System Reliability Assessment for a Rock Tunnel with Multiple Failure Modes

This paper presents a practical procedure for assessing the system reliability of a rock tunnel. Three failure modes, namely, inadequate support capacity, excessive tunnel convergence, and insufficient rockbolt length, are considered and investigated using a deterministic model of ground-support interaction analysis based on the convergence–confinement method (CCM). The failure probability of each failure mode is evaluated from the first-order reliability method (FORM) and the response surface method (RSM) via an iterative procedure. The system failure probability bounds are estimated using the bimodal bounds approach suggested by Ditlevsen (1979), based on the reliability index and design point inferred from the FORM. The proposed approach is illustrated with an example of a circular rock tunnel. The computed system failure probability bounds compare favorably with those generated from Monte Carlo simulations. The results show that the relative importance of different failure modes to the system reliability of the tunnel mainly depends on the timing of support installation relative to the advancing tunnel face. It is also shown that reliability indices based on the second-order reliability method (SORM) can be used to achieve more accurate bounds on the system failure probability for nonlinear limit state surfaces. The system reliability-based design for shotcrete thickness is also demonstrated.     

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

For tunnel constructed by New Austrian Tunnelling Method, the crown is the upper part of tunnel section, constructed during excavation process and supported by shotcrete. The stability of the crown has great influence on the safety of tunnel itself and the buildings above, which correlates, among others, with geometrical setup of tunnel and material properties of shotcrete and soil/rock. In this paper, aiming at analyzing the stability of shotcrete supported crown, a recently presented numerical method discontinuity layout optimization is adopted, which introduces a great amount of potential discontinuities cross over one another and provides a wide search space for efficient upper limit analysis. In the analysis, a well‐established hydration model of cementitious material is implemented for accounting the hydration of shotcrete. Then assumptions based on convergence‐confinement method are used for accounting the 3‐dimensional effect in 2‐dimensional analysis, finally providing time‐space–dependent assessments of stability of shotcrete supported crown.     

隧道围岩稳定性正算反演分析研究——以厦门海底隧道穿越风化深槽施工安全监控为例介绍

为了降低海底隧道施工风险,确保隧道施工顺利穿越海底几处风化深槽和风化囊区域,解决难以获得隧道围岩力学参数的技术难题,采用位移反分析方法建立了动态反演预测模型;作为比较,还简单介绍了弹塑性反演的一种全局优化方法。根据隧道典型断面实际监控量测的围岩拱顶沉降量和周边收敛位移量,结合先行服务隧道揭露的水文地质情况,进行优化反演分析,得到该类围岩初期支护后的等效弹性模量和等效侧压力系数。在相应的同类地质条件下,对后续将开挖的左、右主洞围岩采用边界元法进行正演数值计算,使之能为主洞施工方案比选以及支护设计参数调整与修正提供定量依据,做到信息化动态设计与施工。工程实例分析表明,利用正算反演分析法得出的围岩等效力学参数是可靠的,可据此对类似地质条件下主隧道围岩进行正演计算分析,预测主洞围岩的变形破坏模式,判断其围岩稳定性。位移反分析法是隧道施工变形理论预测分析与工程实际相联系的有效平台,为工程设计施工技术决策提供了一种切实有效的途径。     

A system of monitoring and dimensioning tunnel support

Summary In this paper a general numerical approach is proposed for the identification of loads acting on tunnel linings made by shotcrete, as a temporary lining, and concrete as a permanent one so as to form a system of monitoring and dimensioning these linings. This method requires a set of in situ displacement measurements of shotcrete layer for back calculation, and the constitutive relationship of the structural materials which are shotcrete, and concrete here is assumed to be linear elastic. The advantage of this method is that it avoids those complicated characteristics of rock masses and the loads from back calculation can reflect the combinative effects of rock surrounding the tunnel. An example was demonstrated for this method.     

软弱围岩隧道取消系统锚杆的现场试验研究

在软弱围岩隧道中,提出初期支护结构由钢架+喷射混凝土+钢筋网+锁脚锚杆+纵向连接筋组成,即取消系统锚杆用钢架联结处的锁脚锚杆代替。以包家山隧道为依托工程,采用现场试验的方法,选取2个试验段,进行锁脚锚杆取代系统锚杆后,有、无拱部锚杆的对比试验研究。对比试验的内容包括：隧道初期支护的净空收敛、围岩压力、钢架应力、喷射混凝土应力、锚杆轴力和纵向连接筋应力等。研究结果表明：2个试验段初期支护变形趋于稳定,结构受力安全,说明取消系统锚杆不影响初期支护结构的安全与稳定;拱部锚杆有受拉,也有受压,但受力都不大,最大拉应力仅为钢材极限强度的11.8%,其支护作用不明显;锁脚锚杆大部分受拉,最大值达到191 MPa,钢架支护作用明显,在支护体系中发挥着重要作用。取消系统锚杆减少了施工工序,降低了工程造价,缩短了工序循环时间,有利于及早封闭围岩以形成完整的支护结构。经济价值和社会效益显著。     

Experiences from the planning,construction and supporting of a road tunnel subjected to heavy rockbursting

Summary A 5360 m long road tunnel along a fjord with mountains rising steeply up to 1500 meters above sea level has recently been completed in Norway. 3 km of the tunnel was subjected to rockbursting caused by high and anisotropic stresses in the Precambrian gneisses. During the construction it was necessary to install 15 000 rock-bolts. Steelfibre reinforced shotcrete was successfylly applied for the first time to help stabilize the spalling rock. Supporting measures were only needed for the half of the tunnel closest to the fjord. 2600 m³ shotcrete was used.The paper outlines the preinvestigations and the design approach used for tunnels subjected to high and anisotropic stresses, and gives information about the construction and the support works carried out. A tunnel mapping system is described together with a classification of rockbursting activity in tunnels. Stresses in the rock were calculated by the use of finite element models and measured with doorstopper cells and the CSIR three-dimensional gauge. Comparisons of calculated and measured stresses are carried out.Rockbursting activity as observed along the tunnel is related to the estimated and observed stresses as well as to the properties of the rocks. Simple classification systems are used to correlate the results. Experiences from the use of the support are given.     

复杂条件下隧道断面形状和支护参数优化

通过有限差分法（FLAC3D）数值计算和现场试验对马蹄形断面和大曲率边墙、似圆形断面形式下隧道的支护受力和围岩变形特征进行了对比分析,得出采用似圆形断面可以有效地控制围岩的变形量和变形速率,尤其是水平收敛变形;现场变形量测时的丢失位移所占总位移比例较大,其中下台阶丢失位移比例最大;通过现场试验,对不同支护刚度下围岩压力、锚杆受力、钢架、混凝土应力以及二次衬砌分担的围岩压力和模筑混凝土受力情况进行分析,结合洞室变形的现场量测,得出二次衬砌接触压力及分担围岩压力比呈现出随着初支刚度增大而增大的规律,并综合确定了板岩段合理的支护参数。该结论对在构造应力发育的软岩地区修筑隧道提供了有益的工程经验     

An empirical method for design of grouted bolts in rock tunnels based on the Geological Strength Index (GSI)

The procedure presented in this paper has been developed for the design of grouted rock bolts in rock tunnels during preliminary design stage. The proposed approach provides a step-by-step procedure to set up a series of practical guidelines for optimum pattern of rock bolting in a variety of rock mass qualities. For this purpose, a new formula for the estimation of the rock load (support pressure) is recommended. Due to its wide-spread acceptance in the field of rock engineering, the Geological Strength Index (GSI) is adopted in support pressure equation. For poor and very poor rock mass where the GSI < 27, the use of Modified-GSI is, instead, recommended. The supporting action is assumed to be provided by rock bolts carrying a total load defined by the rock load height. The mechanism of bolting is assumed to rely on roof arch forming and suspension principle. Integrated with support pressure function, the bolt density parameter is modified in order to provide an optimized bolt pattern for any shape of tunnel. The modified bolt density can also be used in analysis of a reinforced tunnel in terms of Ground Reaction Curve (GRC) in such a way as to evaluate the reinforced rock mass and the tunnel convergence. By doing so, the effectiveness of the bolting pattern is well evaluated. The proposed approach based on GSI is believed to overcome constrains and limitations of existing empirical bolt design methods based on RMR or Q-system, which are doubtful in poor rock mass usage. The applicability of the proposed method is illustrated by the stability analysis and bolt design of a rail-road tunnel in Turkey.     

Effects of tunnelling on existing support systems of perpendicularly crossing tunnels

The interactions between perpendicularly crossing tunnels in the Sydney region are investigated using a full three-dimensional (3D) finite element analysis coupled with elasto-plastic material models. Special attention is paid to the effect of subsequent tunnelling on the support system, i.e. the shotcrete lining and rock bolts, of the existing tunnel. The results of the analysis show that in a region such as Sydney, with relatively high horizontal stresses, installation of the new tunnel causes the shotcrete lining of the existing tunnel to be in tension in the side facing towards the tunnel opening and in compression at the crown and invert. The pre-stressed rock bolts are usually tensioned more in the sections closest to the tunnel opening. For this particular study, if a new tunnel is driven perpendicularly beneath an existing tunnel, significant increases are induced in the bending moments in the shotcrete lining at the lateral sides of the existing tunnel and in the axial forces at its crown and invert. The increase in side bending moments causes further tensile cracking but the crown and invert stresses remain within the thresholds for both compressive failure and tensile cracking for shotcrete lining of typical concrete quality. Moreover, the driving of the new tunnel causes the tensile forces in the existing side rock bolts to increase and those in the existing crown rock bolts to decrease. In contrast, if the new tunnel is driven perpendicularly above the existing tunnel, compressive failure of the existing shotcrete lining is induced at the crown of the deeper tunnel for concrete of typical capacity and a significant tensile force increase of the existing rock bolts around the crown. It is concluded that in order to ensure the stability of the existing tunnel, local thickening is needed at the sides of the existing shotcrete lining if the shallow tunnel is installed first and local thickening is needed at the crown if the deep tunnel is installed first.     

基于接触应力反分析的隧道初期支护结构内力研究

利用现场监控量测的数据及时分析和评价支护结构的内力是隧道动态设计和施工的关键问题,对保证隧道施工的安全具有重要意义。根据初期支护中喷射混凝土自身特点,将喷层结构视为弹性地基曲梁,并运用弹性地基曲梁理论,通过喷射混凝土与围岩接触应力推求喷层结构内力的解析解,从而得到喷层结构的应力集中部位,方便后续制定施工安全措施。经台阶法开挖的隧道工程实例分析表明,从喷层与围岩接触应力出发来求解喷层结构内力解析式是隧道内力分析一种新的有效方法,为隧道结构的安全评估提供比较可靠的依据     

基于量测位移的隧洞围岩弹性抗力系数反演方法

在水工隧洞工程中,岩石弹性抗力系数K反映了岩石弹性抗力的大小,是设计环节中需要确定的一个极为重要的基础计算参数。水工隧洞工程中需用水压法试验测定弹性抗力系数,由于水压法测定抗力系数不仅耗时、费工、且试验工艺复杂。本文通过对比分析弹性状态下深埋圆形隧洞开挖支护与水压法试验力学效应关系,提出一种基于量测隧洞位移的围岩抗力系数的反演方法,该法可根据量测隧洞位移直接反演得到弹性抗力系数。结合北京市南水北调配套工程南干渠工程试验段工程实践,对浅埋水工隧洞位移进行监测,利用提出的反演方法,得到了隧洞围岩的弹性抗力系数。提出的反演方法为复杂水工隧洞不同围岩应力状态问题的弹性抗力系数反演提供参考和借鉴。     

Rheological analysis of tunnel excavations by means of coupled finite element (FEM)–boundary element (BEM) analysis

To facilitate the practical numerical analysis of tunnel structures by means of the finite element method in the case of viscoplastic properties of the rock mass and viscoelastic properties of the shotcrete, this method is coupled to boundary elements. In this way, the unchanged properties of the boundary element region provide enormous savings in computing time. In order to improve the numerical stability of such calculations, a variable time-step analysis was employed for each time step with an iterative correction method. Characteristic values are obtained from measured values by back-analysis.     

隧道喷射混凝土强度增长规律及硬化速度对初期支护性能影响试验研究

隧道结构的围岩-支护特征曲线理论表明,初期支护强度变化及支护时机将极大地影响隧道周围围岩的变形及应力分布。相应地,作为初期支护重要组成部分的喷射混凝土,其喷射后的强度增长变化规律及硬化速度也极大地影响着围岩的变形及应力重分布。为探明喷射混凝土的强度增长规律及其硬化速度对初期支护性能的影响,结合隧道工程实践,进行了一系列喷射混凝土现场试验,建立了喷射混凝土强度和弹性模量增长规律,确定了喷射混凝土硬化速度对初期支护性能的影响规律。分析表明：（1）隧道喷射混凝土早期强度发展较快、较平稳,24 h抗压强度平均值为6.4 MPa,48 h抗压强度平均值为11.4 MPa。（2）在软弱围岩中提高喷混凝土的早期强度十分重要,是控制围岩变形和稳定的关键,喷混凝土早期强度越大,隧道初期支护作用越明显。（3）喷混凝土硬化速度对控制拱顶沉降变形效果较显著。与慢速硬化相比,喷射混凝土快速硬化时拱顶沉降减少10.4%,拱脚处减小17%,边墙水平收敛减少了30.7%。（4）喷射混凝土硬化速度对控制围岩塑性变形方面差异较小。（5）应充分考虑喷射混凝土的强度硬化过程,不考虑喷射混凝土硬化速度会在一定程度上高估初期支护性能,使其相应支护结构位移明显小于考虑硬化速度时相应的结构位移。     

Engineering classification of rock masses for the design of tunnel support

SummaryEngineering Classification of Rock Masses for the Design of Tunnel Support An analysis of some 200 tunnel case records has revealed a useful correlation between the amount and type of permanent support and the rock mass qualityQ, with respect to tunnel stability. The numerical value ofQ ranges from 0.001 (for exceptionally poor quality squeezing-ground) up to 1000 (for exceptionally good quality rock which is practically unjointed). The rock mass qualityQ is a function of six parameters, each of which has a rating of importance, which can be estimated from surface mapping and can be updated during subsequent excavation. The six parameters are as follows; theRQD index, the number of joint sets, the roughness of the weakest joints, the degree of alteration or filling along the weakest joints, and two further parameters which account for the rock load and water inflow. In combination these parameters represent the rock block-size, the interblock shear strength, and the active stress. The proposed classification is illustrated by means of field examples and selected case records.Detailed analysis of the rock mass quality and corresponding support practice has shown that suitable permanent support can be estimated for the whole spectrum of rock qualities. This estimate is based on the rock mass quality Q, the support pressure, and the dimensions and purpose of the excavation. The support pressure appears to be a function ofQ, the joint roughness, and the number of joint sets. The latter two determine the dilatency and the degree of freedom of the rock mass.Detailed recommendations for support measures include various combinations of shotcrete, bolting, and cast concrete arches together with the appropriate bolt spacings and lengths, and the requisite thickness of shotcrete or concrete. The boundary between self supporting tunnels and those requiring some form of permanent support can be determined from the rock mass qualityQ. With 8 Figures     

喷锚支护在水工隧洞施工中的应用浅说

简要地介绍了对水工地下洞室施工中对围岩不稳定体,即碎裂岩体、松动岩体、软弱结构面、楔形体结构面等围岩喷锚支护结构的作用,喷锚支护结构的使用。     

公路隧道型钢喷射混凝土初期支护安全评价研究

公路隧道常采用复合式衬砌,按“新奥法”原理进行设计和施工。对于软弱围岩段,采用型钢拱架（或格栅拱架）+注浆+锚喷网联合初期支护形式,型钢喷射混凝土初期支护的安全性评价方法是实现支护动态设计的关键。对初期支护安全性评价进行系统研究,建立了型钢喷射混凝土安全性评价数值计算方法。首先,根据监测数据分析围岩最终沉降量、水平收敛值,作为围岩力学参数反演的依据;其次,采用反演的力学参数,通过地层-结构法数值计算型钢拱架喷射混凝土初期支护内力;最后,采用型钢混凝土安全系数计算方法计算和评价初期支护安全性。研究发现,型钢拱架喷射混凝土初期支护能发挥型钢强支护作用,而喷射混凝土达到设计强度后,混凝土起主要支撑作用,型钢间距对提高初期支护安全系数不显著。     

径向基函数神经网络在地应力场反演中的应用

初始地应力场是地下洞室设计所需的基本指标。基于江边电站引水隧洞沿线区域的地质资料,利用快速拉格朗日分析程序FLAC3D建立了该区域的数值计算模型,使用了随深度变化的侧压力系数以及应力和位移的混合边界条件,通过模拟引水隧洞沿线不同岩性的岩石、断层破碎带和蚀变带进行正分析计算。根据工程现场实测点的主应力数据,基于径向基函数（RBF）神经网络原理,反演了计算区域的岩体力学参数和初始地应力场。其计算结果与实测地应力值基本吻合,满足精度要求,说明反演结果与工程实际相符,所使用的反演方法是合理的。     

Geotechnical parameter estimation in tunnelling using relative convergence measurement

Accurate estimation of geotechnical parameters is an important and difficult task in tunnel design and construction. Optimum evaluation of the geotechnical parameters have been carried out by the back‐analysis method based on estimated absolute convergence data. In this study, a back‐analysis technique using measured relative convergence in tunnelling is proposed. The extended Bayesian method (EBM), which combines the prior information with the field measurement data, is adopted and combined with the 3‐dimensional finite element analysis to predict ground motion. By directly using the relative convergence as observation data in the EBM, we can exclude errors that arise in the estimation of absolute displacement from measured convergence, and can evaluate the geotechnical parameters with sufficient reliability. The proposed back‐analysis technique is applied and validated by using the measured data from two tunnel sites in Korea. Copyright © 2005 John Wiley & Sons, Ltd.     

各向异性岩应力-渗流耦合问题的反分析

在岩土工程实践中对于诸如各向异性岩体的应力-渗流耦合分析等复杂问题,建立用于同时确定多类参数的反分析方法具有重要意义。以位移量测信息为基础信息,对基于复变量微分法的优化算法（Levenberg-Marquit法）引入异步长因子矩阵 ,建立同时反演确定初始地应力、围岩性态参数和渗透系数的协同优化变步长反演算法。对不同的参数借助搜索迭代过程,确定不同的步长因子系数。异步长因子矩阵可使在峰值附近不收敛的参数重新选择搜索方向,使其收敛至精确值。算例表明,异步长因子矩阵可成功地用于协调各类参数敏感性之间的差异,从而有效改进多参数耦合反演的收敛性和收敛速度,使算法具有更好的适应性和有效性,为岩土工程的复杂问题的求解提供一种方法。