2. SPECIAL TRANSPORTATION STRUCTURES(Notes for Guidance ) Highway Design Procedures/Route Geometric Design/Vertical Alignment/The route in Longitudinal Profile/The transverse Profile Radu ANDREI, PhD, P.E., Professor of Civil Engineering Technical University “Gh. Asachi” IASI Lecture Eleven

3. Route Geometric Design/Vertical Alignment/The route in Longitudinal Profile/The transverse Profile Vertical alignment. The longitudinal profile Vertical curves. Vertical connections.Classification The road in transverse profile Problems Additional Readings

4. Vertical Alignment/The Route in Longitudinal Profile The vertical alignment of a highway consists of straight sections of highway, known as grades, or tangents, connected by vertical curves. The projection of a vertical plane of the intersection of the vertical surface generated by the vertical line passing through the axis with the platform defines the so called vertical alignment or the longitudinal profile of a land transportation infrastructure. ( See the next slide )

5. Vertical Alignment/The Route in Longitudinal Profile The longitudinal profile as shown in the figure from the previous slide consists of two lines: - the ground line or the terrain line obtained by the projection of the intersection of this vertical surface with the ground surface. - -the proposed grade line obtained by the projection of the intersection of this surface with the platform if the land transportation infrastructure.

6. Vertical Alignment/The Route in Longitudinal Profile In relation with the figure from the previous slide, all elevations should be based on sea level datum, carried from the nearest geological survey bench mark. The profile should show datum lines: - the profile of the surface of the proposed centre line; - tops of rails of all grade crossings; - the proposed grade line; - the length of vertical curves, the elevations and description of all bench marks;

7. Vertical Alignment/The Route in Longitudinal Profile The vertical alignment of a highway consists of straight sections of highway, known as grades, or tangents, connected by vertical curves. The design of vertical alignment involves the selection of suitable grades for the tangent sections and the design of vertical grades. The topography of the area through which the road traverses has a significant impact on the design of vertical alignment

8. Vertical Alignment/The Route in Longitudinal Profile/Grades The selection of the maximum grades for a highway depends on the design speed and the design vehicle. It is generally accepted that grades of 4 to 5 percent have little or no effect on on passenger cars. As the grade increase above 5 percent, speeds of passenger cars decrease on upgrades and increase on downgrades

9. Vertical Alignment/The route in Longitudinal Profile/Grades Grades has a greater impact on trucks then on passenger cars, the truck speed may increase up to 5 percent on downgrades and decrease by 7 percent on upgrades, depending on the percent and the length of the grade. Therefore the maximum grades have been established, based on the operating characteristics of the design vehicle on the highway.

10. Vertical Alignment/The route in Longitudinal Profile/Grades The maximum grades vary from 5 percent for a design speed of 70 mph and 12 percent for a sedign speed of 30mpa, depending of the type of highway. When grade length are less the 500 ft and roads are one-way in the downgrade direction, maximum grades may increased by 1 to 2 percent, particularly in low volume, rural roads.

11. Vertical Alignment/The route in Longitudinal Profile/Grades Minimum grades depend on the drainage condition of the highway. It is customary to use a minimum 0,5 percent in most cases, although this may be reduced to 0,3 percent on high-type pavement constructed on suitable crowned,firm ground.

12. Vertical Alignment/The route in Longitudinal Profile/Vertical curves Vertical curves are used to to provide a gradual change from one tangent grade to another, so that vehicles may run smoothly as they traverse the highway. These curves are usually parabolic in shape and the expressions developed for minimum length of vertical curves are based on the property of parabola. They are classified as crest or sag vertical curves.

13. Vertical Alignment/The route in Longitudinal Profile/ Crest Vertical curves

14. Main criteria used for the design of crest vertical curves: Case 1: the real sight distance is greater then the the length of the vertical curve (S >L). The minimum length which can provide a minimum stopping site distance S is calculated with the relation: Lmin =2S-1329/A, where A is the algebraic difference between the grades G1 and G2

15. Vertical Alignment/The route in Longitudinal Profile/ Crest Vertical curves Main criteria used for the design of crest vertical curves: Case 2: the real sight distance is less then the the length of the vertical curve (S <L). The minimum length which can provide a minimum stopping site distance S is calculated with the relation: Lmin =AS^2/ 1329, where A is the algebraic difference between the intersecting grades G1 and G2

16. Vertical Alignment/The route in Longitudinal Profile/ Sag Vertical curves Main criteria used for the design of sag vertical curves: Case 1: S>L The minimum length which can provide a minimum stopping site distance S is calculated with the relation: Lmin =2S - (400 + 3,5S)/A, where A is the algebraic difference between the intersecting grades G1 and G2

17. Vertical Alignment/The route in Longitudinal Profile/ Sag Vertical curves Main criteria used for the design of sag vertical curves: Case 2: S<L The minimum length which can provide a minimum stopping site distance S is calculated with the relation: Lmin =AS^2/(400 + 3,5S), where A is the algebraic difference between the intersecting grades G1 and G2

18. Vertical Alignment/The route in Longitudinal Profile/Vertical curves From practical experience it was found that only the algebraic difference of the intersecting grades is less than one half, or one percent do vertical curves become unnecessary. All distances along vertical curves are measured horizontally, and all offsets from the tangents to the curves are measured vertically. Accordingly, the length of a vertical curve is its horizontal projection. The errors resulting from this assumption is negligible in practice, since the curve is quite flat.

19. Vertical Alignment/The route in Longitudinal Profile/Vertical curves Unless otherwise defined, vertical curves are symmetrical in the sense that tangents are equal in length. In relation with the figure from the next slide, the vertical curve AB is refereed to rectangular axes, where x & y, with origin at A (the PVC - point of vertical curvature) represent the horizontal and vertical co- ordinates for any point P on the curve.

20. Vertical Alignment/The route in Longitudinal Profile/Vertical curves

21. In relation with the previous slide, let g 1 and g 2 be the percent grades of tangents AV & BV respectively, using plus for grades according forward and minus for grades descending. Also let A=g 2 -g 1, be the algebraic difference in grades (percent) of the grade tangents, or their rate of divergence.

22. Vertical Alignment/The route in Longitudinal Profile/Vertical curves With these notations clear, the other notations follows: L - total length of curve, in stations l - vertical offsets (in meter or feet) from the vertex V (called PVI.) to the middle of the curve. Since l is the vertical distance from the vertex to the middle of the curve, it is measured downward in a negative direction for all crest curves. A different situation we have for usage for sag curves. There the algebraic sign of l indicates weather elevations along the curve are to be obtained by adding or subtracting offsets from the corresponding tangent elevations.

23. Vertical Alignment/The route in Transverse Profile A typical cross section of the pavements as shown in the next slide, drawn at a suitable scale should show the various slopes of cut and fill, the crown of the finished pavement, the width of the shoulders, the thickness of various courses of pavement or resurfacing, the position of the profile grade line, the centreline of pavement and the limits of the right of way.

24. Vertical Alignment/The route in Transverse Profile Vertical Alignment/The route in Transverse Profile Typical cross sections with conventional terms applied to two-lane highways

25. Problems WORKSHOP No.3 Based on the knowledge delivered during the course, for your best selected route, proceed with the vertical alignment as follows: Draw at a convenient scale the vertical profile of your selected route using a horizontal scale of 1:1000 and a vertical scale of 1:100

26. Problems WORKSHOP No.3 Establish the levels of the ground ( terrain ) line and those of the grade ( red) line, at each intersection point of the route centerline with the map contours.

27. Problems WORKSHOP No.3 Calculate and complete all the rows with specific longitudinal profile data, such as grades, and grade length, differences, along the centerline, between the ground and the red line, pegs and distances between,mileage, the graphical scheme of the horizontal alignment, Km, hm, relative reference level, and any other reference points Connect the series of tangents forming the grade line, by using vertical connection curves and calculate their main functions.

28. Additional Readings Andrei R. Land Transportation Engineering, Technical Publishers, Chisinau, 2002Andrei R. Land Transportation Engineering, Technical Publishers, Chisinau, 2002 Garber j.N., Hoel A.,L, Traffic and Highway Engineering, revised second edition, PWS Publishing,1999Garber j.N., Hoel A.,L, Traffic and Highway Engineering, revised second edition, PWS Publishing,1999

29. Additional Readings Zarojanu Gh.H. Popovici D., Drumuri- Trasee, Editura VENUS, Iasi,1999 STAS 863-85 Road works. Geometrical elements of Lay out. Design specifications Hikerson F.T. RouteLocation and Design, Mc GRAW- HILL, Fifth Edition, 1967