路基不均匀沉降下无砟轨道受力与变形传递规律及其影响

向俊; 林士财; 余翠英; 袁铖; 苏玮

doi:10.19818/j.cnki.1671-1637.2019.02.007

路基不均匀沉降下无砟轨道受力与变形传递规律及其影响

doi: 10.19818/j.cnki.1671-1637.2019.02.007

向俊^1,,
林士财¹,
余翠英^{1, 2},
袁铖¹,
苏玮¹

1.
中南大学土木工程学院, 湖南长沙 410075
2.
华东交通大学理学院, 江西南昌 330013

基金项目:

国家自然科学基金项目 U1261113

高等学校博士学科点专项科研基金项目 20100162110022

牵引动力国家重点实验室开放课题 TPL0901

牵引动力国家重点实验室开放课题 TPL1214

江西省教育厅科技计划项目 GJJ151173

江西省教育厅科技计划项目 GJJ151175

详细信息

作者简介:
向俊(1968-), 男, 湖南溆浦人, 中南大学教授, 工学博士, 从事铁道工程相关研究

中图分类号: U213.2
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出版历程
- 收稿日期: 2018-10-23
- 刊出日期: 2019-04-25

Transfer rules and effect of stress and deformation of ballastless track under uneven subgrade settlement

1.
School of Civil Engineering, Central South University, Changsha 410075, Hunan, China
2.
School of Science, East China Jiaotong University, Nanchang 330013, Jiangxi, China

More Information

Author Bio:
XIANG Jun (1968-), male, professor, PhD, jxiang@mail.csu.edu.cn

摘要

摘要: 针对路基上CRTSⅠ和CRTSⅡ型板式无砟轨道的结构特点, 分别建立了相应的有限元模型, 研究了路基不均匀沉降作用下不同板式无砟轨道受力与变形的传递规律及其影响。分析结果表明: 路基不均匀沉降发生后, 上部轨道结构的垂向变形具有一定跟随性, 变形与沉降曲线相近但不完全重合; 底座板伸缩缝的存在对轨道结构的受力和变形有较大影响, 在20 mm/20 m沉降条件下, CRTSⅠ、CRTSⅡ型板的垂向位移分别达沉降幅值的90%和60%, 相对CRTSⅠ型板而言, 沉降对CRTSⅡ型板的垂向位移影响较小, 但后者更易形成较大范围的离缝, 离缝长度达6.52 m, 为CRTSⅠ型板离缝长度的1.92倍; 当沉降幅值位于底座板中心时, 离缝主要集中在伸缩缝、沉降端部和沉降中心, 但当沉降幅值位于伸缩缝处时, 离缝主要集中在伸缩缝两侧和沉降端部; 沉降波长或幅值改变时, 会导致最大离缝位置出现偏移; 在路基不均匀沉降作用下, CRTSⅠ型板的底座板纵向最大拉应力均大于轨道板的纵向最大拉应力, 而CRTSⅡ型板的情形则相反; 从混凝土强度考虑, CRTSⅠ型板沉降控制标准应以底座板的拉应力控制为主, 而CRTSⅡ型板应以轨道板和底座板的拉应力综合控制。
- 铁道工程 /
- 无砟轨道 /
- 不均匀沉降 /
- 受力特性 /
- 变形 /
- 垂向位移 /
- 离缝
Abstract: The finite element models were established base on the characteristics of CRTS Ⅰ and CRTS Ⅱ slab ballastless track structures on the subgrade. The transfer laws of stress and deformation of different slab ballastless tracks and their effects were analyzed under the role of uneven subgrade settlement. Analysis result indicates that the vertical deformation of the upper track structure deforms accordingly with the subgrade after uneven subgrade settlement occurs. The deformation and settlement curves are similar but not completely coincident. The expansion joints that exist in the base plate have great influence on the stress and deformation of track structure. Under the condition of 20 mm/20 m, the vertical displacements of CRTS Ⅰ and CRTS Ⅱ slabs reach 90% and 60% of settlement amplitude, respectively, the vertical displacement of CRTS Ⅱ slab is less affected by the settlement compared with CRTS Ⅰ slab, but the latter is more likely to form a larger range of seam, and the length of the seam is 6.52 m and 1.92 times the length of the seam of CRTS Ⅰ slab. When the settlement amplitude is located at the center of base plate, the seams are mainly concentrated at the expansion joint, settlement end and settlement center. But when the settlement amplitude is located at the expansion joint, the seams are mainly concentrated on both sides of the expansion joint and settlement end. With the change of settlement wavelength or amplitude, it will cause the maximum position of seam to shift. Under the role of uneven subgrade settlement, the longitudinal maximum tensile stress of the base plate of CRTS Ⅰ slab is greater than that of slab, while the CRTS Ⅱ slab is opposite. Considering the strength of concrete, the settlement control standard of CRTS Ⅰ slab should be based on the tensile stress of base plate, while the settlement control standard of CRTS Ⅱ slab should be based on the tensile stresses of slab and base plate comprehensively.
- railway engineering /
- ballastless track /
- uneven settlement /
- stress characteristic /
- deformation /
- vertical displacement /
- seam

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图 1 板式无砟轨道-路基有限元模型

Figure 1. Finite element models of slab ballastless track-subgrade

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图 2 余弦型不均匀沉降曲线

Figure 2. Uneven settlement curve of cosine type

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图 3 CRTS Ⅰ型板式无砟轨道各结构层变形

Figure 3. Deformations on structural layers of CRTS Ⅰ slab ballastless track

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图 4 CRTS Ⅱ型板式无砟轨道各结构层变形

Figure 4. Deformations on structural layers of CRTS Ⅱ slab ballastless track

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图 5 CRTS Ⅰ型板式无砟轨道各结构层变形(幅值位于伸缩缝)

Figure 5. Deformations on structural layers of CRTS Ⅰ slab ballastless track (amplitude is located at expansion joint)

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图 6 轨道板和底座板的纵向应力分布

Figure 6. Longitudinal stress distributions of slabs and base plates

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图 7 最大垂向位移变化规律(L=20 m)

Figure 7. Variation rules of maximum vertical displacements (L=20 m)

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图 8 最大垂向位移变化规律(L=20 m, 幅值位于伸缩缝)

Figure 8. Variation rules of maximum vertical displacements (L=20 m, amplitude is located at expansion joint)

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图 9 最大垂向位移变化规律(f=10 mm)

Figure 9. Variation rules of maximum vertical displacements (f=10 mm)

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图 10 最大垂向位移变化规律(f=10 mm, 幅值位于伸缩缝)

Figure 10. Variation rules of maximum vertical displacements (f=10 mm, amplitude is located at expansion joint)

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图 11 CRTS Ⅰ型板离缝纵向分布(L=20 m)

Figure 11. Longitudinal distribution of seam of CRTS Ⅰ slab (L=20 m)

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图 12 CRTS Ⅰ型板离缝纵向分布(L=20 m, 幅值位于伸缩缝)

Figure 12. Longitudinal distributions of seam of CRTS Ⅰslab (L=20 m, amplitude is located at expansion joint)

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图 13 CRTS Ⅱ型板离缝纵向分布(L=20 m)

Figure 13. Longitudinal distributions of seam of CRTS Ⅱ slab (L=20 m)

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图 14 CRTS Ⅰ型板离缝纵向分布(f =10 mm)

Figure 14. Longitudinal distributions of seam of CRTS Ⅰ slab (f =10 mm)

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图 15 CRTS Ⅰ型板离缝纵向分布(f =10 mm, 幅值位于伸缩缝)

Figure 15. Longitudinal distributions of seam of CRTS Ⅰ slab (f =10 mm, amplitude is located at expansion joint)

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图 16 CRTS Ⅱ型板离缝纵向分布(f =10 mm)

Figure 16. Longitudinal distributions of seam of CRTS Ⅱ slab (f =10 mm)

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图 17 钢轨上拱幅值(L=20 m)

Figure 17. Buckling amplitudes of rails (L=20 m)

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图 18 钢轨上拱幅值(f=10 mm)

Figure 18. Buckling amplitudes of rails (f =10 mm)

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图 19 轨道板和底座板纵向最大拉应力

Figure 19. Longitudinal maximum tensile stresses of slabs and base plates

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表 1 板式无砟轨道材料参数

Table 1. Material parameters of slab ballastless tracks

结构	参数	CRTS Ⅰ型	CRTS Ⅱ型
轨道板	弹性模量/MPa	36 000	36 000
	宽度/m	2.40	2.55
	厚度/m	0.19	0.20
砂浆层	弹性模量/MPa	200	7 000
	宽度/m	2.40	2.55
	厚度/m	0.05	0.03
底座板	弹性模量/MPa	32 500	32 500
底座板	厚度/m	0.30	0.30
基床表层	弹性模量/MPa	180	180
基床底层	弹性模量/MPa	120	120
扣件	垂向刚度/ (kN·m^-1)	50	60

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表 2 垂向位移比较

Table 2. Comparison of vertical displacements mm

结构	CRTS Ⅰ型		CRTS Ⅱ型
结构	计算值	文献结果	计算值	文献结果
钢轨	1.60	1.38	1.65	1.43
轨道板	0.12	0.10	0.16	0.14

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表 3 CRTS Ⅰ型板的最大离缝(L=20 m)

Table 3. Maximum seams of CRTS Ⅰ slab (L=20 m) mm

沉降幅值/mm	5	10	15	20
伸缩缝处离缝	0.31	0.71	1.10	1.48
中心处离缝	0.07	0.40	0.86	1.91

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表 4 CRTS Ⅰ型板的最大离缝(L=20 m, 幅值位于伸缩缝)

Table 4. Maximum seams of CRTS Ⅰslab (L=20 m, amplitude is located at expansion joint) mm

沉降幅值/mm	5	10	15	20
中心两侧处离缝	0.12	0.62	1.40	2.29
上拱处离缝	0.01	0.09	0.21	0.35

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表 5 CRTS Ⅱ型板的最大离缝(L=20 m)

Table 5. Maximum seams of CRTS Ⅱ slab (L=20 m) mm

沉降幅值/mm	5	10	15	20
上拱处离缝	0.03	0.14	0.30	0.41
中心处离缝	0.03	0.80	3.67	7.52

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表 6 CRTS Ⅰ型板的最大离缝(f =10 mm)

Table 6. Maximum seams of CRTS Ⅰ slab (f =10 mm) mm

波长/m	5	10	15	20	25	30	35	40
伸缩缝处离缝	0.00	0.38	0.68	0.71	0.41	0.11	0.01	0.00
中心处离缝	9.70	7.64	2.71	0.40	0.13	0.04	0.02	0.01

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表 7 CRTS Ⅰ型板的最大离缝(f =10 mm, 幅值位于伸缩缝)

Table 7. Maximum seams of CRTS Ⅰ slab (f =10 mm, amplitude is located at expansion joint) mm

波长/m	5	10	15	20	25	30	35	40
中心两侧处离缝	9.46	4.28	1.36	0.62	0.23	0.10	0.04	0.04
上拱处离缝	0.01	0.18	0.16	0.09	0.11	0.30	0.21	0.19

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表 8 CRTS Ⅱ型板的最大离缝(f =10 mm)

Table 8. Maximum seams of CRTS Ⅱ slab (f =10 mm) mm

波长/m	5	10	15	20	25	30	35	40
上拱处离缝	0.02	0.10	0.16	0.14	0.10	0.02	0.01	0.01
中心处离缝	9.76	8.49	5.25	0.80	0.03	0.02	0.01	0.01

下载: 导出CSV

参考文献(25)

[1]	YU Cui-ying, XIANG Jun, MAO Jian-hong, et al. Influence of slab arch imperfection of double-block ballastless track system on vibration response of high-speed train[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018, 40 (2): 1-14.
[2]	周洋, 向俊, 余翠英, 等. 温度荷载作用下高速铁路无砟轨道伤损反演分析[J]. 铁道科学与工程学报, 2016, 13 (1): 1-8. doi: 10.3969/j.issn.1672-7029.2016.01.001 ZHOU Yang, XIANG Jun, YU Cui-ying, et al. Inversion analysis of damage of ballastless track in high-speed railway under temperature loads[J]. Journal of Railway Science and Engineering, 2016, 13 (1): 1-8. (in Chinese). doi: 10.3969/j.issn.1672-7029.2016.01.001
[3]	VARANDAS J N, HÖLSCHER P, SILVA M A G. Settlement of ballasted track under traffic loading: application to transition zones[J]. Journal of Rail and Rapid Transit, 2014, 228 (3): 242-259. doi: 10.1177/0954409712471610
[4]	LI Xin, NIELSEN J C O, PALSSON B A. Simulation of track settlement in railway turnouts[J]. Vehicle System Dynamics, 2014, 52 (S1): 421-439.
[5]	AL SHAER A, DUHAMEL D, SAB K, et al. Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains[J]. Journal of Sound and Vibration, 2008, 316 (1-5): 211-233. doi: 10.1016/j.jsv.2008.02.055
[6]	GUO Yu, ZHAI Wan-ming. Long-term prediction of track geometry degradation in high-speed vehicle-ballastless track system due to differential subgrade settlement[J]. Soil Dynamics and Earthquake Engineering, 2018, 113: 1-11. doi: 10.1016/j.soildyn.2018.05.024
[7]	肖威, 郭宇, 高建敏, 等. 高速铁路路基不均匀沉降对CRTS Ⅲ板式轨道受力变形的影响[J]. 铁道科学与工程学报, 2015, 12 (4): 724-730. doi: 10.3969/j.issn.1672-7029.2015.04.002 XIAO Wei, GUO Yu, GAO Jian-min, et al. Effect of uneven subgrade settlement on the CRTS Ⅲ slab track stress and deformation of high-speed railway[J]. Journal of Railway Science and Engineering, 2015, 12 (4): 724-730. (in Chinese). doi: 10.3969/j.issn.1672-7029.2015.04.002
[8]	赵立宁, 蔡小培, 曲村. 地面沉降对路基上单元板式无砟轨道平顺性的影响分析[J]. 铁道标准设计, 2013 (10): 15-18. https://www.cnki.com.cn/Article/CJFDTOTAL-TDBS201310005.htm ZHAO Li-ning, CAI Xiao-pei, QU Cun. Influence of land subsidence on the regularity of the ballastless track with unit slabs[J]. Railway Standard Design, 2013 (10): 15-18. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDBS201310005.htm
[9]	蔡小培, 刘薇, 王璞, 等. 地面沉降对路基上双块式无砟轨道平顺性的影响[J]. 工程力学, 2014, 31 (9): 160-165. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201409023.htm CAI Xiao-pei, LIU Wei, WANG Pu, et al. Effect of land subsidence on regularity of double-block ballastless track[J]. Engineering Mechanics, 2014, 31 (9): 160-165. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201409023.htm
[10]	陈兆玮, 孙宇, 翟婉明. 高速铁路桥墩沉降与钢轨变形的映射关系(Ⅰ): 单元板式无砟轨道系统[J]. 中国科学: 技术科学, 2014, 44 (7): 770-777. https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201407015.htm CHEN Zhao-wei, SUN Yu, ZHAI Wan-ming. Mapping relationship between pier settlement and rail deformation of high-speed railway—Part (Ⅰ): the unit slab ballastless track system[J]. Scientia Sinica: Technologica, 2014, 44 (7): 770-777. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201407015.htm
[11]	陈兆玮, 孙宇, 翟婉明. 高速铁路桥墩沉降与钢轨变形的映射关系(Ⅱ): 纵连板式无砟轨道系统[J]. 中国科学: 技术科学, 2014, 44 (7): 778-785. https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201407016.htm CHEN Zhao-wei, SUN Yu, ZHAI Wan-ming. Mapping relationship between pier settlement and rail deformation of high-speed railway—Part (Ⅱ): the longitudinal connected ballastless track system[J]. Scientia Sinica: Technologica, 2014, 44 (7): 778-785. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201407016.htm
[12]	何春燕, 陈兆玮, 翟婉明. 高速铁路路桥过渡段不均匀沉降与钢轨变形的映射关系及动力学应用[J]. 中国科学: 技术科学, 2018, 48 (8): 881-890. https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201808008.htm HE Chun-yan, CHEN Zhao-wei, ZHAI Wan-ming. Mapping relationship between uneven settlement of subgrade and rail deformation in subgrade-bridge transition section and its dynamic application[J]. Scientia Sinica: Technologica, 2018, 48 (8): 881-890. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201808008.htm
[13]	陈仁朋, 王作洲, 蒋红光, 等. 基于轨道板抗弯疲劳强度的不均匀沉降控制[J]. 浙江大学学报(工学版), 2013, 47 (5): 796-802. doi: 10.3785/j.issn.1008-973X.2013.05.009 CHEN Ren-peng, WANG Zuo-zhou, JIANG Hong-guang, et al. Control standard of differential settlement in high-speed railway slab based on bending fatigue strength[J]. Journal of Zhejiang University (Engineering Science), 2013, 47 (5): 796-802. (in Chinese). doi: 10.3785/j.issn.1008-973X.2013.05.009
[14]	徐庆元, 李斌, 周智辉. CRTS-Ⅰ型板式无砟轨道线路路基不均匀沉降限制研究[J]. 中国铁道科学, 2012, 33 (2): 1-6. doi: 10.3969/j.issn.1001-4632.2012.02.01 XU Qing-yuan, LI Bin, ZHOU Zhi-hui. Study on the limited value for the uneven settlement of subgrade under CRTS-Ⅰ type slab track[J]. China Railway Science, 2012, 33 (2): 1-6. (in Chinese). doi: 10.3969/j.issn.1001-4632.2012.02.01
[15]	徐庆元, 范浩, 李斌, 等. CRTS-Ⅱ型板式无砟轨道线路路基不均匀沉降限值研究[J]. 中南大学学报(自然科学版), 2013, 44 (12): 5038-5044. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201312036.htm XU Qing-yuan, FAN Hao, LI Bin, et al. Limited value for uneven settlement of subgrade under CRTS-Ⅱ type slab track[J]. Journal of Central South University (Science and Technology), 2013, 44 (12): 5038-5044. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201312036.htm
[16]	宋欢平, 边学成, 蒋建群, 等. 高速铁路路基沉降与列车运行速度关联性的研究[J]. 振动与冲击, 2012, 31 (10): 134-140. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201210029.htm SONG Huan-ping, BIAN Xue-cheng, JIANG Jian-qun, et al. Correlation between subgrade settlement of high-speed railroad and train operation speed[J]. Journal of Vibration and Shock, 2012, 31 (10): 134-140. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201210029.htm
[17]	张小会, 周顺华, 宫全美, 等. 路基不均匀沉降对车车辆和轨道动力响应的影响[J]. 同济大学学报(自然科学版), 2015, 43 (8): 1187-1193, 1253. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201508010.htm ZHANG Xiao-hui, ZHOU Shun-hua, GONG Quan-mei, et al. Effect of subgrade differential settlement on dynamic response and slab track vertical coupled system[J]. Journal of Tongji University (Natural Science), 2015, 43 (8): 1187-1193, 1253. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201508010.htm
[18]	周萌, 宫全美, 王炳龙, 等. 路基不均匀沉降值对板式轨道动力响应的影响[J]. 铁道标准设计, 2010 (10): 1-4. doi: 10.3969/j.issn.1004-2954.2010.10.001 ZHOU Meng, GONG Quan-mei, WANG Bing-long, et al. Influence of uneven sedimentation value of subgrade on dynamic response of slab tracks[J]. Railway Standard Design, 2010 (10): 1-4. (in Chinese). doi: 10.3969/j.issn.1004-2954.2010.10.001
[19]	程群群. 路基不均匀沉降对无砟轨道结构的动力影响与沉降限值研究[D]. 南京: 东南大学, 2015. CHENG Qun-qun. Research on the dynamic response of ballastless track and limit value of uneven settlement subgrade[D]. Nanjing: Southeast University, 2015. (in Chinese).
[20]	唐进锋, 刘文峰, 王浩, 等. 路基不均匀沉降对车辆-CRTS Ⅲ型轨道系统动力特性影响[J]. 铁道科学与工程学报, 2018, 15 (10): 2455-2462. https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201810001.htm TANG Jin-feng, LIU Wen-feng, WANG Hao, et al. Influence of subgrade uneven settlement on dynamic characteristic of vehicle-CRTS Ⅲ slab track system[J]. Journal of Railway Science and Engineering, 2018, 15 (10): 2455-2462. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201810001.htm
[21]	郭宇, 高建敏, 孙宇, 等. 路基沉降与双块式无砟轨道轨面几何变形的映射关系[J]. 铁道学报, 2016, 38 (9): 92-100. doi: 10.3969/j.issn.1001-8360.2016.09.014 GUO Yu, GAO Jian-min, SUN Yu, et al. Mapping relationship between subgrade settlement and rail deflection of the double-block ballastless track[J]. Journal of the China Railway Society, 2016, 38 (9): 92-100. (in Chinese). doi: 10.3969/j.issn.1001-8360.2016.09.014
[22]	郭宇, 高建敏, 孙宇, 等. 板式无砟轨道轨面变形与路基沉降的映射关系[J]. 西南交通大学学报, 2017, 52 (6): 1139-1147, 1215. doi: 10.3969/j.issn.0258-2724.2017.06.014 GUO Yu, GAO Jian-min, SUN Yu, et al. Mapping relationship between rail deflection of slab track and subgrade settlement[J]. Journal of Southwest Jiaotong University, 2017, 52 (6): 1139-1147, 1215. (in Chinese). doi: 10.3969/j.issn.0258-2724.2017.06.014
[23]	裴国史, 高建敏, 郭宇. 路基不均匀沉降对共享路权有轨电车轨道结构受力的影响[J]. 铁道科学与工程学报, 2018, 15 (11): 2772-2779. https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201811007.htm PEI Guo-shi, GAO Jian-min, GUO Yu. Influence of uneven subgrade settlement on track structure stress of tramcar on sharing road right[J]. Journal of Railway Science and Engineering, 2018, 15 (11): 2772-2779. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201811007.htm
[24]	赵国堂. 高速铁路无砟轨道-路基变形计算模型的研究[J]. 中国铁道科学, 2016, 37 (4): 1-8. doi: 10.3969/j.issn.1001-4632.2016.04.01 ZHAO Guo-tang. Calculation model of ballastless track and subgrade deformation on high-speed railway[J]. China Railway Science, 2016, 37 (4): 1-8. (in Chinese). doi: 10.3969/j.issn.1001-4632.2016.04.01
[25]	易南福. 高速铁路不同类型无砟轨道在不同荷载作用下的受力与变形研究[D]. 长沙: 中南大学, 2010. YI Nan-fu. Analysis of stress and deformation of different types of ballastless track on high-speed railway under different loads[D]. Changsha: Central South University, 2010. (in Chinese).