Analytical‐numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts

This paper presents an analytical‐numerical approach to obtain the distribution of stresses and deformations around a reinforced tunnel. The increase in the radial stress of the reinforced tunnel, based on the performance of a bolt, is modeled by a function, which its maximum value is in the vicinity of the bolt periphery and it exponentially decreases in the far distance from the bolt. On the basis of this approach, the shear stiffness between the bolt and the rock mass and the shear stress distribution around the bolt within the rock mass are also analytically obtained. The results are compared with those obtained by the assumption of ‘uniform increase of radial stress’ method, which is made by the previous studies. The analyses show when the bolts' spacing is large, the safety factor must be increased if the ‘uniform increase of radial stress’ method is used for the design. Finally, a procedure is introduced to calculate the non‐equal deformation of the rock mass between the bolts at any radius that can be useful to compute the bending moment in shotcrete layer in New Austrian Tunnelling Method (NATM) approach. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

金华山软岩铁路隧道施工过程围岩屈服接近度分析

隧道施工过程中围岩处于复杂应力状态下,隧道围岩屈服区演化特征的确定对于围岩稳定性分析和开挖支护方案优化具有重要的意义。采用屈服接近度指标衡量围岩破坏接近程度可以合理地描述复杂应力状态下围岩的应力危险性,对Mohr-Coulomb类岩体材料的屈服接近度函数进行了相应的推导,并在非线性有限元用户子程序上编程予以实现。介绍了赣州-龙岩铁路DKl33+095～DKl38+237段软弱围岩单线隧道正台阶步施工方案以及湿喷纤维混凝土支护方案。为了对该隧道施工过程中隧道围岩屈服区的演化特征进行合理评价,采用非线性有限元法对软弱围岩条件下的铁路隧道施工过程进行了数值模拟,分析了施工过程中隧道围岩屈服接近度分布特征,判定了隧道台阶步施工过程中隧道围岩的稳定性。分析结果表明:该隧道施工过程中围岩破坏区主要发生在下台阶步施工过程中;屈服接近度指标比传统的塑性区分布提供的信息更加丰富,有利于工程技术人员定量地评价隧道开挖支护方案。     

拉西瓦水电工程岩体裂隙透水性反分析研究

80年代以来。由裂隙水在石油工程、水利工程、水资源评价以及工业废料和核废料的储存方面,起着至关重要的作用和影响,因此,裂隙水研究得到了各方面专家的广泛重视。渗透张量是研究岩体裂隙透水性的非常重要的参数。本文以拉西瓦水电工程为实例,把流场中若干点的水头实测值与计算值之误差作为目标函数,给出一种在任意四边形网格上求解裂隙流控制方程的局部坐标有限分析法,用优化单纯形法反求裂隙岩体渗透张量。本文中提出的反分析法特点在于充分研究了岩体所处的地质、水文地质环境,考虑到岩体裂隙结构面的控渗作用,反求岩体渗透性参数。 水流方向有关,增加了反分析的未知数。文章中给出的反分析法有三方面的优点:其一不仅可以求出岩体的渗透张量,而且能求出各组裂隙的渗透系数;其二减少了反分析问题中未知数个数;其三解具有唯一性。     

Analytical modeling of a deep tunnel inside a poro-viscoplastic rock mass accounting for different stages of its life cycle

An analytical approach of the viscoplastic behavior of a porous saturated rock mass surrounding a deep tunnel in different stages of a simplified life cycle is presented. The viscoplasticity is modeled by means of a simple (linear) Norton-Hoff’s law. Some numerical examples are performed to examine the consistency and relevance of the solutions. Parametric studies illustrate the influence of key parameters such as rock mass viscosity, Poisson’s ratio, rock mass permeability, lining emplacement, etc. This analytical approach constitutes a useful reference to facilitate more complex numerical simulation and making it possible to obtain practical estimations of the poromechanical behavior of underground structures.     

东巨寺沟隧道湿喷纤维混凝土支护结构和围岩稳定性位移模糊判别

湿法喷射混凝土可有效地改善隧道内作业环境、反弹量小、喷射质量高,是隧道支护结构施工值得推广的工艺。首次在宝鸡－兰州铁路复线东巨寺沟铁路隧道选取试验段,实施湿喷工艺喷射聚丙烯纤维混凝土,作为支护结构兼作永久性支护,免除二次衬砌工作,并进行水平位移收敛监测。采用非线性最小二乘法对该隧道水平收敛曲线进行回归分析,同时采用隧道稳定性模糊概率分析理论对不同断面位置处的隧道围岩稳定性进行判别分析。分析结果表明,采用湿喷纤维混凝土支护的隧道围岩处于稳定状态,可靠度指标高。     

Multiphase model for inclusion‐reinforced geostructures: Application to rock‐bolted tunnels and piled raft foundations

A multiphase model is proposed to describe the mechanical behaviour of geomaterials reinforced by linear inclusions. This macroscopic approach considers the reinforced soil or rock mass as the superposition of continuous media. Equations of motion and constitutive laws of the model are first derived. Its implementation in a finite element computer code is then detailed. A modified implicit algorithm for elastoplastic problems is proposed. The model and its implementation are fully validated for rock‐bolted tunnels (comparison with scale model experiments) and piled raft foundations (comparison with the classical ‘hybrid method’). The Messeturm case history is finally presented to assess the handiness of the approach for real structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of Numerical and Analytical Methods to Geotechnical Engineering

This is a summing-up report of the topic on application of numerical and analytical methods to geotechnical engineering, presented in the Third National Symposium on Numerical and Analytical Methods in Geomechanics. The application to rock mass and engineering is emphasized in this paper, based on the papers submitted to this symposium.     

数值解及解析解在岩体工程中的应用

本文是在第三届全国岩土力学数值分析和解析方法讨论会上所作的专题综述报告,是据提交给会议的部分论文,着重从数值方法在岩体工程的应用方面进行概括。它包括以下若干方面的课题,如岩体本构方程的模拟、锚喷支护的分析、岩体工程的反分析计算、洞室及竖井的围岩稳定与支护以及高边坡的稳定分析。从所提交的会议论文来看,在研究上述课题时,所采用的方法种类繁多,并具有独特的见解,它们在工程上的应用也已经取得了可喜的成效。     

Analysis of the in situ Hydromechanical Behavior of a Fractured Calcareous Rock Mass

Summary. Hydromechanical experiments have been carried out since 1997 within a small fractured calcareous rock mass in southeastern France, at a site called Coaraze. Simultaneous measurements of fluid pressure and joint displacement were performed during these experiments. The interpretation generated has led to characterizing various types of hydromechanical behavior of the jointed rock mass and has provided several lessons. An original analytical interpretation, coupled with a modeling approach, has allowed one to derive the in situ normal joint stiffness, which proves to be highly non-linear. It has been shown that a coefficient able to take into account stiffness contribution from the surrounding rock mass must be included in order to fully interpret the pressure-displacement curves. This analytical interpretation also yields an estimate of the normal stress across the fracture. A comparison between in situ data and laboratory tests is also presented.     

Rock–support interaction analysis based on numerical modelling

The use of yield in supports to control the final loading that develops upon a support system has been one of the most important deformation control techniques used by tunnelling engineers, both historically and currently. Successful use of this approach requires a thorough understanding of the process of rock–support interaction as it is an approach that can fail dramatically if incorrectly applied. There is a fine line between the yield support technique improving the conditions, and the approach resulting in the development of a large area of failed rock, which could ultimately be detrimental. The relationship between the support action and the rock has historically been studied using analytical approaches with the application of significant simplifying assumptions.This paper presents a new approach, where a state-of-the-art numerical model is run repeatedly to develop rock–support interaction curves. This has the advantage of allowing more realistic tunnel geometry, stress states and ground conditions to be simulated. It does, however, use the familiar output form of the relatively simple rock–support interaction curve as opposed to complex and voluminous graphics. Its disadvantage lies in the considerable number of computer runs required to develop the full solutions. Computer software has, however, been written to automate much of this process using a programming language within the modelling package.The analysis approach has been further improved by plotting not one rock–support interaction curve but a whole family of curves representing variations in the rock mass quality of the assumed ground, since this is the most variable of the input parameters for most tunnelling situations. This form of output allows engineers to study the practical range of yield they may require for their rock conditions and also to define at what rock mass quality they can expect the yielding approach to cease to be an effective strategy. This new approach has been presented on a test case history with idealized rock mass properties to illustrate the approach. However, it is an approach that can be specially tailored to any set of rock conditions, tunnel geometry or stress.     

Numerical modelling of reinforced jointed rock masses I. Theory

The concept of reinforced multi-laminates has been developed and applied to the analysis of reinforced jointed rock masses. The discontinuities and reinforcements in the rock mass are assumed to occur in regular sets, with relatively close spacing within sets. The constitutive equations are established for an ‘equivalent material’, this being identical in its mechanical response to the reinforced jointed rock mass, consisting of its components, i.e. rock material, sets of discontinuities, and sets of reinforcements with associated sets of interfaces. An elasto-visco/plastic algorithm is used so that each component is described by its elastic, failure and flow properties together with its relative orientation. The constitutive equations for the ‘equivalent material’ can be applied to determine optimal reinforcement arrangements for problems of various levels of complexity. Several practical examples illustrating this are contained in a companion paper.     

Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework

Rock mass failure is a particularly complex process that involves the opening and sliding of existing discontinuities and the fracturing of the intact rock. This paper adopts an advanced discretisation approach to simulate rock failure problems within the discontinuous deformation analysis (DDA) framework. The accuracy of this approach in continuum analysis is verified first. Then, the advanced discretisation approach for fracturing modelling is presented, and the discretisation strategy is discussed. Sample rock static failures are simulated and the results are compared with experimental results. Thereafter, with a generalised definition of the artificial joints, this approach is further extended and applied in the simulation of blast-induced rock mass failures in which the instant explosion gas pressure obtained by the detonation pressure equation of state is loaded on the main blast chamber walls and the induced surrounding connected fracture surfaces. In the simulation instance of rock mass cast blasting, the whole process, including the blast chamber expansion, explosion gas penetration, rock mass failure and cast, and the formation of the final blasting pile, is wholly reproduced.     

裂隙岩体变形模量尺寸效应研究Ⅱ:解析法

通过分开考虑岩块和裂隙对岩体变形的贡献,研究了任意裂隙分布岩体等效变形模量的解析计算方法,并用正交裂隙岩体对该方法进行了验证,得到的结果和经典解析解完全一致。此外,通过该方法对锦屏Ⅱ级电站辅助洞中段随机裂隙岩体进行不同尺寸、不同方位下等效变形模量的计算,计算结果显示,随着岩体尺寸的增大,不同方位的变形模量值趋于稳定,该裂隙岩体变形模量的特征单元对(REV)尺寸为8 m,和有限元计算结果一致。结果表明该方法可以用来研究裂隙岩体等效变形模量尺寸效应和各向异性特性,研究成果对于裂隙岩体等效变形参数取值具有重要意义。     

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     

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 2: Stochastic Approach

Summary This paper reports the second part of the study carried out by the authors on the underground explosion-induced stress wave propagation and damage in a rock mass. In the accompanying paper reporting the first part of the study, equivalent material properties were used to model the effects of existing cracks and joints in the rock mass. The rock mass and its properties were treated as deterministic. In this paper, existing random cracks and joints are modeled as statistical initial damage of the rock mass. In numerical calculation, an anisotropic continuum damage model including both the statistical anisotropic initial damage and cumulative damage dependent on principal tensile strain and stochastic critical tensile strain is suggested to model rock mass behavior under explosion loads. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. The suggested models and statistical solution process are also programmed and linked to Autodyn3D as its user's subroutines. Numerical results are compared with the field test data and those presented in the accompanying paper obtained with equivalent material property approach.     

A 2D coupled finite element and boundary element scheme to simulate the elastic behaviour of jointed rocks

In this paper a coupled finite and boundary element formulation is developed for the analysis of excavation in jointed rock. The presence of joints in the rock mass has been included implicitly by treating it as an appropriate anisotropic elastic continuum. The boundary element formulation for an anisotropic medium is briefly discussed. Good agreement has been found between numerical and analytical solutions for several example problems, demonstrating the accuracy of the present formulation. Numerical solutions are also presented for the problems of a deep circular tunnel and a basement excavated in a variety of jointed rock masses.     

Analytical model for the design of grouted rock bolts

An analytical model which represents the behaviour of a reinforced rock mass near a circular underground opening in a homogeneous, uniform stress field has been developed. The theory adopts the concepts of elastoplasticity and considers a proper interaction mechanism between the ground and the grouted (or friction) bolts. It highlights the influence of the bolt pattern on the extent of the yield zone and tunnel deformation. A dimensionless parameter is introduced as a design tool which relates the tunnel convergence to the bolt spacing for a given bolt length. This publication contains the derivation of the analytical model and an illustration of the effect of bolts on the stress and displacement field near an opening. Its application to tunnel design is discussed briefly. The verification of the theory by laboratory simulation and field measurements will be presented, in detail, in a future publication.