Post-failure behavior of two mine pillars confined with backfill

Researchers from the National Institute for Occupational Safety and Health used a series of instruments (borehole extensometers, earth pressure cells, and embedment strain gauges) to study the post-failure behavior of two pillars confined by backfill in a test section at the Buick Mine near Boss, MO, USA. Evaluation of these pillars was part of a research project to assess the safety of the test section when high-grade support pillars were mined.Data from borehole extensometers installed in several backfill-confined pillars and numerical modeling indicated that these pillars failed during extraction of the support pillars. Failure was corroborated by the post-yield pillar strain response in which the immediate elastic strain was negligible compared to the time-dependent strain component measured between blasting rounds.A three-dimensional, finite-element program with an elastic perfectly plastic material model was calibrated using extensometer data to estimate rock mass modulus and unconfined compressive strength. The resulting rock mass modulus was 45–60% of the average deformation modulus obtained from laboratory tests, and the calibrated compressive strength was 40% of average laboratory values. A rock mass modulus equal to 52% of the average laboratory deformation modulus was calculated using the rock mass rating (RMR) system. Rock mass strength was calculated with the generalized Hoek–Brown failure criterion for jointed rock and indicated that in situ strength was 33% of laboratory strength. Post-failure stresses calculated by the finite-element model were larger for confined pillars than post-failure stresses in unconfined pillars calculated using empirical plots. Data from the calibrated model provided a strain-hardening stress-versus-strain relationship. This knowledge is critical for the design of mines that use partially failed pillars to carry overburden load.     

Modelling a mine-by test at the Mont Terri rock laboratory, Switzerland

An instrumented mine-by test was conducted at the Mont Terri rock laboratory, Switzerland in 1997–1998 to assess issues associated with tunnel excavation in a middle Jurassic claystone known as the Opalinus Clay. Excavation-induced stresses resulted in unusually large deformations and the development of an excavation disturbed zone (EDZ) around the tunnel where the observed dominant mode of yielding consisted of extensional fracturing. From field and laboratory observations, it has been observed that Opalinus Clay exhibits responses that often are not represented adequately by linear-elastic or elasto-plastic models. In particular, strong non-linear elastic behaviour at low stresses was observed in laboratory tests. This behaviour has been captured by a phenomenological-based model, known as the stress-dependent modulus (SDM) model. The concepts of the SDM model have been extended to a piece-wise pore pressure formulation that captures the hydromechanical rockmass response. These models were implemented into a finite difference method numerical code and used to simulate the short-term deformations and pore pressure response of the ED-B mine-by test. These simply calibrated models provided a reasonable fit to the field data, particularly in regions of unloading where rockmass deformations were not dominated by dilation.     

Obtaining dynamic complete stress–strain curves for rock using the Split Hopkinson Pressure Bar technique

The feasibility of using the Split Hopkinson Pressure Bar (SHPB) technique to obtain complete dynamic stress–strain curves for rock is established in the laboratory. The SHPB test system, in conjunction with a mean strain hypothesis, can be used not only for obtaining the rock’s constitutive curve before the peak strength but also after the peak strength — and so it is possible to analyze and characterize the post-failure behaviour of rock with the SHPB method. Some typical complete dynamic curves for marble and granite are given in this paper, together with an interpretative discussion on the shapes of the curves.     

A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses

This paper presents a simple procedure for the ground response curve of a circular tunnel excavated in elastic-strain softening rock mass compatible with a linear Mohr–Coulomb or a nonlinear Hoek–Brown yield criterion. The numerical stepwise procedure proposed by Brown et al. [Brown, E.T., Bray, J.W., Ladanyi, B., Hoek, E., (1983). Ground response curves for rock tunnels. J. Geotech. Eng. ASCE 109, 15–39] is modified by including the effects of elastic strain increments and variable dilatancy within the plastic region. The accuracy and practical application of the proposed procedure are shown through some examples. Four different combinations of dilatancy angle and softening parameter are considered to investigate the effects of elastic strain increments and variable dilatancy within the plastic region. The effects of variable dilatancy and peak dilatancy angle on the ground response curve are investigated for tunnels in poor-to-good-quality rock masses. The results show the importance of correctly estimating peak dilatancy angle in elastic-perfectly plastic and elastic-strain softening Hoek–Brown media.     

Methodology for tunnel and portal support design in mixed limestone, schist and phyllite conditions: a case study in Turkey

The purpose of this study is to present a methodology for tunnel and support design in mixed limestone, schist and phyllite conditions through investigating two highway tunnel case studies that are located along the Antalya–Alanya Highway in southern Turkey. The main lithologies of the project area are regularly jointed, recrystallized limestone and the weak lithologies of the schist unit (i.e., pelitic schist, calc schist, graphitic phyllite and alternations of these lithologies). A detailed geological and geotechnical study was carried out in the project area, and the tunnel ground support types and categories were determined according to the Q-system, rock mass rating method and New Austrian Tunneling Method (NATM). The shear strength parameters and geomechanical properties of the rock masses were obtained by using the geological strength index (GSI). The deformation moduli and post-failure behavior of the rock masses have been determined. Slope stability analyses were performed at the portal, side or cut slope sections. Kinematic and limit equilibrium analyses incorporating the effects of water pressure were performed for the regularly jointed failed rock slopes. Circular failure analogy was used for the slope stability analyses of irregularly jointed, highly foliated lithologies. Slope support system recommendations were made. A back analysis on a failed slope was performed. The results of the back analysis compared well with the results obtained through the GSI method. The tunnel grounds were divided into sections according to their rock mass classes. The deformations and stress concentrations around each tunnel section were investigated and the interactions of the empirical support systems with the rock masses were analyzed by using the Phase² finite element software. The regularly jointed rock masses were modeled to be anisotropic and the irregularly jointed, highly foliated and very deformable soil-like lithologies were modeled to be isotropic in the tunnel finite element analyses.     

岩石峰后剪胀效应研究综述

岩石破裂后会发生体积膨胀且仍具有一定的承载能力,煤矿中多利用岩石的该性质进行支护.作者从研究岩石峰后特性的重要工程意义着手,叙述了岩石峰后剪胀的概念、发展历史和研究现状,以及目前研究中存在的问题,强调了研究岩石峰后剪胀效应的重要性.     

Effect of rock mass quality on construction time in a road tunnel

On the basis of the existing NTNU (Norwegian University of Science and Technology) advance rate model and field experiences, an estimation model which can analyze construction time for a broad range of works related to tunnel construction by drill and blast has been established. The model includes the time spent for excavation, rock support, various installations in the tunnel, and site preparation. The model is developed as a spreadsheet. Furthermore, by the use of the model, analyses on various effects of rock mass quality on construction time and advance rate for four Q-values of 0.01, 0.1, 1.0 and 10.0 on seven sizes of road tunnels applied in Norway were made. The results show that construction time increases up to 30–40% with cross sectional area varying from T5 (35.2 m²) to T12 (86.9 m²) under the assumption that the same Q-value is applicable to the entire tunnel length. Standard advance rate considering the effect of rock mass quality may be about 50% lower for Q = 0.01 than in the case of not considering the same effect in a 3 km tunnel. The gap between the two standard advance rates is gradually decreasing with increased Q-value.     

Uncertainty analysis of tunnel squeezing for two tunnel cases from Nepal Himalaya

Weak rocks such as shale, slate, phyllite and schist, and the rock mass of weakness/fault zones are incapable of sustaining high tangential stress. Severe tunnel squeezing is therefore common in the tectonically active Himalayan rock mass and is one of the major areas of concern regarding stability. A reliable prediction of the extent of squeezing is essential so that a strategy can be established regarding stabilizing measures and for optimizing the support well in advance (during planning and design). In this paper, a probabilistic approach to uncertainty analysis that focuses on the effect of the variations in each input parameter of squeezing is used for analyzing and predicting the extent of tunnel squeezing for two tunnel cases in Nepal; Kaligandaki “A” (completed) and Middle Marsyangdi (under construction). A semi-analytical method suggested by Hoek and Marinos [Predicting tunnel squeezing problems in weak heterogeneous rock masses. Tunnels Tunnell Int, 2000; 32(11 and 12): 45–51 and 34–36] for predicting squeezing, an empirical formula proposed by Panthi [Analysis of engineering geological uncertainties related to tunnelling in Himalayan rock mass conditions. PhD thesis, Department of Geology and Mineral Resources Engineering. Norwegian University of Science and Technology (NTNU), Norway, 2006] and the Palisade's 2002 version of @Risk statistical software program have been used for the uncertainty analysis. The analysis results for Kaligandaki indicate fairly good correlation between predicted and actually measured squeezing. The same approach has been used for predicting the degree of tunnel squeezing at Middle Marsyangdi tunnel. It is concluded that the methodology proposed in this paper has potential for predicting the squeezing of future tunnel projects in weak rock mass conditions.     

Load-capacity estimation and collapse analysis of thin-walled beams and columns—recent advances

The present paper is devoted to the recent results of research in the area of load-capacity and post-failure behaviour of thin-walled beams and columns (among them thin-walled cold-formed profiles). It deals with ultimate load and collapse of box-section girders (tubes) of different cross-sections under bending, as well as of lipped and plain channel-section beam-columns. The paper contains the presentation of theoretical analysis and experimental investigation of plastic mechanisms of failure and collapse behaviour of these thin-walled sections. The short review of results obtained in recent years in general precedes those obtained by the Department of Strength of Materials and Structures, TUL. The problem of post-failure behaviour is solved using the rigid-plastic theory adopted and modified for the purposes of the solution taking into consideration strain-hardening of the member’s material. On the basis of experimental investigations theoretical models of plastic mechanisms of failure are produced for different sections. Theoretical analysis is based on the principle of virtual velocities. The problem is solved in an analytical–numerical way. The particular attention has been paid to the influence of the strain-hardening of the material after yielding upon the collapse structural behaviour and also to the influence of cross-section shape and dimensions on the character of collapse. The upper-bound estimation of the load-carrying capacity of analysed thin-walled sections by combining results of non-linear, elastic post-buckling analysis with the results of plastic mechanism analysis is carried out. Results are presented in diagrams showing post-failure curves as well as curves representing structural behaviour in the whole range of loading up to and beyond the ultimate load. Some results are compared with experimental results and those obtained from FE analysis. A comparison of lower- and upper-bound estimation of the load-carrying capacity is discussed and illustrated in diagrams. Conclusions dealing with the influence of strain-hardening phenomenon displayed by the material upon the load-carrying capacity and collapse behaviour of examined sections are derived. Also conclusions concerning different upper- and lower-bound estimations of the load-carrying capacity of analysed sections are presented.     

等效岩体技术在岩体工程中的应用

 以某露天矿边坡为工程背景,结合岩石力学参数室内和现场原位试验,基于颗粒流理论和PFC3D程序,运用等效岩体技术,建立充分反映节理分布特征并考虑细观破裂效应的等效岩体模型,采用Fish语言编制加卸载命令流,研究岩体的强度和力学效应。研究结果表明：(1) 等效岩体在单轴压缩时,轴向应力–应变曲线分为弹性变形阶段、非稳定破裂塑性阶段和破裂后阶段,抗压强度和弹性模量与标准岩块试样相比,有较大幅度降低;(2) 随围压增大,等效岩体抗压强度和残余强度明显提高,延性特征增强,逐渐向理想塑性过渡;(3) 等效岩体技术能有效地描述岩体受节理分布影响而表现的各向异性特征;(4) 等效岩体内部微裂纹主要沿节理走向分布并扩展,破坏形式受主导节理面产状及性质控制。     

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%).     

A three-dimensional hybrid boundary element method for non-linear analysis of a weak plane near an underground excavation

A three-dimensional hybrid boundary element method is developed for the analysis of non-linear behaviour of weak planes near underground excavations. The hybrid model adopts the fictitious stress method for the simulation of underground excavation and the displacement discontinuity method for the weak planes. Besides, the hybrid model employs linear elastic behaviour for the rock and the Barton-Bandis non-linear model for the weak plane. The developed model was verified and applied to analyze the problem of a tunnel penetrating a weak plane, in which the geometrical and material parameters were adopted from a tunnel project in central Taiwan. For the problem with the strike of the weak plane perpendicular to the tunnel axis, the numerical results show that: (1) the smaller the approaching angle, between the tunnelling direction and the dip direction of the weak plane, the larger the failure zone and the roof deformation; (2) the larger the RMR value, the smaller the deformation and failure zone; and (3) the larger the K (= σ_h/σ_u) ratio the larger failure zone will occur around the tunnel.     

Design and construction aspects of deep tunnels (with particular emphasis on strain softening rocks)

A series of railway tunnels will be dug through the European Alps at depths exceeding 2000 m over long stretches. The prevailing high stresses are expected to cause rock burst, large deformations and creep, depending on the nature of the rock. In the first part of the paper the theoretical relations between support pressure and tunnel wall displacements are briefly discussed. Emphasis is given to the post-failure behaviour of the rock mass and its influences on the tunnelling conditions. Frequently encountered strain softening rock types are shown to exhibit a strong dependence of the tunnel stability on the softening rate, which itself varies with the applied confinement pressure. Also discussed are results of laboratory tests and field observations which yield a critical deformation value for a given rock type. Beyond this value, the required support pressures are shown to increase sharply. Systematic monitoring of the rock deformations due to tunnelling can help to define the most adequate support measures and to improve the input values for static calculations by back analyses. Deep tunnels require support types able to control the tunnel wall displacements efficiently. They should oppose significant support pressures from incipient deformations up to large displacements. Various constructive solutions are discussed for-drill & blast as well as for TBM excavation. The last section briefly addresses time-dependent tunnel deformation and their influence on the time of placing the final lining.     

Effects of inelastic volume increase on fractured rock behaviour

This study investigated the correlation between inelastic volumetric deformation and the bearing capacity of fractured rock. Triaxial compression tests on marble specimens have been performed under constant and controlled deformation rates using a servocontrolled loading machine supported by an electro-hydraulic volume-measuring unit connected to a data acquisition system. The triaxial compression tests were carried out on two different marble samples under constant confining pressures ranging from 1–12.5 MPa. The results indicate that stress–inelastic volumetric strain curves are generally linear through the initial part of the post-failure curve where fractured rock behaviour is dominant. It was found that brittle rock loses its strength in the post-failure region depending on volumetric deformation; the slopes of post-failure curves change with an increase in confining pressure. As a result it is concluded that there is a relationship between strength and volumetric strain of fissured rock. Electronic Publication     

Geotechnical considerations in an unlined high pressure tunnel at Lower Kihansi in Tanzania

The Lower Kihansi unlined high-pressure tunnel is the first of its kind to be constructed in Tanzania. The pressure tunnel consists of a 500 m vertical shaft and a 2.195 km inclined headrace tunnel. The cross sectional area of the shaft is 25 m² and that of the headrace tunnel is 30–37.5 m². The headrace tunnel slopes 1:7 towards the powerhouse cavern. The pressure tunnel acts as waterway towards the underground hydroelectric power generation plants with a maximum generating capacity of 180 MW. The Kihansi River has been deviated through the shaft and headrace tunnel from an elevation of 1,146–300 m above sea level. The maximum water pressure created by this deviation is 8.5 MPa.The decision not to steel line the pressure tunnel was reached after the excavation and documentation of the underground rock mass. The hydraulic jacking and hydro-fracturing tests confirmed the rock to have a minimum acceptable confining stress of 9.6 MPa, capable of withstanding the expected water pressure in the tunnel. The permeability of the rock mass is relatively low and any poor zones were sealed by grouting.The discontinuities had a favourable orientation with respect to the tunnel axis such that rock bolts and steel fibre reinforced shotcrete could be used to provide the necessary support. No failures occurred and the decision not to line the Kihansi high-pressure tunnel has proved both technically acceptable and economical.     

A theoretical solution for analysis of tunnels below groundwater considering the hydraulic–mechanical coupling

An analytical solution for the analysis of tunnels below groundwater table in plane strain axisymmetric condition is presented. Seepage body force and secondary permeability of the rock mass due to the mechanical–hydraulic coupling are taken into account. The strain-softening behavior model and Hoek–Brown empirical strength criterion for the rock mass are used in the analysis. As the derived analytical equations do not have closed form solutions, a computer program has been prepared for solving the corresponding equations numerically and examining the analysis. It is shown that the tunnel stability depends on the seepage and the pore water pressure particularly in the case of high pore pressure gradient.     

Rigid-link and FE models for first-generation sheet-section failure

First-generation sheet-sections, loaded by bending moment and a concentrated load, fail by three distinct post-failure modes, the rolling, yield arc, and yield eye post-failure modes. This article shows a new, systematic study of a sheet-section failing by the yield eye post-failure mode, using a rigid-link (RL) and a finite-element (FE) model for a specific set of imperfections. The rigid-link model explains the complex, i.e., snap-back behaviour of sheet-sections if loaded by a load bearing plate. This snap-back behaviour will result in an abrupt decrease in load if displacement control is used. The FE model predicts, besides the post-failure modes mentioned, additionally the roof post-failure mode [Mahendran M. Thin-walled Struct 1997; 27(3): 245–61]. This failure mode always goes together with an abrupt decrease in load, and sometimes results in convergence problems. If the results of the RL and the FE models are compared, it can be shown that the RL model cannot explain FE convergence problems, as was believed in the past [Hofmeyer H, Kerstens JGM, Snijder HH, Bakker MCM. J Constr Steel Res 2002; 58(12): 1509–29].     

Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis

A powerful numerical method that can be used for modeling rock-structure interaction is the discontinuous deformation analysis (DDA) method developed by Shi in 1988. In this method, rock masses are treated as systems of finite and deformable blocks. Large rock mass deformations and block movements are allowed. Although various extensions of the DDA method have been proposed in the literature, the method is not capable of modeling water-block interaction, sequential loading or unloading and rock reinforcement; three features that are needed when modeling surface or underground excavation in fractured rock. This paper presents three new extensions to the DDA method. The extensions consist of hydro-mechanical coupling between rock blocks and steady water flow in fractures, sequential loading or unloading, and rock reinforcement by rockbolts, shotcrete or concrete lining. Examples of application of the DDA method with the new extensions are presented. Simulations of the underground excavation of the ‘Unju Tunnel’ in Korea were carried out to evaluate the influence of fracture flow, excavation sequence and reinforcement on the tunnel stability. The results of the present study indicate that fracture flow and improper selection of excavation sequence could have a destabilizing effect on the tunnel stability. On the other hand, reinforcement by rockbolts and shotcrete can stabilize the tunnel. It is found that, in general, the DDA program with the three new extensions can now be used as a practical tool in the design of underground structures. In particular, phases of construction (excavation, reinforcement) can now be simulated more realistically. However, the method is limited to solving two-dimensional problems.     

Three-dimensional nonlinear analysis for the coupled problem of the heat transfer of the surrounding rock and the heat convection between the air and the surrounding rock in cold-region tunnel

According to the basic theories of heat transfer, geocryology and fluid mechanics, taking the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding the tunnel into account, three-dimensional calculating model of the coupled problem are presented. The finite element formulae of this problem are obtained by Galerkin’s method, and the computer program of the finite element is compiled. Using the program, three-dimensional nonlinear analyses for the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding Fenghuo mountain tunnel on the Qinghai–Tibet Railway are made. The agreement between the calculated results and the in-situ observed data is seen to be very good. The calculated results illustrate that the freezing–thawing situation of the rock surrounding the tunnel can correctly be predicted even if the air temperature distribution along the tunnel is unknown. In thus way, the large cost of in-situ observation for the air temperature in the tunnel can be saved.     

连拱隧道围岩压力的释放率分析

连拱隧道作为公路隧道新的结构型式,理论上还不成熟.以云南省元磨高速公路的两座连拱隧道作为工程背景,按弹性阶段相似原则进行两组连拱隧道室内模型试验,包括隧道处于常规应力状态下和偏压状态下的模型试验.采用压力盒量测施工过程中隧道围岩压力,并提出了围岩压力释放率的概念,对连拱隧道开挖过程中围岩压力的变化特征进行了分析,同时对两种应力状态下的试验结果进行了对比分析.得出的结论对连拱隧道的设计和施工有积极的指导作用.