dynamic stress analysis of railway track bed under train passage

8/17/2019 Dynamic stress analysis of railway track bed under train passage

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Dynamic Stress Analysis of a Railway Track Bed during

Train Passage

Project-2 (CE47006) report submitted toIndian Institute of Technoo!"# $hara!pur

in partia fufiment for the a%ard of the de!ree of

&acheor of Technoo!" ('ons)

InCii En!ineerin!

VIVEK KUAR

!"#E$!%!"

*nder the superision of

Prof& Su'it Kumar Das(

De)artment of #i*il Engineering

Indian Institute of Tec(nology+ K(arag)urS)ring Semester+ "%!,-!.

"/t( A)ril+ "%!.

+


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DE#0ARATI12

I certif" that(a) The %or, contained in this report has been done b" me under the !uidance of m"

superisor

(b) The %or, has not been submitted to an" other Institute for an" de!ree or dipoma

(c) I hae conformed to the norms and !uideines !ien in the Ethica Code of Conduct of the Institute

(d) heneer I hae used materias (data# theoretica ana"sis# fi!ures# and te.t) from other

sources# I hae !ien due credit to them b" citin! them in the te.t of the thesis and !iin!their detais in the references /urther# I hae ta,en permission from the cop"ri!ht o%ners of

the sources# %heneer necessar"

ate1 ie, $umar

Pace1 $hara!pur +2CE3+0+2

DEPARTE2T 13 #IVI0 E24I2EERI24

2


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I2DIA2 I2STITUTE 13 T5E#5210146+ K5ARA4PUR

K5ARA4PUR-7"!$%"+ I2DIA

CERTIFICATE

This is to certif" that the project report entited 8Dynamic Stress Analysis of a

Railway Track Bed during train )assage submitted b" Vi*ek Kumar

9!"#E$!%!": to Indian Institute of Technoo!"# $hara!pur to%ards partia

fufiment of reuirements for the a%ard of de!ree of &acheor of Technoo!"

('ons) in Cii En!ineerin! is a record of bonafide %or, carried out b" him under

m" superision and !uidance durin! 5prin! 5emester 20+-+6

Prof& Su'it Kumar Das(Date; De)artment of #i*il

Engineering

Place; K(arag)ur Indian Institute of

Tec(nology

K(arag)ur+ India

3


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2 ;ITE8ET'99;9?=::::::::::::::::::+3

4 8E5*;T5:::::::::::::::::::::+6

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&aast and sub-baast a"ers are important components of a conentiona rai%a" trac,

s"stem 9ne of their main functions is to preent the transmission of dama!in! stress

chan!es to the under"in! natura !round or sub!rade 5pecification of the a"er thic,ness

needed to do this %as for man" decades based ar!e" on custom and practice ore recent %or, hi!hi!hted the potentia importance of the rotation in principa stresses

%ithin the sub!rade as trains pass (&ro%n +@@6# ?rabe and Ca"ton 200@)# and su!!ested

%a"s in %hich the compe. patterns of stress chan!e induced b" train passa!e coud be

appro.imated in aborator" tests (Po%rie 2007)

!&!

Aim of t(e Study

The aim of this thesis is to ana"Ae the d"namic effects of the rai%a" trac, In the present

stud" d"namic effects are studied usin!


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" 0ITERATURE REVIE<

"&! Pro)erties of track com)onents

6


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"&!&! Rail

The rai beam mode is supported on" at the boundaries The rai ma" be modeed either asan ordinar" Euer-&ernoui (E-&) beam or as a 8a"ei!h-Timoshen,o (8-T) beam

Euler-Bernoulli Beam (E-B beam)

In the E-& beam theor" on" bendin! of the rai is ta,en into account# and in case of

ibrations# on" the mass inertia in transation of the beam is incuded To obtain an euation

for the transerse ibration in a t%o-dimensiona beam the foo%in! structure is studied

The beam is subjected to an e.terna force and has a distributed mass and fe.ura ri!idit" EI

%hich can ar" %ith position and time# %hich is sho%n in /i!ure +

Figure 1: (a) Beam and applied force, (b) force acting on

an element

"&!&" T(e Rail )ads and 3astening

/rom a trac, d"namic point of ie%# the rai pads pa" an important roe The" infuence the

oera trac, stiffness < soft rai pad permits a ar!er defection of the rais %hen the trac, is

oaded b" the train 'ence the a.e oad from the train is distributed oer more seepers

&esides# since soft rai pads can suppress the transmission of hi!h-freuenc" ibrations

7


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do%n to the seepers and further do%n into the baast# the" aso contribute to isoate hi!h-

freuenc" ibration

The most common" used ph"sica mode of a rai pad is the sprin!-damper s"stem The

sprin! can be assumed to be inear# and the dampin! is assumed to be proportiona to the

deformation rate of the rai pad


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The effect of the baast is to distribute the oads from the seepers to the soi *sua"# a

a"er of sub-baast preents the penetration of the baast partices into the soi or ice ersa

&aast is a compe. medium because of its !ranuar properties The baast is constituted b"

stone partices The behaior of the baast is not %e-,no%n because of the compe.it" of

the interactions bet%een partices < !ranuar media can hae behaior both i,e soids and

iuids1 on one hand# the baast supports seepers on the other hand# the iuefaction of

baast is a dan!erous probem %hich can cause deraiment ithout an" train oadin!s#

interna forces in the baast are o% urin! train passa!es# the friction bet%een partices

increases and the baast is compressed b" the train oadin! To proide safet" a!ainst baast

instabiit"# the European and 5%edish codes specified a imit of 3 mBs2 ma.ima ertica

dec, acceeration (CE# 2002 and The 5%edish ationa 8ai


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/i!ure 21 Painting line on the ballast during measurements.

# a stiffness $ and a

dampin! C


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of a static oad and a d"namic component superimposed on the static oad The static oad is

the dead %ei!ht of the train and superstructure# %hie the d"namic component# %hich is

,no%n as the d"namic increment# depends on the train speed and the trac, condition The

hi!h sueeAin! force of maintenance tampin! has been found to cause si!nificant dama!e to

baast &esides these t%o main forces# baast is aso subjected to atera and on!itudina

forces %hich are much harder to predict than ertica forces

The dead %hee oad can be ta,en as the ehice %ei!ht diided b" the number of %hees

The d"namic increment aries %ith train section as it depends on trac, condition# such as

rai defects and trac, irre!uarit"

3igure $; Distri>ution of load from w(eels to su>->allast

"&$ Dynamic effects

"namic finite-eement ana"ses carried out b" ?rabe (2002) and ?rabe and Ca"ton (200@)

indicated that a static ana"sis# in %hich d"namic effects are i!nored# mi!ht be acceptabe for

speeds up to 240 ,mBh (67 mB s) on a firm sub!rade 'o%eer# hi!h-speed rai%a"s %ith ine

speeds of up to 300 ,mBh are increasin!" bein! constructed1 thus the adeuac" of a static

ana"sis to assess the chan!es in stress e.perienced b" the sub!rade durin! train passa!e

cannot be ta,en for !ranted It is ,no%n that resonance-t"pe effects mi!ht resut in e.cessie

++


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!round moements if the speed of the train approaches the 8a"ei!h %ae eocit" for the

soi Timoshen,o +@27 $r"o +@@# +@@6

c Cs

here C depends on the Poissons ratio# and !enera" ran!es from 0@++ to 0@ sshear

%ae eocit" This is uni,e" to be a probem for most sub!rades# for %hich the 8a"ei!h

%ae eocit" %i be in the order of 00 mBs# but has been obsered in sois such as peats

and soft ca"s %ith a 8a"ei!h %ae eocit" of 40J0 mB s (>adshus and $a"nia 2000)The

effects of train speed on the stress paths to %hich soi eements in the sub!rade beo% a

baasted rai%a" trac, are inesti!ated in this paper b" means of a d"namic finite-eement

mode

$ ET51D10146

$&! 3inite-Element odel

The finite-eement mode is based on a section of rai%a" tac, at &ouban,# 60 ,m south of

r"heid on the &roodsn"erpaas to 8ichards &a" C9


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The rai%a" %as recent" reconstructed to 5poornet hea" hau standards to carr" 26 t a.e

oads This inoed repacin! the natura !round beo% the trac, %ith four a"ers of made

!round# desi!nated 55 5 ! rais aid to a !au!e

of +#06 mm# %ith concrete seepers paced at a spacin! of 60 mm on a 300 mm depth of

baast

The rai%a" trac, %as modeed as a t%o-dimensiona (2) d"namic s"stem usin! the finite-

eement pac,a!e


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Fig.5 Finite element mesh of 2D model

TABLE 1

+4

Component

escription

=oun!s

>oduus(E)

(>Pa)

Poissons ratio ensit" ($!Bm3)

8ai 2+0#000 03 7#D0

5eeper 30#000 02 2400

&aast +00 03 +D00

5ub-&aast 32+ 03 2300

55& 2@6 03 2200


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=& RESU0TS

=&! es( #on*ergence Study

>esh coner!ence stud" %as done for three mesh siAes 02# 0+ and 00 and it %as found

out that there %as a si!nificant deiation in cacuated resuts dependin! upon the mesh siAe

This impies that stress aues depend upon mesh siAe and !ie accurate resuts %ith sma

mesh siAe eements In the present stud" the resuts are cacuated for a mesh siAe of 00

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-80000

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

10000

Mesh Convergence

mesh=0.2 mesh=0.1 mesh=0.05

Time9sec:

2ormal Stress9Pa:

+


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=&" Stress *ariation wit( De)t(

In the present stud" norma stresses in " direction are cacuated aon! the depth of the

mode at a depth of 0# 02# 04# and 0D (in m) b" ta,in! baast depth as reference %ith the

passa!e of train in different a"ers as &aast# 5 55& and


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-120000

-100000

-80000

-60000

-40000

-20000

0

20000

Normal Sress variaion !ih "e#h

d=0 d=0.2 d=0.4 d=0.6 d=0.8

ime(m$s)

Normal sress(%a)

Ta>le "

#om)arison wit( stresses com)uted >y 4ra>e 9"%%,: using 4E1TRA#K

epth beo% baast a"er(mm) Cacuated usin! ?E9T8


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

20

40

60

80

100

120

Ma& Normal S ress 'ariaion ! ih "e#h

"e#h(m)

ma& normal sress(%a)

=&$ Stress *ariation in t(e locality of an unsu))orted slee)er

Poor draina!e or differentia settement of the subbase ma" ead to some seepers not bein!

fu" supported# or een compete" unsupported# resutin! in increased defections and

%hee-rai contact forces at the nearb" seepers If one seeper is unsupported# the

nei!hbourin! seepers must carr" a hi!her oad eadin! to oca" increased stresses in the fi

+D


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andBor sub!rade a"ers The chan!es in stress in the fi and in the natura !round that ma"

occur as a resut of an unsupported seeper %ere inesti!ated usin! the finite-eement mode

3ig 7 #ontour of *ertical stresses near unsu))orted slee)er

=&= Effects of Train S)eed on Stress

The estimated =oun!s moduus of a"er


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therefore inesti!ated Train speeds are e.pressed as a function of the 8a"ei!h %ae

eocit"# c

In this stud" "oun!s moduus of a"er Pa and the effect of train

speed %as monitored usin! 2


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30 35 40 45 50 55 60 65 70 7550000

55000

60000

65000

70000

75000

80000

Ma& Normal Sress

veloci,(m$s)


Variation of max normal stress ith !elo"it# "hange

=&, Effect of acceleration and Braking on stress

In addition to ertica oads# a moin! train %i e.ert on!itudina forces at the %hee rai

interface /or a train traein! at a constant speed# for%ard forces %i be reuired to

oercome the effects of roin! and %ind resistance /or a constant speed these forces are

!enera" sma but in case of acceeration and bra,in! these forces can increase to +00 times

of the forces in case of Aero acceerationBbra,in! Ese (200+)

In this mode these resuts %ere incorporated b" increasin! the friction coefficient bet%een

%hee and rai 5tresses %ere compared %ith friction coefficient aues of 0# 02 and 04

2+


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

12000

Shear Sress variaion ! ih cceleraion

=0 =0.25 =0./

+ime(sec)

Shear sress(%a)

=&. Stress Variation wit( slee)er gauge distance

5eepers are an essentia part of rai%a" trac, These are most inte!ra part of trac, in

distributin! the oad appied b" train %hee to the baast


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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-140000

-120000

-100000

-80000

-60000

-40000

-20000

0

20000

Normal Sress 'ariaion ! ih slee#er "isance

"=0. "=0.* "=0.*5 "=0.

ime(sec)

normal sress(%a)

23


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0.6 0.65 0.7 0.75 0.8 0.8580000

90000

100000

110000

120000

130000

140000

ma&imum Normal Sress

slee#er ga#


,& SUAR6 A2D #12#0USI12

24


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< 2 d"namic finite-eement ana"sis has been used to inesti!ate the effect of train speeds#

acceerationBbra,in!# seeper !au!e distance and unsupported seepers on the stress paths

e.perienced b" eements of soi in the subbase and the under"in! natura !round durin!

train passa!e

"namic effects be!in to hae an effect on the stresses imposed on the soi as the train speed

approaches 8a"ei!h %ae speed and there is steep increment in the stress aue after train

speed crosses 8a"ei!h %ae speed


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?rassie# 5 ;# and Co.# 5 L M+@DM GThe d"namic response of rai%a" trac, %ith

unsupported seepersH $. %utomobile Eng. Po%rie# # =an!# ;

dynamic stress analysis of railway track bed under train passage

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