Analysis of the overall response of mountain-isolation layer-tunnel under P-wave incidence
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摘要:
采用高精度间接边界元方法（IBEM）开展了山体−隔震层−隧道的整体响应分析，研究了P波入射下柔性隔震层对高斯形山体内双线隧道地震动响应的减弱作用。在隔震层与围岩之间考虑了碎土的错动滑移，以模拟不完美交界面，并系统讨论了隔震层弹性模量、厚度、P波入射频率等因素对隧道地震动响应的影响。数值模拟结果表明：适当增加隔震层厚度可以显著降低隧道应力，有效提升隔震效果，应力降低幅度约达50%以上，且使得结构受力更为均匀；随着隔震层材料的弹性模量减小，隧道动应力数值明显减小，有效减少了其应力放大区的面积，从而有效避免因地震而导致的衬砌裂缝。
Abstract:As an important transportation facility, the safety and stability of mountain tunnels are of great concern when natural disasters such as earthquakes occur. Seismic wave reflection and coherence effect will occur in the mountain body, and the mountain body, seismic isolation layer, and tunnel as “scattering body” and “secondary source” can change the spatial distribution of ground shaking distribution and values of seismic ground motion. In order to study the influence of isolation measures on seismic wave scattering in double line tunnels within mountains, we uses high-precision indirect boundary element method （IBEM） to analyze the overall response of mountains, isolation layers, and tunnels under P-wave incidence. The isolation effect of flexible isolation layers on double line tunnels crossing Gaussian-shaped mountains.
Firstly, a comprehensive computational model was developed. A two-lane lined tunnel is traversed within the Gaussian-shaped mountain, and a seismic isolation layer is set between the tunnel and the mountain site. It is assumed that the mountain site, the tunnel and the seismic isolation layer are all linear isotropic media. In this article, there is not complete consolidation between the tunnel and the surrounding rock, but rather dislocation slip. Therefore, a series of virtual linear springs and dampers are used to connect the isolation layer and the surrounding rock, and a viscoelastic boundary is set to simulate this imperfect boundary.
Secondly, wave field analysis was conducted based on elastic wave theory. The formulas for the free field and scattering field are provided in the article, and an equilibrium equation is established based on the displacement and stress continuity conditions at the interface of each computational domain. Solving this equation can obtain the virtual wave source density. Multiplying the concentration of the virtual wave source by the corresponding Green’s function can obtain the scattering field of observation points in each domain. The superposition of scattering field and free field yields the full wave field.
Thirdly, the correctness of the results is also verified. Due to the lack of an accurate analytical solution for mountainous tunnels under P-wave incidence in current research, we degenerates the model into a half space tunnel model and compares it with published results, with the same setting of the calculation parameters. It can be found that the results of this paper are in good agreement with those of published paper, thus verifying the accuracy of this method.
Finally, the effects of the modulus of elasticity, thickness, and incident frequency of the seismic isolation layer on the seismic ground motion response of the tunnels were discussed in detail, and the displacements and stresses of the tunnel inside the mountain and the displacements on the mountain surface are obtained. The research results can provide some reference for seismic isolation design and construction of double-line tunnel in mountain site. The following main conclusions are obtained:
1） IBEM can accurately solve the seismic dynamic response of lined tunnels in mountain, including the amplification effect of seismic ground motion in mountain ranges and the stress concentration effect of the lining, etc. Setting up seismic isolation and damping measures can effectively change the distribution of the stress and give full play to the load-bearing capacity of the surrounding rock, thus playing a role in protecting the tunnel lining.
2） As the modulus of elasticity of the isolation layer material decreases, there is a significant reduction in the values of dynamic tunnel stresses. The structural response of the flexible seismic isolation layer for suppressing high-frequency waves is more obvious. When high-frequency waves are incident, an isolation layer with elastic modulus of 12 MPa can reduce the tunnel peak stress to 25.4% of which without an isolation layer. At the same time, when the modulus of elasticity is small, it can effectively reduce the area of its stress amplification zone, thus effectively avoiding lining cracks caused by seismic action.
3） The seismic isolation layer can make the lining circumferential stress distribution tend to be uniform, and with the increase of the thickness of the vibration isolation layer, the tunnel lining dynamic stress gets smaller, and the reduction can be about 50% or more.
4） Considering the efficiency of seismic isolation as well as the cost of the project, among the several sets of parameters studied in this paper, the combined effect of a seismic isolation layer with a modulus of elasticity of 12 MPa and a thickness of 20 cm is superior.
5） Considering the existence of broken soil between the tunnel and the surrounding rock, a staggered slip boundary is introduced on the boundary. The staggered slip boundary model proposed in this paper is still simplified and does not take into account the nonlinear effects such as elastic-plasticity and large deformation.
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图 1 山体内双圆形衬砌隧道计算模型（a）和错动滑移边界构造（b）
L3和L5分别表示左右隧道衬砌内边界；L7和L8分别表示左右隧道衬砌外边界；D2和D3代表隧道域；r1和r2为隧道内外半径；r3为隔震层外半径；t为衬砌厚度，下同
Figure 1. Calculation model of double circular lining tunnel in the mountain （a） and staggered slip boundary structure （b）
L3 and L5 are the inner boundaries of the left and right tunnels，respectively；L7 and L8 are the outer boundaries of the left and right tunnels，respectively；D2 and D3 represent tunnel domains；r1 and r2 are the inner and outer radii of the tunnel，respectively；r3 is the outer radius of the isolation layer；t is the thickness of the lining，the same below
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图 2 隧道—山体系统域划分及边界离散
（a） 弹性半空间域D1；（b） 隔震层域D4 和D5；（c） 隧道域D2 和D3
Figure 2. Domain-division of the tunnel-hill system and boundary discrete elements
（a） Elastic half-space domain D1；（b） Seismic isolation layer domain D4 （D5）；（c） Tunnel domain D2 （D3）
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图 3 当前模型退化结果同Luco和de Barros （1994）对P波垂直入射所得结果对比
（a） 地表位移；（b） 衬砌环向应力
Figure 3. The comparison of the present results with the degenerated results of Luco and Barros （1994） for vertical incident P waves
（a） Surface displacement；（b） Lining circumferential stress
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图 4 P波垂直入射下隔震层d和弹性模量$\eta $不同时左隧道的动应力集中因子DSCF
（a） 无隔震层；（b） 隔震层弹性模量100 MPa；（c） 隔震层弹性模量50 MPa；（d） 隔震层弹性模量12 MPa
Figure 4. DSCF of the left tunnel with different elastic modulus of isolation layer under vertical incident P wave
（a） No isolation layer；（b） Elastic modulus of isolation layer 100 MPa；（c） Elastic modulus of isolation layer 50 MPa；（d） Elastic modulus of isolation layer 12 MPa
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图 5 P波垂直入射下不同隔震层厚度d和弹性模量$\eta $时DSCF
（a） 隔震层厚度10 cm；（b） 隔震层厚度20 cm；（c） 隔震层厚度40 cm
Figure 5. DSCF of the left tunnel with different shock absorption layer thickness under P wave incidence
（a） Isolation layer thickness 10 cm；（b） Isolation layer thickness 20 cm；（c） Isolation layer thickness 40 cm
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图 6 P波垂直入射下不同隔震层厚度的左隧道加速度时程（不设隔震层时的加速度时程为参照，如灰色线条所示）
（a） 隔震层厚度为0 cm与10 cm对比图；（b） 隔震层厚度为0 cm与15 cm对比图；（c） 隔震层厚度为0 cm与20 cm对比图
Figure 6. Acceleration time history of the left tunnel with different seismic isolation layer thickness under P wave incidence （taking the acceleration time histories without isolation layer as reference，which are denoted by gray curves）
（a） Comparison of isolation layer thickness 0 cm and 10 cm；（b） Comparison of isolation layer thickness 0 cm and 15cm；（c） Comparison of isolation layer thickness 0 cm and 20 cm
表 1 材料参数
Table 1 Material parameters
介质 弹性模量
/MPa密度
/（kg·m−3）剪切波速
/（ m·s−1）泊松比 围岩 5000 2000 1000 0.25 隧道 32000 2500 2260 0.25 隔震层① 12 1000 70 0.38 隔震层② 50 1200 130 0.38 隔震层③ 100 1400 170 0.38 
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李天斌. 2008. 汶川特大地震中山岭隧道变形破坏特征及影响因素分析[J]. 工程地质学报,16(6):742–750. doi: 10.3969/j.issn.1004-9665.2008.06.003 Li T B. 2008. Failure characteristics and influence factor analysis of mountain tunnels at epicenter zones of great Wenchuan earthquake[J]. Journal of Engineering Geology,16(6):742–750 (in Chinese).
梁清华,刘中宪,周晓洁,何颖. 2018. 基于粘性—滑移界面接触模型半空间隧道衬砌对平面P波的散射[J]. 世界地震工程,34(3):111–123. Liang Q H,Liu Z X,Zhou X J,He Y. 2018. Scattering of plane P waves by a lined tunnel in a half-space based on viscous-slip interface contact model[J]. World Earthquake Engineering,34(3):111–123 (in Chinese).
梅松华,盛谦,崔臻,梅贤丞. 2022. 黏弹性阻尼减震层的吸能特性试验研究[J]. 岩土工程学报,44(6):997–1005. Mei S H,Sheng Q,Cui Z,Mei X C. 2022. Experimental study on energy absorption property of viscoelasticity damping layer[J]. Chinese Journal of Geotechnical Engineering,44(6):997–1005 (in Chinese).
杨长卫,张良,张凯文,岳茂,童心豪,温浩. 2023. 山岭隧道跨断裂带段及洞口段地震响应大型振动台模型试验研究[J]. 岩石力学与工程学报,42(4):993–1002. Yang C W,Zhang L,Zhang K W,Yue M,Tong X H,Wen H. 2023. Large scale shaking table model test on seismic response of mountain tunnel portal section passing through fault zone[J]. Chinese Journal of Rock Mechanics and Engineering,42(4):993–1002 (in Chinese).
禹海涛,李晶,王祺. 2022. 软土隧道基于地震响应的输入地震动排序[J]. 地震学报,44(1):123–131. doi: 10.11939/jass.20210166 Yu H T,Li J,Wang Q. 2022. Ranking the seismic input motion based on seismic response of soft soil tunnels[J]. Acta Seismologica Sinica,44(1):123–131 (in Chinese).
Ba Z N,Yin X. 2016. Wave scattering of complex local site in a layered half-space by using a multidomain IBEM:Incident plane SH waves[J]. Geophys J Int,205(3):1382–1405. doi: 10.1093/gji/ggw090
Bobet A. 2009. Elastic solution for deep tunnels:Application to excavation damage zone and rockbolt support[J]. Rock Mech Rock Eng,42(2):147–174. doi: 10.1007/s00603-007-0140-0
Fang X Q,Jin H X,Liu J X,Huang M J. 2016. Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves[J]. Tunnell Undergr Space Technol,56:226–231. doi: 10.1016/j.tust.2016.03.008
Huang L,Liu Z X,Wu C Q,Liang J W. 2019. The scattering of plane P,SV waves by twin lining tunnels with imperfect interfaces embedded in an elastic half-space[J]. Tunnell Undergr Space Technol,85:319–330. doi: 10.1016/j.tust.2018.12.024
Jiang X L,Wang F F,Yang H,Sun G C,Niu J Y. 2018. Dynamic response of shallow-buried small spacing tunnel with asymmetrical pressure:Shaking table testing and numerical simulation[J]. Geotech Geol Eng,36(4):2037–2055. doi: 10.1007/s10706-017-0444-0
Lin Z,Yan L,Xiang C,Yang H Y. 2020. Study on dynamic response laws and shock absorption measures of mountain tunnel under strong earthquake[J]. Adv Civil Eng:1671838.
Luco J E,de Barros F C P. 1994. Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space[J]. Earthq Eng Struct Dyn,23(3):321–340. doi: 10.1002/eqe.4290230307
Ma X,Wang F M,Guo C C,Sun B. 2020. Seismic isolation effect of non-water reacted two-component polymeric material coating on tunnels[J]. Appl Sci,10(7):2606. doi: 10.3390/app10072606
Meng G W,Gao B,Zhou J M,Cao G D,Zhang Q. 2016. Experimental investigation of the mechanical behavior of the steel fiber reinforced concrete tunnel segment[J]. Constr Build Mater,126:98–107. doi: 10.1016/j.conbuildmat.2016.09.028
Su L J,Liu H Q,Yao G C,Zhang J L. 2019. Experimental study on the closed-cell aluminum foam shock absorption layer of a high-speed railway tunnel[J]. Soil Dyn Earthq Eng,119:331–345. doi: 10.1016/j.soildyn.2019.01.012
Wang W L,Wang T T,Su J J,Lin C H,Seng C R,Huang T H. 2001. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi earthquake[J]. Tunnell Undergr Space Technol,16(3):133–150. doi: 10.1016/S0886-7798(01)00047-5
Wang Z,Zhu W,Zhang Z. 2012. Seismic isolation effect of a tunnel covered with a buffer layer[J]. Dis Adv,5(4):1372–1376.
Xu X Y,Wu Z J,Sun H,Weng L,Chu Z F,Liu Q S. 2021. An extended numerical manifold method for simulation of grouting reinforcement in deep rock tunnels[J]. Tunnell Undergr Space Technol,115:104020. doi: 10.1016/j.tust.2021.104020
Yi C P,Zhang P,Johansson D,Nyberg U. 2014. Dynamic response of a circular lined tunnel with an imperfect interface subjected to cylindrical P-waves[J]. Comput Geotech,55:165–171. doi: 10.1016/j.compgeo.2013.08.009
Zhou X H,Cheng X S,Qi L,Wang P,Chai S F,Liu Y J. 2021. Shaking table model test of loess tunnel structure under rainfall[J]. KSCE J Civ Eng,25(6):2225–2238. doi: 10.1007/s12205-021-1064-z
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