for SSD, K=55, L= 4*55 = 220 m for PSD, K=235, L= 4*335 = 1340 m

34 Factors governing the vertical alignment Earthwork quantities (cut & fill) Control points (existing road, canal, water level, bridge, etc.) Max & min grade Critical length of the grade Design speed & sight distance

35 Additional factors controlling the vertical alignment a) A smooth grade line is better than a line with numerous breaks b) The roller-coaster or hidden dip should be avoided c) Broken back grade (two vertical curves in the same direction separated with short tangent) should be avoided not pleasing d) On long grade, it is preferred to put steepest grade at the bottom and least grade near top or to break grade by short interval of less grade e) At intersections, reduce gradient f) Climbing lane should be considered when critical length is exceeded and DHV exceeds capacity

36 a) Smooth grade line

37 b) Roller coaster

38 Local dip eliminated Local dip on long grade

39 d) Broken back grade Crest Sag

40 e) Steepest grade at bottom

41 Short hump and dip preceding horizontal curve

42 Out-of-phase vertical and horizontal alignments

43 Improper design of vertical alignment Where does the road go?