Demonstration of spatial anisotropic deformation properties for jointed rock mass by an analytical deformation tensor

This paper develops a joint deformation tensor (JD), which considers all of the joint's mechanical and geometrical parameters that affect the deformability of the rock mass. The method based on JD (JD method) and an elastic deformation anisotropy index (EDAI) are deduced for estimating the spatial anisotropy deformation of a jointed rock mass. The numerical modeling and in situ true triaxial compressive experiments well verified the effectiveness of the EDAI and JD method for the rock mass containing one joint set, orthogonal joint sets or the rock mass containing any types of joint network with unity stiffness ratio.     

An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

In this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second‐order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd.     

Critical review on shear strength models for soil-infilled joints

An infilled rock joint is likely to be the weakest plane in a rock mass. The presence of infill material within the joint significantly reduces the friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the infill material governs the overall shear strength, and the joint walls (rock) play no significant role. Several models have been proposed to predict the peak shear strength of soil-infilled joints under both constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a). CNS models provide a more realistic picture of the soil-infilled joint behaviour in the field. This paper presents a critical review on the existing mathematical models for predicting the shear strength of soil-infilled rock joint and verifies the normalised peak shear stress model with further laboratory investigations carried out on idealised saw-tooth rock joints at the University of Wollongong. Based on the prediction of the experimental data, the normalised peak shear stress model is slightly modified by the authors. A simplified approach for using this model in practice is presented and a new expression for prediction of dilatation at peak shear stress is suggested.     

Stability analysis of a jointed beam

A numerical step-by-step procedure, analogous to the ‘Initial Stress Method,’ is presented for the analysis of a single-layer jointed rock beam subjected to gravity loads and in-plane in situ formation pressure. The joints are permitted to open at locations where the flexural stresses exceed flexural strength. The material properties may be different for each rock block and joint. A detailed algorithm is given for the solution of the problem. The results of several analyses indicating the relative effects of initial formation pressure, transverse load, stiffness of the joint material, and joint spacing on the response of a jointed beam are presented. The convergence characteristics of the numerical procedure are included. The joint material is assumed to be ‘no-tension’ type. Both the geometric and material non-linear effects are considered.     

Distinct element modeling and analysis of mining-induced subsidence

Summary The influence of rock discontinuities on mining-induced subsidence is addressed in this paper. A two-dimensional rigid block computer model was used to simulate discontinuities within strata overlying a longwall coal mine. Input for the model was available from a previous field study and numerical experiments were performed by varying the simulated joint stiffness, joint roughness, and vertical joint density. A comparison of simulated and measured displacements both within the overburden and on the surface provides insight into the influence of rock discontinuities. For the case in which all contacts had a relatively low stiffness, the maximum simulated subsidence was 293 mm whereas the case involving variable, but higher contact stiffness produced a maximum subsidence of only 73 mm reflecting the influence of increased overall stiffness. By comparison, the maximum measured subsidence was 580 mm. Consequently, the model behaved more stiffly than the actual rock mass but still provided a reliable simulation of block caving and strata separation. A comparison of simulated and observed displacements within the overburden suggests that horizontal discontinuities not included in the rigid block mesh above the zone of caving controlled rock mass compliance.List of Symbols c joint stiffness ratio [dimensionless] - d strata thickness ratio [dimensionless] - e strata modulus ratio [dimensionless] - E _a modulus of stratum a [MPa] - E _b modulus of stratum b [MPa] - E _equiv equivalent rock mass modulus [MPa] - E _u unconfined compression modulus of intact rock [MPa] - F _n contact normal force [N] - h overburden thickness [m] - k _a normal spring stiffness of stratum a [N/m] - k _b normal spring stiffness of stratum b [N/m] - k _equiv equivalent rock mass spring stiffness [N/m] - K _n normal material stiffness of joint [MPa/m] - K _s shear material stiffness of joint [MPa/m] - m mined thickness of coal seam [m] - q _u unconfined compressive strength of intact rock [MPa] - Sh shale - Ss sandstone - Sh/Ss shale/sandstone interbeds - S _max maximum subsidence [m] - SLEX Slope Indicator inclinometer/Sondex extensometer - T _a thickness of stratum a [m] - T _b thickness of stratum b [m] - T _j joint thickness [m] - u _a compression of stratum a [m] - u _b compression of stratum b [m] - u _j compression of joint [m] - u _total total compression of strata and included joint [m] - w width of longwall panel [m] - _n normal stress [MPa]     

Effect of rock discontinuities on certain rock strength and fracture energy parameters under uniaxial compression

Summary Five series of test blocks of Pendeli marble with artificially created discontinuities of different crack densities (simulating three mutually orthogonal joint sets) were tested in uniaxial compression in order to study the effect of discontinuities on: (a) the compressive strength and the modulus of elasticity, and (b) certain fracture energy parameters expressed by the ratio W _A/W _V, where W _A is the surface energy and W _V the volume elastic strain energy. Mathematical relationships are derived similar to those suggested by other authors relating strength parameters to crack densities. Such relationships clearly show a reduction in strength with increased crack density. The experimental results obtained permit the extension of Persson's relation (which refers to ideal intact rock) to the more realistic case of discontinuous rock mass by introducing the appropriate term that takes into consideration the effect of rock mass discontinuities on the energy ratio W _A/W _V. A comparison between laboratory results and field observations was subsequently carried out assuming the rock mass to behave as a linearly elastic material, obeying the Hoek and Brown failure criterion. This comparison showed that laboratory results can be extended to larger scale. Furthermore, in order to predict the in situ strength and stability of a rock mass in uniaxial compression (which is of major importance in underground excavations) certain concepts are proposed based on laboratory tests, in situ investigations and first principles of linear elastic fracture mechanics.     

Limiting equilibrium versus BS3D analysis of a tetrahedral rock block

In order to analyze the stability of a 3D rock block using a limiting equilibrium method, some simplifications must be introduced, such as neglecting the effects of deformability of the rock block, fractures, and the surrounding rock mass, the progressive failure and the mobilization of shear strength of fractures, and changes in in situ stresses with block displacement. These limitations may cause some errors when calculating the factor of safety of the block. This paper quantifies the error caused by these simplifications comparing the results against those obtained with a numerical method (BS3D). In addition, the effects of the normal stiffness of the fractures, dilatancy, the tunnel radius, and the block size on stability of the tetrahedron are investigated using the numerical tool to demonstrate the importance of the effects eliminated by the limiting equilibrium approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental Study of Ultrasonic Waves Propagating Through a Rock Mass with a Single Joint and Multiple Parallel Joints

Experiments were conducted to study the relationship between the transmission ratio (TR) and normal stress, joint roughness, joint number and frequency of incident waves, respectively, when ultrasonic waves pass across a rock mass with one joint and multiple parallel joints oriented normally. The ultrasonic waves were generated and received by pairs of piezoelectric transducers and recorded by an ultrasonic detector. The specimens were subjected to normal stress by a hydraulic jack and loading frame. The jointed rock mass was produced by superposing rock blocks in the study. Rough joints were produced by grooving notches on the planar joints formed by sawing directly. In the case of multiple parallel joints, the overall thickness of specimens was maintained while the joint number changed. Three pairs of P-wave transducers and one pair of S-wave transducers with different frequencies were, respectively, applied and all transducers emitted signals perpendicular to the joints in the experiment. The results indicate that TR increases with increasing normal stress while the increment rate decreases gradually. This is particularly so when the normal stress is high enough that TR will approximate 1 even if the rock mass has many joints. In addition, the experiments indicate that the higher the wave’s frequency, the lower its TR, and this phenomenon is gradually reduced as the normal stress increases. In response to S-waves, TR increases with increase in joint roughness; however, in response to P-waves, TR decreases gradually with increase in joint roughness. For multiple parallel joints in a fixed thickness rock mass with normally incident P-waves, TR does not always decrease with increase in the number of joints, and there is a threshold joint spacing for a certain incident wave: when the joint spacing is smaller than the threshold value, TR will increase with a decrease in joint spacing. The experimental results support similar conclusions based on analytical results drawn by Cai and Zhao (Int J Rock Mech Min Sci 37(4):661–682, 2000), Zhao et al. (Int J Rock Mech Min Sci 43(5):776–788, 2006b) and Zhu et al. (J Appl Geophys 73:283–288, 2011a).     

砂岩型铀矿微区原位U-Pb同位素定年技术方法研究

铀矿物定年一直是成矿年代学中的难点,随着微区原位U-Pb同位素定年技术的发展,可以直接针对矿石矿物(铀矿物)进行同位素定年;但是其中的砂岩型铀矿由于其存在状态复杂,在原位定年中剥蚀要求高,也缺乏合适的外部校正标准物质,所以定年准确度有待提高。本文研究了两种微区原位U-Pb同位素测年的方法,对砂岩型铀矿定年进行了尝试,试图解决铀矿测年中的无基体匹配问题并提高砂岩型铀矿定年水平。一是建立了一种激光剥蚀多接收电感耦合等离子体质谱仪联合电子探针进行微区原位U-Pb同位素测年的技术(LA-MC-ICP-MS&EMPA)。通过优化实验方法,对秦岭陈家庄花岗岩型铀矿进行了测试,获得与同位素稀释热电离质谱法(ID-TIMS)一致的年龄结果,证明了微区原位U-Pb同位素测年无基体匹配标准物质分析的可行性;并利用此法获得鄂尔多斯盆地红庆河和塔然高勒砂岩型铀矿的微区原位U-Pb同位素年龄信息。二是尝试了利用飞秒激光剥蚀多接收电感耦合等离子体质谱法(fsLA-MC-ICP-MS)对红庆河和宁夏宁东砂岩型铀矿样品进行微区原位U-Pb同位素定年,并获得了微区原位U-Pb同位素年龄,表明飞秒激光剥蚀技术在砂岩型铀矿定年中有很好的应用前景。本文提出,比较单一且年龄偏老的单矿物样品可以选择LA-MC-ICP-MS&EMPA联合法进行分析,需要高空间分辨率的样品建议使用fsLA-MC-ICP-MS法。     

Tunnel blasting techniques in difficult ground conditions

Summary The quality of tunnelling can be improved by proper blast design which takes into account the rock mass conditions. The effects of different rock mass properties on tunnel blast performance need to be assessed. The strength of the formation and joint orientation critically affected fragmentation and overbreak in a model study of blasting. Similar effects were noted in situ when the performance of a blast pattern in different rock mass conditions in the Tandsi inclines (Bihar, India) were analysed. Accordingly, the on-going blast pattern was modified for the poor ground conditions prevailing in the rest of the inclines. Improved fragmentation and smooth profile were obtained as a result; the rate of drivage improved considerably and the cost of excavation was reduced. Based on the observations in the model studies and the investigations at Tandsi, some guidelines for optimum blast design in difficult ground conditions are suggested.     

Visualization of rock mass classification systems

A rock mass classification system is intended to classify and characterize the rock masses, provide a basis for estimating deformation and strength properties, supply quantitative data for mine support estimation, and present a platform for communication between exploration, design and construction groups. In most widely used rock mass classification systems, such as RMR and Q systems, up to six parameters are employed to classify the rock mass. Visualization of rock mass classification systems in multi-dimensional spaces is explored to assist engineers in identifying major controlling parameters in these rock mass classification systems. Different visualization methods are used to visualize the most widely used rock mass classification systems. The study reveals that all major rock mass classification systems tackle essentially two dominant factors in their scheme, i.e., block size and joint surface condition. Other sub-parameters, such as joint set number, joint space, joint surface roughness, alteration, etc., control these two dominant factors. A series two-dimensional, three-dimensional, and multi-dimensional visualizations are created for RMR, Q, Rock Mass index RMi and Geological Strength Index (GSI) systems using different techniques. In this manner, valuable insight into these rock mass classification systems is gained.     

The Potassium‐Argon Laser Experiment (KArLE): In Situ Geochronology for Planetary Robotic Missions

Geochronology is a fundamental measurement for planetary samples, providing global and solar system context for the conditions prevailing on the planet at the time of major geological events. The potassium (K)‐Argon (Ar) laser experiment (KArLE) will make in situ noble gas geochronology measurements aboard planetary robotic missions such as rovers and landers. Laser‐induced breakdown spectroscopy (LIBS) is used to measure the K abundance in a sample and to release its noble gases; the evolved Ar is measured by mass spectrometry, and relative K content is related to absolute Ar abundance by sample mass, determined by optical measurement of the ablated volume. This approach allows K and Ar to be measured on identical volumes multiple times to create an isochron, which improves the age determination and reveals irregularities in the rock if they exist. The KArLE technique measures a whole‐rock K‐Ar age with 10% uncertainty or better for rocks 2 Ga or older, sufficient to resolve the absolute age of many planetary samples. The LIBS–mass spectrometry approach is attractive because the analytical components have been flight‐proven, do not require further technical development and provide essential measurements (complete elemental abundance, evolved volatile analysis, micro‐imaging) as well as in situ geochronology.     

峰前循环剪切作用下岩石节理剪切力学特性

微震、工程爆破等低应力循环剪切荷载作用对节理岩体工程失稳破坏具有重要影响。为研究峰前循环剪切加卸载作用下岩石节理剪切力学特性,采用RDS-200型岩石节理剪切试验系统对人工劈裂黄砂岩节理进行了峰前循环剪切下的直剪试验。通过与未进行峰前循环剪切加卸载时岩石节理力学参数预测值对比,得到峰前循环剪切加卸载作用对峰前剪切刚度、峰值剪切强度、峰值剪切位移与残余剪切强度的影响。结果表明：（1）峰前循环剪切加卸载后,当法向应力为2 MPa时,岩石节理峰前剪切刚度增大,当法向应力为4～10 MPa时,岩石节理峰前剪切刚度在循环剪切应力幅值范围内增大,在超出循环剪切应力幅值时减小;（2）峰前循环剪切加卸载后,峰值剪切强度降低了10%～20%,降低百分比随法向应力增大整体呈对数函数增大;峰值剪切位移增加了2%～40%,增加百分比随法向应力增大整体呈对数函数减小;（3）峰前循环剪切加卸载后,岩石节理残余剪切强度无明显变化,峰值剪切强度与残余剪切强度差值减小,峰后剪切应力做功损失百分比降低。     

Enriched finite element procedures for analyzing decoupled bolts installed in rock mass

Numerical procedures are developed to analyze interaction between fully grouted bolts and rock mass using ‘enriched finite element method (EFEM)’. A solid element intersected by a rock bolt along any arbitrary direction is termed as ‘enriched’ element. The nodes of an enriched element have additional degrees of freedom for determining displacements, stresses developed in the bolt rod. The stiffness of the enriched element is formulated based on properties of rock mass, bolt rod and grout, orientation of the bolt and borehole diameter. Decoupling at grout–bolt interface and elasto‐plastic behavior of rock mass have also been incorporated into the EFEM procedures. The results of this method are compared with analytical pull‐out test results presented by Li and Stillborg (Int. J. Rock Mech. Min. Sci. 1999; 36 :1013–1029). In addition, a numerical example of a bolted tunnel is provided to demonstrate the efficacy of the proposed method for practical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

The First James K. Mitchell Lecture In situ soil testing: from mechanics to interpretation†

The current use of fundamental mechanics in developing rational interpretation methods for deriving soil properties from in situ test results is reviewed and evaluated. The focus is on some of the most widely used in situ test devices including cone penetrometers with and without pore pressure measurements (CPTU and CPT), self-boring and cone pressuremeters (SBPMT and CPMT), and flat dilatometers (DMT). In situ tests in both cohesive and frictional soils for measuring strength and stiffness properties, in situ state parameters, consolidation coefficients, stress history, and in situ stresses are considered in detail.     

A three-dimensional equivalent continuum constitutive model for jointed rock masses containing up to three random joint sets

A three dimensional constitutive model is formulated for deformation analysis of jointed rock masses containing up to three joint sets with arbitrary spatial configurations. A representative elementary volume (REV) that represents the deformational response of the rock mass is defined and the constitutive relationships are developed based on superposition of deformations of the REV components. By representing the constitutive relationships in a tensorial form, the model is able to implement deformation anisotropy of jointed rock masses. The Mohr-Coulomb failure criterion with tension cut-off is used for the intact rock and the joint sets. The model is implemented in FLAC^3D and the deformations and strength values calculated by the model are compared with the results from a 3DEC model and analytical solutions. The model results are in good agreement with those obtained from 3DEC.     

Manuel Rocha Medal Recipient Wave interaction with underground openings in fractured rock

Summary The objective of this work is to lead to improved models of seismic wave propagation around underground openings by studying the interaction of the waves with the fractured rock surrounding these openings. It demonstrates that seismic models can help in stability problems such as rockbursting in deep-level mining, or in the interpretation of micro-fracturing at waste storage sites. A significant emphasis is placed on comparing the models with observations from controlled experiments. These comparisons demonstrate that the wave propagation can be reliably and accurately modelled, and in so doing it motivates their application to the larger rock engineering problems. Seismic wave models are first applied to laboratory experiments on multiple fractures. Simulation through multiple displacement discontinuities yields strikingly similar waveforms to the experiments, while also identifying the need to build stress dependence into the fracture models, such as stress dependent fracture stiffness. The wave-fracture modelling is extended to in situ fractures in rock at the surface of a deep tunnel, using data collected during an acoustic emission experiment at the URL Mine-by tunnel. Waveforms from the velocity scans are compared against those from elastic models and various models of fracture, such as random assemblies of small open fractures (cracks) and larger fractures with fracture stiffness. Results indicate that it is possible to account for the wave-speeds and amplitudes using models with fractures. A generic method is then proposed for calculating the frequency variation of wave-speed and amplitude for any collection of cracks. The models of fracture are then applied to the rockburst problem, to investigate how the excavation affects the amplitude and the distribution of ground motion. The results provide important insights into the causes of the apparent amplification observed by researchers in this field. The thesis also covers the theory of the models used, including novel numerical work on dispersion and new grid schemes. The full detail of the work cannot be covered in this paper which instead seeks to summarize the main achievements.     

Shear Load Transfer Characteristics of Drilled Shafts Socketed in Rocks

This paper presents a shear load transfer function and an analytical method for estimating the load transfer characteristics of rock-socketed drilled shafts subjected to axial loads. A shear load transfer (f–w) function of rock-socketed drilled shafts is proposed based on the constant normal stiffness (CNS) direct shear tests. It is presented in terms of the borehole roughness and the geological strength index (GSI) so that the structural discontinuities and the surface conditions of the rock mass can be considered. An analytical method that takes into account the coupled soil resistance effects is proposed using a modified Mindlin’s point load solution. Through comparisons with load test results, the proposed methodology is in good agreement with the general trend observed in in situ measurements and represents an improvement in the prediction of the shear behavior of rock-socketed drilled shafts.