An analytical solution for deforming twin‐parallel tunnels in an elastic half plane

The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.     

Analytical study of ground responses induced by the excavation of quasirectangular tunnels at shallow depths

The construction of quasirectangular tunnels at shallow depths is becoming increasingly common in urban areas to efficiently utilize underground space and reduce the need for backfilling. To clarify the mechanical mechanism of the stresses and displacements around the tunnels, this study proposes analytical solutions that precisely account for quasirectangular tunnel shapes, the ground surface, the tunnel depth, and the ground's elastic/viscoelastic properties. The Schwarz alternating method combined with complex variable theory is employed to derive the elastic solution, and convergent and highly accurate solutions are obtained by superposing the solutions in the alternating iterations. Based on the solution and the extended corresponding principle for the viscoelastic problem, the time-dependent analytical solutions for the displacement are obtained for the ground assuming any viscoelastic model. The analytical solutions agree well with the finite element method (FEM) numerical results for models that are completely consistent, and qualitatively agree with field data. Furthermore, based on the stress solution combined with the Mohr-Coulomb failure criterion, the predicted initial plastic zone and propagation directions around the tunnels are qualitatively consistent with those determined by the limit analysis. A parametric study is performed to investigate the influences of the rectangular/quasirectangular tunnel shape, burial depth, and supporting pressure on the ground stresses and displacements.     

软岩浅埋隧道施工工法比选

目前在高速公路软岩浅埋隧道施工中均不同程度地出现了围岩坍塌、地表产生大面积沉降等问题。广福隧道某浅埋段,地质条件复杂,断面大、岩性差,受构造影响比较严重,而且顶板厚度比较薄,易发生坍塌、冒顶现象。为确保浅埋段隧道的施工安全,尽量减少隧道开挖引起的地层沉降和围岩变形,采用FLAC3D对4种施工工法全断面法、短台阶法、单侧壁导坑法和双侧壁导坑法进行模拟,分析了4种工法下地表沉降、隧道围岩周边位移和塑性区的变化特点,选出一种技术可行、经济合理的施工工法,得出一些有意义的结论。     

偏压小间距公路隧道施工的三维数值模拟

以云南平年隧道为工程背景,采用MARC三维非线性有限元法程序,对新奥法修建的偏压、错台、浅埋小间距隧道模拟了先行隧道不同超前距离情况下的动态施工过程。掌子面距离的变化对洞室的横向位移的影响大于竖向位移,且对于左洞更为显著;随着左右洞掌子面距离的增大,洞周位移、中间岩柱位移均减小,但部分范围内地表沉降值有所增大,局部区域受力、变形恶化。     

Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading

The stability of circular tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels/openings in cohesive-frictional soils. In this study, continuous loading is applied to the ground surface, and both smooth and rough interface conditions are modelled. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical use, the results are presented in the form of dimensionless stability charts with the actual tunnel stability numbers being closely bracketed from above and below. As an additional check on the solutions, upper-bound rigid-block mechanisms have been developed and the predicted collapse loads from these are compared with those from finite element limit analysis. Finally, an expression that approximates the ultimate surcharge load has been devised which is convenient for use by practising engineers.     

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     

Elasto‐plastic seepage‐induced stresses due to tunneling

When tunneling is carried out beneath the groundwater table, hydraulic boundary is altered, resulting in seepage entering into the tunnel. The development of flow into the tunnel induces seepage stresses in the ground and the lining is subjected to additional loads. This can often cause fine particles to move, which clog the filter resulting in the long‐term hydraulic deterioration of the drainage system. However, the effect of seepage force is generally not considered in the analysis of tunnel. While several elastic solutions have been proposed by assuming seepage in an elastic medium, stress solutions have not been considered for the seepage force in a porous elasto‐plastic medium. This paper documents a study that investigates the stress behavior, caused by seepage, of a tunnel in an elasto‐plastic ground and its effects on the tunnel and ground. New elasto‐plastic solutions that adopt the Mohr–Coulomb failure criterion are proposed for a circular tunnel under radial flow conditions. A simple solution based on the hydraulic gradient obtained from a numerical parametric study is also proposed for practical use. It should be noted that the simple equation is useful for acquiring additional insight into a problem on a tunnel under drainage, because only a minimal computational effort is needed and considerable economic benefits can be gained by using it in the preliminary stage of tunnel design. The proposed equations were partly validated by numerical analysis, and their applicability is illustrated and discussed using an example problem. Comments on the tunnel analysis are also provided. Copyright © 2010 John Wiley & Sons, Ltd.     

A new approach for estimating the transverse surface settlement curve for twin tunnels in shallow and soft soils

Increasing demand on infrastructures has led to increased attention to shallow soft ground tunneling methods in urbanized areas. Especially in metro tunnel excavations, it is important to control the surface settlements which are observed before and after excavation, which may cause damage to surface structures. Unlike motorway, sewage and other infrastructure tunnels, metro tunnels generally have to be excavated as twin tunnels and must have a larger diameter. Metro tunnels also have shallow depth. Due to their shallow depth, metro tunnels generally have been constructed in weak rocks or weak soils in cities. The construction of twin tunnels will generate ground movements which have the potential to cause damage to existing surface and subsurface structures. To solve this settlement problem, experts have used the Earth pressure balance machine (EPBM) and the slurry balance machine. In such excavations, especially in twin tunnels, the main challenges for constructers are estimating the maximum surface settlement, controlling the interaction of transverse surface settlement and shaping the settlement curve. Incorrect estimation of these parameters can lead to significant problems above the tunnels and in nearby structures. This paper focuses on surface settlement measurements, on the interaction of twin tunnel transverse surface settlement and on the relationship between shield parameters and transverse surface settlement for parallel tunnels using EPBM shields in clay and sand soils in shallow depth. Also, a new equation is proposed for estimating the transverse settlement curve of twin tunnels. The results from this proposed equation are compared with the results of field observations. The transverse settlement curve values obtained from the proposed equation have good agreement with the actual results for the Otogar–Kirazli metro case studies.     

Stresses and displacements in an elastic mass due to distributed loading by discretization technique

Numerical solutions have been obtained for stresses and displacements in a linear elastic half space due to distributed loads of circular, rectangular and elliptical shapes. The technique primarily involves use of a multi-dimensional numerical integration technique to integrate point load solutions over the distributed loading after discretizing the area into a finite number of elements. Both uniform vertical and shear loads have been considered as well as vertical conical loads and inward shear loads. The technique evolved facilitates the determination of stresses and displacements by the use of mini-computers and is neither as tedious and cumbersome as the use of tables and charts nor as costly as FEM solutions. A detailed comparison has been presented between the results obtained by the numerical solutions and those of the existing analytical solutions wherever they are available. It is found that the agreement between the two is within one per cent for displacements at all depths for the different cases studied. The matching is also good in the case of stresses, except at shallow depths.     

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.     

近间距双线大直径泥水盾构施工相互影响研究

对上海复兴东路越江公路隧道--近间距双线盾构隧道同向施工时相互影响的现场监测进行了研究。首先简要介绍了工程背景及其概况,然后介绍了为研究近间距盾构隧道相互影响而布设的监测项目,包括深层土体水平位移、地表沉降以及深层土体沉降、北线隧道三维位移、圆周变形、接缝宽度、北线隧道所受水土压力、北线隧道衬砌内力和土体中的超孔隙水压力。对监测数据进行了详细研究,得到了后建隧道推进时对地面沉降、深层土体位移变化、超孔隙水压力产生和消散、先建隧道衬砌位移、变形、内力的影响规律。从现场监测的分析结果来看,后进隧道对周围土体和先建隧道的影响是十分明显的。研究结果可以为大直径近间距双线推进的越江盾构隧道的设计和施工提供更加科学的指导。     

考虑围岩软化特性和应力释放的圆形隧道黏弹塑性解

将围岩的塑性应变软化特性引入到考虑应力释放的圆形隧道黏弹塑性解中,并且在围岩的软化和残余强度阶段考虑围岩的塑性体积膨胀特性,提出了考虑塑性软化以及塑性体积膨胀和围岩应力释放的圆形隧道弹塑性解。当软化系数k = ∞、膨胀系数h = s时,该解转化为黏弹-脆塑性解;当k = 0、h = s时,则转化为黏弹-理想塑性解,进一步令h = s = 1,则转化为不考虑塑性体积膨胀的黏弹-理想塑性解。通过具体实例计算,分析了掌子面与研究断面间距x、围岩的软化系数k、膨胀系数h和s、支护结构等对围岩塑性区、破碎区半径和变形的影响。当开挖面与研究断面间距x在(0~4)D（D为隧道直径）范围内,随着时间增加塑性圈和破碎区迅速增大;超过4D,塑性区和破碎区半径增量逐渐变小,趋于稳定值;围岩中包含塑性区和破碎区时,二者半径的比值只取决于围岩的性质,与支护结构无关,但支护结构可以限制塑性区及破碎区的范围;考虑应变软化和塑性体积膨胀时,围岩径向位移和塑性区及破碎区半径均大于不考虑应变软化和塑性体积膨胀时的结果;软化系数k增大,围岩位移、塑性区和破碎区半径增加、塑性区半径和破碎区半径之间的比值变小。得到的结果对于隧道工程设计和施工具有一定的指导性和参考价值。     

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.     

A numerical Round Robin on tunnels under seismic actions

Although the seismic behaviour of shallow circular tunnels in soft ground is generally safer than aboveground structures, some tunnels were recently damaged during earthquakes. In some cases, damage was associated with strong ground shaking and site amplification, which increased the stress level in the tunnel lining. Pseudo-static and simplified dynamic analyses enable to assess transient changes in internal forces during shaking. Nevertheless, experimental evidences of permanent changes in internal loads in the tunnel lining would suggest that a full dynamic analysis including plastic soil behaviour should be performed when modelling the dynamic interaction between the tunnel and the ground. While sophisticated numerical methods can be used to predict seismic internal forces on tunnel structures during earthquakes, the accuracy of their predictions should be validated against field measurements, but the latter are seldom available. A series of centrifuge tests were therefore carried out at the University of Cambridge (UK) on tunnel models in sand, in the framework of a research project funded by the Italian Civil Protection Department. A numerical Round Robin on Tunnel Tests was later promoted among some research groups to predict the observed behaviour by means of numerical modelling. In this paper, the main results of five selected numerical predictions are summarized and compared with the experimental results.     

An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

活动性断裂带错动下隧道纵向响应的解析解

震害调研表明，活动性断裂带区域的隧道灾害最为严重。针对错动作用下穿越活动性断裂带隧道的纵向响应进行了研究，推导了隧道纵向力学响应的解析解并进行了验证。考虑断裂破碎带围岩力学性质较差且处于错动变形的主要影响区，将隧道沿纵向进行分区，包括错动影响区、过渡影响区和非影响区。采用Pasternak双参数弹性地基梁，假定不同分区的地基参数和计算模式不同，建立了满足变形和内力连续的隧道纵向力学解析模型并进行了求解。解析计算结果与数值模拟结果、室内试验数据基本一致，验证了解析解的正确性。结果表明：错动作用下，活动性断裂带区域的隧道内力和变形发生了显著变化；隧道纵向挠曲变形与错动方向一致，但在断裂带与上下盘交界区域发生了反向的挠曲；在正断层错动下，纵向弯矩在断裂带与上下盘交界区域达到最大值，且上、下盘区域的隧道拱顶分别出现受拉和受压区域；断裂带区域内的剪力远大于其他区域，且受到较大弯矩，隧道结构易发生破坏。上述计算结果与实际调研结果相一致，表明了提出的解析计算方法可用于活动性断裂带错动下的隧道纵向响应分析。最后，针对地基系数和断裂带宽度两个关键参数进行了敏感性分析，得到了有益规律，可为该类区域的隧道设计和施工提供技术支撑。     

Tunnel stability analysis during construction using a neuro‐fuzzy system

This paper presents an alternative strategy to evaluate the stability of tunnels during the design and construction stages based on a hybrid system, composed by neural, neuro‐fuzzy and analytical solutions. A prototype of this system is designed using a database formed by 261 cases, 45 real and the rest synthetic. This system is capable of reproducing the displacements induced at the periphery of the tunnel before and after support installation. The stability of the excavation process is evaluated using a criterion that considers dimensionless parameters based on the shear strength of the media, the induced deformation level in the ground, the plastic radii and the advance of excavation without support. The efficiency and validity of the prototype is verified with two examples of actual tunnels, one included in the database used to train the system and the other not included. The results of both examples show a better approximation than other commonly used techniques. Copyright © 2005 John Wiley & Sons, Ltd.     

Improving the existing roadway tunnels capacity by adding new tunnels—a structural approach

The roadway tunnel is considered a good solution for the success of modern roadway networks. It can help to overcome possible traffic congestion and considerably reduce journey time. The continuous growth of traffic volumes leads to increase congestion and decrease safety. This leads to the need for extra tunnel space. The extra tunnel space can be achieved either by the widening of the existing tunnel or by adding a new one. The choice of the suitable method is dependent on many factors like tunnels alignment, site conditions, construction method, tunnel operation, risk assessment…etc. The current research investigates the second alternative through a specific case study as an example. The method comprises adding two new tunnels to an existing twin roadway tunnels. The investigated problem considers the new tunnels to be added vertically or horizontally. The influence of the new tunnel construction on the existing tunnels is investigated considering both the variation of relative position and spacing distance in a parametric study context. Several numerical models are employed to check the construction sequence and the tunnelling safety. These models are used to evaluate the induced stresses in surrounding ground for two different soil types, straining actions in tunnels’ liner and deformations of both ground and liner. The result demonstration shows how to find out the minimum practical and safe spacing distance between the driven new tunnels and the existing ones without the need for the relatively expensive soil strengthening techniques.     

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.     

A new closed‐form solution for analysis of unlined pressure tunnels under seepage forces

In this study, a simplified analytical closed‐form solution, considering plane strain and axial symmetry conditions, for analysis of a circular pressure tunnel excavated underwater table, is developed. The method accounts for the seepage forces with the steady‐state flow and is based on the generalized effective stress law. To examine the effect of pore pressure variations and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. The proposed method can be applied for analysis and design of pressure tunnels. Illustrative examples are given to demonstrate the performance of the proposed solution and also to examine the effect of seepage forces on the stability of tunnels. The simplified analytical solution derived in this study is compared with numerical analyses. It is concluded that the classic solutions (Lame's thick‐walled solution), considering the internal pressure as a mechanical load applied to the tunnel surface, are not applicable to pervious media and can result in an unsafe design. Copyright © 2012 John Wiley & Sons, Ltd.