Lined Circular Tunnels in Elastic Transversely Anisotropic Rock at Depth

Closed-form solutions for displacements and stresses of both the liner and the rock are presented for a deep circular tunnel excavated in transversely anisotropic rock above or below the water table subjected to static or seismic loading. The solutions are obtained with the assumption of elastic response of rock and liner, tied contact between rock and liner, impermeable liner, plane strain conditions along the tunnel axis and simultaneous excavation, and liner installation. The liner of a tunnel placed below the water table must support, in addition to the rock stresses, the full water pressure, while a tunnel located above the water table must support only the rock pressures. The solutions presented for static loading show, however, that displacements and stresses of the liner and rock are the same when the tunnel is placed above or below the water table as long as the total far-field stresses are the same. With rapid loading, e.g. seismic loading, excess pore pressures may be generated in saturated rock, which induce a different response than that of a tunnel excavated in dry rock. The analyses indicate that stresses and displacements are more uniform when excess pore pressures are produced, which seems to indicate that pore pressure generation tends to reduce non-uniform response in anisotropic rock.     

Stresses around Pressure Tunnels with Semi-permeable Liners

Summary. The liner of a pressure tunnel needs to be designed such that it can withstand the loads from the ground, the internal pressure, and minimize the development of significant pore pressures at the liner-ground interface. Pore pressures behind the liner reduce the effective stresses in the ground immediately in contact with the liner and can ultimately produce loss of support from the ground. Deformations and loads of the liner are intimately connected to the interplay that exists between liner, ground, and pore pressures in the ground. A closed-form analytical solution has been derived that accounts for the inter-relation between liner, ground, and pore pressures. Elastic response of the liner and ground, and plane strain conditions at any cross-section of the tunnel are assumed. The solution shows that stresses in the ground depend on the following dimensionless factors: relative stiffness of the ground and liner, ground Poisson’s ratio, surface slope angle, coefficient of earth pressure at rest, relative tunnel depth, and magnitude of the pore pressure behind the liner relative to the internal pressure. The minimum ground effective tangential stresses at the ground-liner interface increase with the relative stiffness of the liner, with the coefficient of earth pressure at rest, and with tunnel depth. They decrease with increasing surface slope angle and pore pressures behind the liner. As leakage through the liner increases, the pore pressures in the ground increase. This results in a decrease of effective radial and tangential stresses in the ground while displacements and loads of the liner are relatively less affected.     

Radial Deformations Induced by Groundwater Flow on Deep Circular Tunnels

Summary. The magnitude and distribution of ground deformations around a tunnel are often monitored during construction and provide key information about ground-support interaction and ground behavior. Thus it is important to determine the effects of different parameters on ground deformations to accurately and effectively evaluate what contributes to ground and support behavior observed during excavation. This paper investigates one such relation: the effects of seepage on radial deformations. A number of numerical analyses have been conducted with the following assumptions: deep circular unsupported tunnel, elastic ground, isotropic far field stresses, dry ground or saturated ground with steady-state water seepage. The analyses cover a wide range of tunnel sizes, effective stresses, and pore pressures. Results from the numerical simulations confirm previous analytical solutions for normalized radial deformations behind the face (i.e. on the tunnel side of the face) of a tunnel excavated in dry ground, and have been used to propose a new analytical formulation for normalized radial displacements ahead and behind the tunnel face for both dry and saturated ground with water flow. Water seepage substantially increases the magnitude and distribution of the normalized radial deformations ahead of the face and at the tunnel face, but does not change much the displacement distribution behind the tunnel face.     

双洞隧道洞口段抗减震模型试验研究

为了解隧道衬砌在地震过程中的动态响应以及减震层在地震过程中对隧道及围岩边坡安全性能的影响,针对双洞隧道洞口段进行室内抗减震模型试验研究。模型试验按有（无）减震层分成2组进行对比。试验结果表明：(1) 设置减震层对围岩破坏的形式没有影响,只能在破坏程度上有所减轻;(2) 减震层的设置对模型中的动应力分布情况有较大影响,并能够在一定程度上减小作用在衬砌上的作用力;(3) 有错距的双洞隧道中,长里程隧道洞身在包含短里程隧道洞口的横截平面附近受力状态复杂,减震层的加入有利于减轻其破坏程度。     

马蹄形隧洞考虑支护滞后过程的应力分析

基于平面弹性复变函数中的保角变换方法,推导出带有衬砌的非圆形隧洞在原始地应力作用下的应力解析解。根据衬砌内边界的应力边界条件及围岩衬砌接触面上的应力和位移连续条件,获得求解围岩和衬砌解析函数的基本方程,计算了围岩和衬砌中的应力和位移。在求解过程中,考虑了支护滞后于开挖的力学过程,并认为围岩和衬砌之间紧密接触,不会相互分开和相对滑动。以马蹄形隧洞为例,获得了围岩开挖边界和衬砌内外边界的切向应力及围岩与衬砌接触面上的接触应力分布规律,并与ANSYS数值方法结果对比,算例表明两种方法的计算结果吻合很好。     

Mechanical Response of Lined and Unlined Heated Drifts

Summary Approximate relations are developed to determine the steady stresses and displacements that may develop in unlined and lined drifts heated above ambient, as representative of conditions in a nuclear waste repository. For a series of parallel, unlined drifts, radial convergence due solely to thermal effects is everywhere null at early-times; at late times it is a maximum inward at springline, and an equivalent maximum outward at crown and invert. Support pressures and hoop stresses are evaluated for a flexible liner placed in intimate contact with the drift wall, following excavation, where a full slip condition is applied at the drift-liner interface. For rock mass moduli of similar order to, or smaller than, the liner modulus, hoop stresses and support pressures are shown insensitive to rock mass parameters. Surprisingly, liner stresses are strongly controlled by liner modulus, liner Poisson ratio, liner thermal expansion coefficient, and instantaneous liner temperature, and only weakly by rock mass modulus. Response is shown independent of thermal expansion coefficient of the rock mass, and temperature distribution beyond the drift wall. The “misfit” expansion of the liner in the drift cavity controls liner stresses that rise linearly with the temperature of the liner, alone. Importantly, the results demonstrate the potential to control magnitudes of thermal stresses by the incorporation of compressible elements within the liner, or within the blocking or backfill behind the liner. Although the results are partly conditioned by the assumptions of a fully flexible liner and full slip conditions at the drift-liner interface, they serve to define the important parametric dependencies in the mechanical response of heated drifts.     

高水位隧道堵水限排围岩与支护相互作用分析

为了保护环境并尽可能降低衬砌结构所受的水压力,提出高水位山岭隧道应采取“以堵为主,限量排放”,即“堵水限排”的防排水设计原则。但对于堵水限排情况下衬砌结构的设计,目前尚没有规范可依,这是目前隧道设计施工亟待解决的问题。在隧道力学和渗流力学的基础上进行理论分析,研究渗流应力耦合作用下围岩的力学特性,利用特征曲线法分析了不同排放量下围岩与支护的相互作用,并与数值方法计算结果进行对比。计算结果表明：不同排水量下围岩特性曲线不同,支护阻力也不同,不同排水条件下围岩有效切向应力和有效径向应力的变化很明显,排水对围岩应力以及支护体系受力的影响是不容忽视的。另外,传统隧道设计方法在全排水时完全不考虑水的作用是不安全的。所得结论可为堵水限排衬砌结构设计提供理论依据。     

Visco-Plastic Behaviour around Advancing Tunnels in Squeezing Rock

Summary  The visco-plastic behaviour of rocks plays a relevant role in the tunnelling works, especially for deep tunnels subjected to large initial stresses for which squeezing conditions may develop. A rheological model is discussed that accounts for visco-elastic (primary) and visco-plastic (secondary) contributions to rock creep. The effects of tertiary creep are included in the model by way of a gradual mechanical damage governed by the cumulated visco-plastic strains. The parameters of the intact rock are first identified based on laboratory test results presented in the literature. Then, after scaling them to those of the rock mass, the potential applicability of the model is tested through axisymmetric and plane strain finite element analyses of the full face excavation of a deep circular tunnel. The results are discussed with particular reference to the short term redistribution of stresses around the opening and to its convergence. The analyses show the relevant influence of tertiary creep on the tunnel closure. In addition, those based on an axisymmetric scheme turn out to be crucial for the correct long term prediction of the interaction between the rock mass and the supporting structure of the opening.     

Elastic Solution for Deep Tunnels. Application to Excavation Damage Zone and Rockbolt Support

Summary  A new formulation is presented for deep circular tunnels in rock with cylindrical anisotropy. The formulation is an exact solution since it satisfies equilibrium, strain compatibility, and the anisotropic constitutive model. Complete solutions have been found for two scenarios: tunnel with excavation damage zone, and tunnel with rockbolt support. The solution is based on the assumption of a deep, circular tunnel in a medium with two homogeneous zones: an inner zone surrounding the tunnel, which is either isotropic or anisotropic, and an outer zone, for the remainder of the medium, which is isotropic. Plane strain conditions, elastic response of rock, rockbolts and support, and simultaneous excavation and support installation are also assumed. For tunnels surrounded by an excavation damage zone with reduced rock properties, the tangential stresses and the radial deformations at the tunnel wall are very sensitive to both the magnitude of stiffness reduction of the damaged rock and the size of the damaged zone. The effect of the rockbolts on the rock is approximated by treating the rockbolt-rock composite as a material with cylindrical anisotropy with stiffnesses related to the properties of the rock and rockbolts, and spacing of the rockbolts. Comparisons between the analytical solution and a numerical method show small differences and provide confidence in the approach suggested.     

Visualizing the effect of excavation rate on rock deformation and fracturing of tunnels using a transparent soft rock surrogate

One of the most important problems during tunneling in soft rock is deformation and fracturing of the rock during tunneling. The problem was successfully explored by using a transparent rock surrogate to simulate the behavior of soft rock, which permitted visualizing conditions within the rock. Synthetic soft rock was made using consolidated fused quartz saturated with a blend of two mineral oils that have the same refractive index as the quartz. The tunnel was simulated using a smooth aluminum tube and two tunneling methods representing machining and blasting were considered. Two observation planes made of seeding particles were pre-placed within the model and used to track soil movements and crack propagation. Images of both planes were captured simultaneously using two orthogonal cameras. Rock deformations were concentrated in the vicinity of the tunnel face, and deformation rates behind the tunnel face were significantly greater than those ahead of the face. However, deformation rates and patterns varied considerably depending on the excavation method/rate. Fracturing mechanisms exhibited similar differences, for machining deformations occurred higher above the crown and propagated toward the tunnel face. Conversely for blasting deformations sprang from the crown upwards. These observations can assist with numerical simulations and in planning tunnel support systems.

     

Analytical‐numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts

This paper presents an analytical‐numerical approach to obtain the distribution of stresses and deformations around a reinforced tunnel. The increase in the radial stress of the reinforced tunnel, based on the performance of a bolt, is modeled by a function, which its maximum value is in the vicinity of the bolt periphery and it exponentially decreases in the far distance from the bolt. On the basis of this approach, the shear stiffness between the bolt and the rock mass and the shear stress distribution around the bolt within the rock mass are also analytically obtained. The results are compared with those obtained by the assumption of ‘uniform increase of radial stress’ method, which is made by the previous studies. The analyses show when the bolts' spacing is large, the safety factor must be increased if the ‘uniform increase of radial stress’ method is used for the design. Finally, a procedure is introduced to calculate the non‐equal deformation of the rock mass between the bolts at any radius that can be useful to compute the bending moment in shotcrete layer in New Austrian Tunnelling Method (NATM) approach. Copyright © 2016 John Wiley & Sons, Ltd.     

节理岩体中双向八车道小净距隧道施工方案优化分析

结合福州国际机场高速公路2期工程魁岐2号双洞八车道特大断面小净距隧道工程,建立了离散元数值模拟分析模型,针对节理岩体中特大断面小净距隧道施工方案进行了优化分析。分别研究了双侧壁导坑法、CRD法和CD法3种施工方案下隧道拱顶下沉、中间岩柱水平位移、围岩水平位移和围岩塑性区的变化规律。基于研究成果,并结合魁岐2号特大断面小净距隧道现场实际情况,在该隧道进口Ⅴ级围岩段,将双侧壁导坑法变更为CRD法,顺利完成了施工,此施工方案的变更对降低施工成本、加快施工进度、缩短施工工期均起到了较好的作用。研究结果可为类似条件下特大断面小净距隧道的设计、施工提供借鉴与参考。     

Dynamic response to fluid extraction from a poroelastic half‐space

In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd.     

移动环形荷载作用下饱和土中圆形衬砌隧洞动力响应研究

基于Biot理论,研究了饱和土中带有衬砌的圆形隧洞在移动环形荷载作用下的动力响应。假定衬砌为弹性体,土体为饱和多孔介质,引入两类势函数来表示土体、孔隙水和衬砌的位移,使隧洞的控制方程解耦。结合边界条件及连续条件,通过傅立叶变换得到频率-波数域中衬砌和土体的应力、位移和孔隙水压力解答,最后用傅立叶积分逆变换得到时-空域中的数值解。计算并比较了3种隧洞模型（弹性土体隧洞、饱和土体隧洞和饱和土衬砌隧洞）的动力响应分析。数值分析结果说明：（1）移动荷载速度对3种隧洞动力响应均具有较大影响;（2）弹性土体隧洞和饱和土体隧洞的动力响应具有明显区别,所以在富水地区的隧洞动力响应中土体应该视为饱和土体;（3）衬砌对隧洞动力响应有较大影响,故隧洞的动力分析中不能忽略衬砌作用。     

Analytical Solutions for the Construction of Deeply Buried Circular Tunnels with Two Liners in Rheological Rock

The construction of underground tunnels is a time-dependent process. The states of stress and strain in the ground vary with time due to the construction process. Stress and strain variations are heavily dependent on the rheological behavior of the hosting rock mass. In this paper, analytical closed-form solutions are developed for the excavation of a circular tunnel supported by the construction of two elastic liners in a viscoelastic surrounding rock under a hydrostatic stress field. In the solutions, the stiffness and installation times of the liners are accounted for. To simulate realistically the process of tunnel excavation, a time-dependent excavation process is considered in the development of the solutions, assuming that the radius of the tunnel grows from zero until its final value according to a time-dependent function to be specified by the designers. The integral equations for the supporting pressures between rock and first liner are derived according to the boundary conditions for linear viscoelastic rocks (unified model). Then, explicit analytical expressions are obtained by considering either the Maxwell or the Boltzmann viscoelastic model for the rheology of the rock mass. Applications of the obtained solutions are illustrated using two examples, where the response in terms of displacements and stresses caused by various combinations of excavation rate, first and second liner installation times, and the rheological properties of the rock is illustrated.     

Effect of excavation stages on stress and pore pressure changes for an underground nuclear repository

This paper provides a brief overview of evolution of deformations, stresses, and pore pressures due to different excavation stages during construction of an URL. Excavation of a rockmass develops damage zone of finite width around the excavated zone which is associated with changes in permeability and affect the fluid flow mechanism. In this study, a coupled hydromechanical (HM) analysis for a water saturated porous rock mass has been done which is caused by sequential excavation and backfill of vertical disposal pit of an URL. For this purpose, an Atomic Energy of Canada Limited’s in-floor concept for a deep geologic repository suitable for Indian condition has been used. Changes in rock deformations, stresses, strains and mechanically induced pore pressure in an undrained condition, during excavation, as well as those caused by mechanically induced rock deformations after backfill of the disposal pit have been modeled. A three-dimensional finite difference tool FLAC^3D (Itasca Consulting Group Inc. FLAC-3D 1997) has been used for the analysis.     

Analytical and Numerical Study of the Mechanics of Rockbolt Reinforcement around Tunnels in Rock Masses

Summary  This paper addresses the problem of quantifying the mechanical contribution of rockbolts installed systematically around tunnels excavated in rock masses. The mechanical contribution referred to here is that of increased stress confinement and decreased tunnel convergences as compared with corresponding stresses and displacements obtained for non-reinforced tunnels. The problem is treated analytically first by presenting a closed-form solution for stress and displacement distributions around a circular tunnel excavated in elastic material and reinforced by grouted or anchored rockbolts. The analytical solution assumes that rockbolts are regularly spaced around the tunnel and that axi-symmetry conditions of geometry and loading apply. The results obtained with the closed-form solution are shown to be equivalent to the results of the same problem solved with traditional numerical methods. Based on the analytical and numerical results and by introducing dimensionless ratios that allow to quantify the increase of radial stresses and the decrease of radial displacements in the reinforced region of the tunnel, the paper shows that reinforcement can have a significant mechanical effect (i.e., increasing the confinement and decreasing the convergences) in tunnels excavated in rock masses of poor to very poor quality. The paper analyzes then the mechanical contribution of rockbolt reinforcement when the rock mass is assumed to behave elasto-plastically. For this case, it is shown that rockbolt reinforcement can also have a critical effect in controlling the extent of the plastic failure zone and the convergences of the tunnel. Correspondence: C. Carranza-Torres, Department of Civil Engineering, University of Minnesota, Duluth Campus, 1305 Ordean Court, Duluth, USA     

Tunnelling in squeezing rocks: Case histories

Summary Squeezing rock conditions have posed and continue to pose a major obstacle to the construction of tunnels through mountains, as experience dating back more than a century shows. The paper deals with the study of past experiences in the light of present geotechnical engineering knowledge. Many of the transalpine tunnels were constructed before geotechnical engineering had been developed, and the principles underlying squeezing were not yet understood. Also construction techniques have changed with time. By studying past experience in the light of our present knowledge in geotechnical engineering (rock and soil mechanics), one may gain more insight into the nature and causes of squeezing ground behaviour. Here, a number of older and newer case histories are summarised, providing substantial insight into the phenomenon of squeezing rock. Squeezing rock behaviour is influenced by rock type and structure. Usually, in squeezing zones the rock is strongly jointed and fractured and has low strength. Overburden has also a significant effect and squeezing behaviour may occur abruptly in a tunnel once a limiting overburden has been exceeded. Water pressures in strongly jointed and often crushed rock are important and so are the adopted construction procedures and sequences. A support of substantial structural strength may be necessary to prevent long-term deformations and to withstand increased loading on the tunnel liner from the rock mass surrounding the tunnel.     

Design criteria applied for the Lower Pressure Tunnel of the North Fork Stanislaus River Hydroelectric Project in California

Summary The application of various criteria and certain new approaches to design is illustrated by the example of the Lower Collierville Pressure Tunnel of the North Fork Stanislaus River Hydropower Project in California. With a maximum internal water pressure of 72 bar, Lower Collierville Tunnel will be, when commissioned in 1989, the highest stressed pressure tunnel in the world not situated in granitic rocks.The geological conditions and the results of the geotechnical investigations are described briefly. For the steel-lined portion of the tunnel, the approach for determining the bearing capacity of the rock mass and the load sharing between steel and rock is discussed. The required length of steel liner was determined on the basis of rock mechanical (hydraulic jacking) and rock hydraulic (seepage losses and extension of saturated zone due to seepage) criteria. The use of a new theory allows the effects of mechanical-hydraulic interaction to be taken into account. Finally the methods of estimating the expected water losses and the sealing effect of the consolidation grouting are described.     

隧道掘进拱部运动力学模型研究

将隧道上覆岩层简化为弹塑性双参数基础梁力学模型,分析研究了拱顶上覆岩层挠曲线微分方程和隧道围岩变形弹性基础梁挠曲线微分方程,探讨了隧道基础屈服区宽度R满足条件,得到了拱顶下沉速度的表达式,从理论上解释了隧道围岩变形问题,为开展隧道监控工作提供了依据。