Analytical stress and displacement due to twin tunneling in an elastic semi‐infinite ground subjected to surcharge loads

The construction of twin tunnels at shallow depth has become increasingly common in urban areas. In general, twin tunnels are usually near each other, in which the interaction between tunnels is too significant to be ignored on their stability. The equivalent arbitrarily distributed loads imposed on ground surface were considered in this study, and a new analytical approach was provided to efficiently predict the elastic stresses and displacements around the twin tunnels. The interaction between 2 tunnels of different radii with various arrangements was taken into account in the analysis. We used the Schwartz alternating method in this study to reduce the twin‐tunnel problem to a series of problems where only 1 tunnel was contained in half‐plane. The convergent and highly accurate analytical solutions were achieved by superposing the solutions of the reduced single‐tunnel problems. The analytical solutions were then verified by the good agreement between analytical and numerical results. Furthermore, by the comparison on initial plastic zone and surface settlement between analytical solution and numerical/measured results of elastoplastic cases, it was proven that the analytical solution can accurately predict the initial plastic zone and its propagation direction and can qualitatively provide the reliable ground settlements. A parametric study was finally performed to investigate the influence of locations of surcharge load and the tunnel arrangement on the ground stresses and displacements. The new solution proposed in this study provides an insight into the interaction of shallow twin tunnels under surcharge loads, and it can be used as an alternative approach for the preliminary design of future shallow tunnels excavated in rock or medium/stiff clay.     

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.     

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。     

Timoshenko beam solution for the response of existing tunnels because of tunneling underneath

An analytical solution for the deflection and internal forces of an existing tunnel because of tunneling underneath is presented. The existing tunnel is modeled as a Timoshenko beam resting on a Winkler foundation, which takes into account the contribution of shear deformation to the total deflection of the existing tunnel. The validity of the analytical solution is verified by a centrifuge test, and the merit of this analytical method is confirmed by comparison with the conventional Euler–Bernoulli beam model. Influential factors on the behavior of the existing tunnel are investigated by consideration of the variations of subgrade modulus, ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Results show that the proposed analytical method is a valid and effective method to evaluate shearing‐induced deformation in existing tunnels with large diameters. Results also show that the pattern and the amplitude of the response of the existing tunnel are affected largely by ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Copyright © 2015 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.     

考虑椭圆化地层变形影响的浅埋隧道弹性解

研究了浅埋隧道周围地层最终变形的计算问题,提出了考虑椭圆化变形影响的计算模型和浅埋隧道位移边界条件,并利用Airy应力函数得到了该问题弹性解析解。在此基础上,通过算例分析了椭圆化变形对竖向位移和水平位移的影响。结果表明,椭圆化变形对水平位移的影响远大于竖向位移。     

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.     

Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary

For slope condition of ground surface, the asymmetrical deformation about the vertical center line and the horizontal center line of the tunnel cross section can be formed. A unified displacement function expressed by the Fourier series is presented to express the asymmetrical deformation of the tunnel cross section. Five basic deformation modes corresponding to the expansion order 2 are a complete deformation mode to reflect deformation behaviors of the tunnel cross section under slope boundary. Such this complete displacement mode is implemented into the complex variable solution for analytically predicting tunneling-induced ground deformation under slope boundary. All of these analytical solutions are verified by good agreements of the comparison between the analytical solutions and finite element method results. A parameter study is carried out to investigate the influence of deformation modes of the tunnel cross section, geometrical conditions of the tunnel and the slope angle, and “Buoyancy effect” on the displacement field. Finally, the proposed method is consistent with measured data of the Hejie tunnel in China qualitatively. The presented solution can provide a simplified indication for evaluating the ground deformation under slope condition of ground surface.     

偏压、错台小间距隧道施工位移场动态模拟分析

采用三维非线性有限元法,对偏压、错台的浅埋小间距隧道在不同开挖顺序下的动态施工过程进行了模拟。通过对位移场的分析,研究了其施工力学特性。由于两隧洞之间的相互影响,并行小间距隧道对围岩的扰动程度大于两独立隧道作用的叠加;相互影响对中间岩柱的作用最为明显,对洞周、地表影响相对较弱。两洞开挖顺序不同,最终位移场的分布规律相同,但量值上存在一定差异。研究给出了在偏压、错台情况下的两洞开挖的合理顺序。     

Investigation of surface and subsurface displacements due to multiple tunnels excavation in urban area

Underground structures are currently widely used and are built as urbanism develops. The interactions between perpendicularly crossing and parallel tunnels in the Tehran region are investigated by using a full three-dimensional (3D) finite difference analysis with elastic-plastic material models. Special attention is paid to the effect of subsequent tunneling on the support system, i.e., the shotcrete lining and rock bolts of the existing tunnel. Eventually, as the tunnels are excavated at certain levels, the interaction between the tunnels will certainly have a significant influence on both stress distribution and consequently deformations. Since multilayer tunneling is a three-dimensional phenomenon in nature, 3D numerical solutions must be utilized for analyzing effect of perpendicularly crossing tunnels at various levels. As Tohid twin tunnels and Line 7 pass beneath the Line 4 metro tunnel, changes in stress distribution, deformations, and surface settlements are studied for various conditions and the results are presented in this paper. Consequently, it is shown that there is a significant interaction between tunnels that necessitate certain preventive measures to maintain a stable tunneling operation.     

大断面小净距隧道围岩稳定性数值分析 大断面小净距隧道围岩稳定性数值分析

结合小净距隧道工程特点,分别建立不同跨度小净距隧道有限元计算模型,对隧道施工过程力学特征及围岩稳定性进行对比分析,以研究三车道大断面小净距隧道区别于两车道小净距隧道的基本力学特征。分析结果表明,对应不同隧道跨度、隧道净距和围岩级别对隧道施工过程中围岩稳定性的影响有显著差别,相同隧道净距条件下,三车道小净距隧道围岩应力状态比两车道隧道差,净距越小,差别越大,而围岩质量越低,差别也越显著;另外,在质量较差的围岩中,大断面小净距隧道围岩受力最薄弱部位主要集中在岩柱雁形部,而两车道小净距隧道则为岩柱中部。研究结果可为大断面小净距隧道的设计、施工提供有益的参考。     

Unsupported advance length in tunnels constructed using New Austrian Tunnelling Method and ground surface settlement

Tunnels constructed using New Austrian Tunnelling Method (NATM) are always based on certain round (unsupported) advance lengths, after which, the temporary lining is placed. The settlement of the ground surface resulting from such construction is of high significance in design and practice. The existing data in this respect, however, is scarce. It is the aim of this paper to propose a semi‐analytical procedure based on three‐dimensional finite element analyses to predict the maximum surface settlement of the ground in NATM tunnels under different combinations of tunnel diameter, overburden depth, round length and soil and lining properties. The comparison of the results with three case histories of real tunnels reveals reasonable accuracy of the present solution. Copyright © 2012 John Wiley & Sons, Ltd.     

Centrifuge modelling of twin-tunnelling induced ground movements in loess strata

A great concern for the safety of large cross-section tunnels, which are being or to be built in the loess strata of China, is attracted. Generally, loess is a multi-phase porous medium and develops complex stress and strain variation while executing a tunnel project. Another problem is that the soil surrounding both tunnel arches is subjected to a complex loading due to the double excavation. To obtain an in-depth knowledge of the mechanism of tunnel deformation induced by the twin-tunnelling, we conducted comprehensive centrifuge tests, which can simulate and reproduce strictly the action process of twin-tunnelling. Through the model tests, the response of twin-tunnelling on loess stratum deformation was obtained. The investigations showed that with the increase of tunnel spacing, the stratum deformation distribution near the vault changes from a single-peak V shape to a double-peak W shape. Additionally, the height of the stratum pressure arch effect increases significantly. The settlement of the preceding tunnel is slightly larger than that of the latter tunnel, and the twin-tunnelling effect gradually decreases with the increase of tunnel spacing. Through comparative analysis of the different combinations of tunnel spacing and tunnel interval, the interaction between two tunnels with different spacing and interval during tunnelling was investigated, further optimizing the reasonable tunnel spacing and construction steps, as well as providing reference for tunnel route selection in the loess strata.     

近间距大直径公路盾构隧道施工相互影响分析

结合一外径11.36 m、近距段净距4.0～5.7 m的上海某公路盾构隧道土体和管片位移及应变的监测成果,就后建隧道施工对先建隧道的影响进行了分析。分析结果表明,盾构的推进使隧道间土体朝掘进方向和已建隧道方向侧移,沿深度的最大侧移量发生在隧道中心深度以上0.2D（D为隧道外径）左右;盾尾到达及管片脱出注浆工况阶段,隧道间土体及已建隧道临近面上拱腰处的侧移量达到最大;已建隧道管片呈现上部内敛、下部外扩的变形形态,且临近后建隧道面变形值较大。     

Interaction of longitudinal surface settlements for twin tunnels in shallow and soft soils: the case of Istanbul Metro

Increasing demands on infrastructures increases the attention on shallow soft ground tunneling methods in urbanized areas. Especially, in metro tunnel excavations, it is important to control the surface settlements observed before and after excavation, which may cause damage to surface structures. To solve this problem, earth pressure balance machines (EPBMs) have widely been used throughout the world. This study focuses on surface settlement measurements, the interaction of twin tunnel surface settlement, and the relationship between shield parameters and surface settlement for parallel tunnels using EPBM shields in clay and sand soils. In this study, the tunnels were excavated using two EPBMs. The tunnels were 6.5 m in diameter, as twin tubes with a 14 m distance from center to center. The EPBM in the first tube followed about 100 m behind the other tube. Segmental lining with 1.4 m of length was employed as a final support. The results from this study showed that (1) the most important parameters for the maximum surface settlements are the face pressure and backfill; (2) in twin tunnel excavation with EPBM for longitudinal profile, the settlement rate reached its peak value when the shield came to the monitoring section and this peak value continued until the shield passed the monitoring section; (3) every shield affected the other tunnel’s longitudinal surface settlement profile by approximately 35–36.8 %; (4) S _A, S _B and S _C values were found to be 38.0, 35.8 and 26.2 %, respectively for an EPBM, and (5) ensuring good construction quality is a very effective way to control face stability and minimize surface settlement.     

A hybridized numerical and regression method for estimating the minimum rock pillar width of twin circular tunnels

Twin tunnels can be used for many applications. Interaction between two tunnels is an important problem in tunnel engineering that should be studied specially. Numerical investigations are well adapted to field data and numerical methods can be used in design of rock pillar of twin circular tunnels. So far, no relationship has been provided to estimate the minimum stable rock pillar width. In this paper, the interaction between twin circular tunnels has been studied using 2D finite element analysis. To do this, a great number of twin tunnels were modeled in Phase2 software with different conditions of rock mass (RMR value) and depth of tunnel. Models were analyzed and minimum stable rock pillar width was determined. This process was repeated for three different ratios of K (ratio of horizontal stress to vertical stress, 0.5, 1, and 1.5). Finally, according to the linear and nonlinear regression methods, the best merit function was fitted to result of numerical analysis. Then, new approximate formula was proposed to estimate the minimum rock pillar width according to RMR value and depth of twin circular tunnels with different K values. The formulae are very accurate (coefficient of correlation equals to minimum 0.96) that can be used for estimating the minimum rock pillar width of twin circular tunnels.     

上海长江隧道过民房段地表变位预测及控制研究

复杂环境条件下大型泥水盾构施工诱发的地表变位的预测与控制是亟待深入研究的重要课题。结合上海长江隧道超大型泥水盾构推进工程,对其上行线隧道穿越民房段前试验段的地表沉降监测数据进行了分析,并采用随机介质理论预测了2条隧道单独及共同施工引起的横向地表变形和位移,据以制定了民房段施工地表变位控制措施。实例分析证明,预测方法和控制措施具有科学性、有效性,有一定的实用价值。     

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.     

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.     

岩溶区隧道围岩--支护体系稳定性研究

岩溶是地下水地质作用的过程和结果，是隧道建设面临的不良地质现象之一。正在建设中的某高速公路隧道出口段岩溶地质作用强烈，溶隙、孔洞发育，且受构造变形及后期淋滤溶蚀作用强烈，力学强度低，岩性复杂。其角砾状粘土岩和水云母粘土岩多已泥化成粘土，遇水易膨胀。岩溶区隧道围岩——支护体系的稳定性是该隧道建设面临的主要问题。文章结合隧道施工过程中的围岩变形监控量测和三维弹塑性有限元数值仿真模拟对隧道围岩——支护体系的稳定性进行了研究。围岩水平收敛和拱顶下沉位移及速率变化特性表明，在监测时段内隧道围岩无趋于稳定的迹象。施工动态力学数值仿真模拟表明，在初期支护条件下，围岩出现了较大范围的塑性破坏区，两隧道之间(间距45．0m)围岩破坏接近度达到0．70，最大竖向位移达到3．0mm，表明隧道全断面施工时，两隧道相互作用影响程度较大。为确保隧道围岩——支护体系的稳定，选择合理的施工方法，制定切实可行的支护方案提供了信息。