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Seismic response of buried metro tunnels by a hybrid FDM-BEM approach

机译：混合FDM-BEM方法对地下地铁隧道的地震反应

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摘要

In this work, we present a 2D elastodynamic model for the seismic response of subway tunnels embedded in a laterally inhomogeneous, multilayered geological region overlying the half-plane. To this end, a finite difference-boundary element methodology (FDM-BEM) is developed, with the latter method embedded in the former so as to capture near-site field effects. More specifically, the FDM is used for simulating in-plane elastic wave propagation from the underlying bedrock through the overlying soil deposits to the surface. A 'box' area is then defined within the original FDM mesh and contains lined tunnels. The 'box' is modeled by the BEM and its upper boundary coincides with the free surface of the geological deposit. This way, seismically-induced motions are imparted from the FDM mesh to the 'box' perimeter, so that the BEM may now be used to efficiently model the near-site layers which contain the tunnels. Verification studies are then successfully conducted for upward moving Gabor pulses, using the FDM alone, the present hybrid FDM-BEM and a hybrid FDM-finite element method formulation. Given that the FDM is defined in the time domain and the BEM in the frequency domain, the fast Fourier transform is used for linking these two constituent parts of the hybrid approach. This methodology is finally applied to a north-south geological cross-section of Thessaloniki, Greece, which contains two Metro tunnels placed directly below an important Roman-era monument known as the Arch of Galerius. Results are then given in the form of free-surface motions stemming from the Thessaloniki 5 July 1978 aftershock recorded at bedrock so as to establish the influence of the ongoing Metro line construction, now temporarily halted because of the economic crisis, on the free surface motions in the city centre where a number historical monuments besides the Arch of Galerius still survive.
机译：在这项工作中，我们为埋在半平面上的横向不均匀，多层地质区域中的地铁隧道的地震反应提供了二维弹性模型。为此，开发了一种有限差分边界元方法（FDM-BEM），后者嵌入了前一种方法，以捕获近场场效应。更具体地说，FDM用于模拟从下层基岩通过上覆的土壤沉积物到地面的面内弹性波传播。然后在原始FDM网格内定义一个“框”区域，其中包含衬砌的隧道。 “盒子”由BEM建模，其上边界与地质矿床的自由表面重合。这样，地震引起的运动就从FDM网格传递到“盒子”周边，因此现在可以使用BEM来有效地模拟包含隧道的近地层。然后，仅使用FDM，本混合FDM-BEM和混合FDM有限元方法公式，就成功地进行了向上移动的Gabor脉冲的验证研究。假定FDM在时域中定义，而BEM在频域中定义，则快速傅里叶变换用于链接混合方法的这两个组成部分。该方法最终应用于希腊塞萨洛尼基的南北地质断面，该断面包含两条地铁隧道，直接位于重要的罗马时代纪念碑加列里乌斯拱门下方。然后以自由表面运动的形式给出结果，该自由表面运动来自于基岩记录的1978年7月5日塞萨洛尼基余震，从而确定了正在进行的地铁线路建设（由于经济危机而暂时停止）对自由表面运动的影响在市中心，除了加莱里乌斯拱门外，还有许多历史遗迹。

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