SKM Technical Paper - Pway Design

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Technical PaperAuthor: Lachlan Daniel

Permanent Way Design

A simplified empirical design method

Sinclair Knight Merz Pty LimitedACN 001 024 095ABN 37 001 024 095100 Christie StreetPO Box 164St Leonards NSWAustralia 1590Telephone: +61 2 9928 2100Facsimile: +61 2 9928 2500

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1. Introduction This paper presents a simplified empirical track design procedure which provides a first orderestimate that is suitable for an initial assessment of track standard requirements. The design procedure is suitable for concept design and has been accepted on projects such asthe New Southern Railway (Sydney, Australia) where it was used, together with performancebased specifications, to enable the client to call tenders for detail design and constructcontracts. A more detailed analysis using sophisticated design procedures, eg computer models, should beundertaken before establishing the final track requirements.


2. The Permanent Way

What does the term ‘The Permanent Way’ actually mean?The permanent way derives its definition from the time when railways were first constructedas it seemed that the track structure of a railway represented a far more permanentconstruction than that of other types of ‘roads’ of the time.

The track structure is composed of the rails, the fastening system, the sleepers and ballast.

In some rail systems the term ‘permanent way’ is used to refer to the total railway reserve(Right of Way) as well.

What is the purpose of the permanent way?Apart from providing a dedicated ‘guidance’ system for the proposed rollingstock thepermanent way provides a track structure which is capable of transferring train loads to theformation.

Load transfer works on the principle of stress reduction, layer by layer, as depictedschematically in Figure 1.0.

The greatest stress occurs between the wheel and the rail and is in the order 300,000 kPa.Between rail and sleeper the stress is two orders smaller and again diminishes betweensleeper and ballast bed down to about 300kPa. Finally the stress on the formation, as a resultof the track structure provided, is in the order of 60kPa.

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3.0 Permanent Way Design

3.1 Introduction

The nature of the rail business will determine the type of traffic that uses the track andthus the main elements of its loading.

Types of traffic include:• Freight

− Fast (eg. Interstate services)− Heavy (eg. coal, iron ore)

• Passenger – Express or Commuter

In most rail systems a mixture of all of the above is found resulting in an array ofloadings on the track.

Table 1.0 shows some representative combinations of axle load and speed for thetypes of traffic noted above.

Table 1Type System Axle Load (t) Speed (km/hr)

Fast Freight NSW 19 115Canada 25 105

Heavy Haul Mt Newman 35 75NSW 25 80Lamco 31 60

Express Passenger NSW 18 160BR 17 200TGV* 17 300

Commuter NSW 15 115LRT * KL 7 50

* Track for exclusive use

Density of traffic is also an important element in the loading characteristics of thepermanent way as it will affect the life expectancy of the chosen components and theprobabilities of the loading variations.

The route of the track will also impact on the loading characteristics, specially thelateral loads developed in tight horizontal radius curves.

Track loadings can also vary greatly due to the type of rollingstock used in operations.The type of vehicle, its mass, loading and suspension are all important contributors tothis variation.


Passenger cars, for instance, are usually light vehicles with relatively longwheelbases whereas the typical ore car is rugged and compact with a short wheelbase resulting in a much higher loading intensity.

Wheel arrangement can also affect the loads on the track structure. A locomotivewith long wheel base bogies will usually generate higher curving forces on sharpcurves compared to those with shorter wheel base.

Characteristics of the track also affect track loading especially those relating to itsuniformity. For design purposes it is usual practise to adopt estimates of trackstiffness which are assumed uniform and then, as the design proceeds, test theestimates by iterative process.

Rollingstock speed can also have a significant affect on the loading characteristics. Ifthe wheel and the rail were perfectly smooth and of uniform stiffness there would benothing to generate variation of response and vertical track loading would remanconstant for all speeds.

The reality is that the wheel and the rail are ‘not perfect’ and hence significantvariations are produced which are directly proportional to rollingstock speed.

3.2 The Design ProcessThe permanent way is an extremely elastic structure which is not readily analysed bysimple design methods.

However, with vast years of experience and testing of permanent way materials,empirical methods have been established which permit the track designer to producea first order estimate that is suitable for an initial assessment of track standardrequirements.

The empirical methods are described in detail in the following sections and follow themethodology described in the flow chart shown overleaf.


Allowable BallastPressure

Assumed RoadbedSupport Modulus

Sleeper Size andSpacing Analysis

VehicleParameters

(Weight and size)

Dynamic ImpactFactor

TrainSpeed Rail Wear Analysis

Rail Size SelectionBeam on Elastic

FoundationAnalysis

Exceeded ?Track Condition

ExperienceFactors

Sleeper SupportAnalysis

Sleeper BendingStress Analysis

Exceeded?Sleeper Strength

Data

Ballast PressureAnalysis

Exceeded?Ballast Strength

Data

SubgradePressure Analysis

Exceeded?

Vary BallastDepth

Soil Test

Rail ThermalStress

Rail Yield

Rail ElectricalRequirements

Rail Cost &Availability

Dynamic WheelForce

Track Modulus

Rail Bending Stress

Allowable RailBending Stress

(Yes)

(No) Rail Deflection

Sleeper Plate Load

(Yes) Allowable SleeperBending Stress

(No) Sleeper Plate Load

Ballast Pressure

(Yes)

Subgrade Pressure

Allowable SubgradePressure

(Yes)

(No) Final Ballast Depth

(No)

Flow Chart for Conventional Ballasted Track Structure


3.3 Dynamic LoadsThe nominal vehicle axle load is usually measured for the static condition, but in thedesign of the permanent way the actual stresses in the various components of thetrack structure and in the rollingstock must be determined from the dynamic verticaland lateral forces imposed by the design vehicle moving at speed.

The major factors affecting the magnitude of the dynamic vertical load have beenidentified in section 3.1 and are summarised below:

• Train speed• Wheel diameter• Vehicle unsprung mass• Track condition (including track modulus, track geometry, joint condition)• Track construction• Static wheel load• Vehicle condition

The general method used in the determination of the design vertical wheel load is toexpress it empirically as a function of the static wheel load, ie:

P’ = ∅ .Ps

Where P’ = design wheel load (kN)Ps = static wheel load (kN)∅ = dimensionless impact factor (always > 1)

The dynamic loading on the track structure has been subject to extensiveinvestigations throughout the world which has led to numerous formulae beingdeveloped which take into account the vehicle and track characteristics.

Table 2 summaries the main formulae which are used in determining the dynamicwheel load.

The AREA (American Railway Engineering Association) method of determining theimpact factor to apply to the static wheel load is simple and often used forcontinuously welded rail.

Impact factor ∅ = 1 + 5.21.V / D

(AREA)

Where V = vehicle speed (km/hr)D = wheel diameter (mm)

Alternatively for general track analysis of CWR track the Eisenmann formula isconsidered quite appropriate, whereas the British Rail formula would be moreappropriate for the examination of vehicle unsprung mass effects.


VEHICLE TRACK

Ve

hic

le a

nd

Tra

ck

pa

ram

ete

rs

Tra

in S

peed

Whe

el D

iam

eter

Sta

tic W

heel

Loa

d

Uns

prun

g W

heel

Mas

s

Cen

tre

of G

ravi

ty fo

Veh

icle

Loco

Mai

nten

ance

con

ditio

n

Tra

ck M

odul

us

Trac

k S

tiffn

ess

Tra

ck jo

int d

ip a

ngle

Can

t def

inci

ency

in c

urve

s

Cur

ve r

adiu

s

Tra

ck M

aint

enan

ce C

ondi

tion

FORMULA IMPACT FACTOR

AREA 1 + 5.21 V/D X X

Eisenmann 1 + δ.η.τ X X

ORE 1 + (α'+ β'+ γ ') X X X X X X

BR1 + 8.784(a1 +a2)V Dj.Pu / g Ps X X X X X

IR 1 + V / (58.14 k ) X X

GERMAN 1+V2 / 3.E4 X

SAR 1 + 4.94 V/D X X

Clarke 1 + 19.65 V/(D. k) X X X

WMATA (1+3.86 E -5.V2)2/3 X

TABLE 2 VEHICLE & TRACK PARAMETERS INCLUDED IN IMPACT FORMULAE


The Eisenmann formula adopts a statistical approach to determine the distribution ofthe loading applied to the track and is considered appropriate where non discretewheel or rail defects are involved.

Impact factor ∅ = 1 + δ.η.τ

(Eisenmann)

The value δ is determined by the quality of the track and the following values havebeen suggested for use:

Where δ = 0.1 for track in very good condition0.2 for track in good condition0.3 for track in average condition0.4 for track in poor condition0.5 for track in very poor condition

η = 1 for speed up to 60 km/hrη = 1 + (V-60) / 140 for speeds > 60 km/hr

The value τ depends on the upper confidence limits (UCL) defining the probability thatthe maximum stresses will not be exceeded.

τ = 0.0 for UCL = 50%1.0 for UCL = 84.1%2.0 for UCL = 97.7% (normally used)3.0 for UCL = 99.9%

By far the most comprehensive method of determining the impact factor is thatdeveloped by the Office of Research and Experiments of the International Union ofRailways (ORE) which is based upon measured track results of locomotives.

The impact factor is defined in terms of the dimensionless speed coefficients α’, β’,and γ’.

Impact factor ∅ = 1 + α’+ β’ + γ’

(ORE)

The coefficient α’ is dependent upon:• Vertical track irregularities• Vehicle suspension• Vehicle speed

In a perfectly levelled track α’ is virtually zero. In tangent track with poor surface andvery fast traffic α’ was found to approach 0.35, whereas in curved track values of α’did not exceed 0.18.

α’ can be expressed empirically as:α’ = 0.04 (V/100)3

where V = vehicle speed (km/hr)


The coefficient β’ is dependent upon:• Vehicle speed• Cant deficiency of the track• The location of the centre of gravity of the vehicle

The coefficent β’ is the contribution resulting from the wheel load shift in curves, andmay be defined by either:β’ = 2d.h / G2 (SCNF)β’ = [V2.(2.h+c)/127.R.g] - [2c.h/G2] (DB)

where G = horizontal distance between rail centre lines (m)h = vertical distance from rail top to vehicle centre of massd = cant deficiency (m)c = cant (m)g = gravitational acceleration (m/sec2)R = curve radius (m)V = vehicle speed (km/hr)

The two formulae are approximately equivalent however the SCNF formula may leadto significant errors at high speed or in sharp curves.

The coefficient γ’ is dependent upon:• Vehicle speed• Track condition• Vehicle design• Maintenance condition of the locomotives

As a first approximation the following formula can be used if experiential data is notavailable.

γ’ = 0.10 + 0.017.(V/100)3

where V = vehicle speed (km/hr)

If the effects of other variables (eg. Locomotive and track maintenance) are to beincorporated then the above formula can be generalised as:

γ’ = γo.ao.bowhere γo = value determined in the equation above

ao = locomotive factor relating to maintenance conditionbo = track maintenance factor

• For normal track with a maximum permissible speed of up to 140km/hr:γo = 0.11ao = 2.0bo = 1.3

• For special track with an authorised speed of 200 km/hr, and ‘new’ rollingstock:γo = 0.24ao = 1.5bo = 1.2

ORE have observed that the maximum value of the impact factor occurs in tangenttrack and consequently the impact factor ∅ can be simplified and expressed as:


∅ = 1.29 + 0.04.(V/100)3

3.4 Rail Contract StressesIt is essential to limit wheel/rail contact stresses if rail surface and sub surfacedefects such as shelling and transverse defects are not to occur on the rail runningsurface, the gauge corner, or body of the head or the rail.

An initial approach is to check that the static wheel load / wheel diameter ratio (Ps/D)does not exceed 0.11 kN/m.

If this ratio is exceeded a simplistic analysis is necessary to check the shear capacityof the rail as follows:

T max. = 410 (2Ps/D)05

T all. = 0.3. tensile strength

3.5 Track StiffnessWhen considering the analysis or selection of track components such as rails, thetrack structure can be thought of as a beam on an elastic foundation.

The stiffness of the total track structure is known as the track modulus (k) and isdefined as the force per unit deflection per unit of track length per rail, ie:

k = Ps/Y.s10-3

where Ps = static wheel load (kN)Y = summed total rail deflection at all sleeper locations at

which deflections occur (mm)s = sleeper spacing (mm)

The following track modulus values are typical for 1435mm standard gauge track,however in practice there can be considerable variation at different locations along thetrack as well as seasonal conditions.

Rail Size (kg) Ballast & Sleeper Track Modulus (k)31 150mm, timber or steel 841 200mm, timber or steel 10

47 or 50 200mm, timber or steel 1253 250mm, timber or steel 1560 250mm, timber or steel 2060 250mm, concrete 2560 300mm, concrete 30

For 1067mm narrow gauge track the track modulus values are generally 5 Mpa lowerthan those indicated in the above table, especially for the heavier rail sizes.

3.6 Rail StressesThe AREA method for estimating rail size assumes the beam on an elastic foundationtheory with rail bending moments calculated as follows:


M = P’ / 4BWhere P’ = dynamics wheel load

B = (k/4.E.I)0.25

k = track modulusI = second moment of inertia of the railE = Youngs Modulus

The AREA allowable stress formula follows:Fall. = fb/(1+A1).(1+B1).(1+C1).(1+D1)

Where fb = allowable bending stressA1 = stress factor for lateral bending (20%)B1 = stress factor for track condition (30%)C1 = stress factor for rail wear (15%)D1 = stress factor for unbalanced cant (15%)

Figure 2 for rail selection is based on this formula and is suitable for a non rigorousfirst analysis.

3.7 Rail Seat LoadThe exact magnitude of the load applied to each rail seat of the sleeper depends uponthe following:• The rail weight• The sleeper spacing• The sleeper stiffness characteristics• The track modulus• The amount of ‘play’ between the rail and the sleeper• The amount of play between the sleeper and the ballast, and• Proud sleeper plates (in the case of timber sleepers)

The rail seat load (q) is critical in determining sleeper bending stresses, ballast depthand formation pressure and is determined by the formula:

Q = S.k.y.F

Where S = sleeper spacing (m)k = track modulus (MPa)y = maximum rail deflection caused by the superposition of alladjacent wheel loads (mm).F = factor of safety to account for varying ballast support tothe sleeper associated with the standard of trackmaintenance.

The above formula can be simplified as follows:Q = 0.75.P’.B.S.

Figure 3 can be used to estimate B (in lieu of formula previously given) for a given railsize.


Determination of Rail Section - Figure 2.0

0.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

0 5 10 15 20 25 30 35 40 45 50 55 60

Track Modulus (N/mm²)

Max

. Allo

wab

le S

ing

le D

ynam

ic W

hee

l Lo

ad (

kN)

AS1085-41AS1085-47AS1085-50AS1085-53AS1085-60


Determination of Beta Factor 'ß' - Figure 3.0

0

2

4

6

8

10

12

14

16

18

20

2.5 5 7.

5 10 12.5 15 17

.5 20 22.5 25 27

.5 30 32.5 35 37

.5 40 42.5 45 47

.5 50 52.5 55 57

.5 60

Track Modulus (N/mmº)

Bet

a (1

0000

mm

-1)

AS1085-31AS1085-41AS1085-47AS1085-50AS1085-53AS1085-60


Figure 4 can be used to derive the rail seat load for a given sleeper spacing, with afactor of safety (F) = 1.5.

Generally the maximum rail seat load will not exceed 0.5 to 0.6 of the dynamic wheelload.

3.8 Ballast Contact PressureThe average ballast contact pressure (p) between the sleeper and the ballast iscritical in the calculation of sleeper bending stresses and in assuring the ballaststructure is not over stressed.

Ballast Contact Pressure can be calculated by the following formula:p = q / b.l

Where b = breadth of the sleeper (m)l = effective length of the sleeper under one rail (m)

For Australian sleeper dimensions the following relationships generally apply:

p = 6.2q timber sleepers, narrow gaugep = 5.5q concrete sleepers, narrow gaugep = 6.4q steel sleepers, narrow gaugep = 5.4q timber sleepers, standard gaugep = 5.8q concrete sleepers, standard gaugep = 4.7q steel sleepers, standard gauge

However, with the development of a new sleeper types, it is recommended that theballast contact pressure is calculated using the formula which takes into account theeffective sleeper support beneath the rail seat. ie: p = q / b.l.

A significant amount of research has been carried out in order to derive the effectivelength of the sleeper under one rail. It is recommended that the following formulae areadopted:

• For standard and / or broad gauge sleepers

L = L – g where L = total sleeper length (mm)where g = distance between the centre line of the rail seats (mm)

• For narrow gauge sleepers

In = 0.8 (L – g)

Generally speaking the average contact pressure between the sleeper and the ballast(p) should not exceed 350 kPa for manually tamped track and 475 kPa for machinetamped track with high quality abrasion resistant ballast.

The AREA design manual recommends a maximum allowable contact pressure (p)of 450kPa for timber sleepers and 590 kPa for concrete sleepers. In both cases thislimit was suggested for high quality, abrasion resistant ballast and should be reducedappropriately if inferior ballast materials are used.


Determination of Single Seat Load - Figure 4.0

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

Single Rail Seat Load (q) - (kN)

Sin

gle

Dyn

amic

Wh

eel

Lo

ad x

Bet

a -

(kN

/mm

/100

0)

Sleeper Spacing (500mm)Sleeper Spacing (600mm)Sleeper Spacing (700mm)


3.9 Depth of Ballast

Figure 5 indicates the depth of ballast required based on allowable formationpressure, loading and sleeper dimensions.

The plots are based on the Boussinesq solution for stress at a point in an elastic,homogenous, isotropic medium below a circular plate.

Suggested safe average bearing pressures for subgrade are:

Alluvial soil, non compacted ground 70 – 105 kPaSoft clay, firm sand, sandy clay 110 – 140 kPaDry clay, firm sand, sandy clay 145 – 210 kPaDry gravel soils 215 to 275 kPaCompacted soils 280 kPa

Queensland Rail currently specify new embankments must have a CBR not less than20. (approximates to 210kPa).

An alternative method for establishing ballast depth and/or formation bearing pressureis to adopt the following empirical relationships:

• For standard and / or broad gauge sleepers (developed by Talbot in 1919).

σz = Pa (1/5.9.z1.25)

were σz = maximum vertical formation pressure

Pa = average pressure between the sleeper and the ballast (ie. Pa= 2.q/A where q = rail seat load (kN) and A = entire ballastcontact area of the underside of sleeper (m2).

z = ballast depth (m)

• For narrow gauge sleepers (developed by the Japanese National Railway)

σz = Pa [58 / (10 + (100z) 1.35)].

Clarke (1957) recommended that the maximum subgrade pressure should notexceed 83kPa for uncompacted formations and 139 kPa for compacted formations.


Determination of Depth of Ballast - Figure 5.0

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400

Depth of Ballast (m)

Ma

x.

All

ow

ab

le F

orm

ati

on

Pre

ss

ure

/Ra

il S

ea

t L

oa

d (

m-2

)

Broad Gauge

Standard Gauge

Narrow Gauge


4. Track Design Examples

4.1 Greenvale Line, Ore Traffic, North QueenslandAxle load = 20 tonneMaximum train speed = 60 km/hrWheel Diameter = 850 mmDetermine rail size, sleeper spacing and ballast depth

Contact StressesRatio Ps/D = 100/850

= 0.12 (which is not less than 0.11, ∴ check shear capacity)

T max = 410 (2Ps/D) 0.5

= 410 (200/850) 0.5

= 199 Mpa

Tall = 0.3 UTS= 0.3.800 for 41, 47, 53 kg/m rail= 240Mpa

Tmax<Tall. ∴ ok.

Dynamic Wheel LoadAREA: ∅ = 1 + 5.21 V/D

= 1 + (5.21.60/850) = 1.37

Eisenmann ∅ = 1 + δ.η.τ = 1 + (0.25 x 1 x 2.0) for good average track & 97.7% UCL = 1.5

ORE ∅ = 1.29 + 0.04.(V/100)3

= 1.29 + 0.04 (60/100)3

= 1.299

Adopt impact factor ∅ = 1.39P’ = 1.39 x 100 = 139 kN

Rail SelectionAssuming a track modulus (k) of 12 MPa, Figure 2 indicates a minimum rail size of 47kg/m.

Rail Seat LoadFrom Figure 3, B = 9.7 x 10-4 mm-1

Alternatively B = (k/4.E.I)0.25

= (12 / 4. 2x105. 15.92 x 106)0.25

= 9.85 x 10-4 mm-1

B.P’ = 9.7 x 10-4 x 139


= 0.134 kn/mm

Assuming a sleeper spacing of 610mm, Figure 3.0 indicates:q = 60 kN

Ballast Contact Pressurep = 6.2q for timber sleepers, narrow gauge = 6.2 x 60 = 372 kPa

pall. = 475kPa for machine tamped track

Ballast Depthq = 60kN

Assume safe average bearing pressure of 200 kPaRatio safe bearing to rail seat load = 200/60 = 3.33From Figure 5.0 minimum depth of ballast required = 200mm

Alternatively adopt JNR equation *:σz = Pa [58/(10 + (100z)1.35)]* JNR equation applies for narrow gauge track onlyz = [((116q/σz.A) – 10) 0.74074]/100

z = 209mm

Workshop ExerciseWhat would be the impact on the permanent way if the operation requirements werechanged such that:• Axle loads increased to 25 tinne• Vehicle speed increased to 80 km/hr

(clue: assume track modulus (k) = 15; P’ = 179kn)


5. ConclusionThis paper provides only a brief introduction to the very extensive subject ofpermanent way design and is aimed at providing a basic understanding.

The design procedures presented in this paper are only approximate solutions thatcan be used as a guide to track component selection as a first order estimate. Moredetailed analysis will, in general, be necessary before selection of the track structurecan be established.

In addition this paper has only dealt with the structural engineering aspects of thepermanent way; of equal importance in the selection of the track structure and itscomponents are the economic factors relating to capital expenditure, life cyclereplacement costs and maintenance costs.

With sophisticated technical / economic analyses it is possible to select the optimumeconomic solution for a range of technical alternatives.


6. References

ROA ‘A review of track design procedures – Volume 1 Rails’

ROA ‘A review of track design procedures – Volume 2 Sleepersand Ballast’

PWI ‘British Railway Track – design, construction andmaintenance’

Hagaman, B.R. ‘Track Design’

Broadley, J ‘Track Loading’

SKM Technical Paper - Pway Design

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