断层错动下隧道外包减震层纵向内力解析解

Analytical Solution for Longitudinal Internal Force of Tunnel Covered by Isolation Layer Under Fault Movement

摘要

为研究断层错动作用下外包减震层对隧道纵向响应的影响,考虑断层场地-减震层-隧道系统各接触面间切向相互作用,推导了断层错动下外包减震层隧道纵向响应解析解。首先,提出隧道-减震层的等效Timoshenko梁模型,建立考虑减震层与围岩间切向与法向相互作用的等效梁-弹性地基模型,推导隧道-减震层的位移挠度解析公式。随后,针对隧道结构,推导出表示减震层-隧道接触面切向相互作用的扭转弹簧刚度表达式,建立隧道梁-弹性地基模型,得到隧道弯曲转角解析公式。最终,基于隧道的挠度与弯曲转角解析公式并结合Timoshenko梁的物理和几何方程,推导出隧道弯矩和剪力解析解。通过与三维实体有限元模型对比,验证了提出的解析解的精度,并研究了减震层弹性模量、厚度及泊松比对跨断层隧道内力响应的影响。结果表明:减震层降低隧道的峰值剪力响应,但放大峰值弯矩响应;隧道的峰值剪力随着减震层弹性模量的增加而增加,峰值弯矩表现出相反趋势;随减震层厚度的增加,隧道峰值剪力降低,峰值弯矩增加;减震层泊松比对隧道纵向响应影响较小。该文提出的解析解可为断层错动作用下跨断层隧道外包减震层纵向内力计算和抗错断优化设计提供理论依据。

Abstract

To investigate the influence of the isolation layer on the tunnel response under the fault movement, the analytical solution for the longitudinal response of the tunnel with an isolation layer under fault movement is derived by considering the tangential interactions at the ground-isolation layer-tunnel interfaces. Initially, an equivalent Timoshenko beam model for the tunnel-isolation layer was proposed. An equivalent beam-elastic foundation model considering the tangential and normal interactions at the ground-isolation layer interface was established. The analytical solution for the displacement of the tunnel-isolation layer system was derived. Second, with regard to the tunnel, the rotation spring stiffness at the interface between the isolation layer and tunnel was derived. A beam-elastic foundation model for the tunnel was established to obtain the analytical solution for the rotation angle of the tunnel. Ultimately, based on the derived analytical solutions for the displacement and rotation angle of the tunnel, and combined with the physical and geometric equations of the Timoshenko beam, the analytical solution for the bending moment and shear force of the tunnel was derived. The accuracy of the proposed analytical solution was verified by comparing them with the finite element model. Furthermore, the influences of the elastic modulus, thickness, and Poisson's ratio of the isolation layer on the internal force response of the tunnel were analyzed. Results show that the isolation layer can significantly reduce the shear force response of the tunnel but amplify the bending moment response. As the elastic modulus of the isolation layer increases, the shear force of the tunnel increases while the bending moment decreases. Increasing the thickness of the isolation layer reduces the shear force but increases the bending moment of the tunnel. The Poisson's ratio of the isolation layer has a relatively small effect on the longitudinal response of the tunnel. This study provides a theoretical basis for calculating longitudinal internal forces and optimization design of cross-fault tunnel with isolation layer under fault movement.

关键词

跨断层隧道 / 断层错动 / 减震层 / 弹性地基梁 / 解析解 / 纵向响应

Key words

cross-fault tunnel / fault movement / isolation layer / elastic foundation beam / analytical solution / longitudinal response

参考文献

[1] 王峥峥, 孙铁成, 张胜林, 等 . 断层破碎带岩溶大断面隧道坍塌事故处理[J]. 北京工业大学学报, 2013, 39(10): 1494-1498.

[2] WANG Z Z, SUN T C, ZHANG S L, et al. Collapse treatment of faulted Karst cave tunnel[J]. Journal of Beijing University of Technology, 2013, 39(10): 1494-1498. (in Chinese)

[3] 王鸿儒, 钟紫蓝, 赵密, 等 . 走滑断层黏滑错动下隧道破坏的模型试验研究[J]. 北京工业大学学报, 2021, 47(7): 691-701.

[4] WANG H R, ZHONG Z L, ZHAO M, et al. Model experimental study of the influence of strike—slip fault dislocation on tunnel[J]. Journal of Beijing University of Technology, 2021, 47(7): 691-701. (in Chinese)

[5] LAI J X, HE S Y, QIU J L, et al. Characteristics of seismic disasters and aseismic measures of tunnels in Wenchuan earthquake[J/OL]. Environmental Earth Sciences, 2017, 76(2): 94[2017—01—20]. https://link.springer.com/article/10.1007/s12665—017—6405—3.

[6] LI T B . Damage to mountain tunnels related to the Wenchuan earthquake and some suggestions for aseismic tunnel construction[J]. Bulletin of Engineering Geology and the Environment, 2012, 71(2): 297-308.

[7] WANG Z Z, GAO B, JIANG Y J, et al. Investigation and assessment on mountain tunnels and geotechnical damage after the Wenchuan earthquake[J]. Science in China Series E: Technological Sciences, 2009, 52(2): 546-558.

[8] 赵旭, 代志杰, 黎若寒, 等 . 考虑围岩松动圈的隧道抗减震措施[J]. 北京工业大学学报, 2020, 46(9): 1027-1038.

[9] ZHAO X, DAI Z J, LI R H, et al. Earthquake mitigation measures for tunnels considering loosen—zone in surrounding rock[J]. Journal of Beijing University of Technology, 2020, 46(9): 1027-1038. (in Chinese)

[10] 信春雷, 高波, 周佳媚, 等 . 跨断层隧道设置常规抗减震措施振动台试验研究[J]. 岩石力学与工程学报, 2014, 33(10): 2047-2055.

[11] XIN C L, GAO B, ZHOU J M, et al. Shaking table tests of conventional anti—seismic and damping measures on fault—crossing tunnels[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(10): 2047-2055. (in Chinese)

[12] 信春雷, 高波, 周佳媚, 等 . 跨断层隧道抗减震措施性能振动台试验研究[J]. 岩土工程学报, 2014, 36(8): 1414-1422.

[13] XIN C L, GAO B, ZHOU J M, et al. Shaking table tests on performances of anti—seismic and damping measures for fault—crossing tunnel structures[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(8): 1414-1422. (in Chinese)

[14] 王帅帅, 高波, 隋传毅, 等 . 减震层减震原理及跨断层隧道减震技术振动台试验研究[J]. 岩土工程学报, 2015, 37(6): 1086-1092.

[15] WANG S S, GAO B, SUI C Y, et al. Mechanism of shock absorption layer and shaking table tests on shaking absorption technology of tunnel across fault[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(6): 1086-1092. (in Chinese)

[16] 范凯祥, 申玉生, 高波, 等 . 穿越软硬围岩隧道设置减震层振动台试验研究[J]. 土木工程学报, 2019, 52(9): 109—120, 128.

[17] FAN K X, SHEN Y S, GAO B, et al. Shaking table test on damping layer applied in tunnel crossing soft and hard surrounding rock[J]. China Civil Engineering Journal, 2019, 52(9): 109—120, 128. (in Chinese)

[18] 崔光耀, 纪磊, 荆鸿飞 . 高烈度艰险山区跨断层隧道减震层减震技术研究[J]. 地震工程学报, 2019, 41(2): 286-291.

[19] CUI G Y, JI L, JING H F . Damping shake technology of the shock absorption layer of fault—crossing tunnels in a dangerous mountainous area with high—intensity earthquakes[J]. China Earthquake Engineering Journal, 2019, 41(2): 286-291. (in Chinese)

[20] XIN C L, WANG Z Z, YU J . The evaluation on shock absorption performance of buffer layer around the cross section of tunnel lining[J/OL]. Soil Dynamics and Earthquake Engineering, 2020, 131: 106032[2020—01—14]. https://www.sciencedirect.com/science/article/pii/S026772611930747X?via%3Dihub.

[21] 彭斌, 杜泽辉, 余鹏, 等 . 穿越断层破碎带特大跨度铁路隧道减震技术研究[J]. 铁道技术标准(中英文), 2023(10): 15-21.

[22] PENG B, DU Z H, YU P, et al. Research on vibration reduction technology for super large span railway tunnels passing through fault fractured zones[J]. Railway Technical Standard (Chinese & English), 2023, 5(10): 15-21. (in Chinese)

[23] 唐垠斐 . 山岭隧道断层破碎带地震动力响应规律及抗减震措施研究[D]. 成都: 西南交通大学, 2018.

[24] TANG Y F . Study on seismic dynamic response and aseismic measures for fault fracture zone in mountain tunnels[D]. Chengdu: Southwest Jiaotong University, 2018. (in Chinese)

[25] 崔光耀, 王明年, 于丽, 等 . 穿越黏滑错动断层隧道减震层减震技术模型试验研究[J]. 岩土工程学报, 2013, 35(9): 1753-1758.

[26] CUI G Y, WANG M N, YU L, et al. Model tests on damping shake technology of shock absorption layer of tunnels crossing stick—slip faults[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(9): 1753-1758. (in Chinese)

[27] 崔光耀, 伍修刚, 王明年, 等 . 高烈度地震区黏滑断层隧道减震层减震模型试验研究[J]. 岩土工程学报, 2017, 39(11): 2125-2131.

[28] CUI G Y, WU X G, WANG M N, et al. Model tests on damping of shock absorption layer of stick—slip fracture tunnel in highly seismic areas[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(11): 2125-2131. (in Chinese)

[29] 王道远, 崔光耀, 袁金秀, 等 . 断裂黏滑错动下隧道减错措施作用效果模型试验研究[J]. 岩土工程学报, 2018, 40(8): 1515-1521.

[30] WANG D Y, CUI G Y, YUAN J X, et al. Model tests on effect of dislocation reducing measures of stick—slip fault of tunnels[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(8): 1515-1521. (in Chinese)

[31] RUSSO M, GERMANI G, AMBERG W . Design and construction of large tunnel through active faults: a recent application[C]// International Conference of Tunneling and Underground Space Use. Switzerland: Lombardi Engineering Limited, 2002: 1-14.

[32] ZHAO M, XU L H, HUANG J Q, et al. Analytical solutions of the tunnels under the fault creeping by elastic foundation beam model with considering tangential interaction[J/OL]. Soil Dynamics and Earthquake Engineering, 2023, 172: 108047[2023—05—31]. https://www.sciencedirect.com/science/article/pii/S0267726123002920?via%3Dihub.

[33] 周光新, 崔臻, 盛谦, 等 . 活动断裂错动位移模式对隧洞变形与内力的影响研究[J]. 防灾减灾工程学报, 2021, 41(6): 1323-1330, 1349.

[34] ZHOU G X, CUI Z, SHENG Q, et al. Study on the deformation and internal force of the tunnel under the displacement pattern of the active fault zone[J]. Journal of Disaster Prevention and Mitigation Engineering, 2021, 41(6): 1323—1330, 1349. (in Chinese)

[35] 蒋树屏, 李鹏, 林志 . 穿越活动断层区隧道的抗断设计对策[J]. 重庆交通大学学报(自然科学版), 2008, 27(6): 1034—1036, 1041.

[36] JIANG S P, LI P, LIN Z . Design strategies of breaking resistance of tunnels crossing active faults zone[J]. Journal of Chongqing Jiaotong University (Natural Science), 2008, 27(6): 1034—1036, 1041. (in Chinese)

[37] ZHAO M, JIAO H Y, HUANG J Q, et al. Analytical solutions for circular tunnels under longitudinally propagating shear waves based on improved foundation beam models considering tangential interaction[J/OL]. Tunnelling and Underground Space Technology, 2022, 123: 104444[2022—03—01]. https://www.sciencedirect.com/science/article/pii/S0886779822000840?via%3Dihub.

[38] 陈涛 . 基于Timoshenko梁的隧道纵向地震响应及减震机理研究[D]. 成都: 西南交通大学, 2017.

[39] CHEN T . Longitudinal seismic response and shock absorption mechanism analysis for tunnels based on Timoshenko beam model[D]. Chengdu: Southwest Jiaotong University, 2017. (in Chinese)

[40] 俞剑, 张陈蓉, 黄茂松 . 被动状态下地埋管线的地基模量[J]. 岩石力学与工程学报, 2012, 31(1): 123-132.

[41] YU J, ZHANG C R, HUANG M S . Subgrade modulus of underground pipelines subjected to soil movements[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(1): 123-132. (in Chinese)

[42] 崔光耀, 王明年, 于丽, 等 . 汶川地震断层破碎带段隧道结构震害分析及震害机理研究[J]. 土木工程学报, 2013, 46(11): 122-127.

[43] CUI G Y, WANG M N, YU L, et al. Study on the characteristics and mechanism of seismic damage for tunnel structures on fault rupture zone in Wenchuan seismic disastrous area[J]. China Civil Engineering Journal, 2013, 46(11): 122-127. (in Chinese)

[44] 张煜 . 断层蠕滑错动作用下隧道衬砌损伤开裂研究及柔性连接抗错断措施[D]. 成都: 西南交通大学, 2016.

[45] ZHANG Y . Research on tunnel lining damage and crack induced by fault creep and anti—breaking measure of flexible connector[D]. Chengdu: Southwest Jiaotong University, 2016. (in Chinese)

基金资助

国家重点研发计划资助项目(2022YFC3004305)

国家自然科学基金资助项目(52378475)