Railway Design Layout - PDF

Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway layout (a) Andrea Baliello | Engineer 5b. Railway design 1 ...

Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway layout (a) Andrea Baliello | Engineer 5b. Railway design 1  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Planimetric and altimetric design Andrea Baliello | Engineer 5b. Railway design 2  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Layout The layout of a railway line is the projection of track axis on a horizontal plane (i.e. the representation of planimetric track trend). In general, the layout is a series of straights and circular curves ▪ Double track lines → traffic in both directions completely separate ▪ Simple track lines → the intersections between two trains takes place in the stations, with a precise time-order To judge the quality of a railway track are used geometric indexes such as: 1. Degree of tortuosity 2. Stretching ratio Andrea Baliello | Engineer 5b. Railway design 3  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Layout The railway line design (the choice of straight or curve track) is based on constraints that are found on the territory by the designer Andrea Baliello | Engineer 5b. Railway design 4  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design 1. Degree of tortuosity The degree of tortuosity τ is defined as the ratio between the extension lc of circular curves (the radius must be less than a given value) and the total length of the line lr: lc = 100 lr ▪ The index allows to assess the ability of an existing railway line to be covered by a train at a speed higher than the project speed, without interventions on track Andrea Baliello | Engineer 5b. Railway design 5  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design 2. Stretching ratio The stretching ratio α is defined by the ratio: l r − l0 = 100 l0 where lr; actual line development l0: distance between the two line ends through a fictitious straight line Andrea Baliello | Engineer 5b. Railway design 6  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout The railway layout is composed by a series of straight lines, circular curves and transition curves ▪ The radius of circular curve is the fundamental planimetric element conditioning the maximum allowable speed on the railway line ▪ The use of lower radii is a problem for the construction cost and for the line project in the territory (due to the conformation of ground) Certain railway agencies fixed the minimum radius: → between 650 m and 1100 m, for principal lines; → between 100 m and 350 m, to inscribe cumbersome vehicles in curves In Italy, the minimum radius is equal to 150 m Andrea Baliello | Engineer 5b. Railway design 7  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout The sequence of two circular curves covered in the same direction, connected by a transition element, constitutes a “continuity”; while the sequence of two circular curves covered in the opposite direction and connected by a transition element is called “inflection” ▪ The time during which the body of the vehicle resumes his original vertical position after the exit from the curve, was estimated equal to 1.5 seconds ▪ It is recommended, therefore, in terms of comfort, the interposition, between two consecutive discordant curves, a straight with a length equal to or greater than: 1,5  V lr = [m] 3,6 with V in [km/h] Andrea Baliello | Engineer 5b. Railway design 8  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout ** Given the previous equation, the length lr is next to V/2 In Italy the values adopted are significantly lower: → 30 m, with a speed between 100 km/h and 160 km/h; → 50 m, with a speed > 160 km/h Andrea Baliello | Engineer 5b. Railway design 9  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout In the vertical plane, the line is subdivided in: the grade line (straight line with a constant slope) and the vertical junctions ▪ The slope of the grade line is not a structural constraint (the high speed line between Paris and Lion has a grade line with slope equal to 35 ‰) but is a indicator of railway operative service In European country, slopes can be up to: → 35 ‰ railway line only for passenger trains → 12,5 ‰ railway line for freight and passenger trains In Italy, the slope for high speed lines max slope is 21 ‰ Andrea Baliello | Engineer 5b. Railway design 10  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout The radii of the vertical circular arcs, that connect two consecutive grade lines, are dimensioned to contain the vertical acceleration of the vehicle ▪ In the existing Italian network, the vertical radius, normally realized, amounts to 3000 m (equivalent to: a speed of 200 km/h and a vertical acceleration of 1.03 m/s2). Actually, this value is incompatible with an acceptable level of comfort also for speeds less than 200 km/h. Therefore, the correct vertical radius is given by: 2 *** V [m] R = v 2 *** for speeds of 200 km/h a centrifugal acceleration of 0.15 m/s2 is produced Andrea Baliello | Engineer 5b. Railway design 11  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout In general, the vertical radius is equal to : Balance equation in the Vertical junction radius vertical plane W W v2 V2  av =  with V in [km/h] Rv = g g Rv 12,96  av 0.15 ≤ av ≤ 0.30 m/s2: range limit for vertical acceleration for traditional train speed Andrea Baliello | Engineer 5b. Railway design 12  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout In the case of convex junction, it necessary to consider that the vertical force decreases the static load value discharged on the rail (and then decreases the adherence). Vice versa, in the case of concave junction, static load increases W  v2 W V 2 Fc = v in [m/s] Fc = V in [km/h] g  Rv 127,14  Rv where, Rv is the vertical curve radius, V or v is the speed and Fc is the centrifugal force (vertical). Considering a variation of static load of 1.5 %: V2 0,015 = V 2 = 1,91  Rv V: 100 Km/h Rv: 5240 m 127 ,14  Rv V: 200 Km/h Rv: 20940 m ▪ The convex junction radius must be grater than 5000 m Andrea Baliello | Engineer 5b. Railway design 13  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Layout design Planimetric and altimetric layout The slope depends on the adherence (fa = 0.140 - 0.200) From the equation of traction the adherence limits the choice of: ▪ v (speed) ▪ Q (load) ▪ i (slope) Example of slope: 10 - 12 ‰ Main lines 15 ‰ secondary lines