Research on the dynamic response of shallow-buried circular non-complete bonded tunnels under anti-plane line source loading
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摘要: 为加深理解波源距离和非完全粘结对地震波散射的影响规律，结合位移不连续模型、波函数展开法、Graf公式和镜像方法推导了反平面线源荷载下浅埋圆形非完全粘结隧道动力响应的级数解，并通过衬砌内外边界条件残余量与级数解截断项数的关系校验了该解的精度。通过对该级数解进行参数分析，系统地探讨了衬砌与围岩的接触刚度、衬砌模量、衬砌厚度、隧道埋深和波源距离等因素对衬砌内表面位移和周向剪应力的影响。结果表明：衬砌与围岩的接触刚度对隧道的动力响应具有显著的影响，尤其在某些较小接触刚度情况下隧道动力响应幅值可能非常大；增大衬砌模量会减小位移，但同时会导致周向剪应力增加；增大衬砌厚度能同时减小位移和周向剪应力；增大隧道埋深会使最大位移和周向剪应力向隧道拱顶附近移动；增大线源与隧道的水平距离会使隧道背波侧相对幅值增大。Abstract: The scattering of seismic waves by shallow-buried underground structures has significant theoretical value in the engineering field. However, previous studies have mainly focused on the case of plane waves or the case of complete bonding between lining and surrounding rock, with little consideration of the effects of source distance and non-complete bonding between lining and surrounding rock. In order to deepen the understanding of the influence of source distance and non-complete bonding on seismic wave scattering, the series solution of the dynamic response of shallow-buried circular non-complete bonded tunnels under the loading of anti-plane line source was derived based on the displacement discontinuity model, wave function expansion method, Graf formula and mirror method. The accuracy of the obtained solution was verified by the relationship between the residuals of the inner and outer boundary conditions of the lining and the number of truncated terms in the series solution. By systematically analyzing the parameters of this series solution, the influence of factors such as the contact stiffness between lining and surrounding rock, lining modulus, lining thickness, tunnel depth and source distance on the displacement and circumferential shear stress on the inner surface of the lining was discussed. The results show that the contact stiffness between lining and surrounding rock has a significant influence on the dynamic response of the tunnel, especially in cases with relatively low contact stiffness, where the amplitude of the dynamic response of the tunnel can be very large. Increasing the lining modulus reduces the displacement but increases the circumferential shear stress. Increasing the lining thickness can simultaneously reduce the displacement and circumferential shear stress. As the tunnel depth increases, the maximum displacement and circumferential shear stress on the inner surface of the lining shifts towards the apex of the tunnel. Increasing the horizontal distance between the line source and the tunnel increases the relative amplitude of the tunnel's back wave side.
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图 2 当η = 1.0和Ks/μ1 = 1.0 m−1时衬砌内外边界的位移和应力残差与截断项数N之间的关系
Figure 2. The relationship between the displacement and stress residuals of the inner and outer boundaries of the lining and the number of truncated terms N when η=1.0 and Ks/μ1=1.0 m−1
图 3 当η = 3.0和Ks/μ1 = 0.1 m−1时衬砌内外边界的位移和应力残差与截断项数N之间的关系
Figure 3. The relationship between the displacement and stress residuals of the inner and outer boundaries of the lining and the number of truncated terms N when η=3.0 and Ks/μ1=0.1 m−1
图 4 衬砌内表面归一化位移和周向剪应力与衬砌和围岩的接触刚度的关系
Figure 4. The relationship between normalized displacement and circumferential shear stress on the inner surface of lining and the contact stiffness between lining and surrounding rock
图 5 衬砌内表面归一化位移和周向剪应力与衬砌模量的关系
Figure 5. The relationship between normalized displacement and circumferential shear stress on the inner surface of lining and lining modulus
图 6 衬砌内表面归一化位移和周向剪应力与衬砌厚度的关系
Figure 6. The relationship between normalized displacement and circumferential shear stress on the inner surface of lining and lining thickness
图 7 衬砌内表面归一化位移和周向剪应力与隧道埋深的关系
Figure 7. The relationship between normalized displacement and circumferential shear stress on the inner surface of lining and tunnel burial depth
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[1] LEE V W. On deformations near circular underground cavity subjected to incident plane SH waves [C]// Proceedings of the Application of Computer Methods in Engineering Conference. Los Angeles, 1977: 951–962. [2] LEE V W, TRIFUNAC M D. Response of tunnels to incident SH-waves [J]. Journal of the Engineering Mechanics Division, 1979, 105(4): 643–659. DOI: 10.1061/JMCEA3.0002511. [3] 李海波, 马行东, 李俊如, 等. 地震荷载作用下地下岩体洞室位移特征的影响因素分析 [J]. 岩土工程学报, 2006, 28(3): 358–362. DOI: 10.3321/j.issn:1000-4548.2006.03.015.LI H B, MA X D, LI J R, et al. Study on influence factors of rock cavern displacement under earthquake [J]. Chinese Journal of Geotechnical Engineering, 2006, 28(3): 358–362. DOI: 10.3321/j.issn:1000-4548.2006.03.015. [4] XIA X, LI H B, LIU Y Q, et al. A case study on the cavity effect of a water tunnel on the ground vibrations induced by excavating blasts [J]. Tunnelling and Underground Space Technology, 2018, 71: 292–297. DOI: 10.1016/j.tust.2017.08.026. [5] 袁晓铭. 地表下圆形夹塞区出平面散射对地面运动的影响 [J]. 地球物理学报, 1996, 39(3): 373–381. DOI: 10.3321/j.issn:0001-5733.1996.03.011.YUAN X M. Effect of a circular underground inclusion on surface motion under incident plane SH waves [J]. Acta Geophysica Sinica, 1996, 39(3): 373–381. DOI: 10.3321/j.issn:0001-5733.1996.03.011. [6] 刘殿魁, 林宏. 浅埋的圆柱形孔洞对SH波的散射与地震动 [J]. 爆炸与冲击, 2003, 23(1): 6–12. DOI: 10.3321/j.issn:1001-1455.2003.01.002.LIU D K, LIN H. Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion [J]. Explosion and Shock Waves, 2003, 23(1): 6–12. DOI: 10.3321/j.issn:1001-1455.2003.01.002. [7] 王国庆, 刘殿魁. SH波对浅埋相邻多个圆孔作用的动力分析 [J]. 哈尔滨工程大学学报, 2003, 24(1): 108–113. DOI: 10.3969/j.issn.1006-7043.2003.01.026.WANG G X, LIU D K. Dynamic analysis for effect of SH-wave on shallow fill multiple circular cavities [J]. Journal of Harbin Engineering University, 2003, 24(1): 108–113. DOI: 10.3969/j.issn.1006-7043.2003.01.026. [8] 陈志刚, 刘殿魁. SH波冲击下浅埋任意形孔洞的动力分析 [J]. 地震工程与工程振动, 2004, 24(4): 32–36. DOI: 10.3969/j.issn.1000-1301.2004.04.006.CHEN Z G, LIU D K. Dynamic response on a shallowly buried cavity of arbitrary shape impacted by vertical SH-wave [J]. Earthquake Engineering and Engineering Vibration, 2004, 24(4): 32–36. DOI: 10.3969/j.issn.1000-1301.2004.04.006. [9] 陈志刚. 各向异性半空间中浅埋孔洞对地表反平面运动的影响 [J]. 地震学报, 2015, 37(4): 617–628. DOI: 10.11939/jass.2015.04.008.CHEN Z G. Effect of shallow buried cavity on anti-plane motion of ground surface in anisotropic half-space [J]. Acta Seismologica Sinica, 2015, 37(4): 617–628. DOI: 10.11939/jass.2015.04.008. [10] 李敏, 刘殿魁, 周瑞芬. 含孔半圆形凸起地形及多个孔洞对SH波的散射 [J]. 哈尔滨工程大学学报, 2008, 29(1): 78–84. DOI: 10.3969/j.issn.1006-7043.2008.01.016.LI M, LIU D K, ZHOU R F. Scattering of SH-waves by a semi-cylindrical hill with a hole and multiple cavities around it in half-space [J]. Journal of Harbin Engineering University, 2008, 29(1): 78–84. DOI: 10.3969/j.issn.1006-7043.2008.01.016. [11] 刘刚, 刘殿魁. SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动 [J]. 固体力学学报, 2007, 28(1): 60–66. DOI: 10.3969/j.issn.0254-7805.2007.01.011.LIU G, LIU D K. The ground motion of an isosceles triangular hill above a subsurface cavity with incident SH-waves [J]. Acta Mechanica Solida Sinica, 2007, 28(1): 60–66. DOI: 10.3969/j.issn.0254-7805.2007.01.011. [12] 齐辉, 赵春香, 黄敏. 出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响 [J]. 振动与冲击, 2013, 32(17): 109–112,122. DOI: 10.3969/j.issn.1000-3835.2013.17.021.QI H, ZHAO C X, HUANG M. Dynamic effect of a subsurface cavity in half space under out-of-plane line source load on a cylindrical elastic inclusion with a semi-cylindrical hill [J]. Journal of Vibration and Shock, 2013, 32(17): 109–112,122. DOI: 10.3969/j.issn.1000-3835.2013.17.021. [13] GAO Y F, DAI D H, ZHANG N, et al. Scattering of plane and cylindrical SH waves by a horseshoe shaped cavity [J]. Journal of Earthquake and Tsunami, 2017, 11(2): 1650011. DOI: 10.1142/s1793431116500111. [14] CHEN X, ZHANG N, GAO Y F, et al. Effects of a V-shaped canyon with a circular underground structure on surface ground motions under SH wave propagation [J]. Soil Dynamics and Earthquake Engineering, 2019, 127: 105830. DOI: 10.1016/j.soildyn.2019.105830. [15] ZHANG X P, JIANG Y J, CHEN L J, et al. Anti-plane seismic performance of a shallow-buried tunnel with imperfect interface in anisotropic half-space [J]. Tunnelling and Underground Space Technology, 2021, 112: 103906. DOI: 10.1016/j.tust.2021.103906. [16] LEE V W, KARL J. Diffraction of SV waves by underground, circular, cylindrical cavities [J]. Soil Dynamics and Earthquake Engineering, 1992, 11(8): 445–456. DOI: 10.1016/0267-7261(92)90008-2. [17] 梁建文, 张浩, LEE V W. 地下洞室群对地面运动影响问题的级数解答—P波入射 [J]. 地震学报, 2004, 26(3): 269–280. DOI: 10.3321/j.issn:0253-3782.2004.03.006.LIANG J W, ZHANG H, LEE V W. A series solution for surface motion amplification due to underground group cavities—incident P waves [J]. Acta Seismologica Sinica, 2004, 26(3): 269–280. DOI: 10.3321/j.issn:0253-3782.2004.03.006. [18] LIANG J W, ZHANG H, LEE V W. A series solution for surface motion amplification due to underground twin tunnels: incident SV waves [J]. Earthquake Engineering and Engineering Vibration, 2003, 2(2): 289–298. DOI: 10.1007/s11803-003-0012-x. [19] MEI W Q, XIA Y Y, HAN G S, et al. Theoretical responses of shallow-buried circular cavity subjected to transient P wave [J]. Computers and Geotechnics, 2021, 139: 104411. DOI: 10.1016/j.compgeo.2021.104411. [20] LIN C H, LEE V W, TODOROVSKA M I, et al. Zero-stress, cylindrical wave functions around a circular underground tunnel in a flat, elastic half-space: incident P-waves [J]. Soil Dynamics and Earthquake Engineering, 2010, 30(10): 879–894. DOI: 10.1016/j.soildyn.2010.01.010. [21] LIU Q J, ZHAO M J, WANG L H. Scattering of plane P, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space [J]. Soil Dynamics and Earthquake Engineering, 2013, 49: 52–63. DOI: 10.1016/j.soildyn.2013.02.007. [22] LUCO J E, DE BARROS F C P. Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space [J]. Earthquake Engineering & Structural Dynamics, 1994, 23(3): 321–340. DOI: 10.1002/eqe.4290230307. [23] LIU Q J, YUE C, ZHAO M J. Scattering of harmonic P1 and SV waves by a shallow lined circular tunnel in a poroelastic half-plane [J]. Soil Dynamics and Earthquake Engineering, 2022, 158: 107306. DOI: 10.1016/j.soildyn.2022.107306. [24] SON M, CORDING E J. Ground–liner interaction in rock tunneling [J]. Tunnelling and Underground Space Technology, 2007, 22(1): 1–9. DOI: 10.1016/j.tust.2006.03.002. [25] ACHENBACH J D. Wave propagation in elastic solids [M]. Amsterdam: Elsevier, 1973. DOI: 10.1016/c2009-0-08707-8. -
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