Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.     

Seismic analysis of deep tunnels in near fault conditions: a case study in Southern Italy

The importance of underground structures in transportation and utility networks makes their vulnerability to earthquakes a sensitive issue. Underground facilities are usually less vulnerable to earthquakes compared to above-ground structures, but the associated risk may be relevant, since even a low level of damage may affect the serviceability of a wide network. Seismic analysis of tunnels close to seismogenic faults is a complex problem, which is often neglected at the design stage for the lack of specific codes or guidelines for the design of underground structures in seismic conditions and also because, as mentioned above, underground structures are considered less vulnerable to earthquake loading. This paper investigates the seismic response of deep tunnels focusing on the required steps for a proper design under both static and dynamic loading. The study aims at contributing to improve the methods currently used for the seismic analysis of underground structures. At this purpose, the seismic response of a deep tunnel in Southern Italy has been investigated along the transversal direction. The infrastructure is part of the railway switch line connecting Caserta to Foggia in the Southern Apennines which is one of the most active seismic regions in Italy. The seismic response in the transversal direction has been analysed by using the pseudo-static approach as well as through advanced numerical modeling using the spectral element method coupled with a kinematic approach for finite fault simulations. The pseudo-static approach has been implemented using a closed-form analytical solution. The results obtained from advanced numerical modeling and the pseudo-static method have been compared to assess their validity and limitations.     

地下隧道轴向地震动土作用分析

以弹性基岩上覆层状场地中刚性衬砌隧道为模型,采用间接边界元方法求解衬砌隧道所受的沿轴向地震动土作用,通过参数分析揭示轴向动土作用的幅值大小、空间分布等基本规律。研究表明,土-隧道动力相互作用对地震动土作用的空间分布形式影响较小,但对地下隧道所受地震动土作用峰值大小具有显著影响,隧道主要位置点的地震动土作用峰值与隧道相应位置处自由场土层应力相比放大1.7~2.4倍。论文最后提出一个轴向地震动土作用的简化计算方法。     

土-结构相互作用分析中几类地震输入方式的比较

地震作用下土-结构动力相互作用的整体有限元分析需要在人工边界处输入地震动。目前可能采用的地震输入方法包括黏弹性边界自由场输入方法、自由场应力方法、自由场位移方法以及侧边界自由方法。由于采用近似人工边界条件或者未完全考虑地震自由场,上述地震输入方法均为近似方法。本文以大开地铁车站二维有限元分析为例,根据规范建议的边界位置,研究了上述地震输入方法的精度,研究成果可为土-结构相互作用分析的合理地震输入提供一定参考。     

Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM

Recent researches have revealed that the seismic ground response above tunnels can be different from the free-field motion during earthquakes. Nevertheless, to the best of the authors׳ knowledge, neither building codes nor seismic microzonation guidelines have yet considered this matter. In the present study, the seismic response of a linear elastic medium including a buried unlined tunnel subjected to vertically propagating incident SV and P waves are addressed. For analysis purposes, a numerical time-domain analysis is performed by utilizing a robust numerical algorithm working based on the boundary element method. It is observed that the amplification of the ground surface underlain by a tunnel is increased in long periods. The variation of the amplification factor and characteristic period of the medium versus the buried depth of the tunnel are depicted as the major results of this study. Some simple and useful relations are proposed for estimating the seismic microzonation of the areas underlain by tunnels. These relations can also be used for the preliminary seismic design of structures located on underground structures.     

Impact of incident angles of P waves on the dynamic responses of long lined tunnels

The impact of the incident angle of earthquake motion on the seismic response of the long lined tunnels is studied. Based on the time‐domain finite element method with the viscous‐spring artificial boundary condition, the earthquake motion of oblique incidence is transformed into the equivalent nodal forces acting on the truncated boundary of finite element model. In the present work, the formulas of equivalent nodal forces for the plane P wave with arbitrary incident angle are deduced and implemented into the commercial software abaqus   1 . The effectiveness of the formulas and its implementation are demonstrated by two numerical examples with the reference solutions. The proposed method is applied to investigate the seismic responses of the long lined tunnels under the obliquely incident P waves. The numerical results indicate that the seismic responses of the long lined tunnels are highly affected by the incident angles of P waves. Copyright © 2016 John Wiley & Sons, Ltd.     

Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking

Immersed tunnels are particularly sensitive to tensile and compressive deformations such as those imposed by a normal seismogenic fault rupturing underneath, and those generated by the dynamic response due to seismic waves. The paper investigates the response of a future 70 m deep immersed tunnel to the consecutive action of a major normal fault rupturing in an earthquake occurring in the basement rock underneath the tunnel, and a subsequent strong excitation from a different large-magnitude seismic event that may occur years later. Non-linear finite elements model the quasi-static fault rupture propagation through the thick soil deposit overlying the bedrock and the ensuing interaction of the rupture with the immersed tunnel. It is shown that despite imposed bedrock offset of 2 m, net tension or excessive compression between tunnel segments could be avoided with a suitable design of the joint gaskets. Then, the already deformed (“injured”) structure is subjected to strong asynchronous seismic shaking. The thick-walled tunnel is modelled as a 3-D massive flexural beam connected to the soil through properly-calibrated nonlinear interaction springs and dashpots, the supports of which are subjected to the free-field acceleration time histories. The latter, obtained with 1-D wave propagation analysis, are then modified to account for wave passage effects. The joints between tunnel segments are modeled with special non-linear hyper-elastic elements, properly accounting for their 7-bar longitudinal hydrostatic pre-stressing. Sliding is captured with special gap elements. The effect of segment length and joint properties is explored parametrically. A fascinating conclusion emerges in all analysed cases for the joints between segments that were differentially deformed after the quasi-static fault rupture: upon subsequent very strong seismic shaking, overstressed joints de-compress and understressed joints re-compress—a “healing” process that leads to a more uniform deformation profile along the tunnel. This is particularly beneficial for the precariously de-compressed joint gaskets. Hence, the safety of the immersed tunnel improves with “subsequent” strong seismic shaking!     

近场地震动格林函数的解析法与数值法对比研究

分析了在均匀弹性介质中，分别用解析方法和三维波动有限元数值方法计算无限全空间近场地震动的格林函数的理论与方法。将震源处理分为：(1)计算单一位错点源单位脉冲引起的格林函数；(2)用有限断层模型将断面划分为若干子源并有时间延迟，叠加所有子源的格林函数。本以1994年美国北岭地震为例，用解析法和数值方法分别计算了LV3、PCD、MCN三个场地的格林函数，并进行了对比分析。     

复杂软土盾构隧道纵向抗震分析

以天津Z2线盾构隧道工程为实例,基于ABAQUS有限元软件,建立三维梁-弹簧模型模拟盾构隧道,采用反应位移法对盾构隧道进行纵向抗震分析.根据盾构隧道接头实际情况,计算环间接头弹簧刚度.将地震作用下的自由场最大水平位移幅值,以简谐波的形式施加到盾构隧道轴向和横向.提出一种同时考虑轴向和横向水平地震动耦联效应的方法,通过调...     

地下综合管廊土-结构接触面参数对地震动力响应的影响数值分析

为研究土-结构接触面参数对地下综合管廊地震动力响应特征的影响,建立动力有限元数值模型,模型边界采用激励侧固定边界、远离激励侧黏性边界、其余侧自由场边界的优化组合动力边界,土体本构采用HSS模型,接触面采用改进Goodman单元,动力荷载考虑三种情况(Rayleigh波的作用、底部激励了美国加利福尼亚Upland地震波以及前两者的共同作用),分别研究不同地震动输入、接触面折减系数的改变对综合管廊内力及加速度的影响。研究结果表明:在相同的折减系数条件下,与静力作用相比,动力作用下的结构内力明显增大,综合管廊设计时应考虑地震荷载作用下内力增大的情况;随着界面折减系数的增加,正弯矩极值减小,负弯矩极值增大,加速度峰值增大;在相同接触面折减系数条件下,底部地震波输入产生的结构内力极值显著高于仅有Rayleigh波输入的情况;考虑Rayleigh波和地震波共同作用条件下,引起的管廊结构内力极值与仅考虑底部地震波输入时的结构内力极值差异不大。研究成果可供地下综合管廊结构地震响应精细化数值模拟及抗震设计参考。     

Shaking table test of utility tunnel under non-uniform earthquake wave excitation

A series of shaking table tests were conducted on scaled utility tunnel models with and without construction joints under non-uniform input earthquake wave excitation. Details of experimental setup are first presented with particular focuses on: design and fabrication of double-axis laminar shear box with a rectangular hole opened on its side walls; design of two devices for measuring the slippage between the interface of test soil and the structure, and the relative deformation and rotation between joints of the structure model; and procedure for construction of input earthquake wave. The experiments were conducted in three phases. Phase 1 is free-field test. A 2-norm index is suggested to quantify the boundary effect and it is found that the designed laminar box does not impose significant boundary effect. Phases 2 and 3 are model tests in longitudinal and transversal directions, respectively. Test results are discussed in items of shear force–slip relationship at the soil–model structure interaction surface, movement and rotation of the construction joint, and effect of non-uniform earthquake input. The comparison shows that structural response under non-uniform earthquake excitation is larger than that under uniform excitation. The effect of spatial distribution of earthquake excitation should be considered in the seismic design of utility tunnel.     

A practical approach for seismic risk assessment of underground structures: A case study of Iranian subway tunnels

Active geological and young faulted zones have made Iran’s territory one of the most seismological active areas in the world according to recent historical earthquakes. Some of the deadliest earthquakes such as Gilan 1990 and Kermanshah 2018 caused tens of thousands fatalities. If such violent earthquakes affect strategical structures of a country, indirect losses would be more concerning than direct losses. Nowadays there is no doubt about the vital role of tunnels and underground structures in urban areas. These facilities serve as nonstop functional structures for human transportation, water and sewage systems and underground pedestrian ways. Any external hazard subjected to underground spaces, such as earthquake could directly affect passenger’s lives and significantly decrease whole system reliability of public transportation. Commonly two earthquake levels of intensities, Maximum Design Earthquake (MDE) and Operating Design Earthquake (ODE) were used in seismic design of underground structures. However, uncertain nature of earthquakes in terms of frequency content, duration of strong ground motion, and level of intensity indicate that only the two levels of earthquake (ODE and MDE) cannot cover the all range of possible seismic responses of structures during a probable earthquake. It is important to evaluate the behavior of tunnel under a wide range of earthquake intensities. For this purpose, a practical risk-based approach which is obtained using the total probability rule was used. This study illustrates a framework for evaluation seismic stability of tunnels. Urban railway tunnels of Tehran, Shiraz, Ahwaz, Mashhad, Isfahan and Tabriz were considered as study cases. Nominal value of seismic risk for three main damage states, including minor, moderate and major were calculated.     

考虑进洞高程效应的黄土隧道洞口段地震动力响应特征研究

通过大型振动台模型试验并采用Midas-GTS有限元软件进行模拟计算,研究黄土隧道洞口段在地震作用下的动力响应特征、破坏过程和地震波在模型中的传递规律,分析影响黄土隧道洞口段地震动力响应的主要因素。结果表明:边坡沿弧形开裂面的垮塌受坡脚剪切和坡顶拉裂的共同作用;边坡会对其卓越频率内的地震波产生明显放大效应,且在1/2坡高以上放大效应出现饱和现象;隧道临空面是影响隧道洞口段地震动力响应的主要因素。考虑进洞高程效应时隧道洞口段抗震设防长度可取距洞口5倍洞径范围。振动台模型试验与数值计算在位移、加速度、应力三个响应特征上吻合较好,证明二者结果合理可靠。研究成果可为隧道工程设计和地下结构抗震理论研究提供有益参考。     

Simplified longitudinal seismic response of tunnels linings subjected to surface waves

This paper presents an engineering approach for analysing the longitudinal behaviour of tunnels subjected to earthquakes. The tunnel is modelled as a Timoshenko beam connected to the far soil by means of continuous elastic support (Winkler model). Seismic free-field inputs, such as those caused by surface waves travelling parallel to the tunnel axis, were imposed at the base of the springs of the Winkler model, generating bending moments and shear forces on the cross-sections of the tunnel. Closed-form expressions of the tunnel displacements, shear forces, and bending moments were determined at any tunnel section in terms of the seismic excitation, tunnel geometry and material properties, and subgrade reaction modulus of the soil. A dimensional analysis was carried out to ascertain directly the maximum tunnel displacement, bending moment, and shear force.     

青海门源M6.9地震典型隧道破坏特征分析与启示

地震引起的断层强烈错断是造成隧道等地下结构严重破坏的重要原因。以2022年青海门源6.9级地震中左旋走滑逆断层错动造成的隧道震害为调查基础,对左旋走滑逆断层错动下的震害特征及震害成因进行研究分析,主要得到如下结论：(1)左旋走滑逆断层造成大梁隧道线位严重错动,水平最大偏移约1.78 m,竖向最大抬升约0.68 m;(2)震害主要集中在断层影响范围内,其中隧道受破坏严重段约350 m,占隧道全长的5.33%,受破坏较严重段分别位于严重段大里程侧402 m和小里程侧646 m范围内,占隧道全长的15.96%,其余段落震害总体轻微;(3)施工缝、仰拱填充层等部位对强震较为敏感,震害表现突出。此次研究通过对震害特征分析得到的有益启示可为同类工程抗震设计提供参考与指导。     

Condensed hyperelements method of non-vertical consistent boundaries for wave propagation analysis in irregular media

The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an analysis of 2D anti- plane problems （Love waves） and 2D in-plane problems （Rayleigh waves） in the frequency domain in media consisting of a near-field irregular and a far-field regular part. The near field part may contain structures and its boundaries with the far-field can be of any shape. In this study, the irregular boundaries of the near-field are treated as consistent boundaries, extending the concept of Lysmer＇s vertical consistent boundaries. The presented technique is called the Condensed Hyperelements Method （CHM）. In this method, the irregular boundary is limited to a vertical boundary at each end that is a consistent boundary at the far-field side. Between the two ends, the medium is discretized with hyperelements. Using static condensation, the stiffness matrix of the far-field is derived for the nodes on the irregular boundary. Examples of the application of the CHM illustrate its excellent accuracy and efficiency.     

Seismic ground amplification induced by box-shaped tunnels

The growing use of underground structures, specifically to facilitate urban transportation, highlights the need to scrutinize the effects of such spaces on the seismic ground response as well as the surrounding buildings. In this regard, the seismic ground amplification variations in the vicinity of single and twin box-shaped tunnels subjected to SV waves have been investigated by the finite difference method. To evaluate the effects, generalizable dimensionless diagrams based on the results of parametric numerical analysis considering factors such as variations in the tunnels’ depth, the distances between the tunnels, tunnel lining flexibility, and input wave frequency, have been presented. In addition, to assess the effects of underground box-shaped tunnels on the response spectrum of the ground surface, seven selected accelerograms have been matched based on a specific design spectrum for the stiff soil condition of Eurocode 8 (CEN, 2006). The results underline the significant amplification effect of the box-shaped tunnels on the ground motions, specifically in the case of horizontal twin tunnels, which should be given more attention in current seismic design practices for surface structures.

     

Antiplane SH-deformations near a surface rigid foundation above a subsurface rigid circular tunnel

The problem on the dynamic response of a rigid embedded foundation in the presence of an underground rigid tunnel and subjected to excitation of incident anti-plane SH waves is analyzed. By using the exact analytical solution for the two-dimensional SH-wave propagation in and around both the surface rigid foundation and subsurface rigid tunnel, those aspects of the resulting ground motions that are of special interest and importance for seismic resistant design in earthquake analyses have been examined. The computed amplitudes of the resulting periodic ground motions display a very complicated wave-interference between the surface foundation and underground tunnel that lead to observed standing wave patterns, together with abrupt changes in the wave amplitudes and large amplification of the incident motions. Supported by: National Science Foundation grant CMS 97-14859     

Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations, a longitudinal integral response deformation method classified as a practical approach is proposed in this paper. The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well. When applying the proposed method, the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads. Then, the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation. Afterwards, the critical longitudinal seismic responses of the tunnel are obtained. The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing, determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-ofplane and in-plane waves. The results show that the proposed method has a clear concept with high accuracy and simple progress. Meanwhile, this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure. Therefore, the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.     

隧道与联络通道连接处地震响应分析

联络通道是长距离盾构隧道结构中不可缺少的部分,常设置于两条隧道之间,用于逃生、防火及排水等。与此同时,联络通道与隧道的连接处构造复杂,空间效应明显。在地下结构截面突变处,在地震荷载作用下易产生应力集中,造成结构的破坏,从而带来不可估量的震害。基于有限差分软件FLAC^3D,以天津的典型粉质黏土为例,建立双线并行隧道及联络通道的三维模型,对场地施加正弦波,分析隧道与联络通道连接处的应力和变形情况,并探讨隧道结构埋深、联络通道的直径和长度等对连接处地震响应的影响。基于Fish语言,建立能模拟不同地震波入射方向有限差分模型,计算表明不同地震波入射方向对结构连接处受力具有显著影响。