Analytical solution for longitudinal equivalent bending stiffness of quasi-rectangular shield tunnels
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摘要: 结合类矩形盾构隧道截面特点，分别对中性轴位于截面上部边缘（环缝完全闭合）、截面上拱部、截面腰部和截面下拱部4种情况进行分析，并进一步考虑螺栓预紧力和环缝影响范围，推导得到类矩形盾构隧道的纵向等效抗弯刚度解析解，并对影响纵向等效刚度的相关因素进行探究。研究表明：当施加弯矩小于环缝启动弯矩时，环缝全部闭合，等效纵向抗弯刚度有效率为1，中性轴位于截面上部外缘；随着弯矩进一步增加，环缝逐渐张开，同时中性轴位置逐步下移，等效纵向抗弯刚度减小；纵向等效抗弯刚度有效率随环缝作用区系数增大呈现先迅速下降而后缓慢减小的趋势；螺栓预紧力越大，纵向等效刚度越大，中性轴位置随之上移；随宽高比增大，等效纵向抗弯刚度有效率逐渐下降，中性轴位置随之下移，并在中性轴位置角与小圆弧圆心角相等时出现转折点。Abstract: According to the sectional characteristics of quasi-rectangular shield tunnels, the neutral axes located at four different positions, the upper section edge (the ring joint is completely closed), the section vault, the section waist and the section invert, are analyzed, respectively. The analytical solution for the equivalent longitudinal bending stiffness of quasi-rectangular shield tunnels is then derived by further considering the pretightening force of bolts and the influence range of circumferential joints. The relative influencing factors on the longitudinal equivalent stiffness are also investigated. It is shown that when the applied bending moment is smaller than the activating one, the circumferential joint is completely closed, the effective efficiency of equivalent bending stiffness is 1, and the neutral axis is located at the upper edge of the section. By further increasing the applied bending moment, the circumferential joint starts to partially separate. Simultaneously, the position of the neutral axis moves down gradually. The equivalent longitudinal bending stiffness decreases with the increase of the applied bending moment. The effective efficiency of the equivalent longitudinal bending stiffness decreases first rapidly and then slowly with the increase of the coefficient of circumferential seam action zone. The greater the pretightening force of bolts is, the larger the equivalent longitudinal bending stiffness is. Subsequently, the position of the neutral axis moves up. With the increase of width-height ratio, the effective efficiency of the equivalent bending stiffness decreases gradually, the position of the neutral axis moves down subsequently, and a turning point appears when the position angle of the neutral axis is equal to the center angle of small arc.
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图 3 类矩形盾构隧道三维结构图
Figure 3. Three-dimensional structure of quasi-rectangular shield tunnel
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图 6 环缝闭合时的环缝影响范围内纵向应力及变形
Figure 6. Longitudinal stresses and deformations under completely closed circumferential joint
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图 7 环缝闭合时环缝影响范围外的纵向应力及变形
Figure 7. Longitudinal stresses and deformations outside influence range of circumferential joint under completely closed circumferential joint
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图 8 中性轴位于类矩形截面腰部时纵向应力和变形
Figure 8. Longitudinal stresses and deformations under neutral axis located at waist of quasi-rectangular section
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图 9 中性轴位于类矩形截面下拱部时纵向应力和变形
Figure 9. Longitudinal stresses and deformations under neutral axis located at invert of tunnel section
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图 10 中性轴位于类矩形截面上拱部时纵向应力和变形
Figure 10. Longitudinal stresses and deformations under neutral axis located at tunnel vault
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图 11 弯矩与纵向等效抗弯刚度和中性轴位置角的关系
Figure 11. Relationship among bending moment, longitudinal equivalent bending stiffness and neutral axis
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图 12 环缝作用区系数χ对等效抗弯刚度有效率的影响
Figure 12. Effects of coefficient of circumferential seam action zone on effective efficiency of equivalent bending stiffness
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图 13 环缝影响系数对中性轴位置变化的影响
Figure 13. Effects of influence coefficient of circumferential seam on position of neutral axis
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图 14 螺栓预紧力对纵向等效抗弯刚度的影响
Figure 14. Effects of pretightening force of bolt on equivalent longitudinal bending stiffness
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图 15 中性轴位置角φ随着螺栓预紧力变化曲线
Figure 15. Effects of pretightening force of bolt on position angle of neutral axis φ
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图 16 宽高比a/b对纵向等效抗弯刚度有效率η的影响
Figure 16. Effects of width-height ratio a/b on effective efficiency of equivalent bending stiffness
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图 17 中性轴位置角φ随宽高比a/b变化关系
Figure 17. Relationship between width-height ratio a/b and neutral axis position
表 1 类矩形盾构隧道衬砌主要设计参数
Table 1 Design parameters for linings of quasi-rectangular shield tunnel
隧道宽度2a/m 隧道高度2b/m 半径R1/m 半径R2/m 偏移s/m 角α/(°) 角β/(°) 环宽ls/m 管片厚度t/m 弹性模量Es/MPa 11.50 6.937 2.975 15.225 11.98 78 12 1.2 0.45 3.45×104 
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表 2 类矩形隧道纵向接头主要参数
Table 2 Parameters for longitudinal joint of quasi-rectangular shield tunnel
纵向螺栓数量n/个 直径/mm 长度lb/mm 弹性模量Eb/MPa 抗拉刚度/(kN·m-1) 30 30 370 2.06×105 3.12×105
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[1] 朱瑶宏, 朱雁飞, 黄德中, 等. 类矩形盾构法隧道关键技术研究与应用[J]. 隧道建设, 2017, 37(9): 1055–1062. https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD201709001.htm ZHU Yao-hong, ZHU Yan-fei, HUANG De-zhong, et al. Development and application of key technologies to quasi-rectangular shield tunneling[J]. Tunnel Construction, 2017, 37(9): 1055–1062. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD201709001.htm
[2] 小泉淳, 村上博智, 西野健三. ツールドトネルの轴方向特性のモデルイヒにつぃて[C]// 土木学会论文集. 1988: 79–88. KOIZUMI A, MURAKAMI H, NISHINO K. A Model of the Directional Properties of Tool de Tonel[C]// Journal of the Japan Society of Civil Engineers, 1988: 79–88. (in Japanese)
[3] 志波由纪夫, 川岛一彦, 大日方尚己, 等. 应答变位法にょるツ—ルドトンネルの地震时断面力の算定法[C]// 土木学会论文集, 1989: 385–394. SHIWA Y, KAWASHIMA K, ODATEKA N, et al. A method for calculating the seismic cross-sectional force of a tunnel with a negative response method[C]// Journal of the Japan Society of Civil Engineers, 1989: 385–394. (in Japanese)
[4] 林永国. 地铁隧道纵向变形结构性能研究[D]. 上海: 同济大学, 2001. LIN Yong-guo. Study on the Performance of Longitudinal Deformation Structure of Metro Tunnel[D]. Shanghai: Tongji University, 2001. (in Chinese)
[5] 廖少明. 圆形隧道纵向剪切传递效应研究[D]. 上海: 同济大学, 2002. LIAO Shao-ming. Study on Longitudinal Shear Transfer Effect of Circular Tunnel[D]. Shanghai: Tongji University, 2002. (in Chinese)
[6] 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: 317–323. doi: 10.1016/j.tust.2015.08.001
[7] 张文杰, 徐旭, 李向红, 等. 广义的盾构隧道纵向等效连续化模型研究[J]. 岩石力学与工程学报, 2009, 28(增刊2): 3938–3944. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2009S2098.htm ZHANG Wen-jie, XU Xu, LI Xiang-hong, et al. Research on generalized longitudinal equivalent continuous model of shield tunnels[J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(S2): 3938–3944. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2009S2098.htm
[8] 叶飞, 何川, 朱合华, 等. 考虑横向性能的盾构隧道纵向等效刚度分析[J]. 岩土工程学报, 2011, 33(12): 1870–1876. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201112010.htm YE Fei, HE Chuan, ZHU He-hua, et al. Longitudinal equivalent rigidity analysis of shield tunnel considering transverse characteristics[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12): 1870–1876. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201112010.htm
[9] 李翔宇, 刘国彬, 杨潇, 等. 基于修正纵向等效连续化模型的隧道变形受力研究[J]. 岩土工程学报, 2014, 36(4): 662–670. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201404012.htm LI Xiang-yu, LIU Guo-bin, YANG Xiao, et al. Deformation and stress of tunnel structures based on modified longitudinal equivalent continuous model[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(4): 662–670. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201404012.htm
[10] 耿萍, 陈枰良, 张景, 等. 轴力和弯矩共同作用下盾构隧道纵向非线性等效抗弯刚度研究[J]. 岩石力学与工程学报, 2017, 36(10): 2522–2534. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201710021.htm GENG Ping, CHEN Ping-liang, ZHANG Jing, et al. Nonlinear longitudinal equivalent bending stiffness of shield tunnel under the combined effect of axial force and bending moment[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(10): 2522–2534. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201710021.htm
[11] 徐凌. 软土盾构隧道纵向沉降研究[D]. 上海: 同济大学, 2005. XU Ling. Study on Longitudinal Settlement of Soft Soil Shield Tunnel[D]. Shanghai: Tongji University, 2005. (in Chinese)
[12] 梁荣柱, 夏唐代, 胡军华, 等. 新建隧道近距离上穿对既有地铁隧道纵向变形影响分析[J]. 岩土力学, 2016, 37(增刊1): 391–399. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2016S1051.htm LIANG Rong-zhu, XIA Tang-dai, HU Jun-hua, et al. Analysis of longitudinal displacement of existing metro tunnel due to construction of above-crossing new tunnel in close distance[J]. Rock and Soil Mechanics, 2016, 37(S1): 391–399. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2016S1051.htm
[13] 许有俊, 陶连金, 文中坤, 等. 新建地铁隧道上穿既有隧道引起的结构隆起变形[J]. 中国铁道科学, 2014, 35(6): 48–54. doi: 10.3969/j.issn.1001-4632.2014.06.08 XU You-jun, TAO Lian-jin, WEN Zhong-kun, et al. Upheaval deformation induced by newly-built metro tunnel upcrossing existing tunnel[J]. China Railway Science, 2014, 35(6): 48–54. (in Chinese) doi: 10.3969/j.issn.1001-4632.2014.06.08
[14] LIANG R Z, XIA T D, HONG Y, et al. Effects of above-crossing tunnelling on the existing shield tunnels[J]. Tunnelling and Underground Space Technology, 2016, 58(9): 159–176.
[15] 康成, 叶超, 梁荣柱, 等. 基坑开挖诱发下卧盾构隧道纵向非线性变形研究[J]. 岩石力学与工程学报, 2020, 39(11): 2341–2350. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202011017.htm KANG Cheng, YE Chao, LIANG Rong-zhu, et al. Nonlinear longitudinal deformation of underlying shield tunnels induced by foundation excavation[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(11): 2341–2350. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202011017.htm
[16] 张子新, 朱叶艇, 朱雁飞, 等. 大断面异形盾构衬砌结构纵向力学性能[J]. 同济大学学报(自然科学版), 2017, 45(5): 684–691. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201705010.htm ZHANG Zi-xin, ZHU Ye-ting, ZHU Yan-fei, et al. Study on the longitudinal mechanical behavior of large shield lining structure with a specialshaped cross-section[J]. Journal of Tongji University (Natural Science), 2017, 45(5): 684–691. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201705010.htm
[17] 黄亮, 梁荣柱, 吴小建, 等. 类矩形盾构隧道纵向抗弯刚度分析[J]. 岩土工程学报, 2019, 41(11): 2094–2102. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201911017.htm HUANG Liang, LIANG Rong-zhu, WU Xiao-jian, et al. Longitudinal bending stiffness of quasi-rectangular shield tunnels[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(11): 2094–2102. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201911017.htm
[18] 鲁志鹏. 基于静态量测数据的盾构法地铁隧道建设和运营安全评价研究[D]. 上海: 同济大学, 2008. LU Zhi-peng. Study on the Safety Evaluation of Tunnel Construction and Operation Based on Static Measurement Data[D]. Shanghai: Tongji University, 2008. (in Chinese)
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