Simulation of Stress Distribution around Tunnels and Interaction between Tunnels Using an Elasto–plastic Model

This article presents a computer simulation of stress distribution around tunnels and interaction between tunnels using an elasto-plastic model. A finite element method using ANSYS software has been used for the analyses of one and two tunnels at different overburden depths with different separating distances between the tunnels. The results of numerical analyses indicate that stress distribution and stress concentration around the tunnels vary with the overburden depths. It is found that the coefficients of stress concentration for elasto-plastic medium are smaller than those for elastic one by 1.9%. Furthermore, the interaction between the two tunnels rapidly decreases with the increase of separation distance between them. In addition, for quantitatively describing the interaction between the two tunnels, a critical separation distance is introduced. The critical separation distances between the two tunnels at different overburden depths are 8 m, 12 m, and 14 m respectively. This fact is very important and essential for the design of mining tunnels and to ensure safety in tunnel engineering.     

Effects of Rock Bolting on Stress Distribution around Tunnel Using the Elastoplastic Model

INTRODUCTIONThe stability of underground structures duringand after excavation is the most i mportant factor fordesigners because any kind of collapse may destroylarge parts of a finished tunnel,thereby causing ma-jor repairs and ti me loss.To avoid this problem,rock bolts are widely used as ani mportant support el-ement.These are economical,have a short installa-tion ti me,and provide reinforcement to maintain theintegrity of the stressed rock.The effect of the bearing capacity of rock b…     

平面P波入射下浅埋平行双洞隧道注浆加固减震机制

地震动作用下小净距隧道双洞之间存在动力放大效应,依托某强震区小净距盾构隧道工程,基于傅里叶贝塞尔级数展开法,给出了平面P波垂直入射下地下半空间弹性介质中圆形双洞复合式衬砌洞室动应力解析解,深入研究了洞室间距、隧道全环注浆加固参数对衬砌动应力集中的影响。研究表明：洞室间距对衬砌的动应力有显著影响,随着洞室之间距离减小,左右洞室衬砌动应力明显放大;2.5倍洞径可以作为双洞洞室动力临界净距,当洞室间距小于2.5倍洞径时,应进行抗减震设计;注浆全环加固隧道周边土体,可以明显降低衬砌动应力,随着注浆加固区土体刚度增加,衬砌动应力幅值减小;结合工程实际,建议注浆加固区厚度取0.5倍的洞室半径值,加固区岩体和围岩剪切波速度之比取1.2。     

Finite element analyses of two-tier geosynthetic-reinforced soil walls: Comparison involving centrifuge tests and limit equilibrium results

This study presents the procedure and results of the finite element (FE) analyses of a series of centrifuge tests on geosynthetic-reinforced soil (GRS) two-tier wall models with various offset distances. The objectives of this study were to evaluate the applicability of FE for analyzing GRS two-tier walls with various offset distances and to investigate the performance and behavior of GRS two-tier walls in various stress states. The FE simulations were first verified according to the centrifuge test results by comparing the locations of failure surfaces. The FE results were then used to investigate the effective overburden pressure, mobilization and distribution of reinforcement tensile loads, and horizontal deformation at the wall faces. The interaction between two tiers was investigated based on the FE results, which were also used to examine the modeling assumption of reinforcement tensile loads in limit equilibrium (LE) analysis and to evaluate the design methods in current design guidelines. This study demonstrated favorable agreement between FE and the centrifuge model in locating the failure surface. The FE results indicated that as the offset distance increased, the reinforcement tensile load and wall deformation decreased in both the upper and lower tiers, suggesting the attenuation of interaction between the two tiers. The maximum tensile loads of all reinforcement layers at the wall failure predicted using FE analysis and LE method assuming uniform distribution of reinforced tensile loads were comparable. Compared with the FE results, the Federal Highway Administration (FHWA) design guidelines are conservative in determining the effect of overburden pressure, required tensile strength, location of maximum tension line (for designing the reinforcement length), and the critical offset distance. Furthermore, the FHWA design guidelines do not account for the influence of the lower tier on the upper tier that was observed in this study.     

Rock Mass Stability Investigation Around Tunnels in an Underground Mine in USA

Stability and deformation of rock masses around tunnels in underground mines play significant roles on the safety and efficient exploitation of the ore body. Therefore, understanding of geomechanical behavior around underground excavations is important and necessary. In this study, a three-dimensional numerical model was built and stress analyses were performed by using 3DEC software for an underground mine in USA using the available information on stratigraphy, geological structures and mechanical properties of rock masses and discontinuities. Investigations were conducted to study the effect of the lateral stress ratio (K₀), material constitutive models, boundary conditions and rock support system on the stability of rock masses around the tunnels. Results of the stress, displacement, failure zone, accumulated plastic shear strain and post-failure cohesion distributions were obtained for these cases. Finally, comparisons of the deformation were made between the field deformation measurements and numerical simulations.     

A Top Pilot Tunnel Preconditioning Method for the Prevention of Extremely Intense Rockbursts in Deep Tunnels Excavated by TBMs

The headrace tunnels at the Jinping II Hydropower Station cross the Jinping Mountain with a maximum overburden depth of 2,525 m, where 80% of the strata along the tunnels consist of marble. A number of extremely intense rockbursts occurred during the excavation of the auxiliary tunnels and the drainage tunnel. In particular, a tunnel boring machine (TBM) was destroyed by an extremely intense rockburst in a 7.2-m-diameter drainage tunnel. Two of the four subsequent 12.4-m-diameter headrace tunnels will be excavated with larger size TBMs, where a high risk of extremely intense rockbursts exists. Herein, a top pilot tunnel preconditioning method is proposed to minimize this risk, in which a drilling and blasting method is first recommended for the top pilot tunnel excavation and support, and then the TBM excavation of the main tunnel is conducted. In order to evaluate the mechanical effectiveness of this method, numerical simulation analyses using the failure approaching index, energy release rate, and excess shear stress indices are carried out. Its construction feasibility is discussed as well. Moreover, a microseismic monitoring technique is used in the experimental tunnel section for the real-time monitoring of the microseismic activities of the rock mass in TBM excavation and for assessing the effect of the top pilot tunnel excavation in reducing the risk of rockbursts. This method is applied to two tunnel sections prone to extremely intense rockbursts and leads to a reduction in the risk of rockbursts in TBM excavation.     

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。     

拉张盆地不同埋深复合地层中隧道围岩变形破坏数值模拟研究

不同埋深的软硬岩层叠置复合地层变形破坏形式复杂而使得软岩大变形和硬岩岩爆位置相关关系不够明确。在拉张盆地中自重应力为主,侧压系数一般较小且多数在1.0以内。本文以在水平和铅垂叠置复合地层中TBM开挖圆形断面隧道为例,采用有限差分程序FLAC3D对拉张盆地中不同埋深、不同叠置型式复合地层中TBM开挖后的三维弹塑性位移变形、主应力和塑性破坏分布变化特征展开数值模拟研究。模拟结果表明,围岩变形主要发生在软岩层地层中,埋深超过800 m后沿隧道轴向软岩大变形藕节状分段开始显现;随埋深增加,硬岩稳定性变差,顶拱位移增加尤其明显;随埋深增加,软岩和硬岩地层之间主应力差异变小,硬岩中储能明显;埋深越大塑性区分布范围越大;埋深较小时岩层以拉张破坏为主,埋深较大时以剪切破坏为主,两种状态的转换埋深(临界深度)约为800 m。由此对拉张盆地中深埋界限值给予了理论验证。     

基于弹性力学的诱导劈裂注浆机制分析

针对隧道内水平超前劈裂注浆中浆液劈裂方向随机性的问题,提出一种诱导劈裂注浆方法,可以控制和改变浆液的劈裂方向。首先,基于弹性力学理论及其基本假定,分析竖向地应力大于水平地应力条件下对单一土层进行劈裂注浆时浆液沿竖向劈裂的力学机制,在此基础上探讨改变浆液劈裂方向为水平劈裂的必要性和诱导方法,并从应力集中的角度分析诱导劈裂注浆的力学机制;其次,采用有限元法研究注浆孔孔周劈裂方向控制点的应力随侧向压力系数和诱导孔与注浆孔间距变化而变化的情况,得出实现诱导劈裂注浆时两孔间距及侧向压力系数应满足的条件,并拟合两孔间距临界值的计算公式。结果表明：在离注浆孔上、下方4倍注浆孔径以内对称布设诱导孔,改变了注浆孔孔周劈裂方向控制点的应力场。当两孔间距小于实现诱导的临界距离值时,注浆孔孔周控制点的应力大小发生转换,浆液的劈裂方向发生改变,将沿水平方向劈裂。诱导孔与注浆孔间距的临界值会随着侧向压力系数的增大而逐渐增大。     

SRC rock mass classification of tunnels under high tectonic stress excavated in weak rocks

This paper describes the application of the SRC rockmass classification system to tunnels under high horizontal tectonic stress excavated in weak rocks. The analysis was performed on 25 tunnels in Spain and Italy, for which it was found that much heavier supports than those estimated by the RMR index were required. SRC and RMR indices and other relevant geomechanical data were obtained during the site investigation and construction stages. Data corresponding to in situ stress measurements, analysis of tectonic structures and instability problems arising during construction were used to asses the state of stress.

The relationship between tunnel section convergence and the SRC and RMR indices was also analysed. Support measurements based on SRC and RMR classification were compared with those actually used during construction. These analyses indicate that for most of the tunnels examined, supports estimated using the SRC were much closer to those actually installed than those predicted by the RMR index.

Based on the case histories presented, the factors mainly contributing to deformability and consequently to assessing support measurements were: high horizontal tectonic stress, low strength of rocks, overburden thickness and structural anisotropy related to tunnel axis orientation. According to these factors, the tunnels investigated were classified as three types. Tunnels classed as type I were those of low overburden thickness under high horizontal tectonic stress excavated in low strength rocks. The supports installed for these tunnels were much heavier than those predicted by the RMR index, being more in line with those indicated by the SRC index. The type II tunnels had thick overburdens and showed similar stress and strength conditions to the former. The supports installed were practically those foreseen by the SRC index, appreciably differing with respect to the RMR index. Finally, tunnels included in the type III class were those under low to moderate tectonics stress, irrespective of overburden thickness. These tunnels gave rise to RMR and SRC indices that provided acceptable results.     

Monitoring of Three-dimensional Additional Stress and Strain in Shield Segments of Former Tunnels in the Construction of Closely-Spaced Twin Tunnels

In recent years, with the development of urbanization, the construction of closely-spaced twin tunnels is becoming more and more common. How to ensure the safety of the former tunnel during the construction of the later tunnel has become the focus of the construction of closely-spaced twin tunnels. To study the safety of the former tunnel segment structure, this paper analyzed the field monitoring data of practical engineering (the section with the minimum separation (4.5 m) between the twin tunnels from Anyuanxi station to Chunshenhu station on the Suzhou Metro Line 4 in Jiangsu, China) and obtained the dynamic change law of additional stress and strain of the former tunnel segment under the influence of the construction of later tunnel. Based on this research, the following conclusions were drawn: (1) The maximum circumferential tensile stress on the segmental structures was shown to be 2.62 MPa at the horizontal position on Section S2 in the side adjacent to the later tunnel, which should be main monitored. (2) The maximum values of the vertical deformation and peripheral convergence of the segments were 16.21 and 17.39 mm, separately, both of which were less than two-thirds of the allowable deformation. Therefore, the shield tunnel deformations were within allowable limits. This research results can provide guidance for similar engineering.     

基于微震监测的深埋煤层顶板导水裂隙带发育特征

导水裂隙带发育高度是矿井水害预测的重要技术参数之一。以彬长矿区文家坡煤矿4103工作面为研究对象,利用井-地联合微震监测技术对顶板导水裂隙带发育特征进行研究。研究结果表明:深埋煤层开采时,微震事件超前工作面回采位置发育,超前影响角最大为35°,最小为28°;断层的存在降低了覆岩稳定性,相较于正常基岩,更易在回采影响下发生应力集中和破坏;断层加大了微震事件发生的超前距,而采空区则使微震事件的高密度区向其所在部位发生偏移,加剧覆岩破坏程度,增大导水裂隙带发育高度;垂向上,4103工作面监测区内的微震事件高密度区域主要集中在高程+400~+520 m,结合微震事件数量和能量分布特征,判定4103工作面垮落带发育高度为50 m,垮采比13.16,导水裂隙带发育高度为117 m,裂采比为30.79。该成果可为彬长矿区类似煤矿深埋煤层顶板导水裂隙带发育高度研究及顶板水防治提供重要依据。移动阅读      

陕南特长公路隧道水压致裂法地应力测量结果及工程地质意义分析

中国西部地区地势复杂,区域构造应力场各向异性显著,了解地区地壳应力状态是判断隧道设计阶段线路布设合理性的基础,也是预测隧道施工过程可能出现岩爆、断层滑动等其他工程灾害的重要参数。为了研究陕南特长高速公路隧道现今地应力状态,基于古仙洞隧道钻孔(ZK10钻孔)与化龙山隧道钻孔(ZK11钻孔)水压致裂地应力测量,获得了两隧道现今地应力分布特征。古仙洞和化龙山特长深埋隧道最大埋深处S_H值分别为13 MPa和22 MPa;古仙洞与化龙山隧道的应力关系分别为S_H>S_h>S_v和S_H>S_v>S_h,水平主应力起主导作用;S_H方向为近北西—北西西向,与区域现今构造活动背景基本一致,主要受秦岭造山带活动断裂影响。基于地应力测量结果、相关理论及判断依据认为:最大水平主应力方向与洞轴线夹角,有利于隧道围岩稳定,研究区内古仙洞与化龙山隧道的总体布置是合理的;采用岩石强度应力比法、陶振宇判据、Russenes判据和岩石应力强度比法综合判定研究区内两隧道不具备发生中等强度以上等级岩爆的可能;利用莫尔-库伦准则及拜尔定律,摩擦系数μ取0.6~1.0,对研究区内两隧道的现今地应力状态分析后发现,两隧道附近断裂带的地应力大小未达到地壳浅部断层产生滑动失稳的临界条件,处于较稳定的应力状态。      

紧邻多孔交叠隧道抗震性能研究

随着我国城市轨道交通建设的飞速发展,盾构隧道之间近距离相互穿越工程将会越来越多。武汉市轨道交通2号线与4号线在洪（洪山广场）中（中南路）区间为4孔紧邻交叠隧道。根据实际工程特点,将其简化为不同间距的4孔平行重叠和4孔垂直交叉隧道,分别建立其三维计算模型,分析了紧邻多孔交叠隧道的三维地震响应,其中考虑了不同地震波幅值、隧道间距、隧道空间位置、隧道管片横、纵向差异以及紧邻多孔盾构隧道间加固层的影响,从结构变形和受力两方面评价了其抗震性能。计算分析表明：（1）隧道间距对隧道地震响应影响不显著;（2）4孔垂直交叉隧道的抗震性能要优于4孔平行重叠隧道;（3）紧邻多孔交叠隧道具有良好的抗震性能,满足抗震要求。其研究成果可为今后类似工程的抗震初步设计提供参考。     

Numerical Analyses of the Influence of Blast-Induced Damaged Rock Around Shallow Tunnels in Brittle Rock

Most of the railway tunnels in Sweden are shallow-seated (<20 m of rock cover) and are located in hard brittle rock masses. The majority of these tunnels are excavated by drilling and blasting, which, consequently, result in the development of a blast-induced damaged zone around the tunnel boundary. Theoretically, the presence of this zone, with its reduced strength and stiffness, will affect the overall performance of the tunnel, as well as its construction and maintenance. The Swedish Railroad Administration, therefore, uses a set of guidelines based on peak particle velocity models and perimeter blasting to regulate the extent of damage due to blasting. However, the real effects of the damage caused by blasting around a shallow tunnel and their criticality to the overall performance of the tunnel are yet to be quantified and, therefore, remain the subject of research and investigation. This paper presents a numerical parametric study of blast-induced damage in rock. By varying the strength and stiffness of the blast-induced damaged zone and other relevant parameters, the near-field rock mass response was evaluated in terms of the effects on induced boundary stresses and ground deformation. The continuum method of numerical analysis was used. The input parameters, particularly those relating to strength and stiffness, were estimated using a systematic approach related to the fact that, at shallow depths, the stress and geologic conditions may be highly anisotropic. Due to the lack of data on the post-failure characteristics of the rock mass, the traditional Mohr–Coulomb yield criterion was assumed and used. The results clearly indicate that, as expected, the presence of the blast-induced damage zone does affect the behaviour of the boundary stresses and ground deformation. Potential failure types occurring around the tunnel boundary and their mechanisms have also been identified.     

覆盖层影响下典型地-井模型瞬变电磁法正演

地-井瞬变电磁法是用于地质找矿的有效方法之一,开展该方法的三维正演研究能对资料处理与解释提供帮助。在时间域有限差分算法的基础上,建立了三维地质模型和覆盖层模型,模拟了该模型下的地-井瞬变电磁响应;引入了参数EA,分析了方形低阻体和覆盖层的响应特征以及覆盖层影响因素。结果显示：低阻体位于发射场源下方时,其响应曲线呈现“双高一低”的极值特征,高峰值分别对应低阻体上下边界,低峰值对应低阻体中心;低阻体位于发射场源旁边时,其响应曲线呈现单极值特征,该特征与覆盖层响应特征相同。当覆盖层电阻率较低时,“趋肤效应”作用使覆盖层的响应强度强于低阻体;但当发射场源离钻孔足够远时,覆盖层影响可以忽略,低阻体响应强度更与覆盖层-低阻体电阻率的比值有关。孔中发射能有效降低覆盖层影响。     

Investigating the effects of lateral stress to vertical stress ratios and caverns shape on the cavern stability and sidewall displacements

Effects of lateral stress to vertical stress ratio on behavior of a cavern in various geomechanical and geometrical conditions were studied. Results indicated that the range of one to two lateral stress to vertical stress ratios was the best condition for cavern stability. The ranges causing tension and compressive failure were specified as well. Two-dimensional stability analyses were carried out by using Phase². Key point location on the cavern side wall was investigated and determined using an equation based on a large number of numerical analyses. Subsequently, in order to predict the elasto-plastic displacement and elastic displacement on a side wall key point, two equations were fitted based on various cavern cross sections considering four basic factors, i.e., rock deformation modulus, overburden depth of caverns, heights of the caverns, and the lateral stress to vertical stress ratio. The proposed equations were utilized to predict displacement at the key points of 10 projects subsequent to which the computation results were compared to in-site measuring results and back analysis results. Finally, using key point displacement as a stability factor, the effects of three different shapes of caverns including mushroom, horse shoe, and elliptical were investigated on cavern stability. The most optimum shape was elliptical in a vast range of lateral stress to vertical stress ratios; mushroom and horse shoe shapes were preferred in uniaxial stress fields concerning the rock quality.     

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     

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.     

Practical Estimate of Deformations and Stress Relief Factors for Deep Tunnels Supported by Shotcrete

Summary. Even though ground-support interaction in the vicinity of the tunnel face is a typical 3D problem, tunnel support design is usually based on simplified plane strain models, which are strongly dependent on the assumed degree of ground stress relief at the time of lining installation. The paper focuses on tunnels supported by shotcrete close to the face, where the interaction between the loading process and progressive hardening of the green shotcrete makes the problem time-dependent. A constitutive law characterized by the time-dependent stiffness and strength of the shotcrete is employed herein. The results of an extensive parametric study based on 3D axisymmetric models are presented in the form of non-dimensional design charts, which can provide guidance to a preliminary evaluation of convergences and support loadings. Moreover a strategy is proposed to enhance the capability of simplified design methods (2D models, Convergence-Confinement Method). This consists in a “guided estimate” of stress relief factors, which again is based on the results of 3D time-dependent analyses. Finally, by way of example, the proposed method is applied to two well-documented case-histories.