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CONTACT LOSS BETWEEN RAILWAY TRACK AND SUBGRADE IN VERTICAL PLANE DURING ROADBED RESEARCH a
Wołodzimierz Bednarek & Alfredas Laurinavičius
b
a
Division of Railway Construction, Institute of Civil Engineering, Faculty of Civil and Environmental Engineering and Architecture, Poznań University of Technology , ul. Piotrowo 5, 61-138 , Poznań , Poland E-mail: b
Dept of Roads , Vilnius Gediminas Technical University , Saulėtekio al. 11, LT-2040 , Vilnius , Lithuania E-mail: Published online: 26 Jul 2012.
To cite this article: Wołodzimierz Bednarek & Alfredas Laurinavičius (2003) CONTACT LOSS BETWEEN RAILWAY TRACK AND SUBGRADE IN VERTICAL PLANE DURING ROADBED RESEARCH, Journal of Civil Engineering and Management, 9:1, 10-15, DOI: 10.1080/13923730.2003.10531295 To link to this article: http://dx.doi.org/10.1080/13923730.2003.10531295
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10 ISSN 1392-3730
JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt!cnglish/cditions
2003, Vol IX No 1, 10-15
CONTACT LOSS BETWEEN RAILWAY TRACK AND SUBGRADE IN VERTICAL PLANE DURING ROADBED RESEARCH Wlodzimierz Bednarek 1, Alfred as Laurinavicius 2 1
Division of Railway Construction, Institute of Civil Engineering, Faculty of Civil and Environmental Engineering and Architecture, Poznan University of Technology, ul. Piotrowo 5, 61-138 Poznan, Poland. E-mail:
[email protected] 2 Dept of Roads, Vilnius Gediminas Technical University, Sauletekio a/. 11, LT-2040 Vilnius, Lithuania. E-mail: aljla@ap. vtu.lt
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Received 09 Oct 2001; accepted 21 Nov 2002 Abstract. In the paper a new method of railway subgrade investigation is analysed. Contact loss between track and subgrade in vertical plane is considered. During the roadbed investigations the rail is jacked up using a plate called ,VSS". It is assumed that variable temperatures have influence on the rail which is laid on a curved roadbed. Elasticity of the railway roadbed is calculated. Finally formulas and dependences of various types of track structures are obtained. Keywords: railway, roadbed, flexibility, curve radius, influence of temperature.
1. Introduction
Since 1994 modernisation of E-20 line is being done in Poland. Geotechnical investigation of sub grade is based mainly on measuring modulus of elasticity (beyond standard geotechnical research - exploratory bore-holes, sounding, laboratory studies) [1-3]. This method, when VSS plate with equipment is used, gives the occasion to static pressure on layer of roadbed. Usually a plate of 30 em diameter is used. Before railway line reconstruction geotechnical research of roadbed was carried out. During the research the problem of measurement of elasticity modulus arose. As the trains pass the rail track, it is impossible to use optional counterbalance. That's why mainly the weight of track is used to carry out measurements. The scheme of the first way of research is shown in Fig 1. There are some doubts about this method (first of all a very heavy supporting rail (4)- difficult transporting and fitting, no direct support of the rail (arose offcentre) and rail movement - (changing state of track). Because of that brand a new method of measurement was created [4].
2
a)
6
2. Research using the new method The new method is applied using a channel bar fastened to the ends of neighbouring sleepers. It results in reducing the movement of track (supported directly above the tested point) and deviation from the centre (Fig 2).
Fig 1. Equipment used during the first measurement: a) plan, b) profile. I -- stiff plate, 2 - tripod, 3 - steel bars to fasten gauges, 4 - supporting rail, 5 - hydraulic lift, 6 - gauges, 7 - stiffing ring, 8 - hydraulic pump
11
W Bednarek, A, LaurinaviCius I JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT- 2003, Vol IX No I, 10-15
-
,---
-
,---
,--
,--
-
,--
,---
,--
,--
-~
X
T.T.T.1.T./f:{.1 .1.1.1.1~ c~lhr
1
j
\ , •rce appW::aliox •• Z a:ds
YPTIWITITITITITITIT~TITITI
MQ
g
. '~-~El
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,.~
k
Fig 2. Diagram of the investigated section: a) horizontal view; b) longitudinal section
0
:...
'I
'!
D
g ... =g
3. Contact loss between railway track and subgrade in vertical plane Fig 3. Computed model
3.1. Model description In this model track is regarded as a clamped beam. In the analysis, lateral applied force, preliminary curve and flexibility of subgrade are considered. It is assumed that: 1) sub grade is flexible; 2) beam length modification is neglected; 3) only half of external force (Q) affects the beam (symmetric configuration); 4) influence of shear force (T) on system of internal active force is neglected. Computed track is loaded by a continuous load g (weight of track) and concentrated force Q (repair machines or testing equipment). The following configuration is calculated [5]: - track as a heavy beam (weight, g); - bending stiffness in vertical plane EI; - compression by lateral force H; - the track is laid on the curved Winkler's roadbed (with radius R0 ) with railway ballast at roadbed coefficient (k) per length segment of the track. The track is lifted by external force (Q) (for example, during research of roadbed) on length (I) (Fig 3) [5]. Because of the system symmetry, only the right side of the beam CBD is considered [6].
For the interval CB (bar without roadbed contact, Fig 3) we obtained a differential equation: ~2
+ H ·(f -
y) +
Q g·x2 · x2 2
For interval BD (bar with roadbed contact, in Fig 3) we have obtained:
H d2v
k
g
k
(2)
El d X 2 + El y( X) = El y p + E/ 0
0
where a slightly curved roadbed deflection is given as a function: x2
(3)
.vo=--, 2· R0
where R0 - radius of a curved Winkler's roadbed. Finally, the equation of deformed beam for interval CB is: d4y dx 4
2
H d y g =--·----· El dx: 2
(4)
El
After substitution:
~2
=
H E·l
(5)
Final solution of the calculated equation (4) is: y
= A-sin~x+B·cos~x+C+D·x-
g·x 2 2·H
.
(6)
Four unknowns A, B, C and D we obtain from the following boundary conditions:
3.2. Static and mathematical analysis
d2y El · ·· = Mc
k ... = k
(1)
X=
dv O· = 0 'dx ' 0
(7)
(8)
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W Bednarek, A, LaurinaviCius I JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT- 2003, Vol IX, No /, 10--15
Considering the above dependences we obtain: from the first condition A=-
2
2-
=d Yl_ ., I -2 x=O dx- x=2 dx
3od_ Y
Q ---.
(9)
2·H·~'
from the second condition
The contact condition [ 10] has to be taken into consideration as well: 0
5 y
(10) Finally we obtain the following form of equation (without the unknowns B and C): Q
.
")
g ·X-
Q
V= - - - .Sin ~X+ B . cos ~X+ c + . X. 2·H·~ 2·H 2·H g·x
l =yporazyO=yp. 2
(19)
From the first of the four conditions we obtained the system of four non-linear equations with four unknowns. From the condition 5° we have:
(20)
yO=yp.
2
(11)
2·H
The following equation is obtained:
Doing similar assumptions for the interval BD (2) we obtain a solution in local coordinate system:
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and
B= g.
(21)
k Substituting the dependences shown above, we obtained the system of non-linear equations:
2
·(C ·sin(
