Dynamic response mechanism of shallow parallel tunnels in saturated strata under incident of SV waves
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摘要: 目前城市核心区交叠紧邻的隧道群大量涌现，其抗震安全性问题日益突出，但近邻隧道之间以及与地层的动力相互作用机制尚不清晰。本文针对饱和地层浅埋平行隧道，基于Biot两相介质理论，采用边界积分方程法分别建立了饱和地层水平和竖向双线隧道动力作用分析模型，并与典型算例精确解对比验证了本模型的有效性；在此基础上，研究了SV波入射频率变化和双线隧道间距变化对隧道结构及周围地层孔隙水压力的影响机制，并以单条隧道分析结果为参照进行对比分析。结果表明：相比单条隧道，相邻隧道的存在改变了既有隧道的动力响应特征，且随着隧道间距的减小隧道响应变化更为明显，同时衬砌环向应力峰值显著增加；双线隧道周围地层孔隙水压力分布主要集中在隧道之间的区域内，且SV波低频入射下孔隙水压力峰值随间距的变小而增大；水平双线隧道的动力响应特征与竖向双线隧道不同，随着相邻隧道间距的减小，水平双线隧道的存在会显著放大隧道结构及周围地层的动力响应，而竖向双线隧道则会对垂直入射的SV波的传播起到阻滞作用，从而导致隧道及上部地表动力响应减弱。本研究可为饱和地层浅埋平行隧道抗震设计提供科学依据。Abstract: At present, a large number of overlapping and adjacent tunnel groups have emerged in the core urban area, and the seismic safety problem of these tunnels has become increasingly prominent. However, the dynamic interaction mechanism between adjacent tunnels and the stratum remains unclear. This paper focuses on shallow parallel tunnels in saturated strata. Based on the Biot poroelasticity theory, the boundary integral equation method is used to establish the dynamic analysis models of horizontal and vertical double-line tunnels in saturated strata, and the proposed model is verified by providing comparisons with the known solutions of typical examples. Furthermore, the response mechanism of the tunnel structure and surrounding pore water pressure under the change of tunnel spacing and SV wave incidence frequency is studied, and the results of a single tunnel were compared and analyzed. The results show that the existence of adjacent tunnels changes the dynamic response characteristics of the existing tunnel compared with a single tunnel, and the tunnel response changes more obviously with the decrease of tunnel spacing. In the meantime, the peak stress of lining increased significantly. The distribution of formation pore water pressure around the double-track tunnel is mainly concentrated in the area between the tunnels, and it increases with the decrease of spacing under the low frequency incidence of SV wave. The dynamic response characteristics of the horizontal double-track tunnel are different from those of the vertical double-track tunnel. As the distance between adjacent tunnels decreases, the existence of horizontal double-track tunnels will significantly amplify the dynamic response of the tunnel structure and surrounding strata, while the vertical double-line tunnel will block the propagation of the vertical incident SV wave, which leads to the decrease of dynamic response of the tunnel and the upper surface. The research can provide a scientific basis for the seismic design of shallow parallel tunnels in saturated strata.
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图 3 地表水平（左）和竖向（右）位移幅值与解析解对比
Figure 3. Comparison of the horizontal （left） and vertical （right） displacement amplitudes of the surface with analytical solutions
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图 4 本文环向应力（左）和地表位移幅值（右）与精确解对比
Figure 4. Comparison of the hoop stress （left） and surface displacement （right） in this paper with the exact solution
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图 5 水平双线隧道地表x （a）和y （b）方向无量纲位移幅值曲线
Figure 5. The amplitude curves of the ground x-direction （a） and y-direction （b） displacement of the horizontal twin tunnels
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图 6 竖向双线隧道地表x （a）和y （b）方向无量纲位移幅值曲线
Figure 6. The amplitude curves of the ground x-direction （a） and y-direction （b） displacement of the vertical twin tunnels
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图 7 水平双线隧道（a）和竖向双线隧道（b）的动应力集中因子
$ \sigma _{\theta \theta }^*$ 幅值曲线Figure 7. Amplitude curves of dynamic stress concentration factor of the horizontal twin tunnels （a） and the vertical twin tunnels （b）
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图 8 不同频率入射下单隧道周围地层孔隙水压力分布图
Figure 8. Distribution of pore water pressure around a single tunnel under different incident frequencies
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图 9 不同频率入射下隧道间距比为3 （a），5 （b），8 （c）时水平双线隧道周围地层的孔隙水压力分布图
Figure 9. Distribution of pore water pressure in the formation around the horizontal twin tunnels under different incident frequencies for tunnel spacing ratio S＝3 （a），5 （b），8 （c）
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