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The Study of Subgrade Operating Conditions at Bridge Abutment Approach
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 189 (2017) 893 – 897
Transportation Geotechnics and Geoecology, TGG 2017, 17-19 May 2017, Saint Petersburg, Russia
The study of subgrade operating conditions at bridge abutment approach Dmitry Serebryakova, Anastasia Konona*, Evgeniy Zaitsevb a
Emperor Alexander I St. Petersburg State Transport University, Moskovsky pr., 9, St. Petersburg, 190031, Russian Federation b Petersburg State University of civil aviation, Pilotov Str., 38, St. Petersburg, 196210, Russian Federation
Abstract There is an ongoing problem of interaction between bridges and rail tracks. Interaction zones suffer early failure because of sudden stiffness change. There are some ways to equalize uneven stiffness – geogrid and geopier reinforcement, cement treatment, using of concrete boxes filled with crushed stone, using ballast glue / bond and so on. The presented study is devoted to oscillation distribution in subgrade at bridge abutment approach. Occurring oscillation was described with vibratory displacement amplitudes. Test sites had versatile stiffness structures – geogrid reinforcement and concrete boxes filled with crushed stone. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and (http://creativecommons.org/licenses/by-nc-nd/4.0/). Geoecology. Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and Geoecology Keywords: bridge transition zone; geogrid reinforcement; oscillation; vibratory displacement
1. Introduction To design railway subgrade, imposed loads should be known. It is important to assess static and dynamic loads. It is known that vibrodynamic impact has significant effect on structure bearing capacity [1-9]. Operation practice shows that railway subgrade often has significant deformations at bridge approach zones. High deformations level at bridge transition zones is connected to sudden stiffness change. This sudden change influences
* Corresponding author. Tel.: +7-921-795-5857. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and Geoecology
doi:10.1016/j.proeng.2017.05.139
894
Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
oscillation level in ballast layer and subgrade greatly. Increased vibrodynamic impact reduces subgrade soil strength properties that may lead to subgrade bearing capacity loss [10-11]. To solve this issue versatile stiffness structures should be constructed [12-15]. The principle of their performance is track stiffness progressive increment while approaching the engineering structure due to summarized stiffness change of superstructure and subgrade. 2. Materials and methods In-situ tests were held by PGUPS researchers to study features and regularities of oscillation distribution in subgrade at bridge abutment approach. The research was made on 5 sites on Saint-Petersburg – Moscow railway line. Versatile stiffness structures included geogrids and reinforced concrete bottomless boxes, filled with crushed stone. All test sites had R65 rails and concrete sleepers. Bridges at test sites were metal. They had 1 span and ballastless coverage with concrete slabs. Test sites characteristics are presented in Table 1. Table 1. Test sites characteristics. Bridge position
Bridge length, m
Versatile stiffness structure type
381 km stake 7
48.4
geogrids
377 km stake 8
18.7
concrete bottomless boxes
151 km stake 9
25.54
geogrids
172 km stake 5
38.26
geogrids
179 km stake 1
26.2
geogrids
At all test sites measuring sets were placed at distance of 5 m, 10 m, 15 m and 30 m from bridge abutment at the sleeper end 20 cm beneath its pad. Measurement points were placed at coming on and off the bridge. To assess versatile stiffness structure influence on oscillation damping depthwise the test pit was made at 10 m from abutment edge up to 1.85 m depth from the sleeper pad. Oscillation sensors were placed at 0.2 m, 0.95 m, 1.35 m and 1.85 m below the sleeper pad. Oscillation damping process was also studied in cross-track direction. Sensors placement is presented in Fig. 1 and 2. Statistical analysis was made to obtain reliable test data. Average and maximal probable values of vibratory displacement amplitude were assessed for determined train speeds values.
Fig. 1. Sensors placement (layout).
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Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
Fig. 2. Sensors placement (cross section).
3. Discussion Test data analysis showed the following. Rolling stock coming off the bridge causes higher vibrodynamic impact than coming on the bridge. Vibratory displacement amplitudes values were bigger at train going from the bridge, than at coming on. This fact can be explained with the following: at train coming off the bridge aт impact blow occurs, that gets recorded with the measurement set. Vibratory displacement amplitudes comparative data for rolling stock coming on and off the bridge is shown at Table 2. Table 2. Vibratory displacement amplitudes (mkm) for rolling stock coming on and off the bridge. 381 km Distance from abutment, m
Ап
Ау
5
377
407
10
316
15 30
377 km
Aп
Ап
Ау
1.08
367
434
360
1.14
250
275
282
1.03
259
265
1.02
Aу
151 km
Aп
Ап
Ау
1.16
180
207
276
1.11
189
242
255
1.06
169
176
1.04
Aу
172 km
Aп
Ап
Ау
1.15
129
157
193
1.02
114
175
168
0.96
143
146
1.02
Aу
179 km
Aп
Aп
Ап
Ау
1.22
85
100
1.17
142
1.25
97
107
1.10
123
137
1.11
91
105
1.15
114
130
1.14
100
95
0.95
Aу
Aу
Note. Ап - train coming on the bridge, Ау - train coming off the bridge.
Rolling stock speed increasing causes significant rise of vibratory displacement amplitude increase rate. It amounts up to 40 mkm per 10 km/h at 5-15 m from abutment edge. Vibratory displacement increase rate is up to 10 mkm for further distance from abutment edge. Vibratory displacement increase rate values depending on train speed are presented in Table 3.
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Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
Table 3. Vibratory displacement increase rate (mkm) values per 10 km/h speed increase. Distance from abutment edge, m
Speed range, km/h
Test site 5
10
15
30
377 km
40
27
13
12
70-100
381 km
34
17
12
14
70-100
151 km
26
29
14
14
70-100
172 km
10
11
13
9
100-160
179 km
12
11
13
8
100-160
Test results of oscillation propagation in ballast layer and subgrade show that vibratory displacement amplitude damping can de described with linear relationship. Vibratory displacement amplitude damps by 20 mkm per 0.5 m depth. Amplitude damping is presented in Table 4. Table 4. Vibratory displacement amplitude damping. Vibratory displacement amplitude, mkm Depth below the sleeper pad, m 0.2 0.95 1.35 1.85
Horizontal alongside the track
cross-track
42 16 15 14
46 40 27 20
Vertical
Resulting
178 148 129 111
189 154 133 114
Vibratory displacement amplitude distribution in cross-track direction shows that amplitude decreasing amounts 30 mkm per meter for distance up to 8 m from vibrodynamic impact source. Further going away from the track amplitude decreasing is 1.5 mkm per meter. Vibratory displacement amplitude damping in cross-track direction is presented in Table 5. Table 5. Vibratory displacement amplitude damping in cross-track direction. Vibratory displacement amplitude, mkm Distance from outer rail head, m 1.7 5 10.5 16.5
Horizontal alongside the track
cross-track
42 13 11 8
46 17 14 10
Vertical
Resulting
177 30 22 14
180 37 28 19
Versatile stiffness structure significantly reduces vibrodynamic impact at bridge abutment approach, equalizing its manifestation along the track. Test results comparison before and after versatile stiffness structure construction gives evident vibratory displacement amplitude reducing in the abutment zone (5 – 15 m) by 20% at the average. Test results comparison is presented in Table 6. Table 6. Test data comparison before and after versatile stiffness structure construction. Distance from abutment edge, m 5 10 15 30
Vibratory displacement amplitude, mkm before versatile stiffness structure after versatile stiffness structure construction construction 525 407 378 350 350 282 277 265
Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
4. Conclusions Presented test results allow to make the following conclusions: x Rolling stock coming off the bridge causes higher vibrodynamic impact than coming on the bridge. x Rolling stock speed increasing rises vibratory displacement amplitude increase rate up to 40 mkm per 10 km/h at 5-15 m from abutment edge. x Vibratory displacement amplitude damping can de described with linear relationship. Vibratory displacement amplitude damps by 20 mkm per 0.5 m depth. x Vibratory displacement amplitude decreases by 30 mkm per meter for distance up to 8 m from vibrodynamic impact source. Further going away from the track amplitude decreasing is 1.5 mkm per meter. x Versatile stiffness structure significantly reduces vibrodynamic impact at bridge abutment approach, equalizing its manifestation along the track. References [1] G.M. Stoyanovich. In situ study of the dynamic vibration magnitude of the impact of a moving load on the ground. Khabarovsk, 2005. [2] V.V.Pupatenko, S.A. Kudryavtsev, E.S. Daniliants. Prediction of accumulation of residual deformations of roadbed taking into account the impact of trains. World of transport. 2008 (2), pp. 136 – 142. [3] A.Petriaev. Stress states of thawed soil subgrade. Sciences in cold and arid regions. Volume 7,Issue 4. (2015) 0348-0353. DOI: 10.3724/SP.J.1226.2015.00348. [4] A.V. Petriaev. Thawing railroad bed and methods of its reinforcing, Computer methods and recent advances in geomechanics, Proceedings of the 14th international conference, Kyoto, Japan. (2015) 265. [5] A.Petriaev. The vibration impact of heavy freight train on the roadbed, Procedia Engineering,Advances in Transportation Geotechnics 3, The 3rd International Conference on Transportation Geotechnics (ICTG 2016), 2016.143: 1136–1143. — DOI: 10.1016/j.proeng.2016.06.110 [6] A.Petryaev, A.Morozova. Railroad bed bearing strength in the period of thawing and methods of its enhancement , Sciences in cold and arid regions, Volum 5, Issue 5, (2013) 548-553. DOI: 10.3724/SP.J.1226.2013.00548. [7] A.V. Petryaev, I.N. Zhuravlev. Modern geomaterials model tests in the laboratory. Contemporary and advanced technologies to track facilities on October Railway, Well. Etc., Proceedings of the 43 scientific and technical conference, St. Petersburg, PGUPS, (2001) 119-122. [8] A.V.Petryaev, V.V Ganchits. The impact of geosynthetic materials on the vibrodynamic process subgrade soil. Problems and prospects of development of railway transport, Proceedings of the Russian Scientific and Technical Conference, Volume 1, Ekaterinburg, (2003) 59-62. [9] A.V.Petryaev, I.N. Zhuravlev. To the issue of practical application of finite element method to calculate stress-strain state reinforced designs, Application of geomaterials for construction and reconstruction of transport facilities, Proceedings of the III International scientific-technical conference, Petersburg state transport University of Emperor Alexander I, (2013), 101-104. [10] Kolos A, Morozova A, 2014. Distribution survey for vibrational acceleration of ballast particles under condition of train traffic with increased axial loads. Proceedings of Petersburg Transport University, 2(39): 29-35. [11] Kolos, A., Konon, A. 2016. Estimation of railway ballast and subballast bearing capacity in terms of 300 kN axle load train operation. In: Askar Zhussupbekov (ed.). Challenges and Innovations in Geotechnics. Proc. intern. conf., Astana, 5-7 August 2016. Rotterdam: Balkema. [12] E. Tutumluer , T. D. Stark, D. Mishra, J.P. Hyslip. Investigation and mitigation of differential movement at railway transitions for US high speed passenger rail and joint passenger/freight corridors. Proceedings of the 2012 Joint Rail Conference (JRC2012). April 17-19, 2012, Philadelphia, Pennsylvania, USA. (2012). [13] S. Kaewunruen. Dynamic responses of railway bridge ends: A systems performance improvement by application of ballast glue/bond. Available at: http://works.bepress.com/sakdirat_kaewunruen/46/ (2014). [14] D. Plotkin. Bridge Approaches and Track Stiffness. Federal Railroad Administration Research Results. RR07-12 (2007). [15]C. Gallage, B. Dareeju, S. Dhanasekar. State-of-the-art : track degradation at bridge transitions. In Pathirana, K.P.P. (Ed.) Proceedings of the 4th International Conference on Structural Engineering and Construction Management 2013, Kandy, Sri Lanka. (2013) pp. 40-52.
897
ScienceDirect Procedia Engineering 189 (2017) 893 – 897
Transportation Geotechnics and Geoecology, TGG 2017, 17-19 May 2017, Saint Petersburg, Russia
The study of subgrade operating conditions at bridge abutment approach Dmitry Serebryakova, Anastasia Konona*, Evgeniy Zaitsevb a
Emperor Alexander I St. Petersburg State Transport University, Moskovsky pr., 9, St. Petersburg, 190031, Russian Federation b Petersburg State University of civil aviation, Pilotov Str., 38, St. Petersburg, 196210, Russian Federation
Abstract There is an ongoing problem of interaction between bridges and rail tracks. Interaction zones suffer early failure because of sudden stiffness change. There are some ways to equalize uneven stiffness – geogrid and geopier reinforcement, cement treatment, using of concrete boxes filled with crushed stone, using ballast glue / bond and so on. The presented study is devoted to oscillation distribution in subgrade at bridge abutment approach. Occurring oscillation was described with vibratory displacement amplitudes. Test sites had versatile stiffness structures – geogrid reinforcement and concrete boxes filled with crushed stone. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and (http://creativecommons.org/licenses/by-nc-nd/4.0/). Geoecology. Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and Geoecology Keywords: bridge transition zone; geogrid reinforcement; oscillation; vibratory displacement
1. Introduction To design railway subgrade, imposed loads should be known. It is important to assess static and dynamic loads. It is known that vibrodynamic impact has significant effect on structure bearing capacity [1-9]. Operation practice shows that railway subgrade often has significant deformations at bridge approach zones. High deformations level at bridge transition zones is connected to sudden stiffness change. This sudden change influences
* Corresponding author. Tel.: +7-921-795-5857. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International conference on Transportation Geotechnics and Geoecology
doi:10.1016/j.proeng.2017.05.139
894
Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
oscillation level in ballast layer and subgrade greatly. Increased vibrodynamic impact reduces subgrade soil strength properties that may lead to subgrade bearing capacity loss [10-11]. To solve this issue versatile stiffness structures should be constructed [12-15]. The principle of their performance is track stiffness progressive increment while approaching the engineering structure due to summarized stiffness change of superstructure and subgrade. 2. Materials and methods In-situ tests were held by PGUPS researchers to study features and regularities of oscillation distribution in subgrade at bridge abutment approach. The research was made on 5 sites on Saint-Petersburg – Moscow railway line. Versatile stiffness structures included geogrids and reinforced concrete bottomless boxes, filled with crushed stone. All test sites had R65 rails and concrete sleepers. Bridges at test sites were metal. They had 1 span and ballastless coverage with concrete slabs. Test sites characteristics are presented in Table 1. Table 1. Test sites characteristics. Bridge position
Bridge length, m
Versatile stiffness structure type
381 km stake 7
48.4
geogrids
377 km stake 8
18.7
concrete bottomless boxes
151 km stake 9
25.54
geogrids
172 km stake 5
38.26
geogrids
179 km stake 1
26.2
geogrids
At all test sites measuring sets were placed at distance of 5 m, 10 m, 15 m and 30 m from bridge abutment at the sleeper end 20 cm beneath its pad. Measurement points were placed at coming on and off the bridge. To assess versatile stiffness structure influence on oscillation damping depthwise the test pit was made at 10 m from abutment edge up to 1.85 m depth from the sleeper pad. Oscillation sensors were placed at 0.2 m, 0.95 m, 1.35 m and 1.85 m below the sleeper pad. Oscillation damping process was also studied in cross-track direction. Sensors placement is presented in Fig. 1 and 2. Statistical analysis was made to obtain reliable test data. Average and maximal probable values of vibratory displacement amplitude were assessed for determined train speeds values.
Fig. 1. Sensors placement (layout).
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Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
Fig. 2. Sensors placement (cross section).
3. Discussion Test data analysis showed the following. Rolling stock coming off the bridge causes higher vibrodynamic impact than coming on the bridge. Vibratory displacement amplitudes values were bigger at train going from the bridge, than at coming on. This fact can be explained with the following: at train coming off the bridge aт impact blow occurs, that gets recorded with the measurement set. Vibratory displacement amplitudes comparative data for rolling stock coming on and off the bridge is shown at Table 2. Table 2. Vibratory displacement amplitudes (mkm) for rolling stock coming on and off the bridge. 381 km Distance from abutment, m
Ап
Ау
5
377
407
10
316
15 30
377 km
Aп
Ап
Ау
1.08
367
434
360
1.14
250
275
282
1.03
259
265
1.02
Aу
151 km
Aп
Ап
Ау
1.16
180
207
276
1.11
189
242
255
1.06
169
176
1.04
Aу
172 km
Aп
Ап
Ау
1.15
129
157
193
1.02
114
175
168
0.96
143
146
1.02
Aу
179 km
Aп
Aп
Ап
Ау
1.22
85
100
1.17
142
1.25
97
107
1.10
123
137
1.11
91
105
1.15
114
130
1.14
100
95
0.95
Aу
Aу
Note. Ап - train coming on the bridge, Ау - train coming off the bridge.
Rolling stock speed increasing causes significant rise of vibratory displacement amplitude increase rate. It amounts up to 40 mkm per 10 km/h at 5-15 m from abutment edge. Vibratory displacement increase rate is up to 10 mkm for further distance from abutment edge. Vibratory displacement increase rate values depending on train speed are presented in Table 3.
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Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
Table 3. Vibratory displacement increase rate (mkm) values per 10 km/h speed increase. Distance from abutment edge, m
Speed range, km/h
Test site 5
10
15
30
377 km
40
27
13
12
70-100
381 km
34
17
12
14
70-100
151 km
26
29
14
14
70-100
172 km
10
11
13
9
100-160
179 km
12
11
13
8
100-160
Test results of oscillation propagation in ballast layer and subgrade show that vibratory displacement amplitude damping can de described with linear relationship. Vibratory displacement amplitude damps by 20 mkm per 0.5 m depth. Amplitude damping is presented in Table 4. Table 4. Vibratory displacement amplitude damping. Vibratory displacement amplitude, mkm Depth below the sleeper pad, m 0.2 0.95 1.35 1.85
Horizontal alongside the track
cross-track
42 16 15 14
46 40 27 20
Vertical
Resulting
178 148 129 111
189 154 133 114
Vibratory displacement amplitude distribution in cross-track direction shows that amplitude decreasing amounts 30 mkm per meter for distance up to 8 m from vibrodynamic impact source. Further going away from the track amplitude decreasing is 1.5 mkm per meter. Vibratory displacement amplitude damping in cross-track direction is presented in Table 5. Table 5. Vibratory displacement amplitude damping in cross-track direction. Vibratory displacement amplitude, mkm Distance from outer rail head, m 1.7 5 10.5 16.5
Horizontal alongside the track
cross-track
42 13 11 8
46 17 14 10
Vertical
Resulting
177 30 22 14
180 37 28 19
Versatile stiffness structure significantly reduces vibrodynamic impact at bridge abutment approach, equalizing its manifestation along the track. Test results comparison before and after versatile stiffness structure construction gives evident vibratory displacement amplitude reducing in the abutment zone (5 – 15 m) by 20% at the average. Test results comparison is presented in Table 6. Table 6. Test data comparison before and after versatile stiffness structure construction. Distance from abutment edge, m 5 10 15 30
Vibratory displacement amplitude, mkm before versatile stiffness structure after versatile stiffness structure construction construction 525 407 378 350 350 282 277 265
Dmitry Serebryakov et al. / Procedia Engineering 189 (2017) 893 – 897
4. Conclusions Presented test results allow to make the following conclusions: x Rolling stock coming off the bridge causes higher vibrodynamic impact than coming on the bridge. x Rolling stock speed increasing rises vibratory displacement amplitude increase rate up to 40 mkm per 10 km/h at 5-15 m from abutment edge. x Vibratory displacement amplitude damping can de described with linear relationship. Vibratory displacement amplitude damps by 20 mkm per 0.5 m depth. x Vibratory displacement amplitude decreases by 30 mkm per meter for distance up to 8 m from vibrodynamic impact source. Further going away from the track amplitude decreasing is 1.5 mkm per meter. x Versatile stiffness structure significantly reduces vibrodynamic impact at bridge abutment approach, equalizing its manifestation along the track. References [1] G.M. Stoyanovich. In situ study of the dynamic vibration magnitude of the impact of a moving load on the ground. Khabarovsk, 2005. [2] V.V.Pupatenko, S.A. Kudryavtsev, E.S. Daniliants. Prediction of accumulation of residual deformations of roadbed taking into account the impact of trains. World of transport. 2008 (2), pp. 136 – 142. [3] A.Petriaev. Stress states of thawed soil subgrade. Sciences in cold and arid regions. Volume 7,Issue 4. (2015) 0348-0353. DOI: 10.3724/SP.J.1226.2015.00348. [4] A.V. Petriaev. Thawing railroad bed and methods of its reinforcing, Computer methods and recent advances in geomechanics, Proceedings of the 14th international conference, Kyoto, Japan. (2015) 265. [5] A.Petriaev. The vibration impact of heavy freight train on the roadbed, Procedia Engineering,Advances in Transportation Geotechnics 3, The 3rd International Conference on Transportation Geotechnics (ICTG 2016), 2016.143: 1136–1143. — DOI: 10.1016/j.proeng.2016.06.110 [6] A.Petryaev, A.Morozova. Railroad bed bearing strength in the period of thawing and methods of its enhancement , Sciences in cold and arid regions, Volum 5, Issue 5, (2013) 548-553. DOI: 10.3724/SP.J.1226.2013.00548. [7] A.V. Petryaev, I.N. Zhuravlev. Modern geomaterials model tests in the laboratory. Contemporary and advanced technologies to track facilities on October Railway, Well. Etc., Proceedings of the 43 scientific and technical conference, St. Petersburg, PGUPS, (2001) 119-122. [8] A.V.Petryaev, V.V Ganchits. The impact of geosynthetic materials on the vibrodynamic process subgrade soil. Problems and prospects of development of railway transport, Proceedings of the Russian Scientific and Technical Conference, Volume 1, Ekaterinburg, (2003) 59-62. [9] A.V.Petryaev, I.N. Zhuravlev. To the issue of practical application of finite element method to calculate stress-strain state reinforced designs, Application of geomaterials for construction and reconstruction of transport facilities, Proceedings of the III International scientific-technical conference, Petersburg state transport University of Emperor Alexander I, (2013), 101-104. [10] Kolos A, Morozova A, 2014. Distribution survey for vibrational acceleration of ballast particles under condition of train traffic with increased axial loads. Proceedings of Petersburg Transport University, 2(39): 29-35. [11] Kolos, A., Konon, A. 2016. Estimation of railway ballast and subballast bearing capacity in terms of 300 kN axle load train operation. In: Askar Zhussupbekov (ed.). Challenges and Innovations in Geotechnics. Proc. intern. conf., Astana, 5-7 August 2016. Rotterdam: Balkema. [12] E. Tutumluer , T. D. Stark, D. Mishra, J.P. Hyslip. Investigation and mitigation of differential movement at railway transitions for US high speed passenger rail and joint passenger/freight corridors. Proceedings of the 2012 Joint Rail Conference (JRC2012). April 17-19, 2012, Philadelphia, Pennsylvania, USA. (2012). [13] S. Kaewunruen. Dynamic responses of railway bridge ends: A systems performance improvement by application of ballast glue/bond. Available at: http://works.bepress.com/sakdirat_kaewunruen/46/ (2014). [14] D. Plotkin. Bridge Approaches and Track Stiffness. Federal Railroad Administration Research Results. RR07-12 (2007). [15]C. Gallage, B. Dareeju, S. Dhanasekar. State-of-the-art : track degradation at bridge transitions. In Pathirana, K.P.P. (Ed.) Proceedings of the 4th International Conference on Structural Engineering and Construction Management 2013, Kandy, Sri Lanka. (2013) pp. 40-52.
897