Effect of imperfect interface on the dynamic response of a circular lined tunnel impacted by plane P-waves

A theoretical method for studying the dynamic response of a circular lined tunnel with an imperfectly bonded interface subjected to plane P-waves is presented in the paper. The wave function expansion method was used and the imperfect interface was modeled with a spring model. Two cases were discussed in the paper. In the first case rock is harder than the lining and vice-versa in the second case. The results indicated that the variation in the stiffness of the interface has much influence on the distribution of dynamic stress concentration factors (DSCF) in the rock and the lining. The imperfection of the interface has a more noticeable influence on the DSCF in the rock mass and the lining at high frequency incident wave’s scenario than low frequency incident wave’s scenario. The resonance scattering phenomena can be observed when the bond is extremely weak. Limiting cases were considered and a good agreement with the solutions available in the literature was obtained.     

两向不等压圆形隧洞弹塑性解析分析

圆形隧洞围岩的弹塑性分析一直是岩石力学所关注的问题。基于Mohr-Coulomb强度准则,解决了圆形隧洞在两向不等压地应力作用下的塑性区确定问题。通过复变函数中的保角变换的方法将物理平面非圆形弹性区域映射到像平面的单位圆外域进行求解,将确定弹塑性区的交界问题转化为映射函数系数的求解问题。其核心是将弹塑性交界面上复杂的应力组合式展开成傅里叶级数,通过求解复线性方程组的方法来确定级数的各项系数,建立含有映射函数系数的非线性方程组。采用混合罚函数最优化方法可以确定圆形隧洞的弹塑性交界。通过算例检验了该方法的正确性,并且分析黏聚力、内摩擦角及侧压力系数对塑性区形状的影响规律。     

各向异性岩体中不同接触衬砌隧洞的解析分析

通过复变函数方法建立分析了非圆形水工衬砌隧洞,在衬砌与围岩处于完全和光滑接触条件下的解析解,考虑了衬砌的支护滞后效应和洞内水压作用。研究了正交各向异性岩体中的马蹄形衬砌隧洞,在不同接触条件和洞内压力工况下,接触边界和衬砌自由边界上的应力和位移解。接触条件对衬砌接触边界的切向应力分布影响最显著,完全接触条件下两底脚的切向压应力最大,光滑接触条件下最小。岩体各向异性和倾斜结构面对衬砌中力学分量的非对称性影响在完全接触条件下明显。完全接触条件可高效发挥衬砌的支撑作用,光滑接触条件使岩体的自承能力充分体现。衬砌在两种接触条件下均承担了大部分由水压引起的张拉效应。     

Numerical study on tunnel damage subject to blast-induced shock wave in jointed rock masses

In this study, numerical modeling on the damage of existing circular tunnel subject to blast-induced shock wave was carried out with DEM-based code UDEC. The disturbed zones including failure zones, open zones and shear zones around circular tunnel and peak particle velocities (PPVs) at tunnel surface are employed to analyze the damage of tunnel. The effects of joint spatial and mechanical properties, initial stress of rock mass, and magnitude of shock wave amplitude to damage of tunnel were evaluated in this study. The difference of damage between non-supported circular tunnel and bolt-supported circular tunnel subject to the same blast-induced shock wave was also studied. It is found that the orientations of joints in rock mass around the tunnel have great effects on tunnel damage. The initial stress around tunnel has relatively small influence on tunnel damage. The bolt support could greatly increase the stability of tunnel by changing the vibration form of particle velocity rather than the decreasing of PPV.     

弹性半空间中衬砌隧道对瑞利波的散射

 采用一种高精度的间接边界积分方程法,对弹性半空间中衬砌隧道对入射瑞利的二维散射问题进行求解分析。结果表明：衬砌隧道和非衬砌隧道对瑞利波的散射具有显著的差别,衬砌刚度对波的散射规律具有重要影响。隧道附近地表动力响应和隧道衬砌动应力集中主要取决于衬砌和围岩的刚度比、隧道的埋深和直径、入射波频率等因素。对于柔性衬砌,浅埋隧道对低频瑞利波会产生显著的位移放大效应;对于刚性衬砌,衬砌内壁的动应力集中效应十分明显。整体上看,随着埋深的增大,隧道周围波的散射逐渐减弱。     

深埋马蹄形隧道开挖围岩应力与位移的复变函数解

利用复变函数解法中的柯西积分法,求解工程中常用的单心圆仰拱马蹄形隧道在弹性半空间内任意一点处的应力值和位移值解析解表达式。由于是深埋隧道,且埋深与孔径之比较大,故不考虑重力梯度影响,直接把重力作用化为无限远处作用有P1、P2的外载;求解出马蹄形隧道孔洞在弹性半空间内任意一点处的应力值和位移值解析解表达式。结合典型断面,利用三维有限元分析软件MADIS/GTS建立二维平面应变模型,对理论推导单心圆马蹄形隧道在弹性平面内的解析解公式进行验证。分析表明,有限元结果和解析解结果有较好的吻合性,证明了新方法的准确性,针对深埋马蹄形隧道开挖工程,可以快捷地评估围岩应力状态及位移变形。     

Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses

We present a novel methodology for estimation of equivalent Mohr–Coulomb strength parameters that can be used for design of supported tunnels in elasto-plastic rock masses satisfying the non-linear empirical Hoek–Brown failure criterion. We work with a general adimensional formulation of the Hoek–Brown failure criterion in the space of normalized Lambe's variables for plane stress, and we perform linearization considering the stress field in the plastic region around the tunnel. The procedure is validated using analytical solutions to a series of benchmark test cases. Numerical solutions are also employed to validate the procedure in cases for which analytical solutions are not available. Results indicate that the stress field in the plastic region around the tunnel, as well as the linearization method employed and the quality of the rock mass, has a significant impact on computed estimates of equivalent Mohr–Coulomb strength parameters. Results of numerical analyses also show that our proposed linearization method can be employed to estimate loads and moments on the tunnel support system. We recommend the equating model responses (EMR) method to compute equivalent Mohr–Coulomb strength parameters when the tunnel support pressure is accurately known, and we further show that our newly introduced linearization method can be employed as an alternative to the best fitting in the existing stress range (BFe) and best fitting in an artificial stress range (BFa) methods, providing performance estimates that are generally better than estimates of the BFe and BFa methods when differences with the response of the Hoek–Brown rock mass are of engineering significance (say more than 10%).     

New analytical method for predicting stresses around rectangular tunnels under arbitrary stress boundary conditions

Rectangular tunnels are often encountered in geotechnical engineering. To clarify the mechanical mechanism of the stresses around tunnels, this study presents new analytical approximant solutions for evaluating stresses around tunnels under arbitrary stress boundary conditions. The solutions consist of two parts: one is the solution for a half-plane before excavation, and the other is the solution for a half-plane with tunnels. The second part can be further decomposed into solutions of a half-plane without tunnels subjected to virtual tractions along the ground surface and solutions of an infinite plane with tunnels loaded by virtual tractions along tunnel boundaries. An efficient iterative procedure is proposed for determining the two sets of unknown virtual tractions, which are transformed into equivalent concentrated forces to simplify the computational process. The solutions agree very well with the results obtained by the finite element method. A parametric study is finally performed to investigate the influences of the tunnel buried depth, the tunnel shape, and surcharge loads on the stresses along the ground and around tunnels. The new proposed solutions potentially provide a potential alternative approach for preliminary designs of future rectangular tunnels.     

含滑移界面复合式衬砌隧道地震响应边界元模拟

采用一种高精度间接边界元方法(IBEM),求解了平面P、SV波入射下“围岩-减震层-浅埋衬砌隧道”体系地震响应及动应力集中效应。引入接触-滑移界面模型,模拟复合式隧道衬砌与围岩之间接触状态。结果表明: 总体上看,随着界面滑移刚度因子增大,衬砌内壁动应力集中因子(DSCF)增大,无滑移状态下应力放大更为显著;SV波入射下,衬砌外壁DSCF则随滑移刚度因子增大而减小;P波垂直入射下,低频情况在隧道左右两端动应力集中十分显著,高频时则在隧道下部应力更为集中。另外,减震层的存在可有效降低衬砌动应力集中效应,随着入射频率增加,减震效果越好,隧道衬砌受力更为均匀;适当降低减震层弹性模量和加大减震层厚度,可取得更好的减震效果。     

Rayleigh波作用下圆形隧洞衬砌横向内力的解析解

 考虑土–结构相互作用,Rayleigh面波入射下隧洞衬砌的横向内力解析解至今比较少见。采用拟静力法,基于地下结构力学和平面弹性波动理论,推导出均匀介质中Rayleigh波以任意角度入射时圆形隧洞衬砌的横向内力解析解,考察土–结构交界面之间存在完全滑移和无滑移2种极限接触状态。算例表明,在Rayleigh波作用下,当其传播方向与隧洞轴向垂直时,衬砌的横向内力取得最大值,且内力在2种极限接触状态下的差别不大;与SV波作用效应相比,Rayleigh波作用下的衬砌横向内力均要大,尤其是轴力要大很多,这是由于Rayleig波中的P波分量造成的。浅埋隧洞衬砌的抗震设计,应充分重视Rayleigh波的作用效应。     

深埋特长公路隧道岩爆预测综合研究

岩爆预测一直是地下工程世界性难题之一。以台缙高速公路苍岭隧道的岩爆预测为例,从隧道区围岩的岩体特征和隧道区初始应力场两方面着手,通过工程地质调查研究和区域地质资料分析,对隧道区进行工程地质分类。划分隧道沿线各洞段隧道围岩类别,通过室内岩石力学试验,掌握隧道沿线围岩的物理力学特性;分析区域地震震源机制解、地应力实测资料,揭示区域构造地应力场环境。在研究过程中选取典型部位,采用水压致裂法实测工程区地应力的大小和方向。通过三维有限元反演工程区的初始应力场,在初始应力场和隧道围岩岩石力学性质研究的基础上,结合各洞段隧道断面开挖数值分析结果和现有国内外多种岩爆判别准则,对苍岭隧道岩爆发生的部位和等级进行预测,为制定合理的开挖支护方案提供依据。     

深埋双隧洞开挖的解析延拓法求解

 将隧洞所处的地下空间转换为平面应变情况下的弹性半空间,考虑两隧洞开挖次序的影响,利用解析延拓法及Schwarz交替法求解出弹性半空间内2个任意形状任意尺寸的双隧洞在任意相对位置下其半空间内任意一点的应力解和位移解的隐式表达式。将双圆形隧洞作为特例,考虑到隧洞埋深与孔径相比比较大,从而不考虑重力梯度的影响,将重力化为作用在边界上的均布外荷载,考虑2个隧洞衬砌法向反力的影响,求解出弹性半空间内圆形双隧洞任意一点处的应力值和位移值解析解的具体显式表达式。最后利用二维有限元分析对理论推导的两圆形孔洞解析解进行验证,表明解的可靠性。     

爆炸荷载作用下煤岩巷道底板破坏的数值分析

以中国西南某煤矿爆破底板透水事故为背景，利用ANSYS／LS-DYNA程序简要分析了爆炸发生时岩层中的应力波传递与巷道混凝土底板的破坏过程，给出了煤岩巷道底板破坏时耦合装药的临界药量，分析了饱和岩石和干燥岩石界面位置对混凝土底板破坏的影响。     

Mechanical behavior of a twin-tunnel in multi-layered formations

Model tests of twin circular tunnels in homogenous material, two-layered formations, and three-layered formations are performed. Induced strains and displacements are measured around the tunnel openings during excavation. A two-dimensional numerical simulation based on the fictitious stress method (FSM) is also developed to study the mechanical behavior of a twin-tunnel of circular cross section in multi-layered formations by considering the continuity equation for stress and displacement at the interface. Different values of initial stress, modulus ratio, and coefficient of earth pressure (K) are considered. The distributions of displacement around the unsupported tunnels are analyzed. The fractured zones around the tunnels are determined based on the Hoek and Brown’s failure criterion under various configurations. The numerical results are found in a good agreement with the experimental results within an error of 2–4%, indicating the FSM model could be regarded as a suitable mean to solve the mechanical behavior of a tunnel excavated in the multi-layered formations. The result also shows that the fractured zones are found to develop along the minor principal stress direction, whereas the major displacement is found to occur in the major principal stress direction.     

围岩稳定性评判方法适用范围探讨

基于修正芬纳公式建立了围岩稳定性评判新方法,该方法基于轴对称模型建立径向位移解析表达式。轴对称的基本假定就是圆形洞室,静水压力和均匀初始应力场,各向同性和均匀围岩条件。通过系统分析轴对称假定条件的偏差范围对围岩稳定性判断方法的适用范围进行研究。基于经典的遵循莫尔-库仑屈服准则理想线弹塑性围岩中的洞室开挖问题,分析了各项异性和非均匀性的初始应力场及城门洞型洞室对洞壁变形的影响。研究结果对围岩稳定性评判方法的合理使用范围、精度与轴对称围岩条件提出了量化评价范围。     

基于Mogi-Coulomb强度准则的隧道围岩理想弹塑性解答

合理选择岩石强度准则对隧道应力及位移预测和支护设计都具有重要意义,基于MogiCoulomb强度准则和理想弹塑性模型,通过中间主应力系数反映中间主应力的影响,推导了圆形隧道围岩应力和位移的解析解,并对所得结果进行比较与验证,得到了中间主应力和围岩抗剪强度参数的影响特性。研究表明:具有广泛的适用性和较好的可比性,Mohr-Coulomb强度准则解答和Matsuoka-Nakai准则解答均为其特例;结果关于中间主应力系数b=0.5对称,较好地反映了岩石强度的中间主应力效应及其区间性;粘聚力及内摩擦角对围岩塑性区半径和隧道洞壁位移的影响显著,应充分考虑中间主应力影响及围岩抗剪强度参数变化对隧道设计与施工的影响。     

Excavation-induced hydraulic conductivity reduction around a tunnel – Part 2: Verification of proposed method using numerical modeling

During tunnel excavation in a jointed rock mass, significant joint closure takes place in the immediate vicinity of tunnel due to joint effective normal stress increase, and the equivalent hydraulic conductivity is largely reduced within a zone approximately one tunnel-radius thick around the tunnel. A significant pressure drop takes place across this zone, and the actual raise of pore-water pressure in the surrounding rock mass is steeper than that estimated from the analytical solution that considers the jointed rock mass around the tunnel as a homogeneous, isotropic medium. This paper presents a numerical modeling of the mechanical and hydraulic behavior of a jointed rock mass around a tunnel and provides estimates of the groundwater inflow rate to be compared to those estimated from generally used analytical solutions. The numerical analysis results presented here verify the validity of the analytical method described in the Part 1 paper for estimating groundwater inflow rate into a tunnel considering excavation-induced hydraulic conductivity reduction.     

乌鞘岭隧道三维地应力场多元有限元 回归拓展分析

 采用三维有限元多元回归分析方法,基于有限测点的地应力量测结果,拓展分析隧道区原始宏观地应力场。建立隧道区两个大规模三维计算模型,通过有限元分析软件ANSYS对重力、水平挤压和剪切等4种工况的构造应力场分别进行计算。编制三维地应力场多元回归分析计算机软件MEBA以及与ANSYS的接口程序MEBAC,实现地应力场的多元回归拓展分析,着重分析乌鞘岭隧道岭脊地段的复杂应力状况、应力值的宏观大小和规律,特别是F4,F5,F6,F7断层及其附近的应力状况。宏观地应力场的分析结果表明,乌鞘岭隧道宏观地应力场的主应力方向为N21.2°E,与隧道轴线的夹角为38.2°,断层区隧道衬砌具有纵向挤压和横向受力不对称的特点。区段地应力值高,在隧道轴线位置,最大垂直地应力为32.10 MPa,垂直于隧道轴线方向最大水平地应力为21.72 MPa。宏观地应力场的分析结果对工程的动态设计与施工具有重要参考价值。     

基于非局部Biot理论下饱和土中深埋圆柱形衬砌对平面弹性波的散射

基于Biot饱和多孔介质理论和非局部弹性理论,构建了非局部Biot运动方程及本构方程。利用波函数展开法及饱和土与衬砌边界连续条件和衬砌内边界自由边界条件,求解了饱和土体中圆柱形衬砌对平面波散射问题的解析解。并通过将该解退化为单相介质中及经典Biot理论下衬砌对平面P波散射稳态解,验证了计算结果的正确性。研究结果表明,衬砌内边界及外边界动应力集中因子均随非局部因子的增大而减小;隧道内边界动应力集中因子分布曲线随非局部因子的减小而扩大;当入射波频率大于0.045 MHz时,饱和土中空隙尺寸及空隙动力的影响将不可忽略;非局部因子一定时,衬砌外径与内径比越大则衬砌内边界动应力集中因子越大,且当衬砌较薄时,衬砌内边界动应力集中因子可能产生负值。     

Assessing in situ microcrack damage using ultrasonic velocity tomography

To characterize the damage induced during excavation of a test tunnel in granite, ultrasonic wave velocity and amplitude measurements were made in situ around one quadrant of the tunnel. Sixteen 1-m deep boreholes were drilled into the tunnel wall; these boreholes spanned the region from tensile stress-induced damage in the sidewall to compressive stress-induced damage in the well-developed notch. Measurements were made by pulsing a source transducer at numerous points within a given borehole and on the tunnel surface, and then capturing the transmitted ultrasonic waves at transducers located in the adjacent borehole. The travel times of the waves between sources and receivers were used to compute the average velocities and to construct two-dimensional (2D) tomographic images. Wave velocities and amplitudes in the tensile stress region are low and show significant anisotropy, indicating the presence of oriented microcracks even as deep as 1 m from the tunnel wall. Velocities and amplitudes are higher in the compressive stress region and show lower anisotropy, indicating the rock is relatively undamaged away from the tunnel wall. The velocity anisotropy indicates that the dominant orientation of microcrack planes is everywhere tangential to the tunnel wall, even though the minimum principal stress is tangential and tensile in the sidewall. The distribution of microcracks inferred from these results is consistent with the extensive microseismicity detected during and after excavation and suggests that both the stress history and current stress state have impacted the current state of damage around the tunnel.