Analytical Solution for Modeling Discharge into a Tunnel Drilled in a Heterogeneous Unconfined Aquifer

Predicting transient inflow rates into a tunnel is an important issue faced by hydrogeologists. Most existing analytical solutions overestimate the initial discharge due to the assumption that drilling was instantaneous over the entire tunnel length. In addition, they assume a homogeneous system. An alternative model was recently developed for tunnels intersecting heterogeneous formations, but its application was reduced to the case of confined flow to deep tunnels in weakly diffusive aquifers. In this paper, we adapt existing analytical solutions for drainage systems to the specific case of a tunnel progressively drilled in a highly diffusive heterogeneous unconfined aquifer. The case of a tunnel overlying an impervious layer is analytically solved by applying the superposition principle, while the case of a tunnel constructed some distance above an impervious layer is solved by discretizing the tunnel length into subsectors. Both models can simulate transient discharge into a tunnel drilled at various speeds through a heterogeneous unconfined aquifer, and allow the prediction of discharge rates in shallow tunnels located in highly diffusive aquifers. We successfully applied this approach to a tunnel in heterogeneous volcanic rock.     

Scattering of plane SH waves by a circular- arc hill with a circular tunnel

IntroductionEarthquakedamageinvestigationsandtheoreticalanalysesshowthatahillamplifiesincidentwavestremendouslyduetomulti-reflectionofthewaveswithinthehill;notabledynamicstressconcentrationisobservedonwallofatunnel(Pao,Mow,1973;Lee,Trifunac,1979).Therefore,itmaybeassumedthattheexistenceofatunnelinahillmighthavegreateramplificationeffectonthegroundmotionnearby,andthedynamicstressconcentrationofthetunnelinthehillmightbemorenotable.Itiscommonthattherailwaysorhighwaysarethroughahilloramountainwi…     

A power flow analysis of a double-deck circular tunnel embedded in a full-space

The purpose of the present investigation is to obtain the mean power flow radiated by a double-deck circular tunnel and compares it to the one radiated by a simple circular tunnel. To achieve this, a harmonic line load is applied on the interior floor of the first one and at the bottom of the second one. For the double-deck tunnel, a new analytical model based on the receptance method is developed. The proposed model describes the dynamics of the interior floor using the thin plate theory and considers the Pipe in Pipe (PiP) model to describe the tunnel and soil coupled system. Plain strain conditions are assumed for both systems and conservative coupling is considered between them. Numerical results show significant differences between the power flow radiated by both tunnels, with the one radiated by the double-deck tunnel reaching much higher values. The effect of modifying the flexural rigidity of the interior floor is also presented.     

A comparison of two numerical models for the prediction of vibrations from underground railway traffic

Two prediction models for calculating vibration from underground railways are developed: the pipe-in-pipe model and the coupled periodic finite element–boundary element (FE–BE) model.The pipe-in-pipe model is a semi-analytical three-dimensional model that accounts for the dynamic interaction between the track, the tunnel and the soil. The continuum theory of elasticity in cylindrical coordinates is used to model two concentric pipes: an inner pipe to represent the tunnel wall and an outer pipe to represent the surrounding soil. The tunnel and soil are coupled accounting for equilibrium of stresses and compatibility of displacements at the tunnel–soil interface. This method assumes that the tunnel is invariant in the longitudinal direction and the problem is formulated in the frequency–wavenumber domain using a Fourier transformation. A track, formulated as an Euler–Bernoulli beam, is then coupled to this model. Results are transformed to the space domain using the inverse Fourier transform.The coupled periodic FE–BE model is based on a subdomain formulation, where a boundary element method is used for the soil and a finite element method for the tunnel. The Craig–Bampton substructuring technique is used to efficiently incorporate the track in the tunnel. The periodicity of the tunnel is exploited using the Floquet transformation to formulate the track–tunnel–soil interaction problem in the frequency–wavenumber domain and to compute the wave field radiated into the soil.An invariant concrete tunnel, embedded in a homogeneous full space is analyzed using both approaches. The pipe-in-pipe model offers an exact solution to this problem, which is used to validate the coupled periodic FE–BE model. The free field response due to a harmonic load in the tunnel is predicted and results obtained with both models are compared. The advantages and limitations of both models are highlighted. The coupled periodic FE–BE model has a greater potential as it can account for the complex periodic geometry of the tunnel and the layering in a soil medium. The effect of coupling a floating slab to the tunnel–soil system is also studied with both models by calculating the insertion gain.     

The safety distance of a tunnel under-traversing a slope body with a landslide-prone zone

At present, substantial scientific research achievements have been made in the research on landslide occurrence, movement mechanism, mitigation measures, and structural stability during tunnel excavation. However, the interaction mechanism of a tunnel under-traversing a slope body with potential landslides is still not well understood. Based on the field data provided by previous investigations in the study area, six sets of 1:100 laboratory experiment model tests were conducted to study the stability of the landslide-prone zone of the slope body with an under-traversing tunnel. The selected distances between the tunnel and the sliding surface are 1.5, 3, and 5 times of the tunnel diameter, respectively. The experiment results show the interaction between the landslide-prone zone and the tunnel, elucidating the effect of potential landslides during the tunnel excavation process and the reaction of the landslide slip on the tunnel structure. Several conclusions are obtained: ① During the process of tunnel excavation, the vertical displacement of the tunnel vault decreases with the increase of the buried depth. ② The vertical displacement of the sliding surface increases with the increase of the buried depth of the tunnel. The horizontal displacement of sliding surface decreases with the increase of the buried depth. ③ After the occurrence of a rainfall-induced landslide, the vertical displacement of the tunnel vault in the 1.5-diameter-distance case is 57.29% greater than that in the 3.0-dismeter-distance case.④ For a two-cave tunnel, it is suggested that the cave farther from the landslide toe should be firstly excavated since it may generate less structural deformation.     

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

基于粘性-滑移模型模拟隧道衬砌和围岩之间的接触状态,采用间接边界积分方程法求解弹性半空间中隧道衬砌对平面P波的散射,着重考察了地表位移放大和衬砌动应力集中效应。结果表明:接触滑移边界的刚度系数和粘度系数对隧道衬砌的动应力分布影响较大,滑移刚度较小时,共振频率段动应力集中效果更加显著;随着粘度系数的增大,衬砌内部环向应力幅值逐渐减小。另外,界面刚度系数和粘度系数对隧道衬砌动力反应的影响程度也受控于入射频率和角度。     

A Simple Model for the Movement of Fire Smoke in a Confined Tunnel

Fires in tunnels are unfortunately frequent occurrences often with tragic outcomes. A recent example is the fire on the funicular train at the ski resort in Kaprun (Austria), which caused nearly 160 deaths. Design engineers and risk analysts require knowledge of the fluid dynamics of the fire and smoke movement to answer questions such as how much oxygen can access and feed the fire, and what concentration of smoke will the people be exposed to. As an example in the Austrian accident the geometry was a long tunnel with fire doors closed at one end, and with a fire initiated near the closed (lower) end. The hot smoke from the fire is a source of buoyancy; the smoke reaches the ceiling of the tunnel, and then develops along the ceiling as a wall-bounded plume. The motion of the smoke is driven by a buoyancy force, but at the same time, mechanisms of turbulent heat and mass transfer act as a brake to this motion. In this paper we present how a generic model describing a semi-enclosed buoyancy-driven flow can be interpreted and used in the modelling of fire smoke movement in a confined tunnel. A consideration of the net pollutant volume flux through the tunnel leads to predictions for the variation of concentrations along the tunnel. The smoke concentrations near the fire smoke source scale linearly with the length of the tunnel, with higher concentrations at the lower section of the tunnel, as could be expected. Similarly the concentration of oxygen making its way through to the fire source decreases linearly with the length of the tunnel. A lower bound estimate of the smoke residence time can be obtained based on smoke concentration predictions from the model.     

水域隧道地震响应分析

本文基于Biot动力固结理论和弹性动力学理论,考虑海床（土壤）的两相性、黏弹性人工边界及流（水）-固耦合作用,建立了隧道-土-流体相互作用的力学模型,讨论了P波作用下有无水的情况以及水深、水域隧道埋深、海床土性质和地震波入射角等因素对隧道及其周围海床应力的影响。结果表明:隧道周围海床土的孔隙水压力和隧道内应力随着水深的增加而增加;地震波特性和海床土特性对隧道的内应力和海床土的孔隙水压力均有较大的影响;海床土的渗透性和隧道埋深对隧道的内应力影响较小,而对隧道周围海床土的孔隙水压力影响较大;地震动的入射角对隧道的内应力和隧道附近土层的孔隙水压力均有较大影响。      

不同强度岩石中开挖圆形巷道的局部化过程模拟

利用FLAC模拟了不同粘聚力条件下圆形巷道的局部化过程。为了模拟巷道开挖,利用编写的F ISH函数删除巷道内部的单元。岩石服从莫尔库仑剪破坏与拉破坏复合的破坏准则,破坏之后呈现应变软化-理想塑性行为。文中模拟分为3步：首先,将静水压力施加在模型上,直到达到静力平衡状态;然后,利用编写的F ISH函数开挖巷道;最后,计算重新开始,直到达到静力平衡状态或者塑性流动状态。模拟结果表明,随着粘聚力的降低,巷道围岩的破坏模式首先由孔壁附近零星单元的破坏向4个对称的小V形坑式剪切破坏转变,然后由包含若干小V形坑的大V形坑式剪切破坏向巷道全断面的破坏转变。前三者破坏发生后,巷道围岩仍然能保持稳定。与最大塑性拉伸应变相比,最大剪切应变增量、最大塑性剪切应变要高得多;最大剪切应变增量、最大塑性剪切应变相差不大;随着粘聚力的增加,三者均越来越小。     

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.     

强震作用下铁路隧道横通道交叉结构抗震措施研究

依托四川茂县跃龙门铁路隧道工程,以主线单线隧道与横通道正交结构为研究对象,通过ABAQUS建立有限元分析模型。选取El-Centro地震波数据,通过应用扩展有限元理论,对横通道与主隧道交叉结构在最不利地震条件下的裂损进行研究,并提出减震层结合柔性接头的抗震措施。研究分析得到:减震层结合柔性接头的设置减小并抑制了交叉结构隧道在强震作用下的开裂范围。柔性接头的设置阻止了纵向裂缝的扩展,在交叉口处中部设置环向柔性接头能完全阻止交叉部位拱顶的裂缝生成;在初期支护和二次衬砌之间设置减震层,给予衬砌更大变形空间,使二次衬砌不易受初期支护变形受力影响而开裂。     

Groundborne vibrations due to trains in tunnels

An analytical procedure is presented for determining groundborne vibrations in buildings due to subway trains. The procedure involves a finite element idealization of the subway-soil-structure interaction problem, using an analytical model for the train loading spectrum at the tunnel invert. Both direct fixation and floating slab track support systems are considered. The train model is verified using the measurements of rail velocities. The proposed procedure is applied to the case of a four-storey podium block enclosing twin double-box subways within the confines of its ribbed wall foundations. The severity of velocity response levels of the building, in relation to vibration standards, is also considered.     

任意圆弧形凸起地形中隧洞对入射平面SH波的影响

借助辅助函数的思想， 采用波函数展开法给出了圆弧形凸起地形中隧洞对入射平面SH波影响问题的一个解析解．数值结果表明，凸起地形中隧洞的存在以及隧洞大小，对凸起地形表面运动，以及凸起地形中的隧洞的动应力集中均具有显著影响．      

On Inflow to a Tunnel in a Fractured Double-Porosity Aquifer

Inflow to a tunnel is a great public concern and is closely related to groundwater hydrology, geotechnical engineering, and mining engineering, among other disciplines. Rapid computation of inflow to a tunnel provides a timely means for quickly assessing the inflow discharge, thus is critical for safe operation of tunnels. Dewatering of tunnels is another engineering practice that should be planned. In this study, an analytical solution of the inflow to a tunnel in a fractured unconfined aquifer is obtained. The solution takes into account either the spherical or slab-shaped matrix block and the unsteady state interporosity flow. The instantaneous drainage water table and anisotropic hydraulic conductivities of the fractures network are also considered. Both uniform flux and uniform head boundary condition are considered to simulate the constant head boundary condition in the tunnel. The effects of the hydraulic parameters of the fractured aquifer on the inflow variation of the tunnel are explored. The application of the presented solution to obtain the optimum location and discharge of the well to minimize the inflow to a tunnel is illustrated.     

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.     

Seismic response of a cut‐and‐cover tunnel isolated by polymer material

An effective method for the seismic retrofitting of the sidewalls of cut‐and‐cover tunnels has not yet been established. Thus, a new method of seismic retrofitting for cut‐and‐cover tunnels, called the ‘polymer isolation method’, is developed here. In this method, thin walls made of polymer materials, called ‘isolation walls’, are inserted between the ground and the sidewalls of a tunnel. We demonstrate the effectiveness of the proposed method in reducing the seismic response of tunnels by using some numerical simulations. It is found that the proposed method depends on the thickness of the soil cover over the tunnel and the ratio of the stiffness between the soil and the structure. Furthermore, a simple chart is proposed for convenience to represent the applicability of the polymer isolation method to the design of seismic retrofits for cut‐and‐cover tunnels. Although this particular chart has been obtained through a limited case, some other typical cases in which the chart can also be implemented for special conditions are addressed, and the applicability and the limitations of this chart are suggested for possible conditions of the ground and of tunnel structures. Copyright © 2012 John Wiley & Sons, Ltd.     

门源MS6.9地震中大梁隧道地震动响应分析

2022年1月8日,青海省门源县发生M_S6.9地震,造成震中附近的兰新高铁大梁隧道受损,导致高铁长时停运。文章通过建立二维平面应变模型,加载双向门源波进行动力时程分析,得到了大梁隧道的地震动响应结果,并对模型在震后的受力变形及震害特征进行详细分析。结果表明：在门源波双向加载下,大梁隧道的地震动响应受水平地震荷载影响很大;沿着y轴正向,隧道的截面形状对纵向位移和加速度的地震动响应有加强作用;拱顶处地震动响应最大,其竖向及横向地震动响应加速度分别为5.206 4 m/s²、4.534 8 m/s²,竖向及横向位移分别为7.070 9 cm、0.641 5 cm;拱底处地震动响应最小,其竖向及横向地震动响应加速度分别为3.287 6 m/s²、4.511 2 m/s²,竖向及横向位移分别为4.851 6 cm、0.625 2 cm;拱肩、拱脚处存在明显的应力集中现象,拱顶、拱底、拱肩及拱脚处内力的受力形式发生变化,但是衬砌应力和内力的极值均发生在拱腰及拱脚处,说明拱腰及拱脚处为震害严...     

地震动非一致性对隧道动力响应的影响分析

针对隧道的抗震安全性,借助有限元软件平台对其地震时程响应进行非线性有限元分析。利用弹性模型考虑混凝土隧道在循环荷载作用下的拉、压应力-应变关系,同时对土体采用MohrCoulomb模型,选用人工边界作为边界条件,以人工合成的多点地震加速度时程作为地震动输入,分别考虑一致输入、行波效应、相干效应及行波加相干效应对隧道的影响。分析结果表明,与一致激励的计算结果相比,非一致地震激励会显著增加隧道结构的内力和位移响应,从而对隧道抗震产生不利影响。研究结论可为长隧道结构的抗震设计和分析提供科学依据。     

双洞八车道大断面隧道地震动力响应数值分析

为研究双洞八车道超大断面隧道在地震力作用下的动力响应特征,以平潭综合实验区牛寨山隧道为工程背景,建立双洞八车道隧道的三维有限元数值计算模型。采用时程分析方法,在模型底部输入水平向地震动荷载,计算隧道结构在地震动荷载作用下的响应,包括位移、加速度及应力的变化。结果表明:最大水平和竖向位移出现在拱顶处,南线浅埋隧道整体呈剪切响应;隧道最大水平加速度出现在南线隧道拱顶偏左处,最大垂直加速度出现在南线隧道拱顶偏右处,南线隧道洞口由于浅埋,关键部位响应差较北线要大;南线的右拱肩埋深最浅,该部位拉应力最大,而北线拱顶的拉应力区最大,拱脚也出现明显的拉或压应力。建议在隧道洞口段的拱顶、拱脚及埋深最浅的部位应加强抗震设防。