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Shaking Table Test Using Full-scale Model for Lateral Resistance Force of Ballasted Tracks During Earthquake
Procedia Engineering Volume 143, 2016, Pages 1100–1107 Advances in Transportation Geotechnics 3 . The 3rd International Conference on Transportation Geotechnics (ICTG 2016)
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Tracks during Earthquake Takahisa Nakamura1*, Yoshitsugu Momoya1†, Kiyonori Nomura1‡ and Yabunaka Yoshihiko2§ 1
Railway Technical Research Institute, Tokyo, Japan 2 West Japan Railway Company, Oosaka, Japan [email protected]
Abstract In Japan where large earthquakes frequently occur, it is important to increase the resistibility of railway structures to earthquakes. The authors performed a shaking table test using a full-scale model to evaluate the lateral resistance force of the ballasted track during earthquakes. In this study, the shaking table test was attempted under test conditions under which the sleeper is given the lateral force to induce track buckling. Two kinds of cross sections of ballasted track for the full-scale model were applied: a straight track and a curved track to evaluate the influence of the difference of the cross section of ballasted track on the lateral resistance force. The results of the shaking table test clarified that the lateral resistance force of the ballasted track decreased during shaking, and the lateral sleeper displacement increased significantly by lateral force smaller than the lateral resistance force of the ballasted track after shaking. In addition, it is considered that the influence of the cross section of ballasted track on the lateral ballast resistance force during shaking and after shaking is small. Keywords: Ballasted track, Shaking table test, Full-scale model, Lateral resistance force during earthquake, Cross section of ballasted track
1 Introduction In Japan where large earthquakes frequently occur, it is important to increase the resistibility of railway structures to earthquakes. As an example of the cases where the running safety of the train was *
Assistant Senior Researcher Senior Chief Researcher, Laboratory Head ‡ Researcher § Assistant Manager †
1100
Selection and peer-review under responsibility of the Scientific Programme Committee of ICTG 2016 c The Authors. Published by Elsevier B.V.
doi:10.1016/j.proeng.2016.06.156
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
endangered due to an earthquake, it was reported that the track buckling of a ballasted track occurred during an earthquake under non-degradation of the substructure beneath the ballasted track (Miura, 1982). Meanwhile, in the wake of 1995 Hyogo earthquake in Japan, design standards for railway infrastructures were updated (RTRI, 2012a). Although design standards for track structure concerning a non-earthquake have been established (RTRI, 2012b), they do not consider seismic influence. In addition, the risk of track buckling might increase during an earthquake because the axial force becomes large especially in sections where continuous welded rails are laid. The lateral force to induce track buckling tends to increase significantly due to the rise of the rail temperature in the intense heat period. However, the deformation performances of the ballasted track during shaking and the lateral ballast resistance force after shaking have yet to be sufficiently clarified. Moreover, it is not clear enough to reveal the difference of the cross section of the ballasted track for the straight track without cant and the curved track with cant for the lateral ballast resistance force. Therefore, the authors performed a shaking table test using a full-scale track model of cross section of ballasted track for both the straight track and the curved track to evaluate the lateral resistance force of ballasted tracks during an earthquake, before and after an earthquake.
2 Large-scale Shaking Table Test 2.1 Test Overview The authors performed the shaking table test to evaluate the lateral resistance force of ballasted tracks during shaking, before and after shaking using the shaking table test equipment of the Railway Technical Research Institute. The soil tank made of steel is 7m in length, 5m in width, 0.6m in height construction and connected rigidly with a bolt on the shaking table. Figure 1 shows the schematic Accelaration transducer Load cell spring rod Displacement transducer 500 1:1.8
Ballast width
200
Cant
1:1.8
Ballast thickness No.1
2kN
Ballast shoulder accleraration Sleeper accleraration Ballast accleraration beneath sleeper
Sleeper displacement
Rail
200
581
No.1
Sleeper
4200
581
2kN No.2
No.2
4kN
1:1.8
200 6000
6000
1050
No.3
6kN
4kN
1050
No.3
6kN unit:mm
0kN
No.4
No.4
0kN
unit:mm 㸦b㸧Curved track 㸦a㸧Straight track Figure 1: Schematic views of full-scale model
Sleeper Rail Ballast shoulder width Ballast thichness Cant 㸦case of curved track 㸧
3H type 60kg 500mm 200mm 200mm
Table 1: Specifications of full-scale model
1101
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
Ballasted track
Spring
Shaking table
Shaking direction
2
Acceleration 㻔m/s 㻕
Figure 2: Shaking test condition of the large-scale shaking table test (curved track) 8 6 4 2 0 -2 -4 -6 -8 0
2
Max:7m/s
10
20
30
Time (s) Figure 3: Chuetsu Earthquake wave views of the full-scale model. Assuming the ballasted track of the standard cross-sectional of the Shinkansen on the viaduct, the ballast thickness was 200mm, the ballast shoulder width was 500mm, and the gradient of the slope of the ballast was 1: 1.8. Two kinds of cross sections of ballasted track were applied: a straight track without a cant and a curved track with a cant of 200mm. The specifications of this model are shown in Table 1. The weight of rail per sleeper was determined based on the sleeper spacing in the ballasted track of Shinkansen (43 sleepers/ 25m rail). Cement boards were installed on the shaking table in consideration of the coefficient of the friction between the ballast bottom and the roadbed of the Shinkansen ballasted track on the viaduct. Then, the ballast layer was constructed using ballast by the vibration methods with achieving a dry density of 1.6t/m3. Four Sleepers were placed on the shaking table to perform the tests of different condition so that they were arranged in the rail longitudinal direction one by one. The sleeper spacing was determined to minimums the influence from adjacent sleepers. Figure 2 shows the test condition of the large-scale shaking table test. Lateral loads corresponding to a load of which the continuous welded rail causes the track to buckle were always applied to the full-scale track model using a spring during shaking. The tension change of the spring used was small, about 15% in the stroke range from 80 mm to 100 mm.
2.2 Test Cases Table 2 shows the test cases of the shaking table test and the lateral ballast resistance test. Two kinds of shaking wave forms, i.e., sine wave (loading frequency 3Hz, 10 waves) and real earthquake wave were applied. Shaking direction was a sleeper longitudinal direction. The earthquake wave is the response wave of the top of the Tokamachi viaduct in 2004 Chuetsu Earthquake in Japan (ARAIC, 2007), (Figure 3) (here after called Chuetsu wave). Lateral loads to be applied by springs under shaking are 0kN, 2kN, 4kN and 6kN. Measurement items of the shaking test are the horizontal displacement of the both ends of the sleeper, the lateral load of the spring, and the horizontal acceleration of the shaking table and the ballast shoulder on the side to which the lateral load of the spring is applied.
1102
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al. Case
1
2
Cross section of ballast
Sleeper No.
Lateral force
Lateral loading test
Shaking wave and magunitude of acceleration
1 2 3 4 1 2 3 4
2kN 4kN 6kN 0kN 2kN 4kN 6kN 0kN
before shaking test after shaking test before shaking test after shaking test
䐟Sine wave of 2m/s2
Straight track
Curved track
䐠Sine wave of 4m/s2 䐡Chuetsu wave of 6m/s2 䐢Chuetsu wave of 7m/s2 䐣Sine wave of 6m/s2 䐤Sine wave of 7m/s2 䐥Sine wave of 8m/s2
Table 2: Test case of shaking table test ㍕Ⲵ⨨ Loading apparatus ㍕Ⲵ᪉ྥ Loading direction (㍕Ⲵ㏿ᗘ㸸 1.15mm/min)
Horizontal displacement transducer ኚ Ỉᖹ᪉ྥ 㸪ኚ 㖄┤᪉ Load Ⲵ cell 㔜
Sleeper ࡲࡃࡽࡂ
㐨ᗋ Ballast
Figure 4: Outline of lateral loading test Horizontal loading tests were conducted at a constant displacement rate of 2 mm/min in the sleeper longitudinal direction, before the shaking tests and after shaking of a sine wave of 8m/s 2, using a loading apparatus shown in Figure 4. Measurement items are the horizontal displacement and the lateral loads of both ends of the sleeper.
2.3 Characteristics of the Lateral Ballast Resistance Force after Shaking The relationship between the lateral ballast resistance force and the sleeper displacement before shaking tests and after shaking of a sine wave of 8m/s2 is shown in Figure 5. At all times, the lateral ballast resistance force before the shaking tests showed a similar trend regardless of whether the cross section of ballasted track was straight track or curved track; 8.4kN with the straight track and 8.2kN with the curved track when the sleeper displacement was 2mm. After the shaking of a sine wave of 8m/s2, the lateral ballast resistance force of both the straight track and the curved track was reduced when the sleeper displacement was 2mm, 5.3kN with the straight track and 6.2kN with the curved track. The decreasing rate by shaking of the straight track was about 37%, and the curved track was about 24%. However, the lateral ballast resistance force showed little difference between the straight track and the curved track when the sleeper displacement exceeded 4mm. According to the above results, it is considered that the influence of the difference of cross section of ballasted track on lateral ballast resistance force before shaking and after shaking is small.
Ballast lateral resistance force(kN)
12 10
Curved track before shaking
Straight track before shaking
8 6 4 Curved track after shaking
2 0
0
1
2
Straight track after shaking
3
4
5
Sleeper displacement(mm) Figure 5: Relationship between the lateral ballast resistance force and the sleeper displacement 1103
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
2.4 Characteristics of the Lateral Ballast Resistance Force during Shaking
20
Sleeper displacement(mm)
Sleeper displacement(mm)
Figure 6 shows the sleeper displacement increment during shaking of a sine wave of 6m/s2 and a sine wave of 7m/s2 under the lateral loads of 0kN, 2kN and 4kN. It can be seen that the sleeper displacement increases regardless of whether the cross section of ballasted track is straight track or curved track when the maximum acceleration increases and lateral loads increase. Residual sleeper displacement reached approximately 10mm and 60mm during shaking for the sine wave of 6m/s2 and 7m/s2 respectively under the lateral force of 4kN, regardless of whether the cross section of ballasted track is straight track or curved track. Next, it can be seen that residual sleeper displacement during shaking for both the sine wave of 6m/s2 and 7m/s2 was very small under the lateral force of 0kN, regardless of whether the cross section of ballasted track is straight track or curved track. These results indicated that residual sleeper displacement increased when the lateral loads act, and residual sleeper displacement was very small when the lateral loads didn’t act. In addition, as for the influence of the cross section of ballasted track, the residual sleeper displacement generally shows a similar trend regardless of whether the cross section of ballasted track is straight track or curved track except in the case of the sine wave of 7m/s2 under lateral loads of 2kN. Figure 7(S-a) 㹼(S-c) shows the acceleration wave of the sleeper, the ballast shoulder and the ballast surface beneath the sleeper in the case of straight track during shaking of a sine wave of 6m/s2 and a sine wave of 7m/s2 under lateral loads of 0kN, 2kN and 4kN. Figure 7(C-a) 㹼(C-c) shows the acceleration wave in the case of the curved track. First, it can be seen that a superposition of the high-frequency waves on the acceleration wave of the ballast shoulder became prominent at the time of the maximum acceleration as lateral force increased, regardless of whether the cross section of ballasted track is straight track or curved track. 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
15 10
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘 㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
5 0
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘 㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
-5㻜
0
㻝
1
㻞
㻟
3 2 Time (s)
㻠
4
1.0 0.5 0.0 -0.5 -1.0
㻞 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟 㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
0㻜
㻡
5
1㻝
2㻞
(b) Lateral force of 2kN
100 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
80 60 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌 㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
40
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
20 0㻜 0
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
1㻝
2㻞
3㻟
4㻠
5㻡
Time (s)
(c) Lateral force of 4kN Figure 6: Sleeper displacement increment during shaking
1104
3㻟
Time (s)
(a) Lateral force of 0kN Sleeper displacement(mm)
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
4㻠
5㻡
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
This is because that the surface of the ballast shoulder on which the accelerometer was fixed showed different behavior from the entire ballast shoulder and the shaking table due to the progress of the plastic deformation of the ballast shoulder at the time of maximum acceleration. In addition, it is considered that the plastic deformation of the ballast shoulder further progresses as the residual sleeper displacement increase as shown in Figure 6 (b) and Figure 6 (c). These results indicate that the 15
Sleeper
Ballast beneath sleeper
㻝㻡
Ballast shoulder
Sleeper
5 0 -5 -10 -15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻜 㻙㻡 㻙㻝㻜 㻙㻝㻡㻝㻜 0
㻝㻡 5
Ballast beneath sleeper
15
Ballast shoulder
10
Acceleration (m/s2)
Acceleration (m/s2)
Sleeper
5 0 -5 -10 Shaking table 㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
Sleeper
Ballast beneath sleeper
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻝㻡 5
㻝㻡 5
Sleeper
Ballast beneath sleeper
Ballast shoulder
Shaking table
5 0 -5 -10 -1510 0
Time (s) (S-b) Lateral force of 2kN, Straight track 15
Shaking table 㻝㻝 1
Time (s) (C-a) Lateral force of 0kN, Curved track
10
-15㻝㻜 0
Ballast shoulder
㻡
Time(s) (S-a) Lateral force of 2kN, Straight track 15
Ballast beneath sleeper
㻝㻜
10
Acceleration (m/s2)
Acceleration(m/s2)
Shaking table
11
1
12
2
13
3
14
15
4
5
Time (s) (C-b) Lateral force of 2kN, Curved track 15
Ballast shoulder
Sleeper
Ballast beneath sleeper
Ballast shoulder
Shaking table
Acceleration (m/s2)
Acceleration (m/s2)
10 5 0 -5 -10
10 5 0 -5
-10 Shaking table
-15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻝㻡 5
-15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
Time (s) Time(s) (C-c) Lateral force of 4kN, Curved track (S-c) Lateral force of 4kN, Straight track Figure 7: Acceleration wave during shaking 1105
㻝㻡 5
100 80 60
Chuetsu wave of 6m/s2 Chuetsu wave of 7m/s2 Sine wave of 6m/s2 Sine wave of 7m/s2 Sine wave of 8m/s2
40 20 0
0
2 4 Lateral force(kN)
6
Residual sleeper displacement (mm)
Residual sleeper displacement (mm)
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al. 100 80 60
Chuetsu wave of 6m/s2 Chuetsu wave of 7m/s2 Sine wave of 6m/s2 Sine wave of 7m/s2 Sine wave of 8m/s2
40 20 0
0
2
4
6
Lateral force(kN)
(a㸧Straight track (b㸧Curved track Figure 8: Residual sleeper displacement superposition of the high-frequency waves became prominent when lateral loads increased because the lateral ballast resistance force decreases due to a decrease in the rigidity of the ballast shoulder caused by the plastic deformation at the time of the maximum acceleration. Next, it can be seen that the superposition of a high-frequency waves on the acceleration wave of the ballast surface beneath the sleeper became prominent at the time of the maximum acceleration when lateral force increased to 4kN, regardless of whether the cross section of ballasted track is straight track or curved track. It is also found that a slight amount of superposition of a high-frequency on the acceleration wave of the sleeper under lateral force of 4kN. This indicates that an increase in the maximum acceleration progresses the plastic deformation and reduce the rigidity of the ballast shoulder, and a increase in the sleeper displacement progresses the plastic deformation of the ballast surface beneath the sleeper and reduce the rigidity of the ballast surface beneath the sleeper. In other words, an increase in maximum acceleration and lateral force reduces the ballast rigidity at the time of the maximum acceleration during shaking, and furthermore tend to reduce the rigidity of the ballast surface beneath the sleeper when sleeper displacement occurs. Therefore, it is considered that sleeper displacement rapidly increased with the reduction of the lateral resistance force. The relationship between the lateral loads and the residual sleeper displacement of each shaking magnitude is shown in Figure 7. It can be seen that the residual sleeper displacement of each shaking magnitude tends to increase with an increase in the lateral force regardless of whether the cross section of ballasted track is straight track or curved track. In addition, each residual sleeper displacement shows a similar trend regardless of whether the cross section of ballasted track is straight track or curved track. Here, we examined the relationship between the residual sleeper displacement and the lateral resistance force both during shaking and after shaking using the result in case of the straight track to compare the lateral force with the lateral ballast resistance force by a lateral loading test performed after the shaking of a sine wave of 8m/s2 as shown in Figure 5. Although the sleeper displacement was 0.6mm when the lateral resistance force was 4kN in the lateral loading test performed after the shaking of a sine wave of 8m/s2, sleeper displacement was 59.4mm when lateral resistance force was 4kNduring the shaking of a sine wave of 7m/s2 as shown in Figure 8(a). Furthermore, although the sleeper displacement was 0.1mm when the lateral resistance force was 2kN in the lateral loading test performed after the shaking of a sine wave of 8m/s2, sleeper displacement was 51.3mm when lateral ballast resistance force was 2kN during the shaking of a sine wave of 8m/s2. This indicated that large residual sleeper displacement occurred during shaking even if the same lateral force was acted on the sleeper after shaking. From this fact, there is a high possibility that the buckling of continuous welded rails occurs due to the dynamic motion acting on ballasted tracks during earthquake. In addition, it is considered that, in
1106
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
general, the deformation and strength characteristics of ballasted tracks on the lateral ballast resistance force during shaking and after shaking are similar regardless of whether the cross section of ballasted track is straight track or curved track.
3 Conclusions In this study, large-scale shaking table test were performed with a full-scale model, and we got the following findings. (1) In order to evaluate the lateral ballast resistance force under shaking, shaking tests were conducted applying the lateral load. It has been revealed that large residual displacement occurs during shaking even if the lateral loads was smaller than the lateral ballast resistance force before and after shaking. (2) It has been revealed that residual sleeper displacement occurred significantly when the lateral loads increased, and residual sleeper displacement was very small when the lateral load was 0kN. (3) The influence of the difference of the cross section of ballasted track between the straight track and the curved track on the lateral ballast resistance force during shaking and after shaking was small.
References Miura,Y., Kirishiki,K. (1982). “Deformation of Railway Track and Running Safety of Train Earthquake”. RTRI Pre-Report. No.82-45. ( in Japanese). Railway Technical Research Institute. (2012a). “Design Standard for Railway Stractures –Seismic Design”. Maruzen. (in Japanese). Railway Technical Research Institute. (2012b). “Design Standard for Railway Stractures –Track Structure”. Maruzen. (in Japanese). Aircraft and Railway Accidents Investigation Commission. (2012b). “Railway accident investigation report”, East Japan Railway Co., Ltd. Between Urasa station and Nagaoka station, Joetsu Shinkansen Line, Nagaoka City, Niigata Prefecture. derailment accident. (in Japanese).
1107
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Tracks during Earthquake Takahisa Nakamura1*, Yoshitsugu Momoya1†, Kiyonori Nomura1‡ and Yabunaka Yoshihiko2§ 1
Railway Technical Research Institute, Tokyo, Japan 2 West Japan Railway Company, Oosaka, Japan [email protected]
Abstract In Japan where large earthquakes frequently occur, it is important to increase the resistibility of railway structures to earthquakes. The authors performed a shaking table test using a full-scale model to evaluate the lateral resistance force of the ballasted track during earthquakes. In this study, the shaking table test was attempted under test conditions under which the sleeper is given the lateral force to induce track buckling. Two kinds of cross sections of ballasted track for the full-scale model were applied: a straight track and a curved track to evaluate the influence of the difference of the cross section of ballasted track on the lateral resistance force. The results of the shaking table test clarified that the lateral resistance force of the ballasted track decreased during shaking, and the lateral sleeper displacement increased significantly by lateral force smaller than the lateral resistance force of the ballasted track after shaking. In addition, it is considered that the influence of the cross section of ballasted track on the lateral ballast resistance force during shaking and after shaking is small. Keywords: Ballasted track, Shaking table test, Full-scale model, Lateral resistance force during earthquake, Cross section of ballasted track
1 Introduction In Japan where large earthquakes frequently occur, it is important to increase the resistibility of railway structures to earthquakes. As an example of the cases where the running safety of the train was *
Assistant Senior Researcher Senior Chief Researcher, Laboratory Head ‡ Researcher § Assistant Manager †
1100
Selection and peer-review under responsibility of the Scientific Programme Committee of ICTG 2016 c The Authors. Published by Elsevier B.V.
doi:10.1016/j.proeng.2016.06.156
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
endangered due to an earthquake, it was reported that the track buckling of a ballasted track occurred during an earthquake under non-degradation of the substructure beneath the ballasted track (Miura, 1982). Meanwhile, in the wake of 1995 Hyogo earthquake in Japan, design standards for railway infrastructures were updated (RTRI, 2012a). Although design standards for track structure concerning a non-earthquake have been established (RTRI, 2012b), they do not consider seismic influence. In addition, the risk of track buckling might increase during an earthquake because the axial force becomes large especially in sections where continuous welded rails are laid. The lateral force to induce track buckling tends to increase significantly due to the rise of the rail temperature in the intense heat period. However, the deformation performances of the ballasted track during shaking and the lateral ballast resistance force after shaking have yet to be sufficiently clarified. Moreover, it is not clear enough to reveal the difference of the cross section of the ballasted track for the straight track without cant and the curved track with cant for the lateral ballast resistance force. Therefore, the authors performed a shaking table test using a full-scale track model of cross section of ballasted track for both the straight track and the curved track to evaluate the lateral resistance force of ballasted tracks during an earthquake, before and after an earthquake.
2 Large-scale Shaking Table Test 2.1 Test Overview The authors performed the shaking table test to evaluate the lateral resistance force of ballasted tracks during shaking, before and after shaking using the shaking table test equipment of the Railway Technical Research Institute. The soil tank made of steel is 7m in length, 5m in width, 0.6m in height construction and connected rigidly with a bolt on the shaking table. Figure 1 shows the schematic Accelaration transducer Load cell spring rod Displacement transducer 500 1:1.8
Ballast width
200
Cant
1:1.8
Ballast thickness No.1
2kN
Ballast shoulder accleraration Sleeper accleraration Ballast accleraration beneath sleeper
Sleeper displacement
Rail
200
581
No.1
Sleeper
4200
581
2kN No.2
No.2
4kN
1:1.8
200 6000
6000
1050
No.3
6kN
4kN
1050
No.3
6kN unit:mm
0kN
No.4
No.4
0kN
unit:mm 㸦b㸧Curved track 㸦a㸧Straight track Figure 1: Schematic views of full-scale model
Sleeper Rail Ballast shoulder width Ballast thichness Cant 㸦case of curved track 㸧
3H type 60kg 500mm 200mm 200mm
Table 1: Specifications of full-scale model
1101
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
Ballasted track
Spring
Shaking table
Shaking direction
2
Acceleration 㻔m/s 㻕
Figure 2: Shaking test condition of the large-scale shaking table test (curved track) 8 6 4 2 0 -2 -4 -6 -8 0
2
Max:7m/s
10
20
30
Time (s) Figure 3: Chuetsu Earthquake wave views of the full-scale model. Assuming the ballasted track of the standard cross-sectional of the Shinkansen on the viaduct, the ballast thickness was 200mm, the ballast shoulder width was 500mm, and the gradient of the slope of the ballast was 1: 1.8. Two kinds of cross sections of ballasted track were applied: a straight track without a cant and a curved track with a cant of 200mm. The specifications of this model are shown in Table 1. The weight of rail per sleeper was determined based on the sleeper spacing in the ballasted track of Shinkansen (43 sleepers/ 25m rail). Cement boards were installed on the shaking table in consideration of the coefficient of the friction between the ballast bottom and the roadbed of the Shinkansen ballasted track on the viaduct. Then, the ballast layer was constructed using ballast by the vibration methods with achieving a dry density of 1.6t/m3. Four Sleepers were placed on the shaking table to perform the tests of different condition so that they were arranged in the rail longitudinal direction one by one. The sleeper spacing was determined to minimums the influence from adjacent sleepers. Figure 2 shows the test condition of the large-scale shaking table test. Lateral loads corresponding to a load of which the continuous welded rail causes the track to buckle were always applied to the full-scale track model using a spring during shaking. The tension change of the spring used was small, about 15% in the stroke range from 80 mm to 100 mm.
2.2 Test Cases Table 2 shows the test cases of the shaking table test and the lateral ballast resistance test. Two kinds of shaking wave forms, i.e., sine wave (loading frequency 3Hz, 10 waves) and real earthquake wave were applied. Shaking direction was a sleeper longitudinal direction. The earthquake wave is the response wave of the top of the Tokamachi viaduct in 2004 Chuetsu Earthquake in Japan (ARAIC, 2007), (Figure 3) (here after called Chuetsu wave). Lateral loads to be applied by springs under shaking are 0kN, 2kN, 4kN and 6kN. Measurement items of the shaking test are the horizontal displacement of the both ends of the sleeper, the lateral load of the spring, and the horizontal acceleration of the shaking table and the ballast shoulder on the side to which the lateral load of the spring is applied.
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Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al. Case
1
2
Cross section of ballast
Sleeper No.
Lateral force
Lateral loading test
Shaking wave and magunitude of acceleration
1 2 3 4 1 2 3 4
2kN 4kN 6kN 0kN 2kN 4kN 6kN 0kN
before shaking test after shaking test before shaking test after shaking test
䐟Sine wave of 2m/s2
Straight track
Curved track
䐠Sine wave of 4m/s2 䐡Chuetsu wave of 6m/s2 䐢Chuetsu wave of 7m/s2 䐣Sine wave of 6m/s2 䐤Sine wave of 7m/s2 䐥Sine wave of 8m/s2
Table 2: Test case of shaking table test ㍕Ⲵ⨨ Loading apparatus ㍕Ⲵ᪉ྥ Loading direction (㍕Ⲵ㏿ᗘ㸸 1.15mm/min)
Horizontal displacement transducer ኚ Ỉᖹ᪉ྥ 㸪ኚ 㖄┤᪉ Load Ⲵ cell 㔜
Sleeper ࡲࡃࡽࡂ
㐨ᗋ Ballast
Figure 4: Outline of lateral loading test Horizontal loading tests were conducted at a constant displacement rate of 2 mm/min in the sleeper longitudinal direction, before the shaking tests and after shaking of a sine wave of 8m/s 2, using a loading apparatus shown in Figure 4. Measurement items are the horizontal displacement and the lateral loads of both ends of the sleeper.
2.3 Characteristics of the Lateral Ballast Resistance Force after Shaking The relationship between the lateral ballast resistance force and the sleeper displacement before shaking tests and after shaking of a sine wave of 8m/s2 is shown in Figure 5. At all times, the lateral ballast resistance force before the shaking tests showed a similar trend regardless of whether the cross section of ballasted track was straight track or curved track; 8.4kN with the straight track and 8.2kN with the curved track when the sleeper displacement was 2mm. After the shaking of a sine wave of 8m/s2, the lateral ballast resistance force of both the straight track and the curved track was reduced when the sleeper displacement was 2mm, 5.3kN with the straight track and 6.2kN with the curved track. The decreasing rate by shaking of the straight track was about 37%, and the curved track was about 24%. However, the lateral ballast resistance force showed little difference between the straight track and the curved track when the sleeper displacement exceeded 4mm. According to the above results, it is considered that the influence of the difference of cross section of ballasted track on lateral ballast resistance force before shaking and after shaking is small.
Ballast lateral resistance force(kN)
12 10
Curved track before shaking
Straight track before shaking
8 6 4 Curved track after shaking
2 0
0
1
2
Straight track after shaking
3
4
5
Sleeper displacement(mm) Figure 5: Relationship between the lateral ballast resistance force and the sleeper displacement 1103
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
2.4 Characteristics of the Lateral Ballast Resistance Force during Shaking
20
Sleeper displacement(mm)
Sleeper displacement(mm)
Figure 6 shows the sleeper displacement increment during shaking of a sine wave of 6m/s2 and a sine wave of 7m/s2 under the lateral loads of 0kN, 2kN and 4kN. It can be seen that the sleeper displacement increases regardless of whether the cross section of ballasted track is straight track or curved track when the maximum acceleration increases and lateral loads increase. Residual sleeper displacement reached approximately 10mm and 60mm during shaking for the sine wave of 6m/s2 and 7m/s2 respectively under the lateral force of 4kN, regardless of whether the cross section of ballasted track is straight track or curved track. Next, it can be seen that residual sleeper displacement during shaking for both the sine wave of 6m/s2 and 7m/s2 was very small under the lateral force of 0kN, regardless of whether the cross section of ballasted track is straight track or curved track. These results indicated that residual sleeper displacement increased when the lateral loads act, and residual sleeper displacement was very small when the lateral loads didn’t act. In addition, as for the influence of the cross section of ballasted track, the residual sleeper displacement generally shows a similar trend regardless of whether the cross section of ballasted track is straight track or curved track except in the case of the sine wave of 7m/s2 under lateral loads of 2kN. Figure 7(S-a) 㹼(S-c) shows the acceleration wave of the sleeper, the ballast shoulder and the ballast surface beneath the sleeper in the case of straight track during shaking of a sine wave of 6m/s2 and a sine wave of 7m/s2 under lateral loads of 0kN, 2kN and 4kN. Figure 7(C-a) 㹼(C-c) shows the acceleration wave in the case of the curved track. First, it can be seen that a superposition of the high-frequency waves on the acceleration wave of the ballast shoulder became prominent at the time of the maximum acceleration as lateral force increased, regardless of whether the cross section of ballasted track is straight track or curved track. 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
15 10
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘 㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
5 0
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘 㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
-5㻜
0
㻝
1
㻞
㻟
3 2 Time (s)
㻠
4
1.0 0.5 0.0 -0.5 -1.0
㻞 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟 㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
0㻜
㻡
5
1㻝
2㻞
(b) Lateral force of 2kN
100 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
80 60 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌 㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
40
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
20 0㻜 0
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻯㼡㼞㼢㼑㼐㻌㼠㼞㼍㼏㼗
1㻝
2㻞
3㻟
4㻠
5㻡
Time (s)
(c) Lateral force of 4kN Figure 6: Sleeper displacement increment during shaking
1104
3㻟
Time (s)
(a) Lateral force of 0kN Sleeper displacement(mm)
㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻢㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗 㻿㼕㼚㼑㻌㼣㼍㼢㼑㻌㼛㼒㻌㻣㼙㻛㼟㻞㻘㻌㻿㼠㼞㼍㼕㼓㼔㼠㻌㼠㼞㼍㼏㼗
4㻠
5㻡
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
This is because that the surface of the ballast shoulder on which the accelerometer was fixed showed different behavior from the entire ballast shoulder and the shaking table due to the progress of the plastic deformation of the ballast shoulder at the time of maximum acceleration. In addition, it is considered that the plastic deformation of the ballast shoulder further progresses as the residual sleeper displacement increase as shown in Figure 6 (b) and Figure 6 (c). These results indicate that the 15
Sleeper
Ballast beneath sleeper
㻝㻡
Ballast shoulder
Sleeper
5 0 -5 -10 -15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻜 㻙㻡 㻙㻝㻜 㻙㻝㻡㻝㻜 0
㻝㻡 5
Ballast beneath sleeper
15
Ballast shoulder
10
Acceleration (m/s2)
Acceleration (m/s2)
Sleeper
5 0 -5 -10 Shaking table 㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
Sleeper
Ballast beneath sleeper
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻝㻡 5
㻝㻡 5
Sleeper
Ballast beneath sleeper
Ballast shoulder
Shaking table
5 0 -5 -10 -1510 0
Time (s) (S-b) Lateral force of 2kN, Straight track 15
Shaking table 㻝㻝 1
Time (s) (C-a) Lateral force of 0kN, Curved track
10
-15㻝㻜 0
Ballast shoulder
㻡
Time(s) (S-a) Lateral force of 2kN, Straight track 15
Ballast beneath sleeper
㻝㻜
10
Acceleration (m/s2)
Acceleration(m/s2)
Shaking table
11
1
12
2
13
3
14
15
4
5
Time (s) (C-b) Lateral force of 2kN, Curved track 15
Ballast shoulder
Sleeper
Ballast beneath sleeper
Ballast shoulder
Shaking table
Acceleration (m/s2)
Acceleration (m/s2)
10 5 0 -5 -10
10 5 0 -5
-10 Shaking table
-15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
㻝㻡 5
-15㻝㻜 0
㻝㻝 1
㻝㻞 2
㻝㻟 3
㻝㻠 4
Time (s) Time(s) (C-c) Lateral force of 4kN, Curved track (S-c) Lateral force of 4kN, Straight track Figure 7: Acceleration wave during shaking 1105
㻝㻡 5
100 80 60
Chuetsu wave of 6m/s2 Chuetsu wave of 7m/s2 Sine wave of 6m/s2 Sine wave of 7m/s2 Sine wave of 8m/s2
40 20 0
0
2 4 Lateral force(kN)
6
Residual sleeper displacement (mm)
Residual sleeper displacement (mm)
Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al. 100 80 60
Chuetsu wave of 6m/s2 Chuetsu wave of 7m/s2 Sine wave of 6m/s2 Sine wave of 7m/s2 Sine wave of 8m/s2
40 20 0
0
2
4
6
Lateral force(kN)
(a㸧Straight track (b㸧Curved track Figure 8: Residual sleeper displacement superposition of the high-frequency waves became prominent when lateral loads increased because the lateral ballast resistance force decreases due to a decrease in the rigidity of the ballast shoulder caused by the plastic deformation at the time of the maximum acceleration. Next, it can be seen that the superposition of a high-frequency waves on the acceleration wave of the ballast surface beneath the sleeper became prominent at the time of the maximum acceleration when lateral force increased to 4kN, regardless of whether the cross section of ballasted track is straight track or curved track. It is also found that a slight amount of superposition of a high-frequency on the acceleration wave of the sleeper under lateral force of 4kN. This indicates that an increase in the maximum acceleration progresses the plastic deformation and reduce the rigidity of the ballast shoulder, and a increase in the sleeper displacement progresses the plastic deformation of the ballast surface beneath the sleeper and reduce the rigidity of the ballast surface beneath the sleeper. In other words, an increase in maximum acceleration and lateral force reduces the ballast rigidity at the time of the maximum acceleration during shaking, and furthermore tend to reduce the rigidity of the ballast surface beneath the sleeper when sleeper displacement occurs. Therefore, it is considered that sleeper displacement rapidly increased with the reduction of the lateral resistance force. The relationship between the lateral loads and the residual sleeper displacement of each shaking magnitude is shown in Figure 7. It can be seen that the residual sleeper displacement of each shaking magnitude tends to increase with an increase in the lateral force regardless of whether the cross section of ballasted track is straight track or curved track. In addition, each residual sleeper displacement shows a similar trend regardless of whether the cross section of ballasted track is straight track or curved track. Here, we examined the relationship between the residual sleeper displacement and the lateral resistance force both during shaking and after shaking using the result in case of the straight track to compare the lateral force with the lateral ballast resistance force by a lateral loading test performed after the shaking of a sine wave of 8m/s2 as shown in Figure 5. Although the sleeper displacement was 0.6mm when the lateral resistance force was 4kN in the lateral loading test performed after the shaking of a sine wave of 8m/s2, sleeper displacement was 59.4mm when lateral resistance force was 4kNduring the shaking of a sine wave of 7m/s2 as shown in Figure 8(a). Furthermore, although the sleeper displacement was 0.1mm when the lateral resistance force was 2kN in the lateral loading test performed after the shaking of a sine wave of 8m/s2, sleeper displacement was 51.3mm when lateral ballast resistance force was 2kN during the shaking of a sine wave of 8m/s2. This indicated that large residual sleeper displacement occurred during shaking even if the same lateral force was acted on the sleeper after shaking. From this fact, there is a high possibility that the buckling of continuous welded rails occurs due to the dynamic motion acting on ballasted tracks during earthquake. In addition, it is considered that, in
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Shaking Table Test using Full-Scale Model for Lateral Resistance Force of Ballasted Nakamura et al.
general, the deformation and strength characteristics of ballasted tracks on the lateral ballast resistance force during shaking and after shaking are similar regardless of whether the cross section of ballasted track is straight track or curved track.
3 Conclusions In this study, large-scale shaking table test were performed with a full-scale model, and we got the following findings. (1) In order to evaluate the lateral ballast resistance force under shaking, shaking tests were conducted applying the lateral load. It has been revealed that large residual displacement occurs during shaking even if the lateral loads was smaller than the lateral ballast resistance force before and after shaking. (2) It has been revealed that residual sleeper displacement occurred significantly when the lateral loads increased, and residual sleeper displacement was very small when the lateral load was 0kN. (3) The influence of the difference of the cross section of ballasted track between the straight track and the curved track on the lateral ballast resistance force during shaking and after shaking was small.
References Miura,Y., Kirishiki,K. (1982). “Deformation of Railway Track and Running Safety of Train Earthquake”. RTRI Pre-Report. No.82-45. ( in Japanese). Railway Technical Research Institute. (2012a). “Design Standard for Railway Stractures –Seismic Design”. Maruzen. (in Japanese). Railway Technical Research Institute. (2012b). “Design Standard for Railway Stractures –Track Structure”. Maruzen. (in Japanese). Aircraft and Railway Accidents Investigation Commission. (2012b). “Railway accident investigation report”, East Japan Railway Co., Ltd. Between Urasa station and Nagaoka station, Joetsu Shinkansen Line, Nagaoka City, Niigata Prefecture. derailment accident. (in Japanese).
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