alternative approach to permanent way alignment design

Alternative Approach to Permanent Way Alignment Design Explained/Challenged

Constantin Ciobanu Senior Pway Engineer

ATKINS

West of England Section18/11/2015

About Constantin Ciobanu

Third generation railway professional

Graduated Technical University of Civil Engineering Bucharest (TUCEB), Romania, in 1998

• Speciality: Railway, Road and Bridge Engineering

Lecturer / Assistant Lecturer – TUCEB, 1998 – 2011

• Track alignment design for plain line and S&C (including light rail and tramway)

• Realignment methods (Hallade and similar)

• Continuous welded rails (CWR) behaviour and CRT management

Joined Atkins in May 2013

• Main projects: Great Western Electrification Project +Great Western Route Modernisation

• ATKINS - BRT Development Group under PhoD

Design Engineer – Romania, 2006 – 2013

• Railway, Light Rail, Tramway, Road designs

• Main project: Romanian sections - IVth Pan-European Railway Corridor (TEN-T)

Lead Track Design Engineer, CRE for two 100km sections

Lateral Acceleration. Cant. Cant Deficiency

• Circular movement - inertial centrifugal acceleration

𝑎𝑐 =𝑣2

𝑅

• The track is inclined towards the centre of the curve with the cross-level angle α to compensate for a part of the centrifugal acceleration

• The traditional way to measure this inclination is the cant, E, defined as “the vertical difference in heights of the two rails of a track, measured at centerline of the rail heads (S)” (TRK2049 – 2010, B.1.1).


The non-compensated lateral acceleration 𝑎𝑞

𝑎𝑞 = 𝑎𝑐𝑐𝑜𝑠 ∝ −𝑔 𝑠𝑖𝑛 ∝ = 𝑎𝑐 − 𝑔𝐸

𝑆=𝑣2

𝑅− 𝑔

𝐸

𝑆where:

• v is the speed of the vehicle

• R is the curve radius

• g is the gravitational acceleration

• E is the applied cant

• S is the cross-level standardised reference for rail heads centerline distance (considered 1505mm in UK)

Cant Deficiency, D, is usually used instead of aq :

𝐷 =𝑆

𝑔𝑎𝑞 =

𝑆

𝑔

𝑣2

𝑅− 𝐸

𝑫 = 𝟏𝟏. 𝟖𝟐𝑽𝟐

𝑹− 𝑬


• The cant, E, defines the track inclination angle, measured as level difference over rail centerlinedistance (not over track gauge)

• The cant deficiency, D, defines the non-compensated lateral acceleration

• Simplifications:

• Suspension behaviour

• Bogie attack angles

• Differences between the suspended and un-suspended mass

• Dynamic behaviour – oscillations, damping effect

• Vehicle centre of mass – brought at track level

• etc

𝑫 = 𝟏𝟏. 𝟖𝟐𝑽𝟐

𝑹− 𝑬 [𝒎𝒎]

Track Geometry Recording. Standard Deviation

• Periodic track measurement is required to maintain an effective railway track system – safe and with good vehicle ride quality.

• Safety – well defined exception (exceedance) levels

Intervention and Immediate remedial actions

• Ride quality – track geometry Standard Deviation (SD)

Quality Index defined based on speed and various classes of lines

Track Geometry Recording. Standard Deviation

Signal Processing. Fourier Analysis. Standard Deviation

Fourier Analysis – signal simplification

Two (three) standard deviation wave length bands:• 35m = 1m to 35m (H) and 0.5m to 35m (V)(general track quality index)• 70m = 1m to 70m (H) and 0.5m to 70m (V)(comfort quality index for passenger trains at higher speed –V≥80mph)• 200m = 1m to 200m (H) and 0.5m to 200m (V)(High Speed track quality index V>250km/h – EN13848)

Signal Processing. Fourier Analysis. Standard Deviation

Track Quality Standard Deviation

• Global track quality index

• Computed based on the inertial response of the measuring bogie to the track irregularities

• Two (three) track quality standard deviation wave length bands:

• 35m = 1m to 35m (H) and 0.5m to 35m (V)

(general track quality index)

• 70m = 1m to 70m (H) and 0.5m to 70m (V)

(comfort quality index for passenger trains at higher speed – V≥80mph)

• 200m = 1m to 200m (H) and 0.5m to 200m (V)

(High Speed track quality index V>250km/h – EN13848)

• Two sets of SD values:• AL – horizontal alignment

• TOP – top of rail - vertical alignment and cant

• WT35 – worst of the two tops (left rail and right rail).

• MT70 – mean top vertical variation (middle track vertical variation)

Any change in the vehicle lateral or vertical acceleration due to the design, is a source of oscillations:

- Horizontal transition (AL35 and AL70)

- Cant transition (WT35 and MT70)

- Gradient change (WT35 and MT70)

- Vertical curve (WT35 and MT70)

Inherent Track geometry Standard Deviation

(SD present in the design and not caused by installation)

Inherent Track Quality Standard Deviation

Rolling design (inherent) track quality

standard deviation

The normal approach is hiding the maximum

SD and its cause.

A better way is to consider in the design

the rolling SDs.

Gives the designer a better understanding

Disclaimer

What will follow should not be considered (yet) a design guidance!

(Except the excerpt from TRK2049)

Applying cant

• The inside rail of the curved track stays at the design level

• The outside rail is lifted with the full cant value

• The outer rail is the one that provides curve guidance for the vehicle

• Vertical Profile for the high rail?

• Vertical curves for cant?

(Classic approach)Cant applied by lifting

the outer rail

Cant applied by lowering the inner rail (Switzerland)

Cant applied symmetrically-High speed track – Shinkansen

- tramway

Ways of applying cant

• For low speed the difference is not significant (there are exceptions)

• As the speed increases and the track tolerances are tighter the difference is starting to be significant in the ride quality and whole life behaviour of the track

• Shinkansen (since 1968) V>160km/h

• Almost all slab track based HS lines

• Californian High Speed

Cant over a reverse curve

• Balancing the curvature variation – proportional transition lengths

• Balancing the cant / rate of change of cant

• Balancing the cant gradient

• Balancing the deficiency / rate of change of cant deficiency

• What else?

Cant over a reverse transition. “The orphan rule”

Romanian Railway track standard Instructia 314 German Railway track standard

RIL 800.0110

Cant over a reverse transition. “The orphan rule”

Austrian Railway track standard OBB – B 50 United Kingdom

Network Rail – Track Design Handbook – TRK 2049

Cant over a reverse curve. “The orphan rule”

All these standards are showing a mysterious triangleAll these standards recommend a lifting of the reverse point

Cant over a reverse curve. “The orphan rule”

Designing a sudden change in curvatureWhen is a transition curve not needed?

…when the cant is constant.

Designing a sudden change in curvatureWhen is a transition curve not needed?

• Horizontal alignment track quality standard deviation - SD (mm) - Al35 Band for a straight to a circular alignment with or without transition curve

X 2.3

• In the case of the actual installation, the sudden change in curvature is practically impossible to be installed on track, as the rails are not kept in place laterally by a perfectly rigid system, especially for a ballasted track.

• An actual sudden change in curvature is in fact impossible to install or maintain, especially on ballasted track, because it will always tend to become a short curvature transition during installation respectively post-installation, due to the modelling effect of the passing trains.

Designing a sudden change in curvature

1. Limit the virtual rate of change of cant deficiency, RcD (VT), calculated based on the assumptions of the principle of Virtual Transition.

This is the design approach used in the UK and defined by the Track Design Handbook – NR/L2/TRK/2049 (2010) for Network Rail and by the track design standard S1157 (2014) for London Underground.

2. Limit the sudden change in curvature by limiting the instantaneous change in cant deficiency (ΔD).

This design approach is the most common used in continental Europe and around the world. It can be found in the European Norm for track alignment design parameters – BS EN 13803-2 (2006).

The Principle of Virtual Transition

TRK2049 - RcDNormal Design Value

Maximum Design Value

Exceptional Design Value

35 mm/s 55 mm/s 70 mm/s

The limits of the Rate of Change of Cant Deficiency(according to the Track Design Handbook TRK2049)

EN 13803-2 - ∆D

Speed

V [km/h]V≤70 70<V≤170 170<V≤230

Recommended

∆Dlim [mm]50 40 30

The limits of the Sudden Change in Cant Deficiency(according to the European Norm EN 13803-2)

Comparison between the design restrictions for a sudden change in curvature

(∆D was computed from RcD for a virtual transition length LVT of 12.2m)

TRK2049Normal Design Value



35 mm/s 55 mm/s 70 mm/s


EN 13803-2

Speed

V [km/h]V≤70 70<V≤170 170<V≤230

Recommended

∆Dlim [mm]50 40 30



(the equivalent virtual RcD for EN13803 is computed for a virtual transition length LVT of 12.2m)




35 mm/s 55 mm/s 70 mm/s


EN 13803-2

Speed

V [km/h]V≤70 70<V≤170 170<V≤230

Recommended

∆Dlim [mm]50 40 30


Speed

[mph]

RIL 800.0110 specifications

Sudden change of Cant

Deficiency

∆D

Equivalent virtual

Rate of change of

Cant Deficiency for

12.2m virtual

transition

RcD [mm/s]

Speed

[km/h]

Minimum radius not

requiring transition

curve [m]

Plain line S&C Plain line S&C Plain line S&C

25 40 220 180 86 105 79 96

32 50 340 280 87 106 100 121

38 60 490 400 87 107 119 147

44 70 670 545 87 107 139 171

50 80 875 710 87 107 159 195

56 90 1110 900 87 107 179 220

63 100 1370 1110 87 107 199 244

69 110 1735 1410 83 102 208 256

75 120 2170 1745 79 98 216 268

81 130 2680 2130 75 94 222 279

87 140 3275 2575 71 90 227 287

94 150 3990 3085 67 87 229 298

100 160 4825 3675 63 83 230 303

106 170 5810 4350 59 79 229 306

112 180 6975 5125 55 75 226 308

119 190 8365 6000 51 71 221 308

125 200 10000 7000 48 68 219 310

Cant deficiency parameters for the minimum radius not requiring transition to straight

according to the German track alignment design standard RIL 800.0110 (2008)




35 mm/s 55 mm/s 70 mm/s


EN 13803-2

Speed

V [km/h]V≤70 70<V≤170 170<V≤230

Recommended

∆Dlim [mm]50 40 30



(the equivalent virtual RcD for EN13803 is computed for a virtual transition length LVT of 12.2m)




35 mm/s 55 mm/s 70 mm/s


EN 13803-2

Speed

V [km/h]V≤70 70<V≤170 170<V≤230

Recommended

∆Dlim [mm]50 40 30


Transition curve shift

When a transition is to be installed between two circular curves one of the curves is shifted towards the centre relative to the other.

This shift (theoretical slue), S, for a clothoid transition, is dependent on the curvature variation ∆K between the two curves:

𝑆 =𝐿2

24∆𝐾 −

𝐿4

2668∆𝐾3 +⋯

where

∆𝐾 =1

𝑅2−

1

𝑅1=𝑅1 − 𝑅2𝑅1𝑅2

Best practice rule in some European countries :

If the required curve shift to install a transition is below 3mm, that transition should not be proposed in

the design as it is practically impossible to be installed on site, on ballasted track.

Transition curve shift

By inserting a 30m transition between R1 and R2, the rate of change of cant deficiency changes as follows:• From 36mm/s to 15mm/s (21mm/s decrease)• From 56mm/s to 23mm/s (33mm/s decrease)• From 71mm/s to 29mm/s (42mm/s decrease).

…when the cant is constant.