An improved numerical approach in surrounding rock incorporating rockbolt effectiveness and seepage force

The solutions of stress and displacement of a circular opening excavated in brittle and strain-softening rock mass incorporating rockbolts effectiveness and seepage force are presented in this study. The evolution equation is reconstructed for the strength parameters that incorporate these factors. Based on the evolution equation, an improved numerical method and stepwise procedure are presented which are compatible with the Mohr–Coulomb (M–C) and the generalized Hoek–Brown (H–B) failure criteria, respectively. Then given three interaction mechanisms between rockbolts and surrounding rock, solutions for stress and displacement are proposed in line with the improved numerical method and numerical stepwise procedure. The proposed approach can be reduced to Fahimifar and Soroush’s (Tunn Undergr Space Technol 20:333–343, 2005) solutions for special cases. The proposed method was validated by field monitoring data and FLAC results of Yanzidong tunnel. Examples under the M–C and generalized H–B failure criteria for rock mass are generated through MATLAB programming. Moreover, parametric studies are conducted to highlight the influence of rockbolts effectiveness in combination with seepage force on the stress and displacement of very good, average, and very poor surrounding rock. Results show that in this case, stress confinement is higher and tunnel convergences are lower than the corresponding stresses and displacements obtained in non-reinforced tunnels. Displacement and plastic radius are also higher than those without considering seepage force.     

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.     

Progressive degradation of rock properties and time-dependent behavior of deep tunnels

Time-dependent response of deep tunnels is studied considering the progressive degradation of the mechanical properties of the rock mass. The constitutive model is based on a rock-aging law for the uniaxial strength of the rock and for the Young’s modulus. A semi-analytical solution is developed for the stresses and displacements around a deep circular tunnel taking into account the face advance. The evolution of the plastic and damage zones over time is determined. Numerical examples are presented for the case of Saint-Martin-La-Porte access adit in France of the Lyon–Turin Base Tunnel. The computed results which are compared with the field data in terms of the convergence of tunnel wall and of the displacements inside the rock mass monitored by multi-point extensometers show the efficiency of the approach to simulate the time-dependent deformation of a tunnel excavated in squeezing ground. Simple relationships are proposed to evaluate the parameters of the constitutive model directly from those of the empirical convergence law presented in previous work.     

A Simple Method for Analysis of Point Anchored Rockbolts in Circular Tunnels in Elastic Ground

Summary. A simple analytical method for the analysis of point anchored rockbolts is presented in this paper. The solution has been derived for elastic ground and rockbolts, for plane strain conditions, and for tunnels with circular cross section. The method provides accurate results for the rockbolts’ loads and displacements and explicitly includes the connection of the rockbolts to the surrounding ground. The addition of such details to a Finite Element numerical model is critical; otherwise the solution obtained may be dependent on the discretization used and on the stiffness of rockbolts and ground. As an alternative to including details of the rockbolt head and anchor point in the numerical model, which could be computationally very expensive, an equivalent spring constant is proposed. The spring constant is obtained by matching numerical with analytical results for a simple case, but keeping the geometry, material properties, and discretization unchanged.     

并设小净距隧道爆破振动响应分析及控爆措施研究

通过大量二维、三维数值模拟计算,分析了围岩、净距、埋深等条件对小净距隧道爆破振动特性的影响,研究了先行隧道不同支护体系、不同中岩墙加固措施及后行隧道不同施工方案等情况下,小净距隧道中后行隧道爆破开挖对先行隧道的影响。根据研究结果,提出了中岩墙加固宜采用注浆加固、先行隧道初期支护宜及时跟进并封闭、掏槽眼宜远离中岩墙以及开挖进尺不宜大于净距的1/3等小净距隧道爆破施工的控爆措施,以供小净距隧道爆破开挖设计、施工借鉴。     

Mechanical response of surrounding rock of tunnels constructed with the TBM and drill-blasting method

There are two kinds of excavation methods in underground engineering: the tunnel boring machine (TBM) and the drill-blasting method. A large number of studies have shown that the deformation and failure, the degree of disturbance, the stability and the reinforcement measures of surrounding rock using the TBM and drill-blasting method vary from each other. To accurately master these macroscopic damages, it is necessary to focus on the investigation of the micro-mechanical responses of the surrounding rock. Scanning electron microscopy tests, acoustic emission tests and tunnel acoustic detection tests were carried out to analyze the mechanical response of surrounding rock of tunnels, which were excavated in marble by, respectively, the TBM and the drill-blasting method. The tests results showed that most of the rock fractures cut by TBM is wipe along the crystal, and the failure mechanism is mainly cutting, while most of the rock fractures induced by the TBM coincide with crystal planes, its mechanism is mainly tensile. The stress–strain curves of rocks cut by the TBM method are rather flat around the peak strength, which means a strong resistance to deformation around the peak load. The response of AE for the rock cut by the TBM method appears after larger strains than the response of the rock constructed by the drill-blasting method. This suggests that the resistance to damage is higher under TBM excavation conditions. The relaxation depths of the tunnel excavated by the drill-blasting method are larger than the tunnel excavated by the TBM method. The research can provide more insight into tunnel failure mechanisms and provide a framework for reinforcement measures.     

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.     

近区锚喷结构的爆破振动特性研究

选用水泥砂浆和玻璃钢分别模拟岩石和锚杆,浇筑2.5 m×1.8 m×2.1 m尺寸的岩体模型,通过模型试验研究近区锚喷结构在掏槽爆破作用下的振动特性。利用测试锚杆测得不同设置情况锚杆上的应变波。试验结果表明,端锚锚杆中部锚固段与锚杆尾部自由段测得的振动波形和变形形式完全不同,中部锚固段振动幅值稍大;在不设置喷层和预应力时,尾部自由段的应变波规律性更强,且持续时间长;随着离爆源距离的增加,锚杆的振动频率和幅值衰减明显,但振动持续时间则稍有增长;通过小波变化的时频方法分析应变波的能量,临近工作面锚杆的振动能量大,但能量分布分散,振动时间有限,稍远的锚杆虽振动能量小,但能量集中,持续时间长;两种不同能量对锚喷结构产生不同的损坏模式。试验和实践发现,爆破容易造成附近喷层的损坏和锚杆的失效,钢纤维混凝土可增加喷层的抗动载性能,调整支护工艺也是减小爆破影响的有效方法。     

Analytical solutions for stresses and displacements around tunnels driven in cross-anisotropic rocks

In this paper, closed-form solutions for the stresses and displacements around unlined circular tunnels excavated in an elastic, orthotropic (cross-anisotropic) medium are developed. The effect of both the elastic parameters characterizing the behaviour of the medium and the anisotropy of the initial stress system on the stresses and displacements induced are evaluated. An example of utilizing the theoretical solution for design analysis is given. For convenience of application, design charts are prepared for the determination of stresses and displacements for given values of initial stresses and the elastic parameters. Copyright © 1999 John Wiley & Sons, Ltd.     

Modeling strategy for jointed rock masses reinforced by rock bolts in tunneling practice

This paper deals with the modeling of jointed rock masses reinforced by rock bolts. It is well known that rock bolts are extremely effective in reinforcing jointed rocks. However, if a continuum approach is adopted for modeling jointed rock masses, it is often misleading to evaluate the effectiveness of the rock bolts by numerical analyses such as the finite element method. This may be due to the fact that since no more joints exist in the continuum, the effectiveness of the rock bolts in constraining the relative displacements along the joints cannot be evaluated properly. In order to investigate the reinforcement effect of rock bolts, physical model tests were performed in the laboratory. The test results revealed that jointed rock masses should be modeled as an equivalent continuum after the installation of rock bolts and that the mechanical parameters of the equivalent continuum should be evaluated by considering the reinforcement effect of the rock bolts. Therefore, the values of the mechanical parameters differ from place to place in accordance with the relation between joint orientation and rock bolt direction, even though joint systems are homogeneous. In conclusion, in the continuum approach for modeling jointed rock masses, it should be emphasized that rock bolts and jointed rock masses should not be modeled separately but should be modeled simultaneously by considering the reinforcement effect of the rock bolts in constraining joint movement. The modeling of shotcrete reinforced by steel ribs is also discussed in comparison to the modeling by rock bolts.     

Experimental investigation of the time-dependent response of unreinforced and reinforced tunnel faces in cohesive soils

In spite of the increasing diffusion of tunnel boring machines, conventional tunnelling is still preferred for economic reasons in case of short tunnels, unconventional cross sections or irregular tunnel trajectories. In conventional tunnelling, the mechanical response of the tunnel front is a main concern and, when tunnels are excavated in cohesive soils, this is dominated by the time factor, related to geometry, to the mean excavation rate and to the hydro-mechanical properties of the materials involved. This is particularly evident during excavation standstill: front displacements progressively increase with time and, in many cases, the system response under long-term conditions becomes unstable. In conventional tunnelling, a common technique employed to improve the system response (under both short- and long-term conditions) is the installation of fibreglass tubes within the advance core. In this paper, the mechanical response of both unreinforced and reinforced deep tunnel fronts in cohesive soils is experimentally analysed. In particular, the results of a series of 1 g small-scale tests, taking into account both the influence of the excavation rate (the unloading time) on the system response and the evolution with time of the tunnel face displacements, induced by a rapid reduction in the horizontal stress applied on the tunnel face, are reported.     

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.     

某工程试验洞的有限元流变计算分析

把岩体作为粘弹塑介质，用组合模型描述岩体流变特性，对某工程试验洞的粘土岩进行有限元流变计算，计算结果与实测结果相当一致。计算表明，岩体流变特性对岩体、特别对软弱岩体的围岩稳定的影响是不容忽视的。在围岩稳定分析中，粘弹塑性方法能更好地预测洞室塑性区的发展和洞周位移的变化情况，并为寻求合理的支护时间、支护形式提供依据。     

Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.     

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。     

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。     

高应力区隧道围岩变形破坏的数值模拟及物理模拟研究

隧道失稳和维护困难是高地应力隧道的普遍问题,对隧道的支护设计提出了更高的要求。研究从地下工程岩体应力环境变化和岩体强度变化的角度探讨了高应力隧道围岩的变形破坏机制。根据重庆某深埋隧道围岩实际情况,运用FLAC3D三维显式有限差分法分析软件,建立了摩尔-库仑剪破坏与拉破坏复合的应变软化模型。通过隧道的三维数值计算,分析了高应力环境下隧道周边塑性区分布、应力场、位移场等的分布特点,得到了高应力隧道围岩在高地应力环境下的破坏规律。通过物理模型验证了高应力隧道围岩的破坏特点,并进行了超载试验,将其与数值模拟进行对比,进一步验证了所建数值模型的科学性。     

ANALYSIS OF ROCKBOLT REINFORCEMENT USING BEAM-COLUMN THEORY

A simple analytical procedure that applies classical beam-column theory for evaluating passive rockbolt roof reinforcement is presented in this paper. The analytical model is derived from first principles and is capable of modelling any number of reinforcing bolts. Each rockbolt is modelled as a linear spring and the model allows for non-uniform bolt spacing. In this study the rock beam is assumed to be isotropic and linearly elastic for the sake of simplicity. However, the analytical model can be extended to include anisotropic rockmass as well as inelastic material behaviour. The solution to the coupled set of governing equations is obtained by using a simple numerical solution procedure. The results from the analytical model indicate that the critical buckling load of a rock beam is strongly influenced by the ambient rock modulus. For salt-rock excavations the rock modulus typically declines with time due to various phenomena, and a diminished modulus could seriously compromise roof stability. The other main conclusion of this study is that rockbolts loose their effectiveness in restraining a roof beam once its critical buckling load is approached. In such a situation, increasing bolt stiffness does not improve its reinforcing action on a roof beam but it enhances the possibility of bolt failure due to anchor pull-out. © 1997 by John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech., vol. 21, 241–253 (1997)     

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.     

软弱泥质砂岩地层中输水隧洞稳定性研究

泥质砂岩属于黏土岩,具有典型的遇水软化特征。在泥质砂岩富水地层中进行隧道开挖是地下工程的一个挑战性问题。研究了围岩软化与未软化条件下泥质砂岩地层中输水隧洞的稳定性和支护时间。首先,介绍了泥质砂岩遇水软化的力学试验结果;然后,采用基于Hoek-Brown强度准则的岩体参数评价方法,评估泥质砂岩在围岩软化与未软化条件下的力学参数;再后,以兰州水源地引水隧洞为依托工程,采用数值模拟方法对泥质砂岩隧洞软化与未软化工况的围岩稳定性进行了计算分析,得出泥质砂岩遇水软化对隧洞安全性存在显著影响;最后,采用位移收敛法,研究了泥质砂岩软化与未软化工况中,保障隧洞施工安全的合理支护时机。研究表明,泥质砂岩未软化工况中,可考虑隧道围岩初期支护在距掌子面4～5 m位置实施;而在泥质砂岩遇水软化工况中,初期支护建议在掌子面开挖后立刻支护。研究成果可为泥质砂岩地层隧洞的安全施工提供依据。