NUMERICAL ANALYSIS ON STATIC LOAD CAPACITY
OF PRESTRESSED CONCRETE SLEEPERS
UNDER HYPOTHETICAL BEARING PRESSURE DISTRIBUTION
WAN AZLAN BIN WAN ABDUL RASHID
A project report submitted in partial fulfillment of the
requirement for the award of the degree of
Master of Engineering (Civil – Structure)
Fakulti Kejuruteraan Awam
Universiti Teknologi Malaysia
JANUARY 2012
ii To my beloved mother and family
iv ACKNOWLEDGEMENT
Countless appreciation to my mother and family who had supporting me
throughout my life.
I must thank my thesis supervisor, Dr. Izni Syahrizal Ibrahim who had given
me the chance to pursue this topic for my thesis. His constant support, motivation
and valuable guidance were very important and I must thank him for all his time on
supervising my thesis.
My special thanks to every staff and students at the Faculty of Civil
Engineering at Universiti Teknologi Malaysia for all the valuable experiences and
knowledge I had obtained during my study for the Masters programme at the
university.
A special acknowledgement to my office mates for being very supportive
and understanding during my study.
Thank you to all my friends for their joy and laughter and not to forget to
anyone who had been involved directly and indirectly in developing this thesis.
This thesis is a dedication to my beloved mother and family.
v ABSTRACT
Prestressed concrete sleepers are currently designed based on permissible
stresses concepts resulting from quasi-static wheel loads. It was designed to exceed
the mean working load to avoid loss of bond in the prestressing due to cracking of
the concrete sleepers. These loads allow for static response of the sleeper due to the
mechanism of vertical load transfer between the rail and sleeper as well as the
sleeper and ballast interaction. In practice, the designer apply uniform pressure
distribution beneath each rail seat which is dependent on the track gauge and
sleeper length as stipulated in many design standards. Applying uniform pressure
distribution beneath each rail seat may not be necessarily applicable to all in-situ
sleepers as the contact pressure distribution between sleepers and ballast is mainly
influenced by the cumulative effect of the traffic loading at various speeds over a
period of time as well as the quality of ballast maintenance. A significant amount of
research has been conducted by researchers worldwide over the century in
postulating a set of hypothetical contact pressure distribution on the sleeper-ballast
interaction. This leads to predicament as to whether the designed sleepers under the
assumption of uniform contact pressure distribution had the adequate static load
capacity to withstand the designed vertical loading but under different contact
pressure distribution pattern. To solve this predicament, numerical analysis using
commercially available finite element package, LUSAS, is carried out and
comparison is made with the experimental test results in validating the finite
element model. The numerical analysis will be useful in predicting the maximum
vertical loading prior to the cracking of the sleeper under various hypothetical
contact pressure distribution patterns. From numerical analysis, prestressed
concrete sleeper that is placed on ballast has reserve strength in static load capacity
with a factor between 2.2 and 2.4 of the positive rail seat test load at crack
initiation.
vi ABSTRAK
Reka bentuk sleeper konkrit prategasan adalah berdasarkan kepada konsep
tekanan yang dibenarkan, hasil daripada aksi beban kuasi-statik roda. Ia direka
bentuk untuk melebihi purata beban kerja bagi mengelakkan kehilangan daya
tarikan di dalam prategasan yang disebabkan oleh keretakan. Beban ini
membenarkan respon statik oleh sleeper yang disebabkan oleh mekanisma
perpindahan beban menegak di antara rel dan sleeper serta interaksi antara sleeper
dan ballast. Pereka bentuk mengenakan tekanan rata yang seragam di bawah setiap
kerusi rel yang bergantung kepada tolok landasan dan panjang sleeper seperti mana
ditetapkan di dalam banyak piawaian. Mengenakan tekanan yang seragam di bawah
kerusi rel mungkin tidak benar untuk semua sleeper di landasan kerana tekanan
permukaan di antara sleeper dan ballast dipengaruhi oleh kesan kumulatif daripada
beban
trafik
pada
pelbagai
kelajuan
pada
suatu
tempoh
serta
kualiti
penyelenggaraan ballast. Jumlah penyelidikan yang ketara telah dilakukan oleh
para penyelidik di seluruh dunia dalam menyediakan satu set hipotesis tekanan rata
bagi interaksi sleeper-ballast. Ini membawa kepada persoalan samada reka bentuk
sleeper dibawah andaian tekanan yang seragam mempunyai kapasiti yang
mencukupi untuk menahan rekaan beban menegak tetapi di bawah pelbagai bentuk
hipotesis tekanan rata. Untuk menyelesaikan persoalan ini, analisis berangka
menggunakan pakej perisian komersil untuk model unsur terhingga, LUSAS,
dijalankan dan perbandingan dibuat dengan keputusan daripada ujian uji kaji dalam
mengesahkan penggunaan model unsur terhingga. Analisis berangka ini sangat
berguna untuk meramalkan beban menegak yang maksima sebaik sebelum
keretakan sleeper dibawah pelbagai bentuk hipotesis tekanan rata. Berdasarkan
kepada keputusan analisis berangka, sleeper konkrit prategasan yang diletakkan di
atas ballast mempunyai kekuatan rizab pada kapasiti beban statiknya iaitu diantara
factor 2.2 dan 2.4 daripada beban ujian positif kerusi kereta api semasa keretakan
mula berlaku.
vii TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DEDICATION
ii
DECLARATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xii
LIST OF SYMBOLS
xx
LIST OF APPENDICES
xxi
INTRODUCTION
1
1.1. Modernization of the ballasted railway track
1
network in Malaysia
1.2. Functions of track components and the load
2
path
2
1.3. Problem statement
4
1.4. Objectives of the study
6
1.5. Scopes of the study
7
LITERATURE REVIEW
8
2.1. Development of prestressed concrete sleepers
8
2.2. Prestressed as the preferred concrete sleepers
9
viii 2.3. Load assessment on prestressed concrete
10
sleepers
2.4. Beams on elastic foundation and the ballast
13
stiffness
2.5. The centre negative moment test experiment
15
2.6. Nonlinear finite element model of railway
18
prestressed concrete sleeper
2.7. Current practice in the theoretical analysis to
22
design sleepers
3
RESEARCH METHODOLOGY
24
3.1. Introduction
24
3.2. Finite element model for the centre negative
25
moment experimental setup
3.2.1.
Creating a new model
25
3.2.2.
Defining the geometry
26
3.2.3.
Defining the mesh – prestressing tendon
29
3.2.4.
Defining the mesh – concrete
30
3.2.5.
Defining the geometric properties
31
3.2.6.
Defining the material properties –
32
prestressing tendon
3.2.7.
Defining the material properties –
34
concrete
3.2.8. Assigning attributes to the prestressing
36
tendons
Assigning attributes to the concrete
38
3.2.10. Supports – Centre negative moment
40
3.2.9.
experimental setup
3.2.11. Loading – Self weight
42
3.2.12. Loading – Initial strain on prestresing
43
tendons
3.2.13. Loading – Vertical point load setup for
the centre negative moment test
45
ix 3.2.14. Nonlinear control
47
3.2.14.1. Loadcase 1
48
3.2.14.2. Loadcase 2
50
3.2.15. Running the analysis
52
3.2.16. Viewing the results
53
3.3. Finite element model with the hypothetical
58
bearing pressure distribution patterns
3.3.1.
Support – Hypothetical bearing
58
pressure distribution patterns
4
RESULTS, ANALYSIS AND DISCUSSIONS
62
4.1. Validation of LUSAS’ nonlinear finite element
62
model
4.2. Numerical analysis on static load capacity of the
64
prestressed concrete sleepers under hypothetical
bearing pressure distribution
4.2.1. Cracking load, ultimate load and crack
65
patterns
4.2.2. Load-deflection response at first crack
67
section
4.2.3. Vertical deflection along the sleeper’s
68
length
4.2.4 Principal stress distribution in x-
70
direction on first crack section
4.3. Summary of static load capacity of the
72
prestressed concrete sleepers under hypothetical
bearing pressure distribution
5
CONCLUSIONS AND RECOMMENDATIONS
75
5.1. Conclusions
75
5.2. Recommendations
76
REFERENCES
77
APPENDICES
80
x LIST OF TABLES
TABLE NO.
2.1
TITLE
Hypothetical bearing pressure distribution of sleeper
PAGE
12
(Sadeghi, 2005)
2.2
Material models used by Kaewunruen and Remennikov
20
(2006b) in ANSYS
4.1
Numerical analysis results of LUSAS’ nonlinear finite
66
element model on the cracking load, ultimate load and
crack patterns of the prestressed concrete sleeper under
hypothetical bearing pressure distributions
4.2
Maximum vertical deflections and comparison with
69
previous work by Sadeghi (2005)
4.3
Maximum principal stress in x-direction and
71
comparison with previous work by Sadeghi (2005)
4.4
Static load capacity between test and numerical analysis
74
A.1
Input for the line geometry in LUSAS
80
A.2.1.1.
Laboratory test (Sadeghi, 2005)
83
A.2.1.2.
Input for spring support stiffness distribution in LUSAS
83
A.2.1.3.
Summary of results at first crack point
84
A.2.2.1.
Tamped either side of rail (Sadeghi, 2005)
86
A.2.2.2.
Input for spring support stiffness distribution in LUSAS
86
A.2.2.3.
Summary of results at first crack point
87
A.2.3.1.
Principal bearing on rails (Sadeghi, 2005)
89
A.2.3.2.
Input for spring support stiffness distribution in LUSAS
89
A.2.3.3.
Summary of results at first crack point
90
xi A.2.4.1.
Maximum intensity at the ends (Sadeghi, 2005)
92
A.2.4.2.
Input for spring support stiffness distribution in LUSAS
92
A.2.4.3.
Summary of results at first crack point
93
A.2.5.1.
Maximum intensity in the middle (Sadeghi, 2005)
95
A.2.5.2.
Input for spring support stiffness distribution in LUSAS
95
A.2.5.3.
Summary of results at first crack point
96
A.2.6.1.
Center bound (Sadeghi, 2005)
98
A.2.6.2.
Input for spring support stiffness distribution in LUSAS
98
A.2.6.3.
Summary of results at first crack point
99
A.2.7.1.
Flexure of sleeper produces variations form (Sadeghi,
101
2005)
A.2.7.2.
Input for spring support stiffness distribution in LUSAS
101
A.2.7.3.
Summary of results at first crack point
102
A.2.8.1.
Well tamped sides (Sadeghi, 2005)
104
A.2.8.2.
Input for spring support stiffness distribution in LUSAS
104
A.2.8.3.
Summary of results at first crack point
105
A.2.9.1.
Stabilized rail seat and sides (Sadeghi, 2005)
107
A.2.9.2.
Input for spring support stiffness distribution in LUSAS
107
A.2.9.3.
Summary of results at first crack point
108
A.2.10.1.
Uniform pressure (Sadeghi, 2005)
110
A.2.10.2.
Input for spring support stiffness distribution in LUSAS
110
A.2.10.3.
Summary of results at first crack point
111
xii LIST OF FIGURES
FIGURE NO.
1.1
TITLE
Cross sectional layout of a typical ballasted track
PAGE
2
(Selig & Waters, 1994)
2.1
Deflections of elastic foundations under uniform
13
pressure: a- Winkler foundation; b- practical soil
foundation (Teodoru, 2009)
2.2
Load distribution region in continuous granular ballast
14
(Zhai et al., 2004)
2.3
Model of ballast under one rail support point (Zhai et
14
al., 2004)
2.4
The modified model of the ballast (Zhai et al., 2004)
14
2.5
Schematic diagram of centre negative moment test
15
experiment (AS 1085.14-2003)
2.6
Load-deflection results by Kaewunruen and
16
Remennikov (2006a)
2.7
Multi-linear stress-strain curve of concrete by
17
Kaewunruen and Remennikov (2006a)
2.8
Multi-linear stress-strain curve of prestressing tendon
18
by Kaewunruen and Remennikov (2006a)
2.9
Finite element model of prestressed concrete sleeper
19
by Kaewunruen and Remennikov (2006b)
2.10
Model for reinforcement in finite element model
(Tavarez, 2001): a) discrete; and b) smeared
20
xiii 2.11
Load-deflection response of experimental and model
21
of the prestyressed concrete sleeper by Kaewunruen
and Remennikov (2006b)
3.1
Inputs for File details and Model details in New Model
26
window
3.2
Selected segments of Line geometry
26
3.3
Surface geometry creation by line sweeping
27
3.4
Surface geometry of concrete excluding the increased
27
section at the rail seat
3.5
Increased section at the rail seat
28
3.6
Surface geometry for the chamfer at rail seat
28
3.7
Structural bar element definition for the line mesh to
29
model the prestressing tendons
3.8
Structural plane stress element definition for the
30
surface mesh to model the concrete
3.9
The cross sectional area to model the geometric line
31
for 4 nos. prestressing tendons
3.10
The concrete thickness to model the Geometric Surface
32
for the concrete
3.11
The isotropic material properties of the prestressing
33
tendon in elastic region
3.12
The isotropic material properties of the prestressing
34
tendon in plastic region using von Mises Stress
Potential model
3.13
The isotropic material properties of the concrete in
35
elastic region
3.14
The isotropic material properties of the concrete in
36
plastic region using Concrete model (Model 94)
3.15
Selection of lines geometry that represents the
37
prestressing tendons
3.16
The assigned properties on the selected line elements
37
3.17
Selection of surface geometry that represents the
38
concrete
xiv 3.18
The meshed surface’s plane stress elements
38
3.19
Selection of line geometry for non-structural line
39
element (None 40 mm) assignment
3.20
Selection of line geometry for non-structural line
39
element (None 1 spacing) assignment
3.21
Surface’s plane stress elements with low aspect ratio
39
and 90 degrees quadrilateral shape and the model
dimensions in LUSAS
3.22
Rotate attributes in Move window
40
3.23
Structural support definition
41
3.24
The assigned structural support on the model
41
3.25
Body Force for the Self Weight
42
3.26
Loading Assignment for the Self Weight
43
3.27
The assigned Self Weight loading on the model
43
3.28
The Initial Strain loading on the prestressing tendons
44
3.29
Loading Assignment for the Initial Strain
44
3.30
The assigned Initial Strain loading on the model
45
3.31
The Vertical Point Load attributes
46
3.32
Loading Assignment for the Vertical Point Load
46
3.33
The assigned Vertical Point Load on the model
47
3.34
The incremental-iterative method for nonlinear
47
solution
3.35
The nonlinear control of loadcase selection
48
3.36
The nonlinear control for Loadcase 1
49
3.37
The Advanced nonlinear control for Loadcase 1
50
3.38
The nonlinear control for Loadcase 2
51
3.39
The selected point at midspan to be set with
51
Termination criteria
3.40
The Advanced nonlinear control for Loadcase 2
52
3.41
Setting the Increment Load Factor to active
53
3.42
The deformed mesh
54
3.43
The nodal number
54
xv 3.44
Load-deflection response form the Graph Wizard
55
3.45
Principal stress distribution in global x-direction (SX)
56
3.46
Crack pattern on the model
56
3.47
Animation Wizard to display animated results of all
57
loadcase
3.48
Compressing the animation using Microsoft Video 1
57
compressor
3.49
Identification of line segments
58
3.50
Spring support stiffness’ Line Variation inputs for
59
Segments 3
3.51
Selecting Segment 3 as the Variation Attribute for the
60
spring support stiffness
3.52
Structural supports to represent the ballast stiffness at
60
Segment 3
3.53
Spring support that represents the ballast stiffness for
61
Principal bearing on rails scenario
4.1
Comparisons of load-deflection response between
63
experimental results and LUSAS model
4.2
Load-deflection response at first crack point
67
4.3
Vertical deflection along the sleeper’s length
68
4.4
Principal stress in x-direction on the first crack section
70
A.1.
Model dimensions in LUSAS
80
Hypothetical bearing pressure distribution patterns
83
A.2.1.1.
(LUSAS model)
A.2.1.2.
Unloaded with external load
84
A.2.1.3.
At initiation of crack (external load = 485 kN)
84
A.2.1.4.
At ultimate state (external load = 649 kN)
84
A.2.1.5.
Load-deflection relation for first crack point (Node
84
no.54 at bottom of railseat)
A.2.1.6.
Vertical deflection along the sleeper length at different
85
load stage
A.2.1.7.
Principal stress in x-direction at first crack section
(Node no.54 at bottom of railseat)
85
xvi A.2.2.1.
Hypothetical bearing pressure distribution patterns
86
(LUSAS model)
A.2.2.2.
Unloaded with external load
87
A.2.2.3.
At initiation of crack (external load = 435 kN)
87
A.2.2.4.
At ultimate state (external load = 658 kN)
87
A.2.2.5.
Load-deflection relation for first crack point (Node
87
no.54 at bottom of railseat)
A.2.2.6.
Vertical deflection along the sleeper length at different
88
load stage
A.2.2.7.
Principal stress in x-direction at first crack section
88
(Node no.54 at bottom of railseat)
A.2.3.1.
Hypothetical bearing pressure distribution patterns
89
(LUSAS model)
A.2.3.2.
Unloaded with external load
90
A.2.3.3.
At initiation of crack (external load = 485 kN)
90
A.2.3.4.
At ultimate state (external load = 645 kN)
90
A.2.3.5.
Load-deflection relation for first crack point (Node
90
no.54 at bottom of railseat)
A.2.3.6.
Vertical deflection along the sleeper length at different
91
load stage
A.2.3.7.
Principal stress in x-direction at first crack section
91
(Node no.54 at bottom of railseat)
A.2.4.1.
Hypothetical bearing pressure distribution patterns
92
(LUSAS model)
A.2.4.2.
Unloaded with external load
93
A.2.4.3.
At initiation of crack (external load = 455 kN)
93
A.2.4.4.
At ultimate state (external load = 652 kN)
93
A.2.4.5.
Load-deflection relation for first crack point (Node
93
no.54 at bottom of railseat)
A.2.4.6.
Vertical deflection along the sleeper length at different
94
load stage
A.2.4.7.
Principal stress in x-direction at first crack section
(Node no.54 at bottom of railseat)
94
xvii A.2.5.1.
Hypothetical bearing pressure distribution patterns
95
(LUSAS model)
A.2.5.2.
Unloaded with external load
96
A.2.5.3.
At initiation of crack (external load = 460 kN)
96
A.2.5.4.
At ultimate state (external load = 653 kN)
96
A.2.5.5.
Load-deflection relation for first crack point (Node
96
no.54 at bottom of railseat)
A.2.5.6.
Vertical deflection along the sleeper length at different
97
load stage
A.2.5.7.
Principal stress in x-direction at first crack section
97
(Node no.54 at bottom of railseat)
A.2.6.1.
Hypothetical bearing pressure distribution patterns
98
(LUSAS model)
A.2.6.2.
Unloaded with external load
99
A.2.6.3.
At initiation of crack (external load = 485 kN)
99
A.2.6.4.
At ultimate state (external load = 648 kN)
99
A.2.6.5.
Load-deflection relation for first crack point (Node
99
no.54 at bottom of railseat)
A.2.6.6.
Vertical deflection along the sleeper length at different
100
load stage
A.2.6.7.
Principal stress in x-direction at first crack section
100
(Node no.54 at bottom of railseat)
A.2.7.1.
Hypothetical bearing pressure distribution patterns
101
(LUSAS model)
A.2.7.2.
Unloaded with external load
102
A.2.7.3.
At initiation of crack (external load = 455 kN)
102
A.2.7.4.
At ultimate state (external load = 647 kN)
102
A.2.7.5.
Load-deflection relation for first crack point (Node
102
no.54 at bottom of railseat)
A.2.7.6.
Vertical deflection along the sleeper length at different
load stage
103
xviii A.2.7.7.
Principal stress in x-direction at first crack section
103
(Node no.54 at bottom of railseat)
A.2.8.1.
Hypothetical bearing pressure distribution patterns
104
(LUSAS model)
A.2.8.2.
Unloaded with external load
105
A.2.8.3.
At initiation of crack (external load = 255 kN)
105
A.2.8.4.
At ultimate state (external load = 347 kN)
105
A.2.8.5.
Load-deflection relation for first crack point (Node no.
105
1168 at top chamfer)
A.2.8.6.
Vertical deflection along the sleeper length at different
106
load stage
A.2.8.7.
Principal stress in x-direction at first crack section
106
(Node no. 1168 at top chamfer)
A.2.9.1.
Hypothetical bearing pressure distribution patterns
107
(LUSAS model)
A.2.9.2.
Unloaded with external load
108
A.2.9.3.
At initiation of crack (external load = 480 kN)
108
A.2.9.4.
At ultimate state (external load = 644 kN)
108
A.2.9.5.
Load-deflection relation for first crack point (Node
108
no.54 at bottom of railseat)
A.2.9.6.
Vertical deflection along the sleeper length at different
109
load stage
A.2.9.7.
Principal stress in x-direction at first crack section
109
(Node no.54 at bottom of railseat)
A.2.10.1.
Hypothetical bearing pressure distribution patterns
110
(LUSAS model)
A.2.10.2.
Unloaded with external load
111
A.2.10.3.
At initiation of crack (external load = 475 kN)
111
A.2.10.4.
At ultimate state (external load = 647 kN)
111
A.2.10.5.
Load-deflection relation for first crack point (Node
111
no.54 at bottom of railseat)
A.2.10.6.
Vertical deflection along the sleeper length at different
load stage
112
xix A.2.10.7.
Principal stress in x-direction at first crack section
112
(Node no.54 at bottom of railseat)
A.3.1.
Schematic diagram of rail seat negative moment test
115
(AS 1085.14-2003)
A.3.2.
Schematic diagram of rail seat positive moment test
(AS 1085.14-2003)
116
xx LIST OF SYMBOLS
Kb
-
Ballast stiffness
hb
-
Depth of ballast
le
-
Effective supporting length of half sleeper
lb
-
Width of sleeper underside
α
-
Ballast stress distribution angle
Eb
-
Elastic modulus of the ballast
fc'
-
Specified compressive strength of concrete
Ec
-
Elastic modulus of the concrete
fct'
-
Tensile strength of the concrete
L1
-
Unloaded with external load
L2
-
Load at initiation of crack
L3
-
Load at ultimate state
D
-
Diamter of prestressing tendon
As
-
Area of prestressing tendon
xxi
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
1.A.
Model dimensions and input for the line geometry
80
1.B.
Cross sectional area of prestressing tendons (As)
81
1.C.
Modulus of elasticity of concrete (Ec)
81
1.D.
Ballast stiffness for the spring supports (kb)
82
2.1.A.
Spring support stiffness input for Laboratory test
83
2.1.B.
Principal stress distribution in x-direction and crack
84
pattern
2.1.C.
Load-deflection at first crack point
84
2.1.D.
Vertical deflection along the sleeper length at different
85
load stage
2.1.E.
Principal stress in x-direction on the first crack section
85
2.2.A.
Spring support stiffness input for Tamped either side of
86
rail
2.2.B.
Principal stress distribution in x-direction and crack
87
pattern
2.2.C.
Load-deflection at first crack point
87
2.2.D.
Vertical deflection along the sleeper length at different
88
load stage
2.2.E.
Principal stress in x-direction on the first crack section
88
2.3.A.
Spring support stiffness input for Principal bearing on
89
rails
2.3.B.
Principal stress distribution in x-direction and crack
90
pattern
2.3.C.
Load-deflection at first crack point
90
xxii
2.3.D.
Vertical deflection along the sleeper length at different
91
load stage
2.3.E.
Principal stress in x-direction on the first crack section
91
2.4.A.
Spring support stiffness input for Maximum intensity at
92
the ends
2.4.B.
Principal stress distribution in x-direction and crack
93
pattern
2.4.C.
Load-deflection at first crack point
93
2.4.D.
Vertical deflection along the sleeper length at different
94
load stage
2.4.E.
Principal stress in x-direction on the first crack section
94
2.5.A.
Spring support stiffness input for Maximum intensity in
95
the middle
2.5.B.
Principal stress distribution in x-direction and crack
96
pattern
2.5.C.
Load-deflection at first crack point
96
2.5.D.
Vertical deflection along the sleeper length at different
97
load stage
2.5.E.
Principal stress in x-direction on the first crack section
97
2.6.A.
Spring support stiffness input for Center bound
98
2.6.B.
Principal stress distribution in x-direction and crack
99
pattern
2.6.C.
Load-deflection at first crack point
99
2.6.D.
Vertical deflection along the sleeper length at different
100
load stage
2.6.E.
Principal stress in x-direction on the first crack section
100
2.7.A.
Spring support stiffness input for Flexure of sleeper
101
produces variations form
2.7.B.
Principal stress distribution in x-direction and crack
102
2.7.C.
pattern
Load-deflection at first crack point
102
2.7.D.
Vertical deflection along the sleeper length at different
103
load stage
xxiii
2.7.E.
Principal stress in x-direction on the first crack section
103
2.8.A.
Spring support stiffness input for Well tamped sides
104
2.8.B.
Principal stress distribution in x-direction and crack
105
pattern
2.8.C.
Load-deflection at first crack point
105
2.8.D.
Vertical deflection along the sleeper length at different
106
load stage
2.8.E.
Principal stress in x-direction on the first crack section
106
2.9.A.
Spring support stiffness input for Stabilized rail seat
107
and sides
2.9.B.
Principal stress distribution in x-direction and crack
108
pattern
2.9.C.
Load-deflection at first crack point
108
2.9.D.
Vertical deflection along the sleeper length at different
109
load stage
2.9.E.
Principal stress in x-direction on the first crack section
109
2.10.A.
Spring support stiffness input for Uniform pressure
110
2.10.B.
Principal stress distribution in x-direction and crack
111
pattern
2.10.C.
Load-deflection at first crack point
111
2.10.D.
Vertical deflection along the sleeper length at different
112
load stage
2.10.E.
3.A.
Principal stress in x-direction on the first crack section
112
Relevant information from KTMB’s Double Track
113
Specification
3.B.
Dynamic Wheel Load
113
3.C.
Rail seat load
114
3.D.
Results from Testing of Prestressed Concrete Sleeper
115
(DNV,2002)
1
CHAPTER 1
INTRODUCTION
1.1.
MODERNIZATION OF THE BALLASTED RAILWAY TRACK
NETWORK IN MALAYSIA
The Government of Malaysia through Keretapi Tanah Melayu Berhad
(KTMB) is embarking on an exciting challenge in modernizing its ballasted railway
track through the implementation of double tracking and electrification of its
railway system on the west coast of the peninsular.
This includes the already completed Rawang-Ipoh Project, the ongoing
Ipoh-Padang Besar Project and the Seremban-Gemas Project as well as the
upcoming Gemas-Johor Bahru Project. Total project cost of the modernization of
this ballasted railway track is approximately RM 30 billion.
The modernized ballasted track is designed to replace the colonial track of
90 km/h top speed with the 140 km/h maximum operational speed which could go
up to its limit of 160 km/h on certain stretches. This will directly reduce the transit
time for both passengers and goods traffic which in return will stimulate
developments and economic growth along its corridor.
Once the network between Johor Bahru and Padang Besar is completed, it
will further spur and enhance the growth of international container traffic through
train services between the ports of Malaysia. It will definitely pave the way for the
success of the Indonesia-Singapore-Malaysia-Thailand Growth Region.
2
1.2.
FUNCTIONS OF TRACK COMPONENTS AND THE LOAD PATH
The design of a railway system is typically divided into two main
components namely the design of trains or rollingstock and the design of the
supporting structure (Remennikov, Kaewunruen, 2008). It is expected that the track
structures will guide and facilitate the safe, economic and smooth passages of any
passenger and freight trains.
By considering the static and dynamic loads acting on the track structure,
railway track structures is primarily analysed and designed to avoid excessive
loading which may induce damage to the track substructure and superstructure.
This include track components such as rails, rail pads, mechanical fasteners and
concrete sleepers (superstructure) as well as geotechnical systems such as ballast,
sub-ballast and subgrade or formation (substructure). Fig. 1.1 shows the cross
sectional layout of a typical ballasted track (Selig & Waters, 1994).
Figure 1.1: Cross sectional layout of a typical ballasted track (Selig & Waters, 1994)
As a longitudinal steel members positioned on the equally spaced sleepers,
rails are the critical component in guiding the rolling stocks. Its main function is to
accommodate and transfer the loads from the rolling stock to the supporting
sleeper. With adequate strength and stiffness in the rails, a steady shape and smooth
track is maintained and various forces exerted by travelling rolling stocks are
resisted. In modern electrified track, rails had additional function of serving as an
electrical conductor for railway signaling system.
3
Both mechanical fasteners and rail pads are the primary components of the
fastening systems. Apart from keeping the rails in position on the sleepers, the
mechanical fasteners withstand the three dimensional forces of vertical, lateral and
longitudinal as well as the overturning movements of the track. Mechanical fastener
also transfer forces caused by wheels, thermal change and natural hazard from rails
to the adjacent set of sleepers.
As the other primary components of the fastening systems, rail pads which
are placed on the rail seat are essential in filtering and transferring the dynamic
forces from the rails and mechanical fastener to the sleepers. The dynamic force is
predominantly from the travelling rolling stocks and the high damping coefficient
of the rail pads considerably reduces the excessive high-frequency force
components to the sleepers. The resiliency provided by the rail pads to rail-sleeper
interaction has resulted in the alleviation of rail seat cracking and contact attrition.
Sleepers are part of the track component that rest transversely on the ballast
with respect to the longitudinal rail direction. It was first made using timber before
evolving to steel, reinforced concrete and to the most common type seen today,
prestressed concrete. This evolution is closely related to improve durability and
longer service life span. In terms of its functionality, sleepers are critical in (i)
providing support and restraint to the rail in vertical, longitudinal and lateral
direction, (ii) transfering load from the rail foot to the underlying ballast bed, and
(iii) retaining proper gauge and inclination of the rail by keeping anchorage for the
rail fastening system.
Underneath the sleepers in providing tensionless elastic support is ballast, a
free-draining coarse aggregate layer typically composed of crushed stones, gravel,
and crushed gravel. Depending on the local availability, basalt and granite are
usually the selected material for ballast due to its strength characteristic for load
transfer. In between the ballast and the underlying subgrade is sub-ballast,
commonly composed of broadly graded slag, broadly sand-gravel or crushed
aggregate. The last support to sustain and distribute the resultant downward
dynamic loading along its infinite depth is subgrade or also known as formation.
Subgrade includes existing soil and rock as well as other structures such as pile
embankment and the recent high performance materials of geotextiles and
4
geofabrics. To prolong track serviceability, the infinite depth of subgrade must have
adequate bearing capacity, provide good drainage and yield tolerable smooth
settlement.
1.3.
PROBLEM STATEMENT
As reviewed by Doyle (1980), one of the main functions of prestressed
concrete sleepers is to transfer the vertical loads to the ballast and formation. This
vertical loads subject the sleeper to bending moment which is dependent on the
pressure distribution exerted by the ballast underneath the sleeper.
In practice, a uniform pressure distribution is assumed in design to calculate
the static load capacity of the sleeper in withstanding the bending stresses. This also
lead to a four point bending moment test at the rail seat in the laboratory (AS
1085.14-2003) based on the assumption that the sleepers would behave similar to
those of the in-situ ones. (Remennikov, Murray, Kaewunruen, 2008)
However, this assumption is not completely true as the bearing pressure
distribution on the sleeper-ballast interaction is mainly depending on the degree of
voids in the ballast underneath the sleeper. The major influence factors in
determining the degree of voids are the traffic loading and train speed. Both factors
are time dependent as cumulative effect of the traffic loading at various speeds will
gradually change the structure of the ballast and the subgrade. A remarkable effort
by Talbot (1913-1940), other researchers and standards have postulated a set of
hypothetical bearing pressure distribution on the sleeper-ballast interaction and
their corresponding bending moment diagrams.
Therefore, quantifying the rail seat load and the bearing pressure
distribution is the most critical steps in designing the sleeper to withstand vertical
loading. Numerical analysis using a commercial finite element package, LUSAS,
was carried out to check on the assumption made on the laboratory test as well as to
check whether the assumption of uniform pressure will provide an overestimate of
5
the sleeper’s static load capacity in relative to other hypothetical bearing pressure
distribution.
The preliminary applied rail seat load in the design and numerical analysis
will be based on 20 tonne axle load which is the maximum imposed load as
regulated by the Malaysian Railway Authority although it is acknowledged
excessive wheel load over 400 kN due to wheel or rail abnormalities may occur
once or twice in the sleeper’s design life span of 50-100 years (Kaewunruen,
Remennikov, 2009). This is considered a rare event and it is not economic to design
sleeper for such a high static load capacity.
Subsequently, the rail seat load will be increased if the bending stress limit
is not exceeded. If the bending stress is exceeded prior to rail seat load based on 20
tonne axle load, a lower load will be applied to predict what load the sleepers will
fail under flexure.
6
1.4 .
OBJECTIVES OF THE STUDY
The objective of this study are :
a) To develop two-dimensional model of presetressed concrete sleepers using
finite element analysis modelling;
b) To compare the finite element analysis model with the load-deflection
response of the centre negative moment experimental test as previously
conducted by Kaewunruen and Remennikov (2006a);
c) To verify if the assumed uniform bearing pressure distribution on the
sleeper-ballast interaction is not underestimating the design if other
hypothetical bearing pressure distribution pattern occurs;
d) To predict the maximum vertical static loading capacity at crack initiation
stage and ultimate state on various hypothetical bearing pressure
distribution patterns.
7
1.5.
SCOPES OF THE STUDY
The scope of this study are :
a) To review the analysis and design of monoblock prestressed concrete
sleepers by referring to Section 4 of AS 1085.14-2003 as practiced by the
track designer of KTM Double Track Projects;
b) To perform numerical analysis using finite element software, LUSAS, with
various hypothetical bearing pressure distribution on the sleeper-ballast
interaction as the controlled variable.
c) To apply specification of sleeper dimension, rail seat loading, material
properties and other technical parameters based on the centre negative
bending moment test carried out by Kaewunruen and Remennikov (2006a).
The ballast stiffness will be based on technical specification used in KTM
Double Track Project.
d) To only consider quasi-static wheel loads in the full scale experiments and
numerical analysis, impact loads are omitted.
e) To only consider independent, closely spaced, discrete and linearly elastic
springs for the beams on elastic foundation. Continuum approach is omitted
as effects on local pressure distribution are assumed negligible in the
transverse direction of the track.
8
CHAPTER 2
LITERATURE REVIEW
2.1.
DEVELOPMENT OF PRESTRESSED CONCRETE SLEEPERS
As described by Taylor (1993), the need for replacement of timber sleepers
emerged in the United Kingdom at the start of World War 2. This is mainly due to
the scarcity of the material for mass production of sleepers in new railway lines, the
introduction of Continous Welded Rail track, the advancement of concrete
technology and pre-stressing techniques (Esveld, 2001). Thus, both reinforced
concrete sleepers and prestressed concrete sleepers designs were concurrently
developed respectively by the Chief Civil Engineer’s Department of London
Midland and Scottish Railway as well as Dr. Mautner from The Prestressed
Concrete Company in the early 1940’s.
In 1941, two designs of reinforced concrete sleepers were manufactured and
tested in branch line near Derby. In the following year, 100 of them were laid in the
Mainline near Watford and survived for just 10 days. This testing was valuable for
providing the experience in strain measurement and highlighting the difficulties of
carrying out research on the real track.
On 21 February 1943, the first prestressed concrete sleepers were laid in the
west coast mainline at Chedington. The durability of the prestressed concrete
sleepers was found to be better than reinforced concrete sleepers. This is the
starting point to the use of prestressed concrete as the preferred sleepers in railway
lines across the world.
9
2.2.
PRESTRESSED AS THE PREFERRED CONCRETE SLEEPERS
In discussing the work by Thomas (1944), Dr. Mautner share the design
basis of the first prestressed concrete sleepers. Permissible stresses concept was
covered in some details and repetition test undertaken by Freyssinet in 1936 was
referred (Taylor, 1993).
According to Dr. Mautner (Thomas, 1944), the bond between concrete and
steel bars in reinforced concrete sleepers was very sensitive to repeated loading.
This is principally due to the inability of the steel bars to response to the plasticity
of the concrete in tension. As a result, slipping would occur between the steel bars
and the concrete and a considerable degree of cracking in the concrete take place
without actually leading to failure.
On the contrary, apart from the development length of the prestressing
strands, discrepancy was non-existent between the steel and concrete strains in the
prestressed concrete as long as no crack developed. Thus, the concrete is only in
compression state instead of tension and both steel and concrete will identically
elongates under loading.
The difference between the behavior of prestressed and reinforced concrete
sleepers lead to different basis in design. Unless the reinforced concrete sleepers are
very heavy and deep, cracking will inevitably occur and its design will be base on
crack should not increase rapidly under repetitions loading in order to prolong its
service life thus minimizing replacement. In contrast, no crack should occur during
the service life forms the basis in the design of prestressed concrete sleepers.
As crack in concrete sleepers will significantly increase the bond stress and
lead to reduced capacity, prestressed concrete sleepers is more durable under
repeated static load hence is preferable as compared to reinforced concrete sleepers.
10
2.3.
LOAD ASSESSMENT ON PRESTRESSED CONCRETE SLEEPERS
As described by Taylor (1993), the American Railway Engineering
Association (AREA) and the American Society of Civil Engineers (ASCE) had set
up special committees under the chairmanship of Professor A.N. Talbot in 1913 to
initiate a scientific study on the deformations and stresses in railway track. A
consistent research between 1918 and 1940 has produced seven important reports
through the development of data and the establishment of procedures for laborary
tests and track trials.
The Talbot Committee had use fixed reference locations to measure the rail
displacement beneath different wheel configuration - single wheels and pairs of
wheels of normal passenger coach and complete locos. Valuable data on the
distribution of wheel loads along the rail to the adjacent sleepers was obtained.
The Talbot Committee also measured the sleeper’s deformation to
determine the ballast’s bearing pressure distributions on sleeper soffits and at depth.
Laboratory test of sleeper on ballast bed was carried out by measuring the pressure
on the ballast through embedment of pressure capsules in the ballast.
Then, the scientific study by the Talbot Committee went on to consider
stresses in rails and joints as well as determining the effect of flat spots on wheels
and the consequential imposed stresses on rails.
Johansen (1944) described the work by the Research Department of London
Midland and Scottish Railway on reinforced concrete sleepers laid at Cheddington
main line from 1942 as well as timber sleepers. The experiments were conducted by
fitting the strain gauges on different position of the sleepers and placed in track for
monitoring. Eleven conclusions were reported by Johansen.
One of the conclusions recognizes ballast as support to the sleeper is the
most influential variable in affecting sleeper stresses. It appears that sleeper stresses
are linearly correlated in general with load and speed under identical sleeper design,
type and spacing. It also appears that concrete sleepers had three times as much
variation in stresses as compared to wood sleepers. This is due to the greater
stiffness of the concrete sleepers and ductility of the wooden sleeper to flex to the
11
contour of the ballast surface to the extent that any increase in a given load would
cause relatively further increase in stress of the wooden sleeper (Thomas, 1944).
Further tests were carried put at Cheddington by Thomas (1944). The focus
was to study the forces to which a concrete sleeper is subjected rather than the
effects of these forces. This includes investigation of the chair reaction and the
distribution of ballast pressure reaction under the sleeper using load cells and ‘ball
sandwich’ respectively.
‘Ball sandwich’ is formed by laying out ball bearings regularly between two
separated metal plates. It was fixed to the soffit of the sleeper to be in contact with
the ballast. The ballast pressure distribution was estimated by measuring the width
of the balls indentation into the outer steel leaves of the sandwich and used with the
information from the calibration.
It appears that in any particular day, there was usually no great variation
between a sleeper and the other. However, the local variation in the intensity of the
ballast’s bearing pressure distribution underneath a sleeper was considerable. This
is due to the slight rearrangement of the ballast which leads to points of high
pressure as the sleeper lifts a little on the approach of the train. Although the ballast
aggregate that causing the local pressure increase were soon pushed down, others
were continually being displaced.
Thomas (1944) also suggested that the method of packing the ballast
beneath the sleeper contribute to the difference in the ballast’s bearing pressure
distribution. It is interesting to note that ballast’s bearing pressure distribution in the
middle of the sleeper was occasionally observed due to the initial conditions of the
ballast during laying of the sleeper. As time from laying increases, the ballast’s
bearing pressure distribution in the center of the sleeper was slowly reduced to zero
as the continual packing under the rails lead to transfer of the ballast’ bearing
pressure distribution nearer to the rail.
After decades of research on understanding the interaction between sleeper
and ballast, Sadeghi (2005) compiled the work of researchers and International
Standards on the proposed hypothetical bearing pressure distribution under railway
sleepers as shown in Table 2.1.
12
Table 2.1 : Hypothetical bearing pressure distribution of sleeper (Sadeghi, 2005)
Item
No.
Distribution of
bearing pressure
Developers
Remarks
ORE, Talbot
Laboratory test
ORE, Talbot,
Tamped either side
Bartlett Clarke
of rail
3
ORE, Talbot
Principal bearing on rails
4
ORE, Talbot
Maximum intensity
at the ends
5
Talbot
Maximum intensity
in the middle
6
Talbot
Center bound
7
Talbot
Flexure of sleeper
produces variations form
1
2
ORE, Talbot,
8
Kerr, Schramm
9
ORE, Talbot
AREA, Raymond,
10
Talbot
Well tamped sides
Stabilized rail seat and
sides
Uniform pressure
Sadeghi (2005) has developed a finite element model to investigate the
stress distribution patterns under the sleeper and the deflection of the sleeper.
Spring supports that represent the ballast stiffness have been adopted in the finite
element modeling.
13
2.4.
BEAMS ON ELASTIC FOUNDATION AND THE BALLAST
STIFFNESS
As described by Teodoru (2009), the analysis of bending of beams on
elastic foundation firstly developed by Winkler in 1867 assuming that the reaction
forces of the foundation are proportional at every point to the deflection of the
beam at that point. The vertical deformation characteristics of the foundation are
defined by independent, closely spaced, discrete and linearly elastic springs as
shown in Figure 2.1.
Figure 2.1 : Deflections of elastic foundations under uniform pressure:
a – Winkler foundation; b – practical soil foundation (Teodoru, 2009)
Although significant research to improve the deficiencies of the Winkler
model in the displacement discontinuity has been developed, discrete and linearly
elastic springs will be applied to the support condition of the numerical analysis
model. This is under the assumption that the effect of local ballast’s bearing
pressure distribution beneath the individual sleeper in the transverse direction of the
track is negligible as compared to set of sleepers in the longitudinal direction.
Zhai et. al (2004) described the work by Ahlbeck et al. (1978) which
assumed stresses of the ballast are uniformly distributed over the cone region and
zero outside the cone. The inclination of the cone is the ballast stress pervasion
angle corresponding to the Poisson’s ratio. Therefore, the effective active region of
the ballast under each sleeper can be determined as shown in Figure 2.2.
14
Figure 2.2 : Load distribution region in continuous granular ballast (Zhai et
al., 2004)
Under this assumption, the continous granular ballast could be modeled as a
series of separate masses as shown in Figure 2.3 by which the analytical process is
greatly simplified.
Figure 2.3 : Model of ballast under one rail support point (Zhai et al., 2004)
Figure 2.4 : The modified model of the ballast (Zhai et al., 2004)
15
Therefore, the supporting stiffness of a ballast mass, Kb is determined as:
(2.1)
where hb is the depth of ballast, le is the effective supporting length of half sleeper,
lb is the width of sleeper underside, α is the ballast stress distribution angle and Eb is
the elastic modulus of the ballast.
2.5.
THE CENTRE NEGATIVE MOMENT TEST EXPERIMENT
Kaewunruen and Remennikov (2006a) performed a centre negative moment
test to investigate the rotational capacity of a monoblock prestressed concrete
sleeper under static hogging moment. The schematic diagram for the experimental
setup is shown in Figure 2.5.
Figure 2.5 : Schematic diagram of centre negative moment test experiment
(AS 1085.14-2003)
16
The boundary conditions, locations of supports and characteristics of
loading for the test were carried out in accordance with the Australian Standards
(AS 1085.14-2003). With a total length of about 2,700 mm, the rail gauge of the
monoblock prestressed concrete sleeper is approximately 1,600 mm. It was
supplied by an Australian manufacturer within the collaboration of the Australian
Cooperative Research Center for Railway Engineering and Technologies (Rail
CRC).
A small rate displacement control with a loading rate of approximately 10
kN/min had been implemented for the test, in accordance to Australian Standards
(AS 1085.14-2003) which had specify that the loading rate should not be greater
than 25 kN/min. To measure the deflection at the point load, Linear Variable
Differential Transformer (LVDT) was used.
Figure 2.6 : Load-deflection results by Kaewunruen and Remennikov (2006a)
17
Through visual inspection by the help of magnifying glass and the use of the
load-deflection relation as shown in Figure 2.6, the visualized crack initiation load
is about 79 kN and the measured one is about 75 kN. The measured crack initiation
load was defined as the intersection between load-deflection relations in stages I
and II (Gustavson, 2002). The maximum load was found as 133.3 kN.
After performing the test, the concrete sleeper was drilled for material
testing. This is important in investigating the mechanical properties of the concrete
material. Subjected to uni-directional axial loading test, the displacement of the
cored concrete under loading was measured using LDVT. This allows a nonlinear
stress-strain curve of the concrete material to be plotted as shown in Figure 2.7. It
was found that the compressive strength of the cored concrete is 88.5 MPa.
Figure 2.7 : Multi-linear stress-strain curve of concrete by Kaewunruen and
Remennikov (2006a)
18
The prestressing tendon has also been tested and the plotted stress-strain
curve is shown in Figure 2.8. It was found that each prestressing tendon has a proof
stress of 1860 MPa and the measured initial strain due to prestressing is about 6.70
mm/m.
Figure 2.8 : Multi-linear stress-strain curve of prestressing tendon by Kaewunruen
and Remennikov (2006a)
2.6.
NONLINEAR
FINITE
ELEMENT
MODEL
OF
RAILWAY
PRESTRESSED CONCRETE SLEEPER
Subsequent to the center negative moment test experiment, Kaewunruen and
Remennikov (2006b) developed a three-dimensional nonlinear finite element model
of railway presstressed concrete sleeper using ANSYS. The nonlinear model
provides nonlinear response analyses of each material component’s complicated
stress-strain behaviours.
Prior to the exceedence of either the specified tensile or compressive
strength of the concrete, the analyses are governed by the elastic linear behavior.
Once the specified tensile or compressive strength of the concrete are exceeded by
the principal stress at the integration points, there will be formation of cracking or
crushing of the concrete. If the external load is continually applied, regions of
19
cracked and crushed concrete will form in perpendicular with the redistributed
residual stresses to the direction of principal stress. Nonlinear iterative solver is
required to model this behavior.
a) Three-dimensional full scale model
c) Cross section of the concrete sleeper
b) Boundary conditions
d) Solid and bar elements connectivity
Figure 2.9 : Finite element model of prestressed concrete sleeper by Kaewunruen
and Remennikov (2006b)
To model the concrete, SOLID65 solid element was used. The solid element
was facilitated by plasticity algorithm to model the compressive crushing of the
concrete while nonlinear material model was used to accommodate the concrete
cracking model in the tension zone. Discrete reinforcement modeling with truss
elements, LINK 8, was utilized as the smeared crack analogy is impracticable due
to the fully prestressed nature throughout the whole cross section of the concrete.
The nonlinear finite element model is shown Figure 2.9.
This is because in the smeared crack analogy, a given fraction of
reinforcement volume is assumed to be distributed over the entire concrete element
and the reinforcement’s strength reinforces the defined region of the concrete mesh.
Perfect bonding between concrete and prestressing tendons in the discrete
20
reinforcement modeling was also assumed by the researcher as shown in Figure
2.10.
(b)
(a) Figure 2.10 : Model for reinforcement in finite element model (Tavarez, 2001):
a) discrete; and b) smeared
For the material models, four cases were investigated as shown in Table 2.2.
Material properties inputs for the concrete model include its specified compressive
strength (fc’) taken as 88.5 MPa. Modulus of Elasticity (Ec) as well as tensile
strength (fct’) was based on the Australia Standard (AS 3600-2001) specified
Ec = 5050 (fc’)0.5 and fct’ = 0.4 (fc’)0.5 , respectively. The Poisson’s ratio for the
concrete was taken as 0.3. For the prestressing tendons model, the material
properties inputs include 0.2% proof stress of 1,700 MPa, ultimate stress of 1,930
MPa and Elastic Modulus of 190 GPa.
Table 2.2 : Material models used by Kaewunruen and Remennikov (2006b) in
ANSYS
Concrete Model
Prestressing Tendon Model
Material
Tension
Compression
Distribution
MAT1
Linear Elastic
Linear Elastic
Discrete
Linear Elastic
MAT2
Linear Elastic
Discrete
Linear Elastic
MAT3
Linear Elastic
Discrete
Multi-linear
Isotropic
MAT4
Cracking
Discrete
Multi-linear
Isotropic
Multi-linear
Isotropic
Multi-linear
Isotropic
Multi-linear +
Crushing
properties
21
To model the nonlinear loading to failure that is consistent with the
experimental data, the applied displacement technique was used for the loaddeflection analysis in order to facilitate the smooth convergence of numerical
iterations of the loading.
The pretensioning of the tendon that corresponds to prestressing force in the
preliminary load stage was modeled by applying 6.70 mm/m initial strain to the
tendon elements. To model the selfweight of the materials, the materials’ density
was entered as a function of the gravitational acceleration of 9.81 ms-2 in the
negative global Z-direction. Then, the load step that is consistent with the testing
data was defined.
The numerical results as shown in Figure 2.11 found that the linear range
(from 0 to 65 kN of loading) of the concrete sleeper’s static behavior can be
predicted using MAT1 model.
Figure 2.11 : Load-deflection response of experimental and model of the
prestressed concrete sleepers by Kaewunruen and Remennikov (2006b)
22
For the nonlinear models of MAT2 and MAT3, both gives similar results in
the same loading range. The finding shows that MAT2 represents the nonlinear
behavior better than MAT3 models. When subjected to larger displacements (after
10-15 mm), MAT2 model yields slightly higher than MAT3 model. It was found
that MAT2 and MAT3 require 126 kN and 125 kN, respectively in comparison to
the maximum experimental load of 133 kN. This gives 4.5% and 5.3% differences
from the experimental results for the MAT2 and MAT3 model respectively.
It is also noticed from the numerical results that MAT4 model that apply
both cracking and crushing model are far from the experimental results due to the
low tensile strength of concrete used thus resulting in lower load-deflection
response than others.
2.7.
CURRENT PRACTICE IN THE THEORETICAL ANALYSIS TO
DESIGN SLEEPERS
Zakeri and Sadeghi (2007) summarize the four main steps applied in current
practices of the analysis and design of railway sleepers as reported by Grassie
(1984).
First, the design vertical wheel load is considered. This is a product of static
wheel load and combined vertical design load factor of not less than 2.5. The
combined vertical design load factor is established to make allowance for the
effects of static load at speed and the effects of dynamic load in addition to the
static wheel load (AS 1085.14-2003). As mentioned by
Kaewunruen and
Remennikov (2006a), the influence of the dead load for prestressed concrete
sleepers is negligible and the design vertical load can be expressed by wheel load
alone (Wakui and Okuda, 1999)
Second, the load transferred to the sleepers from the rails is defined as a
percentage of the design vertical wheel load. This percentage is linearly correlated
with the centre-to-centre spacing of the sleeper. AS 1085.14-2003 recommended
for rails of equal to or heavier than 47 kg/m, centre-to-centre spacing of the sleeper
23
between 500 mm and 750 mm is used and the distribution factor to be adopted on a
single sleeper are respectively ranging from 45 to 60 percent of the rail load.
Product of design vertical wheel load and the distribution factor is the design rail
seat load.
Third, a pressure distribution pattern of the ballast beneath the sleeper is
considered. AS 1085.14-2003 considers uniform pressure distribution beneath each
rail seat which is dependent on the track gauge and sleeper length. However, the
pressure distribution under the sleeper is very dependent on the condition of the
sleeper-ballast interaction. A set of hypothetical contact pressure distribution for
sleeper-ballast interaction has been reported by Sadeghi (2005).
Fourth, after assuming loading pattern on rail-sleeper interaction and
pressure distribution on sleeper-ballast interaction, bending moment at the rail seat
and at the centre of the sleeper are calculated. Thus, capacity of the sleeper will be
designed according to this calculated bending moment, which is resulted from the
action of vertical static load from the rail onto the sleeper.
It is to be noted that only flexural stresses is checked through calculation if
the design is complied with all clauses in AS 1085.14-2003, specifically related to
shape and dimension of the prestressed concrete sleeper. However, prestressed
concrete sleepers capacity to carry shear and principal tension could be measured
by carrying out load test.
In addition to its static load capacity, the performance of sleepers is also
measured in terms of its capability to withstand lateral and longitudinal loading.
The contributing factors to these include the sleeper size, shape, surface geometry,
weight and spacing (Doyle, 1980).
24
CHAPTER 3
RESEARCH METHODOLOGY
3.1.
INTRODUCTION
A set of numerical analysis of the monoblock prestressed concrete sleepers
was performed by developing two-dimensional nonlinear plane stress finite element
models using LUSAS. Nonlinear models were developed to analyse the nonlinear
response of each material components that possess complicated stress-strain
behavior (Kaewunruen and Remennikov, 2006b) (see Section 2.6). The concrete
was modeled using plane stress elements (QPM8) and the prestressing wire using
bar element (BAR3). Perfect bonding was assumed between these two elements due
to the superposition of nodal degrees of freedom. To simulate the nonlinear
behavior of multi-crack concrete in tension and compression, concrete’s plane
stress elements (QPM8) was assigned with crushing material model (LUSAS’
Model 84), based on a multi-surface plasticity approach. The nonlinear behavior of
the prestressing wire was simulated by assigning von Mises stress potential model
to the prestressing wire’s bar element (BAR3).
The two-dimensional nonlinear plane stress finite element model of the
monoblock prestressed concrete sleeper was first validated by evaluating the loaddeflection relationship from the experimental work carried out by Kaewunruen and
Remennikov (2006a) (see section 2.5). Once validated, the support of the concrete
sleeper model was replaced using elastic spring support element to represent the
ballast stiffness. The support element was also distributed according to the
hypothetical bearing pressure distribution pattern. To predict the load at failure
25
through nonlinear iterative algorithms, incremental load analysis utilizing the
Newton Raphson method as modeled in LUSAS was applied.
3.2.
FINITE ELEMENT MODEL FOR THE CENTRE NEGATIVE
MOMENT EXPERIMENTAL SETUP
The finite element model of the monoblock prestressed concrete sleeper was first
modelled according to the center negative moment experimental setup as conducted
by Kaewunruen and Remennikov (2006a) (see section 2.5). This finite element
model considered all parameters identical to the experimental setup for validation
of the initial results.
3.2.1. CREATING A NEW MODEL
A new model was created by starting the LUSAS Modeller session. A
LUSAS Modeller Startup window will prompt and Create new model was selected.
If continuing from an existing LUSAS Modeller session, the menu command File >
New was selected to start a new model file.
Subsequently in the New Model window, File details and Model details
were entered as shown in Figure 3.1.
26
Figure 3.1 : Inputs for File details and Model details in New Model window
The group of kN, mm, kt, s and C were selected to represent the units for the
loading, length, mass, time and temperature, respectively.
3.2.2. DEFINING THE GEOMETRY
To start defining the geometry, 14 segments of connected line were created
through the menu command Geometry > Line > Coordinates. Coordinates as listed
in Appendix 1.A. were entered into the Enter Coordinates window and the OK
button was clicked to finish.
Figure 3.2 : Selected segments of Line geometry
27
By selecting all segments of connected line as shown in Figure 3.2, a series
of surface were then created through the menu command Geometry > Surface > By
Sweeping. Sweep window as shown in Figure 3.3 will prompt and translation value
of 30.0 mm in Y direction was entered to create the surface geometry.
Figure 3.3 : Surface geometry creation by line sweeping
With all segments of connected line at the top of each surface were selected
in each case, the above processes were repeated five times to create the surface
geometry as shown in Figure 3.4.
Figure 3.4 : Surface geometry of concrete excluding the increased section at the
rail seat
28
`To create the enlarged section at the rail seat, the respective segments of
connected line were selected and translation of 40 in Y direction was entered in the
Sweep window to create the surface geometry as shown in Figure 3.5.
Figure 3.5 : Increased section at the rail seat
The last step in defining the geometry was to create the three point surface
that chamfer the rail seat. This chamfer was useful in reducing the stress
concentration at the change of section between rail seat and the rest of the sleeper.
By selecting the respective three points as shown in Figure 3.6, the three points
surface was created through the menu command Geometry > Surface > Points.
Select Type window will prompt and General Surface type was selected and the OK
button was clicked to finish.
Figure 3.6 : Surface geometry for the chamfer at rail seat
29
3.2.3. DEFINING THE MESH – PRESTRESSING TENDON
The prestressing tendon was modelled using line mesh through the menu
command Attributes > Mesh > Line. On the prompted Line Mesh window, twodimensional Bar structural element type with Quadratic Interpolation Order were
selected under the Element description option. Alternatively, BAR3 element was
entered under the Element name option. Bar element was selected to model the
prestressing tendon because of its behavior which acts in axial tension and
compression only.
To create a uniform mesh, Element length of 40.0 mm was entered. For
identification, this attributes was named Bar element 40 mm and the summary of
the attributes is shown in Figure 3.7.
Figure 3.7 : Structural bar element definition for the line mesh to model the
prestressing tendons
30
3.2.4. DEFINING THE MESH – CONCRETE
The concrete was modelled using surface mesh through the menu command
Attributes > Mesh > Surface. On the prompted Surface Mesh window, Plane
Stress’ Structural element type of Quadrilateral Element shape and Quadratic
Interpolation order were selected under the Element description option.
Alternatively, QPM8 element was entered under the Element name option.
Plane Stress element was selected to model the concrete because of the
smaller z dimension of the monoblock prestressed concrete sleeper as compared to
the in-plane x and y dimensions. With the load to act only in this x-y plane, the
normal stress and the shear stress normal to the plane were assumed to be zero.
Regular mesh was selected and named as Plane stress for ease of
identification. The summary of the attributes is shown in Figure 3.8.
Figure 3.8 : Structural plane stress element definition for the
surface mesh to model the concrete
31
To further control the mesh density and also to have regular mesh
quadrilateral shape, non-structural Line mesh with 40 mm spacing and one division
of spacing were created. Both attributes were named as None 40 mm and None 1
spacing, respectively.
3.2.5. DEFINING THE GEOMETRIC PROPERTIES
The inputs for geometric properties were needed for structural element
meshes namely the bar elements (BAR3) and the plane stress elements (QPM8).
Figure 3.9 : The cross sectional area to model the geometric line for 4 nos.
prestressing tendons
For the bar elements (BAR3), the menu command Attributes > Geometric >
Line was selected to prompt the Geometric Line window. Two attributes need to be
created for 4 nos prestressing tendons and 6 nos prestressing tendons, respectively.
To be consistent with the element’s structural type, the Bar/Link tab was selected to
prompt for input of the Cross sectional area (A) of the tendon. A value of 78.5 mm2
32
and 117.8 mm2 were entered as the cross sectional area value for 4 nos prestressing
tendons and 6 nos prestressing tendons respectively. The calculation for cross
sectional area for the prestressing tendon is shown in Appendix 1.B. and the
summary for the 4 nos prestressing tendon attributes is shown in Figure 3.9.
For the plane stress elements (BAR3), the menu command Attributes >
Geometric > Surface was selected to prompt the Geometric Surface window.
Thickness value of 245.0 mm was entered and named as Concrete thickness as
shown in Figure 3.10.
Figure 3.10: The concrete thickness to model the Geometric Surface for the concrete
3.2.6. DEFINING THE MATERIAL PROPERTIES – PRESTRESSING
TENDON
The prestressing tendon will be defined with the nonlinear material
properties which require the specification of yield stresses that is based on the multi
linear stress-strain curve from the prestressing tendon material testing when
defining the yield surface (LUSAS, 2008a).
To define the nonlinear material properties of the prestressing tendon, the
menu command Attributes > Material > Isotropic was selected to prompt the
Isotropic window. On the Elastic tab, Young’s modulus of 190.0 kN/mm2,
33
Poisson’s ratio of 0.27 and Mass density of 8.0E-12 kt/mm3 were entered as shown
in Figure 3.11.
Figure 3.11 : The isotopic material properties of the prestressing tendon in
elastic region
For the prestressing tendon to behave in nonlinear manner, the Plastic
option was selected for the Plastic tab to appear. Von Mises’ Stress potential model
with hardening properties option was selected. Among the three methods in
defining the nonlinear hardening of the prestressing tendon, the Total strain option
was selected as a direct input from the multi linear stress-strain curve from the
material testing (see Figure 2.8) could be directly applied. The tensile stress and
strain value for σ1, ε1, σ2 and ε2 were 1.86 kN/mm2, 0.0097895, 1.93 kN/mm2 and
0.053 respectively.
34
This attributes is named as Prestressing Tendon Material and the summary
is as shown in Figure 3.12.
Figure 3.12 : The isotopic material properties of the prestressing tendon in plastic
region using von Mises Stress Potential model
3.2.7. DEFINING THE MATERIAL PROPERTIES – CONCRETE
The concrete will be defined with the multi-crack Concrete model (Model
94) to simulate the nonlinear behavior of the concrete. These plastic-damagecontact models will form damage planes according to a principal stress criterion
before it develop as embedded rough contact planes. To control the basic softening
curve used in the model, a fixed softening curve that is applicable to reinforced
concrete applications or a fracture-energy controlled softening curve that depends
35
on the element size and applicable to un-reinforced concrete applications could be
applied (LUSAS, 2008b).
To define the nonlinear material properties of the concrete, the menu
command Attributes > Material > Isotropic was selected to prompt the Isotropic
window. On the Elastic tab, Young’s modulus of 47.5 kN/mm2 (see Appendix 1.C.),
Poisson’s ratio of 0.30 and Mass density of 2.5E-12 kt/mm3 were entered as shown
in Figure 3.13.
Figure 3.13 : The isotopic material properties of the concrete in elastic region
For the concrete to behave in nonlinear manner, the Plastic option is
selected for the Plastic tab to appear. Concrete model (Model 94) with Reinforced
concrete option was selected. Based on the multi linear stress-strain curve from the
concrete material testing (see Figure 2.7), the value for Uniaxial compressive
strength (fc’), Uniaxial tensile strength (fct’) and Strain at peak uniaxial
compression (εc) were entered as 0.0885 kN/mm2, 0.009 kN/mm2 and 0.0037
respectively.
Other
parameters
value
were
entered
recommendation and explanation provided by LUSAS (2008b).
according
to
the
36
This attributes is named as Concrete Material and the summary is as shown
in Figure 3.14.
Figure 3.14 : The isotopic material properties of the concrete in plastic
region using Concrete model (Model 94)
3.2.8. ASSIGNING ATTRIBUTES TO THE PRESTRESSING TENDONS
After defining the attributes for the line’s mesh, geometric properties and
material properties, these attributes will be assigned to the prestressing tendon’s
lines geometry in order for it to behave as prestressing tendons in the model. This
was done by first selecting the respective lines geometry that represents the
prestressing tendons as shown in Figure 3.15.
37
Figure 3.15 : Selection of lines geometry that represents the prestressing tendons
Subsequently, the selected lines’ geometry were meshed with the bar
element by dragging the Bar element 40 mm attributes from the Attributes treeview
and dropped into the Graphics window. This step must not be preceded by
geometric properties and material properties assignment as any structural element
shall be meshed first to activate the finite element model.
With the prestressing tendon’s line geometry still selected, the 4 nos
prestressing tendons and 6 nos prestressing tendons of the geometric properties as
well as the Prestressing Tendon Material of the material properties were dragged
from the Attributes treeview and dropped into the Graphics window.
To check whether all respective attributes has been assigned to the
respective prestressing tendon’s line geometry, the respective line on the Graphic
window was right-clicked and the Properties option was selected to prompt the
Properties window as shown in Figure 3.16. The assigned attributes can be checked
on the respective Mesh, Geometric and Material tabs.
Figure 3.16 : The assigned properties on the selected line elements
38
3.2.9. ASSIGNING ATTRIBUTES TO THE CONCRETE
Similar to prestressing tendons, the concrete need to be assigned with
surface’s mesh, geometric properties and material properties that has been
previously defined in order for all surface geometry in the model to behave as
concrete. This was done by first selecting all surfaces geometry that represents the
concrete as shown in Figure3.17.
Figure 3.17 : Selection of surface geometry that represents the concrete.
Subsequently, the surfaces geometry were meshed with the surface element
by dragging the Plane Stress attributes from the Attributes treeview and dropped
into the Graphics window. This step must not be preceded by geometric properties
and material properties assignment as any structural element shall be meshed first
to activate the finite element model.
With the concrete’s surface geometry still selected, the Concrete thickness
of the geometric properties attribute and the Concrete Material of the material
properties attribute were dragged from the Attributes treeview and dropped into the
Graphics window.
Figure 3.18 : The meshed surface’s plane stress elements.
From Figure 3.18, it can be seen that the surface mesh had irregular size of
quadrilateral shape. A regular size of quadrilateral shape with low aspect ratio and
corner angles of 90 degrees are targeted since the sections of the monoblock
prestressed concrete sleepers does not differs greatly to each other thus low stress
gradient region was expected.
39
To regulate the size of the quadrilateral shape, the horizontal perimeter lines
as shown in Figure 3.19 were selected. Then the selected lines are meshed with
None 40 mm attribute by dragging the non structural line from the Attributes
treeview and dropped into the Graphic window.
Figure 3.19 : Selection of line geometry for non-structural line element (None
40 mm) assignment
Then, the vertical lines as shown in Figure 3.20 were selected in order to
give an approximate aspect ratio of 1.0 to the quadrilateral shape. This was done by
dragging None 1 spacing attribute from the Attributes treeview and dropped into the
Graphic window to mesh the selected lines.
Figure 3.20 : Selection of line geometry for non-structural line element (None 1
spacing) assignment
As a result, a uniform and regular quadrilateral shape of surface mesh with
low aspect ratio and 90 degrees corner for the plane stress elements of the concrete
were created as shown in Figure 3.21.
Thickness = 245 mm
180 mm
240 mm
1,600 mm
80 mm
2,680 mm
380 mm
Figure 3.21 : Surface’s plane stress elements with low aspect ratio and
90 degrees quadrilateral shape and the model dimensions in LUSAS
40
3.2.10. SUPPORTS – CENTRE NEGATIVE MOMENT EXPERIMENTAL
SETUP
To simulate the support that is identical to the centre negative moment test
setup (see Figure 2.5), the prestressed monoblock concrete sleeper model need to be
rotated 180 degrees along the global Cartesian x-axis. This was done by selecting
all elements of the model in the Graphic window, right-clicked and Move option
was selected to prompt the Move window. Rotate option was then selected and
about the X-axis, 180 degrees of rotational angle was entered as shown in Figure
3.22.
Figure 3.22 : Rotate atttibutes in Move window
Once rotated, the support for the monoblock prestressed concrete sleeper was
defined by selecting the menu command Attributes > Support to prompt the
Structural Supports window. On the Structural Supports tab, Translation in Y
direction was fixed and the attribute is named Vertical Pin Support as shown in
Figure 3.23.
41
Figure 3.23 : Structural support definition
Then, the Vertical Pin Support was assigned to the centerline of the rail seat
by first clicking the respective point before dragging the attribute from the
Attributes treeview and dropped into the Graphic window. Assign Support window
will prompt and Assign to points as well as All loadcase options were selected.
Once OK to finish, the model was assigned with the Vertical Pin Support attribute
as shown in Figure 3.24.
Figure 3.24 : The assigned structural support on the model
42
3.2.11. LOADING – SELF WEIGHT
The self weight of the monoblock prestressed concrete sleeper could be
modeled by applying a gravity acceleration in the negative Y direction to the bar
and plane stress elements that have been assigned with the respective mass density
through material properties attribute.
To define the self weight, the menu command Attributes > Loading was
selected to prompt the Structural Loading window. On the Structural options Body
Force was selected and clicked Next to enter -9.81E3 mms-2 for the Linear
acceleration in Y direction as shown in Figure 3.25. The attribute was named Self
Weight.
Figure 3.25 : Body Force for the Self Weight
To assign, all bar and plane stress elements were first selected before the
Self Weight attribute was dragged from the Attributes treeview and dropped in the
Graphic window. Loading Assignment window will prompt for the Assign to
surface and Assign to lines to be selected with Loadcase 1 and Load factor of 1.0 to
be entered as shown in Figure 3.26.
43
Figure 3.26 : Loading Assignment for the Self Weight
Once OK to finish, the model was assigned with the Self Weight attribute as
shown in Figure 3.27.
Figure 3.27 : The assigned Self Weight loading on the model
3.2.12. LOADING – INITIAL STRAIN ON PRESTRESSING TENDONS
The initial strain on prestressing tendons was modeled by selecting the
menu command Attributes > Loading to prompt the Structural Loading window.
On the Structural options Stress and Strain was selected and clicked Next to enter
6.7E-3 for the Initial Stress and Strain Type as shown in Figure 3.28. The attribute
was named Initial Strain.
44
Figure 3.28 : The Initial Strain loading on the prestressing tendons
By first selecting all structural bar elements (see Figure 3.15), the Initial
Strain attribute was then dragged from the Attributes treeview and dropped in the
Graphic window. Loading Assignment window will prompt to select for the Assign
to lines with Loadcase 1 and Load factor of 1.0 were entered as shown in Figure
3.29.
Figure 3.29 : Loading Assignment for the Initial Strain
45
Once OK to finish, the model was assigned with the Initial Strain attribute
as shown in Figure 3.30.
Figure 3.30 : The assigned Initial Strain loading on the model
3.2.13. LOADING – VERTICAL POINT LOAD SETUP FOR THE
CENTRE NEGATIVE MOMENT TEST
The centre negative moment test that was carried out in accordance with
Australian Standards (AS 1085.14-2003) require the point load from a single source
to be distributed on two points with each is located at 75 mm away from the
centerline of the monoblock prestressed concrete sleeper (see Figure 2.5).
To define the vertical point load, the menu command Attributes > Loading
was selected to prompt the Structural Loading window. On the Structural options
Concentrated was selected and clicked Next to enter -1.0 kN for the for the
Concentrated load in Y Direction as shown in Figure 3.31. The attribute was named
Vertical Point Load.
46
Figure 3.31 : The Vertical Point Load attributes
By first selecting the respective two points, the Vertical Point Load attribute
was then dragged from the Attributes treeview and dropped in the Graphic window.
Loading Assignment window will prompt to select Assign to points with Loadcase 2
and Load factor of 1.0 were entered as shown in Figure 3.32.
Figure 3.32 : Loading Assignment for the Vertical Point Load
47
Once OK to finish, the model was assigned with the Vertical Point Load
attribute as shown in Figure 3.33.
Figure 3.33 : The assigned Vertical Point Load on the model
3.2.14. NONLINEAR CONTROL
As stress distribution is no longer possible to be directly obtained through
equilibrium with a given set of external loads in the nonlinear analysis, the
nonlinear control that is defined as a property of a loadcase could be applied in
terms of incremental load. The incremental load will linearly predict the nonlinear
response and the subsequent iterative corrections are performed to eliminate the out
of balance or residual forces in order to restore the equilibrium. The extent of the
achieved equilibrium state depends on the convergence criteria of the iterative
corrections process. This solution procedure is commonly referred to as an
incremental-iterative method as shown in Figure 3.34. In LUSAS, the nonlinear
solution is based on the Newton-Raphson procedure (LUSAS, 2008c).
Figure 3.34 : The incremental-iterative method for nonlinear solution
48
The nonlinear control need to be defined for both Loadcase 1 and Loadcase
2 on the Loadcase treeview. Loadcase 1 represents the constant unfactored load of
the Self Weight and the Initial Strain whereas Loadcase 2 represents the
incremental Vertical Point Loads applied 75 mm away from the centre of the
monoblock prestressed concrete sleeper model.
3.2.14.1. Loadcase 1
To define the nonlinear control for Loadcase 1, the Nonlinear and Transient
was selected under the Controls option after right-clicking the Loadcase 1 icon on
the Loadcase treeview tab as shown in Figure 3.35.
Figure 3.35 : The nonlinear control of loadcase selection
Nonlinear & Transient window will prompt as shown in Figure 3.36. The
nonlinear option was selected and the Incrementation was set to Automatic to allow
the Loadcase 1 to be factored by a fixed 1.0 Load factor as defined previously. This
was done by setting the Starting load factor as 1.0, Max change in load factor as
0.0 and Max total load factor as 1.0. This setting means both Self Weight and Initial
Strain will be factored as 1.0 initially and with no change in load factor, the max
total load factor remains as 1.0.
49
Figure 3.36 : The nonlinear control for Loadcase 1
The Adjust load based on convergence option was selected to allow the
Iterations per increment option to be activated and a value of 20 to be entered.
Commonly, a value of between 10 and 20 were sufficient for the number of
iterations per increment needed in the Newton-Raphson procedure. Max time steps
or increments was set to default value of zero as there is no termination criteria set
for Loadcase 1.
On the Solution Strategy, Same as previous loadcase option was not
selected. Max number of iterations was set to 25, an additional of 5 iterations of 20
as set for the Iterations per increment previously. To achieve convergence of the
solution at each load increment of less than 0.1% of the reactions for the out of
balance forces, the Residual force norm was set as 0.1 and the Incremental
displacement norm was set to 1 for change in displacement to be less than 1% of
the displacements for that load increment.
50
On the Advanced option in the Incrementation section, all default setting is
maintained and Allow step reduction option is clicked as shown in Figure 3.37.
Figure 3.37 : The Advanced nonlinear control for Loadcase 1
3.2.14.2. Loadcase 2
The procedures in defining the nonlinear control for Loadcase 2 were
similar to Loadcase 1.
For Loadcase 2, the Vertical Point Load will be factored by variable
increments. This was done by setting the Starting load factor as 1.0, Max change in
load factor as 2.0 and Max total load factor as 0.0. Limiting the Max change in
load factor to 2.0 means that the second and subsequent load increment factors for
the Vertical Point Load is restricted to a factor of 2.0 in order for sufficient points
to be obtained thus load deflection behavior of the beam could be observed better.
Max total load factor was set to zero for the solution to be terminated on limiting
displacement at a certain point that will be set in the Advanced option of the
Incrementation section.
51
All other inputs on the Nonlinear & Transient window for Loadcase 2 were
identical to Loadcase 1 and the summary is shown in Figure 3.38.
Figure 3.38 : The nonlinear control for Loadcase 2
To set the Termination criteria, a point on the midspan was selected first as
shown in Figure 3.39.
Figure 3.39 : The selected point at midspan to be set with Termination criteria
52
Then, after clicking the Advanced option in the Incrementation section on
the Nonlinear & Transient window, Terminate on value of limiting variable was
selected. The selected point at midspan will appear in the Point number drop down
list and V that represents the vertical displacement as well as -40.0 that represents
40.0 mm in negative direction were entered
in the Variable type and Value
termination criteria respectively. Other settings were similar to Loadcase 1 and the
summary of the Advanced Nonlinear Incrementation Parameters is shown in
Figure 3.40.
Figure 3.40 : The Advanced nonlinear control for Loadcase 2
3.2.15. RUNNING THE ANALYSIS
Now, the model is complete and it is ready for analysis. To run the analysis,
the Solve Now button was clicked.
53
3.2.16. VIEWING THE RESULTS
Once the analysis for the model completed, the results will be loaded on top
of the model and the 1:Increment 1 Load Factor = 1.00000 of Loadcase 1 was set
to active by default. Any load increment can be set to active by right-clicking on the
particular Increment Load Factor and select the Set Active option as shown in
Figure 3.41.
Figure 3.41 : Setting the Increment Load Factor to active
To view the deformed shape, right-clicked in a blank part of the Graphic
window that has no selected features and select the Deformed mesh option to add
the deformed mesh layer to the Layer treeview. Alternatively, the menu command
View > Insert Layer > Deformed mesh was selected to prompt the Properties
window and commonly the defaults setting was applied. To only display the
deformed mesh as shown in Figure 3.42, other layers such as Geometry, Attribute
and Mesh layers were disabled.
54
Figure 3.42 : The deformed mesh
The load-deflection graph at the midspan could be plotted by using the
Graph Wizard. This was done by first identifying the respective nodal number of
the intended load and deflection values that need to be plotted. The nodal number
could be displayed by right-clicking in a blank part of the Graphic window that has
no selected features and select the Labels option to prompt the Properties window.
Then, Node’s Name with Label attributes using IDs are selected to display the
nodal number as shown in Figure 3.43.
Figure 3.43 : The nodal number
To plot the load-deflection graph of nodal number 45 as shown in Figure
3.44, the menu command Utilities > Graph Wizard was selected to prompt the
Graph Wizard window and Time history type was chosen. For X Attribute of the
Time History Graph, Nodal for the Entity data with All Loadcases for the Sample
loadcases option were selected. For the input of the Nodal data, Displacement in y
55
direction of DY were selected and nodal number 45 was specified as the single
node. For Y Attribute of the Time History Graph, Nodal for the Entity data with All
Loadcases for the Sample loadcases option were selected. For the input of the
Nodal data, Loading in y direction of FY are selected and nodal number 45 was
specified as the single node.
Figure 3.44 : Load-deflection response from the Graph Wizard
The stress distribution on the model could be viewed by right-clicking in a
blank part of the Graphic window that has no selected features and selects the
Contours option to prompt the Properties window. To view the component of
principal stress in the x direction as shown in Figure 3.45, Stress – Plane Stress
option with SX Component were selected in the respective drop down list. It is
reminded that the viewed stress distribution corresponds to the activated Increment
Load Factor case.
56
Figure 3.45 : Principal stresses distribution in global x-direction (SX)
As the Concrete Material attributes was assigned with the multi-crack
Concrete model (Model 94) to simulate the nonlinear behavior of the concrete, the
crack pattern on the concrete could be viewed in the results. This is done by rightclicking in a blank part of the Graphic window that has no selected features and
selects the Vectors option to prompt the Properties window. To view the crack
patterns as shown in Figure 3.46, Stress – Plane Stress option of Crack type were
selected in its respective drop down list. It is reminded that the crack patterns
correspond to the activated Increment Load Factor case.
Figure 3.46 : Crack pattern on the model
Alternatively, the change of stress and crack pattern can be animated instead
of viewing the results individually for each loadcase. To animate the results, the
menu command Utilities > Animation Wizard was selected to prompt the
Animation Wizard window and Load history was chosen for the Animation type.
With All loadcase option selected, the animated results of all loadcase will be
displayed in the Animation window as shown in Figure 3.47.
57
Figure 3.47 : Animation Wizard to display animated results of all loadcase
To save the animation for replay in windows player, the animation was
saved by selecting the menu command File > Save As AVI when the Animation
window was still active. Save As window will prompt and selected file name was
entered for the automatic .avi file extension. Once Save button was clicked, the
Video Compression window as shown in Figure 3.48 will prompt and Microsoft
Video 1 as the Compressor with Compression Quality of 100 percent were selected.
Figure 3.48 : Compressing the animation using Microsoft Video 1 compressor
58
3.3.
FINITE ELEMENT MODEL WITH THE HYPOTHETICAL
BEARING PRESSURE DISTRIBUTION PATTERNS
Once the finite element model has been validated with the experimental
results, the study was continued with the distribution of the spring support element
that follows the hypothetical bearing pressure distribution pattern (see Table 2.1)
under the bottom of the previously validated monoblock presstressed concrete
sleeper model. This is to predict the failure load of the monoblock prestressed
concrete sleeper under various hypothetical bearing pressure distribution patterns.
3.3.1. SUPPORT – HYPOTHETICAL BEARING PRESSURE
DISTRIBUTION PATTERNS
To start, the validated model used for the centre negative moment
experiment is rotated 180 degrees along the X-axis and saved as different file name
for each hypothetical bearing pressure distribution pattern.
The important first step in assigning a variable spring support stiffness that
represents the hypothetical pressure distribution was to add identification number
onto each line segments on the bottom of the monoblock prestressed concrete
sleeper model as shown in Figure 3.49.
Figure 3.49 : Identification of line segments
59
By taking the Principal bearing on rails (see Table 2.1) as an example, line
segment with identification number 3 was clicked and the menu command Utilities
> Variation > Line was selected to prompt the Line Variation window. On the Line
Variation window, Interpolation Type was chosen and Linear was specified as the
Order with Distance type as Parametric. Then, the corresponding parametric
distance and spring support stiffness value were entered in Distance (x) and Value
(y) boxes respectively (also see Table A.2.3.2, Appendix 2.3.A.). This utility was
named as Segment 3 as shown in Figure 3.50. Once OK button was clicked,
Segment 3 utility will appear in Utilities treeview.
Figure 3.50 : Spring support stiffness’ Line Variation inputs for Segments 3
After defining Segment 3 utility, it will be used in defining the spring
stiffness value. This was done by selecting the menu command Attributes >
Support to prompt the Structural Support window. For Translation in Y Direction,
Spring stiffness was chosen to allow for the input value to be entered. On the input
box, variation attribute option was clicked in order to select the previously defined
Segment 3 utility in the drop down list as shown in Figure 3.51.
60
Figure 3.51 : Selecting Segment 3 as the Variation Attribute for the spring support
stiffness assignment
Once OK button on the Select A Variation Attribute window was clicked,
the spring stiffness value was assigned as 1*Segment 3. Then, the attribute was
named as Ballast stiffness – Segment 3 and the summary of the assigned structural
support is shown in Figure 3.52.
Figure 3.52 : Structural supports to represent the ballast stiffness at Segment 3
61
This process is repeated for the remaining 13 segments of line by entering
the corresponding value of Distance (x) and Value (y) as listed in Appendix 2.1.A.
until Appendix 2.10.A. The completed assignment of variable spring support
stiffness to represents the Principal bearing on rails’ hypothetical pressure
distribution pattern (see Appendix 2.3.A.) is shown in Figure 3.53.
Figure 3.53 : Spring support that represents the ballast stiffness for Principal
bearing on rails scenario
62
CHAPTER 4
RESULTS, ANALYSIS AND DISCUSSIONS
4.1.
VALIDATION OF LUSAS’ NONLINEAR FINITE ELEMENT
MODEL
Prior to performing a numerical analysis on static load capacity of
prestressed concrete sleepers under hypothetical bearing pressure distribution, the
LUSAS’ nonlinear finite element model of the prestressed concrete sleeper is
validated with the experimental load-deflection response as performed by
Kaewunruen and Remennikov (2006a) (see Section 2.5).
The comparison of load-deflection responses between experimental and
LUSAS’ nonlinear finite element model is shown in Figure 4.1.
Gustavson (2002) has defined crack initiation as the intersection between
load-deflection relations in stages I and II. This method provides a slightly higher
cracking load as compared to reading the first deviation point from the linear elastic
region into the plastic region of the load-deflection relationship. From the cracking
pattern, it is noted that the first crack of both experimental and nonlinear finite
element model are in flexure.
By referring to Figure 4.1, the measured crack initiation load from the experimental
results was approximately 75 kN while the LUSAS model is approximately 78 kN.
The difference is approximately 4.0%.
63
140
Ultimate load ≈ 133 kN 130
Load at initiation of crack ≈ 78 kN 120
110
Ultimate load ≈ 131 kN
100
Load (kN)
90
80
70
Load at initiation of crack ≈ 75 kN 60
50
40
30
20
10
0
0
5
10
15
20
25
Deflection (mm)
Experimental results
30
35
40
LUSAS model
Figure 4.1 : Comparison of load-deflection response between experimental results
and LUSAS model
By applying the incremental loading after first cracking of both
experimental and LUSAS’s model, the prestressed concrete sleeper behaves
plastically and reaches its ultimate load and failed. From Figure 4.1, the ultimate
load from the experimental results was approximately 133 kN while the LUSAS
model is approximately 131 kN. The difference is approximately 1.5%.
From the comparison with the experimental results, it is found that the
LUSAS’ model can provide good prediction of measured crack initiation load and
ultimate load. This validation allows the LUSAS’ model to perform numerical
analysis on static load capacity of prestressed concrete sleepers under hypothetical
bearing pressure distribution
.
64
4.2.
NUMERICAL ANALYSIS ON STATIC LOAD CAPACITY OF THE
PRESTRESSED CONCRETE SLEEPERS UNDER HYPOTHETICAL
BEARING PRESSURE DISTRIBUTION
The validated LUSAS’ model is then used to perform numerical analysis on
static load capacity of prestressed concrete sleepers under hypothetical bearing
pressure distribution (see Table 2.1).
Three load points are of particular importance in reading the results of
(i) cracking load, ultimate load and crack patterns; (ii) load-deflection response at
first cracking point; (iii) vertical deflection along the sleepers length; and (iv) the
principal stress distribution in x-direction on the first crack section.
These load points are :
i.
L1 - Unloaded with external load;
ii.
L2 - Load at initiation of crack; and
iii.
L3 - Load at ultimate state.
All results is then analysed and validated with the work done by previous
researchers (Kaewunruen and Remennikov, 2006a) (see Section 2.5 and 2.6) in
order to propose the static load capacity of the prestressed concrete sleepers under
different scenarios of hypothetical bearing pressure distribution patterns.
Subsequently, comparisons are made with the designed static load capacity and the
experimental result.
Appendix 2 shows each result on every scenario of the hypothetical bearing
pressure distributions while the designed static load capacity and the experimental
results are shown in Appendix 3.
65
4.2.1. CRACKING LOAD, ULTIMATE LOAD AND CRACK PATTERNS
By referring to Table 4.1, the first crack occurs beneath the rail seat in all
scenarios except for Item No. 8 where the first crack occurs at top chamfer. As the
external vertical load at rail seat increases, the crack propagates until the sleeper
fails at its ultimate capacity. All cracks occur in flexure.
The cracking patterns shows that the most critical part of the prestressed
concrete sleeper is at its rail seat as it is where the first crack occurs and had the
most damaging crack at its ultimate capacity. Other affected parts that cracks at
ultimate load include the top and bottom surface at the center of the prestressed
concrete sleeper.
There is consistency between the vertical deflection and the stress
distributions pattern in the principal x-direction along the prestressed concrete
sleeper. The principal stress in x-direction is in flexural tensile on the particular
surface that deflects vertically along the sleeper’s length.
The cracking load for first crack that occurs beneath the rail seat ranges
between 435 kN and 485 kN while for first crack that occurs at top chamfer is 255
kN. These values are higher than the designed rail seat load of 125.9 kN for the 20
tonne axle load requirement as well as 164.0 kN and 198.0 kN for the first crack
that occurs during negative and positive moment test at the rail seat respectively
(see Appendix 3).
At ultimate state, the prestressed concrete sleepers fail at load ranges
between 644 kN and 658 kN for failure beneath the rail seat while the failure load
at the top chamfer is 347 kN. Only the result from the ultimate state of the positive
moment test is available and the value is 434 kN (see Appendix 3), lower than the
numerical results.
It can be seen that the prestressed concrete sleeper had a higher static load
capacity under hypothetical bearing pressure distributions as compared to designed
and experimental results.
Table 4.1 : Numerical analysis results of LUSAS’ nonlinear finite element model on the cracking lo
crack patterns of the prestressed concrete sleeper under hypothetical bearing pressure distributions.
Item
no.
Distribution of
bearing pressure
Remarks
At intiation of crack
Crack patterns
Load
1
Laboratory test
485 kN
2
Tamped either
side of rail
435 kN
3
Principal bearing on rails
485 kN
4
5
Maximum intensity
at the ends
Maximum intensity
in the middle
455 kN
460 kN
6
Center bound
485 kN
7
Flexure of sleeper
produces variations form
455 kN
8
Well tamped sides
255 kN
9
Stabilized rail seat
and sides
480 kN
10
Uniform pressure
475 kN
Cr
67
4.2.2. LOAD-DEFLECTION RESPONSE AT FIRST CRACK SECTION
Previously, it was acknowledged that first crack occurs beneath the rail seat
in all scenarios except for Item No. 8 where the first crack occurs at top chamfer. In
particular, first crack occurs at node no. 54 beneath the rail seat and node no. 1168
at top chamfer of the LUSAS model. The load-deflection response on these
particular nodes shows nonlinear behavior and this is plotted in Figure 4.2.
700
600
Load (kN)
500
400
300
200
100
0
0
0,05
Item 1
Item 6
0,1
0,15
Item 2
Item 7
0,2
0,25
Deflection (mm)
Item 3
Item 8
0,3
0,35
Item 4
Item 9
0,4
0,45
Item 5
Item 10
Figure 4.2 : Load-deflection response at first crack point
From Figure 4.2, it can be seen that the load capacity beneath the rail seat at
the ultimate state is between 644 kN and 658 kN while the corresponding
deflection is between 0.187 mm and 0.413 mm. From the load-deflection response
at node no. 54, the nonlinear behavior beneath the rail seat is approximately similar
although not identical. The differences may due to the degree of voiding in the
ballast under the sleeper hence its hypothetical bearing pressure distributions
Load-deflection response at node no. 1168 shows that top chamfer has
lower capacity and this may due to stress concentration region and decreased
sectional area of the concrete material.
68
4.2.3. VERTICAL DEFLECTION ALONG THE SLEEPER’S LENGTH
The vertical deflection along the sleeper’s length of all hypothetical
bearing pressure scenarios at each load points (1-L1, 1-L2, 1-L3 … 10-L1, 10-L2,
10-L3) is shown in Figure 4.3 (see Chapter 4.2).
Distance along the sleeper's length
‐0,2
0
200 400 600 800 1.000 1.200 1.400 1.6001.800 2.000 2.200 2.400 2.600 2.800
Deflection (mm)
0
0,2
0,4
0,6
0,8
1
1‐L1
3‐L1
5‐L1
7‐L1
9‐L1
1‐L2
3‐L2
5‐L2
7‐L2
9‐L2
1‐L3
3‐L3
5‐L3
7‐L3
9‐L3
2‐L1
4‐L1
6‐L1
8‐L1
10‐L1
2‐L2
4‐L2
6‐L2
8‐L2
10‐L2
2‐L3
4‐L3
6‐L3
8‐L3
10‐L3
Figure 4.3 : Vertical deflection along the sleeper’s length
From Figure 4.3, it can be seen that all scenarios have a similar vertical
deflection pattern except for well tamped side scenario (Item No. 8). The maximum
vertical deflection for Item No. 8 is on the centre while others are on the rail seat.
This may due to the absence of support along the gauge of the prestressed concrete
sleeper for Item No. 8.
At L1, only self-weight is acting and the vertical deflection is
approximately zero and negligible. The vertical deflection increases as the external
vertical rail seat load increases to L2 and L3. All maximum vertical deflection is in
69
the downward direction. The distance between point of zero deflection along the
sleeper’s length ranges between 675 mm and 1067 mm, as compared to 660 mm
for the rail seat positive moment test setup (see Figure A.3.2.).
Table 4.2 : Maximum vertical deflections and comparison with previous work by
Sadeghi (2005)
Item
No.
Distribution of
bearing pressure
Remarks
Maximum vertical
deflection (∆y) (mm)
Numerical
Results
Sadeghi
(2005)
1
Laboratory test
0.196
0.207
2
Tamped either side
of rail
0.386
0.109
3
Principal bearing on
rails
0.220
0.212
4
Maximum intensity
at the ends
0.300
0.491
5
Maximum intensity
in the middle
0.413
0.311
6
Center bound
0.200
0.263
7
Flexure of sleeper,
variations form
0.259
0.138
8
Well tamped sides
0.069
0.242
9
Stabilized rail seat
and sides
0.863
0.218
10
Uniform pressure
0.189
0.102
From Table 4.2, the value of maximum vertical deflections for prestressed
concrete sleepers under hypothetical bearing pressure distributions from the
numerical analysis is compared with the previous work done by Sadeghi (2005).
The value of maximum vertical deflections ranges between 0.102 mm and 0.863
mm while the differences for each item ranges between 0.008 mm and 0.645 mm.
70
The differences may due to longitudinal track and dynamic modeling for
Sadeghi (2005) whereas this numerical analysis only considers an individual
sleeper on the transverse direction of the track and static modeling. Also, there are
variations in parameters’ input between both models. Although there are
differences, the value is considered small and there are consistencies between of
both models. It is noted that maximum vertical deflection occurs at the rail seat
except for Item No. 8.
4.2.4. PRINCIPAL STRESS DISTRIBUTION IN X-DIRECTION ON FIRST
CRACK SECTION
The principal stress distribution in x-direction on the first crack section of
all hypothetical bearing pressure scenarios at each load points (1-L1, 1-L2, 1-L3 …
10-L1, 10-L2, 10-L3) (see Section 4.2) is shown in Figure 4.4.
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
1‐L1
3‐L1
5‐L1
7‐L1
9‐L1
‐0,02
‐0,01
0,00
Principal stress in x‐direction (kN/mm2)
1‐L2
3‐L2
5‐L2
7‐L2
9‐L2
1‐L3
3‐L3
5‐L3
7‐L3
9‐L3
2‐L1
4‐L1
6‐L1
8‐L1
10‐L1
0,01
2‐L2
4‐L2
6‐L2
8‐L2
10‐L2
0,02
2‐L3
4‐L3
6‐L3
8‐L3
10‐L3
Figure 4.4 : Principal stress in x-direction on the first crack section
71
At L1, only self-weight is acting and the principal stress distribution in x-direction
is approximately zero and negligible. The principal stress distribution in x-direction
increases as the external vertical rail seat load increases from L1 to L2. However,
as external vertical rail seat load increases from L2 to L3, the principal stress
distribution in x-direction decreases and this is due to the loss of sectional area of
the concrete material as crack propagates.
To validate the value of principal stress distributions in x-direction, a
comparison was made to previous numerical analysis work by Sadeghi (2005). The
comparison is tabulated in Table 4.3.
Table 4.3 : Maximum principal stress in x-direction and comparison with previous
work by Sadeghi (2005)
Item Distribution of bearing
No.
pressure
Remarks
Maximum principal stress
in x-direction (MPa)
Numerical
Results
Sadeghi
(2005)
1
Laboratory test
8.50
8.32
2
Tamped either
side of rail
5.86
8.85
3
Principal bearing
on rails
8.52
8.51
4
Maximum intensity
at the ends
8.14
17.7
5
Maximum intensity
in the middle
20.1
18.6
6
Center bound
19.8
15.4
7
Flexure of sleeper,
variations form
8.41
8.61
8
Well tamped sides
7.90
10.4
9
Stabilized rail seat
and sides
8.53
10.5
10
Uniform pressure
8.55
7.07
72
From Table 4.3, the maximum value of principal stress distribution in xdirection for prestressed concrete sleepers under hypothetical bearing pressure
distribution ranges between 5.85 MPa and 20.1 MPa while the differences for each
item ranges between 0.01 MPa and 9.56 MPa.
Although there are differences between the numerical results and the
previous work by Sadeghi (2005), the value is considered small and there are
consistencies between both models. The differences may due to longitudinal track
and dynamic modeling for Sadeghi (2005) whereas this numerical analysis only
considers an individual sleeper on the transverse direction of the track and static
modeling. Also, there are variations in parameters’ input between both models.
4.3.
SUMMARY
OF
STATIC
LOAD
CAPACITY
OF
THE
PRESTRESSED CONCRETE SLEEPERS UNDER HYPOTHETICAL
BEARING PRESSURE DISTRIBUTION
From the numerical analysis, the static load capacity of the prestressed
concrete sleepers under hypothetical bearing pressure distribution is higher than the
design requirement and experimental test value.
The design requires the prestressed concrete sleepers to withstand a static
load of 20 tonne from the axle and also a dynamic factor of 2.5 that takes into
account an impact load having a frequency between 30 and 100 Hz (AS 1085.142003). By specifying the sleeper spacing, rail seat load is derived and the
prestressed concrete sleeper must have the capacity to resist this action load. From
KTMB specifications, the rails seat load is 125.9 kN (see Appendix 3).
In the manufacturing of the prestressed concrete sleepers, acceptance tests are
mandatory to ensure that the prestressed concrete sleepers could function well in
(1) providing support and restraint to the rail in vertical, longitudinal and lateral
direction; (2) transfering load from the rail foot to the underlying ballast bed; (3)
retaining proper gauge and inclination of the rail by keeping anchorage for the rail
fastening system. There are various tests involved and the most critical is the
73
positive and negative moment test at the rail seat. These test are done on every
manufacturing cycles and the tested prestressed concrete sleeper must exceed 198
kN and 164 kN of rail seat load at the crack initiation (see Appendix 3).
Table 4.4 shows that the prestressed concrete sleepers that are placed on
ballast have reserve strength in static load capacity with a factor between 2.2 and
2.4 of the positive rail seat test load at crack initiation. For Item No. 8, the reserve
strength in static load capacity is 1.6 times the negative rail seat test load and this
may due to stress concentration region at the top chamfer and also decreased
sectional area of the concrete. At ultimate state, the reserve strength in static load
capacity for prestressed concrete sleepers on ballast is 1.5 times the positive rail
seat test load at ultimate state.
Results from the numerical analysis shows that this reserve strength in static
load capacity is the main factor in ensuring the serviceability of the in-situ
prestressed concrete sleeper as the excessive wheel load over 400 kN due to wheel
or rail abnormalities may occur once or twice in the sleeper’s design life span of
50-100 years (Kaewunruen, Remennikov, 2009).
Negative rail seat test load at crack initiation
= 164 kN
,
Positive rail seat test load at ultimate state =
434 kN
Positive rail seat test load at crack initiation
=
,
KTMB’s specification on axle load action =
20 ton
198 kN
Table 4.4 : Static load capacity between test and numerical analysis
Crack initiation
Item
No.
Distribution of bearing
pressure
Ultimate state
Numerical
Analysis’ Rail
Seat Load (kN)
Numerical /
Test ratio
Axle load
(tonne)
Numerical
Analysis’ Rail
Seat Load (kN)
Numerical /
Test ratio
Axle load
(tonne)
1
485
2.4
78
649
1.5
104
2
435
2.2
70
658
1.5
105
3
485
2.4
78
645
1.5
103
4
455
2.3
73
652
1.5
104
5
460
2.3
74
653
1.5
104
6
485
2.4
78
648
1.5
104
7
455
2.3
73
647
1.5
103
8
255
1.6
41
347
n/a
55
9
480
2.4
77
644
1.5
103
10
475
2.4
76
647
1.5
103
75
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1.
CONCLUSIONS
The LUSAS software enables the discrete nonlinear finite element model to
predict the behavior and static load capacity of the prestressed concrete sleeper.
Two-dimensional plane stress and bar elements were used for the concrete and
prestressing tendon mesh respectively. The inputs for the nonlinear properties of
the material were based on the laboratory test of the respective material. The model
was validated with previous work done experimentally and numerically by
Kaewunruen and Remmennikov (2006a) as well as Sadeghi (2005).
From the numerical analysis, the prestressed concrete sleeper that is placed
on ballast has reserve strength in static load capacity with a factor between 2.2 and
2.4 of the positive rail seat test load at crack initiation. This is the main factor in
ensuring the serviceability of the in-situ prestressed concrete sleeper as the
excessive wheel load over 400 kN due to wheel or rail abnormalities may occur
once or twice in the sleeper’s design life span of 50-100 years (Kaewunruen,
Remennikov, 2009).
76
5.2.
RECOMMENDATIONS
For future study, a numerical analysis on dynamic load capacity on
prestressed concrete sleeper under hypothetical bearing pressure distribution is
recommended. This may involve the effect of train speed variation, track stiffness,
track damping, effective unsprung mass of the vehicle and longitudinal modeling.
This type of study may give a better representation of the in-situ prestressed
concrete sleeper behavior hence the prediction on its serviceability.
For a more advance study, consideration on impact load of high frequency
is recommended.
77
REFERENCES
1. Ahlbeck, D.R. , Meacham, H.C. , Prause, R.H. (1978) The development of
analytical models for railroad track dynamics, in: A.D. Kerr (Ed.), Railroad
Track Mechanics & Technology, Pergamon Press, Oxford.
2. Det Norske Veritas Pte. Ltd. (2002), Testing of Prestressed Concrete Sleeper
for Associated Concrete Products (M) Sdn. Bhd., Det Norske Veritas Technical
Report, DNV/SL/R20021139.
3. Doyle, N.F. (1980) Railway Track Design : A Review of Current Practice,
Occasional Paper No. 35, Bereau of Transport Economics, Commonwealth of
Australia, Canberra ; Chapter 4:125-175.
4. EDP Consulting Group Sdn. Bhd. (2003), Design calculation of concrete
sleepers, Projek Landasan Berkembar Elektrik Rawang-Ipoh, Keretapi Tanah
Melayu Berhad.
5. Esveld, C. (2001) Modern Railway Track, 2nd edition, MRT-Productions, The
Netherlands.
6. Grassie, S.L. (1984) Dynamic modeling of railway track and wheel sets, invited
paper, Second International Conference on Recent Advances in Structural
Dynamics, University of Southampton.
7. Gustavson, R. (2002) Structural behavior of concrete railway sleepers, PhD
Thesis, Department of Structural Engineering, Chalmers University of
Technology.
8. Johansen, F.C. (1944) Experiments on reinforced concrete sleepers, Proc. ICE,
Railway Division, pp 3-20.
9. Kaewunruen, S. , Remennikov, A. (2006a) Rotational capacity of prestressed
concrete
sleeper
under
http://ro.uow.edu.au/engpapers/318.
static
hogging
moment,
78
10. Kaewunruen, S. , Remennikov, A. (2006b) Nonlinear finite element modeling
of railway prestressed concrete sleeper, http://ro.uow.edu.au/engpapers/319.
11. Kaewunruen, S. , Remennikov, A.M (2009) Impact capacity of railway
prestressed concrete sleepers, Elsevier, Engineering Failure Analysis ; 16:15201532.
12. LUSAS (2008a) Modeller Reference Manual, LUSAS Version 14.3 : Issue 1,
Chapter 5 : Model Attributes, Stress Potential (von Mises, Hill, Hoffman) pp
143-146.
13. LUSAS (2008b) Modeller Reference Manual, LUSAS Version 14.3 : Issue 1,
Chapter 5 : Model Attributes, Multi Crack Concrete (Model 94), pp 151-155.
14. LUSAS (2008c) Modeller Reference Manual, LUSAS Version 14.3 : Issue 1,
Chapter 6 : Running an Analysis, Nonlinear Solution Procedure, pp 255-262.
15. Remennikov, A.M. , Kaewunruen, S. (2008) A review of loading conditions for
railway track structures due to train and track vertical interaction, Structural
Control Health Monitoring ; 15:207-234.
16. Remennikov, A.M. , Murray, M.H. , Kaewunruen, S. (2008) Conversion of AS
1085.14 for prestressed concrete sleepers to limits states design format,
http://ro.uow.edu.au/ engpapers/400.
17. Sadeghi, J. (2005) Investigation on the accuracy of current practices in analysis
of railway track sleepers, International Journal of Civil Engineering; 3(1):3451.
18. Standard Australia (2003) Railway track material – Part 14 : Prestressed
Concrete Sleepers, Australian Standard : AS 1085.14-2003.
19. Tavaarez, F.A. (2001) Simulation of Behaviour of Composite Grid Reinforced
Concrete Beams Using Explicit Finite Element Methods, Master’s Thesis,
University of Wisconsin-Madison, Madison, Wisconsin.
79
20. Taylor, H.P.J. (1993) The railway sleeper : 50 years of pretensioned,
prestressed concrete, The Structural Engineer, Volume 71, No. 16, 281-295.
21. Teodoru, I.B. (2009) Beams on elastic foundation : The simplified continuum
approach, Buletinul Institutu;ui Politehnic Din Iasi, Publicat de Universitatea
Tehnica, Gheorghe Asachi’’ din Iasi, Tomul LV (LIX), Fasc. 4, Sectia,
Constructii. Arhitectura.
22. Thomas, F.G. (1944) Experiments on concrete sleepers, Proc. ICE, Railway
Division, pp 21-66.
23. Wakui, H. , Okuda, H. (1999) A study on limit-state design method for
prestressed concrete sleepers, Concrete Library of JSCE, Vol. 33, 1999, pp. 125.
24. Zakeri, J.A. , Sadeghi, S. (2007) Field investigation on load distribution and
deflections of railway track sleepers, Journal of Mechanical Science and
Technology; 21:1948-1956.
25. Zhai, W.M. , Wang, K.Y. , Lin, J.H. (2004) Modelling and experiment of
railway ballast vibrations, Journal of Sound and Vibration ; 270:673-683.
80
Appendix 1.A. : Model dimensions and input for the line geometry
Thickness = 245 mm
180 mm
240 mm
1,600 mm
380 mm
80 mm
2,680 mm
Figure A.1 : Model dimensions in LUSAS
Table A.1 : Input for the line geometry in LUSAS
Global Cartesian Coordinates System
X - axis
Y - axis
Z - axis
1
0
0
0
2
300
0
0
3
380
0
0
4
540
0
0
5
740
0
0
6
820
0
0
7
1260
0
0
8
1340
0
0
9
1420
0
0
10
1860
0
0
11
1940
0
0
12
2140
0
0
13
2300
0
0
14
2380
0
0
15
2680
0
0
81
Appendix 1.B. : Cross sectional area of prestressing tendons (As)
i) Diameter of prestressing tendon (D) = 5 mm
ii) Area of prestressing tendon (As)
=
=
19.6 mm2
iii) 4 nos prestressing tendons
= 4 As = 4 x 19.6 mm2 =
78.6 mm2
iv) 6 nos prestressing tendons
= 6 As = 6 x 19.6 mm2 = 117.8 mm2
=
Appendix 1.C. : Modulus of elasticity of concrete (Ec)
From AS 3600-2001, Modulus of elasticity of concrete (Ec) =
where,
5,050
= Ultimate compressive strength of concrete at 28 days = 88.5 MPa
Modulus of elasticity of concrete (Ec) =5,050 √88.5 = 47,508 MPa = 47.5kN/mm2
82
Appendix 1.D. : Ballast stiffness for the spring supports (kb)
From Zhai, et al. (2004) and 1085.14-2003,
Spring stiffness (kb)
where,
=
le = L-g = 2,680 mm – 1,600 mm = 1,080 mm
lb = 250 mm
α
= 35°
hb = 300 mm
Eb = 0.088 kN/mm2
Spring stiffness (kb)
=
=
0.088
156.6 kN/mm
83
Appendix 2.1.A. : Spring support stiffness input for Laboratory test
Item
No.
Distribution of
bearing pressure
1
Developers
Remarks
ORE, Talbot
Laboratory test
Table A.2.1.1. : Laboratory test (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation >
Specify Order : Parabolic > Distance Type : Parametric
Figure A.2.1.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 0.5
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
0
113.1
132.2
156.6
160.9
154.6
36.5
0
36.5
64.7
113.1
18.9
18.9
113.1
113.1
132.2
156.6
160.9
154.6
36.5
0
36.5
154.6
10
154.6
158.3
160.9
11
160.9
162.4
156.6
12
156.6
146.7
132.2
13
132.2
123.3
113.1
14
113.1
64.7
0
123.3
146.7
162.4
158.3
Table A.2.1.2. : Input for spring support stiffness distribution in LUSAS
84
Appendix 2.1.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.1.2. : Unloaded with external load
Figure A.2.1.3. : At initiation of crack (external load = 485 kN)
Figure A.2.1.4. : At ultimate state (external load = 649 kN)
Appendix 2.1.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
Deflection (mm)
Node …
Figure A.2.1.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
485
0.132
Ultimate state
649
0.196
Table A.2.1.3. : Summary of results at first crack point
85
Appendix 2.1.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.1.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.1.E. : Principal stress in x-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.1.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
86
Appendix 2.2.A. : Spring support stiffness input for Tamped either side of rail
Item
No.
Distribution of
bearing pressure
2
Developers
Remarks
ORE, Talbot,
Bartlett Clarke
Tamped either side
of rail
Table A.2.2.1. : Tamped either side of rail (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.2.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
156.6 ( x = 0.5 )
156.6
156.6
156.6 ( x = 0.4 )
156.6
156.6
0
0
156.6 ( x = 0.727 )
156.6
156.6
156.6 ( x = 0.5 )
156.6
156.6
156.6 ( x = 0.273 )
0
0
156.6
10
156.6
156.6
11
156.6
156.6 ( x = 0.6 )
12
156.6 ( x = 0.5 )
156.6
13
156.6
156.6
14
156.6
156.6 ( x = 0.5 )
Table A.2.2.2. : Input for spring support stiffness distribution in LUSAS
87
Appendix 2.2.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.2.2. : Unloaded with external load
Figure A.2.2.3. : At initiation of crack (external load = 435 kN)
Figure A.2.2.4. : At ultimate state (external load = 658 kN)
Appendix 2.2.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,1
0,2
0,3
0,4
0,5
Deflection (mm)
Node …
Figure A.2.2.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
435
0.172
Ultimate state
658
0.386
Table A.2.2.3. : Summary of results at first crack point
88
Appendix 2.2.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
Deflection (mm)
0
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.2.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.2.E. : Principal stress in x-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,05
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.2.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
89
Appendix 2.3.A. : Spring support stiffness input for Principal bearing on rails
Item
No.
Distribution of
bearing pressure
3
Developers
Remarks
ORE, Talbot
Principal bearing on rails
Table A.2.3.1. : Principal bearing on rails (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.3.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
0
87.0
110.2
156.6
117.5
101.8
15.7
0
15.7
87.0
110.2
156.6
117.5
101.8
15.7
0
15.7
101.8
10
101.8
117.5
11
117.5
156.6
12
156.6
110.2
13
110.2
87.0
14
87.0
0
Table A.2.3.2. : Input for spring support stiffness distribution in LUSAS
90
Appendix 2.3.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.3.2. : Unloaded with external load
Figure A.2.3.3. : At initiation of crack (external load = 485 kN)
Figure A.2.3.4. : At ultimate state (external load = 645 kN)
Appendix 2.3.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack
300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
Deflection (mm)
Node …
Figure A.2.3.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
485
0.150
Ultimate state
645
0.220
Table A.2.3.3. : Summary of results at first crack point
91
Appendix 2.3.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.3.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.3.E. : Principal stress in x-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.3.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
92
Appendix 2.4.A. : Spring support stiffness input for Maximum intensity at the
ends
Item
No.
Distribution of
bearing pressure
4
Developers
Remarks
ORE, Talbot
Maximum intensity
at the ends
Table A.2.4.1. : Maximum intensity at the ends (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.4.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
156.6
121.5
112.2
93.5
70.1
60.8
9.4
0
9.4
121.5
112.2
93.5
70.1
60.8
9.4
0
9.4
60.8
10
60.8
70.1
11
70.1
93.5
12
93.5
112.2
13
112.2
121.5
14
121.5
156.6
Table A.2.4.2. : Input for spring support stiffness distribution in LUSAS
93
Appendix 2.4.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.4.2. : Unloaded with external load
Figure A.2.4.3. : At initiation of crack (external load = 455 kN)
Figure A.2.4.4. : At ultimate state (external load = 652 kN)
Appendix 2.4.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
Deflection (mm)
Node …
Figure A.2.4.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
455
0.180
Ultimate state
652
0.300
Table A.2.4.3. : Summary of results at first crack point
94
Appendix 2.4.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.4.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.4.E. : Principal stress in x-direction on the first crack section
240
210
180
Elevation (mm)
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0,00
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.4.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
95
Appendix 2.5.A.: Spring support stiffness input for Maximum intensity in the
middle
Item
No.
Distribution of
bearing pressure
Developers
Remarks
Talbot
Maximum intensity
in the middle
5
Table A.2.5.1. : Maximum intensity in the middle (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.5.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
0
35.1
44.4
63.1
86.5
35.1
44.4
63.1
86.5
95.8
6
7
8
9
95.8
147.3
156.6
147.3
147.3
156.6
147.3
95.8
10
95.8
86.5
11
86.5
63.1
12
63.1
44.4
13
44.4
35.1
14
35.1
0
Table A.2.5.2. : Input for spring support stiffness distribution in LUSAS
96
Appendix 2.5.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.5.2. : Unloaded with external load
Figure A.2.5.3. : At initiation of crack (external load = 460 kN)
Figure A.2.5.4. : At ultimate state (external load = 653 kN)
Appendix 2.5.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,1
0,2
0,3
0,4
0,5
Deflection (mm)
Node …
Figure A.2.5.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
460
0.255
Ultimate state
653
0.413
Table A.2.5.3. : Summary of results at first crack point
97
Appendix 2.5.D. : Vertical deflection along the sleeper length
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
Deflection (mm)
0
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.5.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.5.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
‐2E‐17
0,01
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
0,02
Figure A.2.5.7. : Principal stress in x-direction at first crack section (Node no. 54
at bottom of railseat)
98
Appendix 2.6.A. : Spring support stiffness input for Center bound
Item
No.
Distribution of
bearing pressure
Developers
Remarks
Talbot
Center bound
6
Table A.2.6.1. : Center bound (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.6.1. : Hypothetical bearing pressure distribution patterns (LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
0
87.0
110.2
156.6
156.6
156.6
156.6
156.6
156.6
87.0
110.2
156.6
156.6
156.6
156.6
156.6
156.6
156.6
10
156.6
156.6
11
156.6
156.6
12
156.6
110.2
13
110.2
87.0
14
87.0
0
Table A.2.6.2. : Input for spring support stiffness distribution in LUSAS
99
Appendix 2.6.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.6.2. : Unloaded with external load
Figure A.2.6.3. : At initiation of crack (external load = 485 kN)
Figure A.2.6.4. : At ultimate state (external load = 648 kN)
Appendix 2.6.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
Deflection (mm)
Node …
Figure A.2.6.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
485
0.140
Ultimate state
648
0.200
Table A.2.6.3. : Summary of results at first crack point
100
Appendix 2.6.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.6.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.6.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.6.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
101
Appendix 2.7.A. : Spring support stiffness input for Flexure of sleeper
produces variations form
Item
No.
Distribution of
bearing pressure
7
Developers
Remarks
Talbot
Flexure of sleeper
produces variations form
Table A.2.7.1. : Flexure of sleeper produces variations form (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Parabolic > Distance Type : Parametric
Figure A.2.7.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
1
2
3
4
5
Parametric
distance (x) =
0.0
90
111
118
109
90
Parametric
distance (x) =
0.5
108
6
7
8
80
50
45
9
50
65
48
48
105
140
10
140
142
145
11
145
150
156.6
12
156.6
150
145
13
145
138
133
14
133
118
108
Segments
115
114
103
85
Parametric
distance (x) =
1.0
111
118
109
90
80
50
45
50
Table A.2.7.2. : Input for spring support stiffness distribution in LUSAS
102
Appendix 2.7.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.7.2. : Unloaded with external load
Figure A.2.7.3. : At initiation of crack (external load = 455 kN)
Figure A.2.7.4. : At ultimate state (external load = 647 kN)
Appendix 2.7.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
0,3
Deflection (mm)
Node …
Figure A.2.7.5. : Load-deflection relation for first crack point (Node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
455
0.162
Ultimate state
647
0.259
Table A.2.7.3. : Summary of results at first crack point
103
Appendix 2.7.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.7.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.7.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,05
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.7.7. : Principal stress in x-direction at first crack section (Node no.
54 at bottom of railseat)
104
Appendix 2.8.A. : Spring support stiffness input for Well tamped sides
Item
No.
Distribution of
bearing pressure
8
Developers
Remarks
ORE, Talbot,
Kerr, Schramm
Well tamped sides
Table A.2.8.1. : Well tamped sides (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.8.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
156.6
156.6
156.6
0
0
0
0
0
0
156.6
156.6
156.6
0
0
0
0
0
0
10
0
0
11
0
0
12
156.6
156.6
13
156.6
156.6
14
156.6
156.6
Table A.2.8.2. : Input for spring support stiffness distribution in LUSAS
105
Appendix 2.8.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.8.2. : Unloaded with external load
Figure A.2.8.3. : At initiation of crack (external load = 255 kN)
Figure A.2.8.4. : At ultimate state (external load = 347 kN)
Appendix 2.8.C. : Load-deflection at first crack point
400
350
Load (kN)
300
250
200
Load at the initiation of crack 150
100
50
0
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
Deflection (mm)
Node …
Figure A.2.8.5. : Load-deflection relation for first crack point (Node no. 1168
at top chamfer)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
255
0.055
Ultimate state
347
0.069
Table A.2.8.3. : Summary of results at first crack point
106
Appendix 2.8.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
Deflection (mm)
0
0,2
0,4
0,6
0,8
1
At initiation of crack
Unloaded with external load
At ultimate state
Figure A.2.8.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.8.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
‐2E‐17
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.8.7. : Principal stress in x-direction at first crack section (Node no.
1168 at top chamfer)
107
Appendix 2.9.A. : Spring support stiffness input for Stabilized rail seat and
sides
Item
No.
Distribution of
bearing pressure
9
Developers
Remarks
ORE, Talbot
Stabilized rail seat
and sides
Table A.2.9.1. : Stabilized rail seat and sides (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.9.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
156.6
156.6
156.6
156.6
117.5
101.8
15.7
0
15.7
156.6
156.6
156.6
117.5
101.8
15.7
0
15.7
101.8
10
101.8
117.5
11
117.5
156.6
12
156.6
156.6
13
156.6
156.6
14
156.6
156.6
Table A.2.9.2. : Input for spring support stiffness distribution in LUSAS
108
Appendix 2.9.B. : Principal stress distribution in x-direction and crack pattern
Figure A.2.9.2. : Unloaded with external load
Figure A.2.9.3. : At initiation of crack (external load = 480 kN)
Figure A.2.9.4. : At ultimate state (external load = 644 kN)
Appendix 2.9.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
0,25
Deflection (mm)
Node …
Figure A.2.9.5. : Load-deflection relation for first crack point (node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
480
0.135
Ultimate state
644
0.196
Table A.2.9.3. : Summary of results at first crack point
109
Appendix 2.9.D. : Vertical deflection along the sleeper length at different load
stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.9.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.9.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.9.7. : Principal stress in x-direction at first crack section (node no. 54
at bottom of railseat)
110
Appendix 2.10.A. : Spring support stiffness input for Uniform pressure
Item
No.
Distribution of bearing
pressure
10
Developers
Remarks
AREA, Raymond,
Talbot
Uniform pressure
Table A.2.10.1. : Uniform pressure (Sadeghi, 2005)
Menu command : Utilities > Variation > Line > Type : Interpolation
> Specify Order : Linear > Distance Type : Parametric
Figure A.2.10.1. : Hypothetical bearing pressure distribution patterns
(LUSAS model)
Spring support stiffness (kN/mm)
Segments
Parametric distance
(x) = 0.0
Parametric
distance (x) = 1.0
1
2
3
4
5
6
7
8
9
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
156.6
10
156.6
156.6
11
156.6
156.6
12
156.6
156.6
13
156.6
156.6
14
156.6
156.6
Table A.2.10.2. : Input for spring support stiffness distribution in LUSAS
111
Appendix 2.10.B. : Principal stress distribution in x-direction and crack
pattern
Figure A.2.10.2. : Unloaded with external load
Figure A.2.10.3. : At initiation of crack (external load = 475 kN)
Figure A.2.10.4. : At ultimate state (external load = 647 kN)
Appendix 2.10.C. : Load-deflection at first crack point
700
600
Load (kN)
500
400
Load at the initiation of crack 300
200
100
0
0
0,05
0,1
0,15
0,2
Deflection (mm)
Node …
Figure A.2.10.5. : Load-deflection relation for first crack point (node no. 54 at
bottom of railseat)
Stage
Load (kN)
Displacement (mm)
Initiation of crack
475
0.128
Ultimate state
647
0.187
Table A.2.10.3. : Summary of results at first crack point
112
Appendix 2.10.D. : Vertical deflection along the sleeper length at different
load stage
Distance along the sleeper from origin (mm)
‐0,2
0
400
800
1200
1600
2000
2400
2800
0
Deflection (mm)
0,2
0,4
0,6
0,8
1
At initiation of crack
At ultimate state
Unloaded with external load
Figure A.2.10.6. : Vertical deflection along the sleeper length at different load stage
Appendix 2.10.E. : Principal stress in X-direction on the first crack section
240
210
Elevation (mm)
180
150
120
90
60
30
0
‐0,04
‐0,03
‐0,02
‐0,01
0
0,01
0,02
Principal stress in x‐direction (kN/mm2)
Initiation of crack
Ultimate state
Unloaded section
Figure A.2.10.7. : Principal stress in x-direction at first crack section (node no.
54 at bottom of railseat)
113
Appendix 3.A. : Relevant information from KTMB’s Double Track
Specification
i)
Axle Load
=
20 tonne
ii)
Train Speed, V
=
160 kph
iii)
Rail Type
=
UIC 54 kg
iv)
Sleeper spacing
=
600 mm
v)
Static Wheel Load
=
98.7 kN
Appendix 3.B. : Dynamic Wheel Load
i)
Using Eisenmann’s Formula (1972)
Dynamic Wheel Load
=
where,
0.1 for track in excellent condition
q
=
Static Wheel Load x (1 + qst)
0.2 for track in good condition
0.3 for track in poor condition
s
=
1 + (V-60)/140
t
=
1.0 for statistical confidence of 84.1%
2.0 for statistical confidence of 97.7%
3.0 for statistical confidence of 99.9%
Dynamic Wheel Load
=
98.7 x ( 1 + 0.2 x 1.7143 x 3 )
=
200.22 kN
Resultant Impact Factor =
2.02857
114
ii)
Using Australian Standard 1085.14-2003
Dynamic Wheel Load
=
2.5 x Static Wheel Load
=
246.75 kN
>
2 x Static Wheel Load, adequate for
sleeper with
additional guardrails
Conclusion
:
Dynamic Wheel Load
= 246.8 kN
Appendix 3.C. : Rail seat load
Sleeper Spacing
=
600 mm
Distribution Factor
=
0.51
Rail Seat Load, R
=
Dynamic Wheel Load x Distribution Factor
=
246.8 x 0.51
=
125.868 kN
115
Appendix 3.D. : Results from Testing of Prestressed Concrete Sleeper (DNV,
2002)
i)
Rail Seat Negative Moment Test
Figure A.3.1. : Schematic diagram of rail seat negative moment test
(AS 1085.14-2003)
Test results :
No structural cracking was observed during
3 minutes holding time at a load of
164 kN > 125.9 kN
116
ii)
Rail Seat Positive Moment Test
Figure A.3.2. : Schematic diagram of rail seat positive moment test
(AS 1085.14-2003)
Test results : i ) No structural cracking was observed during 3 minutes
holding time at a load of 198 kN > 125.9 kN
ii) After repeated load of 15 kN to 228 kN (1.15 P2) for 3
million cycles at 5.6 Hz, rail seat was able to support a
load of 228 kN for 3 minutes.
iii) Ultimate load recorded at 434 kN