Citation: | YANG Chengyong, MA Wenhui, FEI Teng, HAN Xueguo, CHENG Lin. Analysis of Longitudinal Deformation of Shield Tunnel Structures with Consideration of Axial Force and Shear Effect[J]. Journal of Southwest Jiaotong University, 2022, 57(1): 139-147. doi: 10.3969/j.issn.0258-2724.20200134 |
The influence of axial force and shear effect on the longitudinal deformation of shield tunnel structures under different loads is investigated by Fourier series method. Taking into account the foundation reaction caused by shear deformation, the governing differential equation of bending deformation is derived, and a formula is proposed to calculate the shear deformation. The correctness of the Fourier series solution is verified by comparison with analytical solutions. Through comparative calculation, the main work is focused on addressing the influence of cross section, end support, type of load, ratio of length to height, and elastic foundation on the shear deformation of shield tunnel, the influence of shear rigidity on bending deformation, shear deformation and internal forces, and the influence of axial load exerted by installation of segment rings on bending deformation and bending moment. Results show that the shear deformation of shield tunnel accounts for more than 20% of the total deformation, which is caused by the form of annular section and low shear rigidity of shield tunnel. When shear deformation is counted, the whole deformation gets larger, but the bending deformation and bending moment are smaller than those without consideration of shear deformation. As shear rigidity decreases, shear deformation increases, and its proportion to the entire deformation also increases. In our case studies, when the shear rigidity decreases from 8×106 to 1×106 kN, the whole deformation goes up by 15.7%; the bending deformation and bending moment go down by 11.7% and 17.1%, respectively; the shear deformation increases 5.77 times; and the percentage of shear deformation to the whole deformation increases from 4.64% to 27.17%. Besides, the bending deformation and bending moment are also increased by installation-caused axial load, but the influence range is limited, often less than 2% in deflection and less than 3% in bending moment.
[1] |
廖少明,门燕青,肖明清,等. 软土盾构法隧道纵向应力松弛规律的实测分析[J]. 岩土工程学报,2017,39(5): 795-803. doi: 10.11779/CJGE201705003
LIAO Shaoming, MEN Yanqing, XIAO Mingqing, et al. Field tests on longitudinal stress relaxation along shield tunnel in soft ground[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(5): 795-803. doi: 10.11779/CJGE201705003
|
[2] |
TIMOSHENKO S P. Strength of materials, part I, elementary theory and problems[M]. Third edition. New York: D. Van Nostrand Company Inc., 1955.
|
[3] |
WU H N, SHEN S L, LIAO S M, et al. Longitudinal structural modelling of shield tunnels considering shearing dislocation between segmental rings[J]. Tunnelling and Underground Space Technology, 2015, 50(8): 317-323.
|
[4] |
梁荣柱,林存刚,夏唐代,等. 考虑隧道剪切效应的基坑开挖对邻近隧道纵向变形分析[J]. 岩石力学与工程学报,2017,36(1): 223-233.
LIANG Rongzhu, LIN Cungang, XIA Tangdai, et al. Analysis on the longitudinal deformation of tunnels due to pit excavation considering the tunnel shearing effect[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(1): 223-233.
|
[5] |
HETENYI M. Beams on elastic foundation[M]. Ann Arbor: University of Michigan Press, 1946.
|
[6] |
杨成永,程霖,余乐,等. 隧道沉降引起的轨道结构变形与脱空[J]. 中国铁道科学,2018,39(6): 37-43. doi: 10.3969/j.issn.1001-4632.2018.06.06
YANG Chengyong, CHENG Lin, YU Le, et al. Deformation and cavity of track structure due to tunnel settlement[J]. China Railway Science, 2018, 39(6): 37-43. doi: 10.3969/j.issn.1001-4632.2018.06.06
|
[7] |
COWPER G R. The shear coefficient in Timoshenko’s beam theory[J]. Journal of Applied Mechanics, 1966, 33(2): 335-340. doi: 10.1115/1.3625046
|
[8] |
HUTCHINSON J R. Shear coefficients for Timoshenko beam theory[J]. Journal of Applied Mechanics, 2001, 68(1): 87-92. doi: 10.1115/1.1349417
|
[9] |
严宗达. 结构力学中的富里叶级数解法[M]. 天津: 天津大学出版社, 1989.
|
[10] |
WANG C M. Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions[J]. Journal of Engineering Mechanics, 1995, 121(6): 763-765. doi: 10.1061/(ASCE)0733-9399(1995)121:6(763)
|
[1] | WANG Junjie, ZHANG Shuai. Large Deformation Control of Tunnel Surrounding Rock Based on Advance Stress Release and Grouting Reinforcement[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20230706 |
[2] | ZHONG Xiaochun, HUANG Siyuan, ZHU Weibin, CHEN Qiaosong, YOU Zhi. Analysis of Sealing Performance of Shield Tail Brush Based on Compression and Grease Escape Test[J]. Journal of Southwest Jiaotong University, 2023, 58(1): 125-132. doi: 10.3969/j.issn.0258-2724.20210814 |
[3] | YE Fei, QIN Nan, LIANG Xing, HAN Xingbo, HAN Xin. Microscopic Model Analysis of Shield Tunnel Backfill Grouting Based on Displacement Effect[J]. Journal of Southwest Jiaotong University, 2022, 57(2): 339-345. doi: 10.3969/j.issn.0258-2724.20200344 |
[4] | XIE Hongming, HE Chuan, FENG Kun, LIANG Minfei, LI Ce, AL-SEBAEAI Maged. Unidirectional Vibration Waterproof Test of Ring Joint of Shield Tunnel under the Action of Earthquake[J]. Journal of Southwest Jiaotong University, 2020, 55(4): 713-718. doi: 10.3969/j.issn.0258-2724.20180456 |
[5] | SHEN Xiang, YUAN Dajun, CAO Yutao, GAO Zhenfeng. Experiments on Material Proportions for Simulating Sandy Layer in Deep Sea[J]. Journal of Southwest Jiaotong University, 2020, 55(3): 628-634. doi: 10.3969/j.issn.0258-2724.20180285 |
[6] | GENG Ping, WANG Qi, GUO Xiangyu, HE Chuan, LU Shujun, XIAO Mingqing. Force Characteristics of Longitudinal Joints of Shield Tunnel under Seismic Action[J]. Journal of Southwest Jiaotong University, 2020, 55(4): 704-712. doi: 10.3969/j.issn.0258-2724.20180634 |
[7] | YE Huawen, WANG Liwu, ZHANG Qing, XU Xun, WEI Xing. Trigonometric Series Solution of Bending Deformation for Composite Beam with Steel Corrugated Webs[J]. Journal of Southwest Jiaotong University, 2019, 54(4): 701-708, 723. doi: 10.3969/j.issn.0258-2724.20170277 |
[8] | WANG Mingnian, HUANG Haibin, TANG Yuan, WANG Chuang, LIU Dagang. Influence of Shield Construction on Pressure Fluctuation of Segment Grout[J]. Journal of Southwest Jiaotong University, 2019, 54(3): 461-467, 586. doi: 10.3969/j.issn.0258-2724.20170199 |
[9] | GENG Ping, HE Chuan, YAN Qixiang. Analysis of Longitudinal Seismic Response of Shield Tunnel[J]. Journal of Southwest Jiaotong University, 2007, 20(3): 283-287. |
[10] | LIWei, HE Chuan, ZHANG Zhi-qiang. M odelTest ofConstructing Shield Tunnel under Large Underground Structure[J]. Journal of Southwest Jiaotong University, 2005, 18(4): 478-483. |
[11] | MAOJian-qiang, ZHOUDe-pei. Deformation Analysis for Landslide-Tunnel Interaction[J]. Journal of Southwest Jiaotong University, 2002, 15(4): 371-376. |
[12] | XIETao, YUANWen-zhong, ZHUMing. The Deformation Behavior of Super-Large Pile Group under Vertical Load[J]. Journal of Southwest Jiaotong University, 2002, 15(4): 377-381. |
1. | 高锋阳,强雅昕,高智山,徐昊,史志龙. 计及驾驶风格的氢燃料电池有轨电车自适应能量管理策略. 铁道科学与工程学报. 2024(04): 1379-1390 . ![]() | |
2. | 刘继宗,张祖涛,王浩,孔苓吉,伊敏熠,朱忠尹. 城轨交通制动能量利用技术研究现状与展望. 西南交通大学学报. 2024(06): 1322-1345 . ![]() | |
3. | 张伟建,崔杰,陈波,周洋,丁俊. 有轨电车混合供电及运行切换方法研究. 机电工程技术. 2022(07): 108-110+252 . ![]() |