Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method(FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory(URL)Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks(DFNs)of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.     

Numerical simulation of hydraulic fracturing and associatedmicroseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress.
2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.     

GPGPU-parallelised hybrid finite-discrete element modelling of rock chipping and fragmentation process in mechanical cutting

Mechanical cutting provides one of the most flexible and environmentally friendly excavation methods.It has attracted numerous efforts to model the rock chipping and fragmentation process,especially using the explicit finite element method(FEM) and bonded particle model(BPM),in order to improve cutting efficiency.This study investigates the application of a general-purpose graphic-processing-unit parallelised hybrid finite-discrete element method(FDEM) which enjoys the advantages of both explicit FEM and BPM,in modelling the rock chipping and fragmentation process in the rock scratch test of mechanical rock cutting.The input parameters of FDEM are determined through a calibration procedure of modelling conventional Brazilian tensile and uniaxial compressive tests of limestone,A series of scratch tests with various cutting velocities,cutter rake angles and cutting depths is then modelled using FDEM with calibrated input parameters.A few cycles of cutter/rock interactions,including their engagement and detachment process,are modelled for each case,which is conducted for the first time to the best knowledge of the authors,thanks to the general purpose graphic processing units(GPGPU) parallelisation.The failure mechanism,cutting force,chipping morphology and effect of various factors on them are discussed on the basis of the modelled results.Finally,it is concluded that GPGPU-parallelised FDEM provides a powerful tool to further study rock cutting and improve cutting efficiencies since it can explicitly capture different fracture mechanisms contributing to the rock chipping as well as chip formation and the separation process in mechanical cutting.Moreover,it is concluded that chipping is mostly owed to the mix-mode Ⅰ-Ⅱ fracture in all cases although mode Ⅱ cracks and mode Ⅰ cracks are the dominant failures in rock cutting with shallow and deep cutting depths,respectively.The chip morphology is found to be a function of cutter velocdty,cutting depth and cutter rake angle.     

New approaches to quantify progressive damage and associated dynamic rock mass blockiness

In the past decade, numerical modelling has been increasingly used for simulating the mechanical behaviour of naturally fractured rock masses. In this paper, we introduce new algorithms for spatial and temporal analyses of newly generated fractures and blocks using an integrated discrete fracture network (DFN)-finite-discrete element method (FDEM) (DFN-FDEM) modelling approach. A fracture line calculator and analysis technique (i.e. discrete element method (DEM) fracture analysis, DEMFA) calculates the geometrical aspects of induced fractures using a dilation criterion. The resultant two-dimensional (2D) blocks are then identified and characterised using a graph structure. Block tracking trees allow track of newly generated blocks across timesteps and to analyse progressive breakage of these blocks into smaller blocks. Fracture statistics (number and total length of initial and induced fractures) are then related to the block forming processes to investigate damage evolution. The combination of various proposed methodologies together across various stages of modelling processes provides new insights to investigate the dependency of structure's resistance on the initial fracture configuration.     

Composite wedge failure using photogrammetric measurements and DFN-DEM modelling

Analysis and prediction of structural instabilities in open pit mines are an important design and operational consideration for ensuring safety and productivity of the operation. Unstable wedges and blocks occurring at the surface of the pit walls may be identified through three-dimensional (3D) image analysis combined with the discrete fracture network (DFN) approach. Kinematic analysis based on polyhedral modelling can be used for first pass analysis but cannot capture composite failure mechanisms involving both structurally controlled and rock mass progressive failures. A methodology is proposed in this paper to overcome such limitations by coupling DFN models with geomechanical simulations based on the discrete element method (DEM). Further, high resolution photogrammetric data are used to identify valid model scenarios. An identified wedge failure that occurred in an Australian coal mine is used to validate the methodology. In this particular case, the failure surface was induced as a result of the rock mass progressive failure that developed from the toe of the structure inside the intact rock matrix. Analysis has been undertaken to determine in what scenarios the measured and predicted failure surfaces can be used to calibrate strength parameters in the model.     

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.     

Space decomposition based parallelization solutions for the combinedfiniteediscrete element method in 2D

The combined finiteediscrete element method （FDEM） belongs to a family of methods of computationalmechanics of discontinua. The method is suitable for problems of discontinua, where particles aredeformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplinesincluding rock mechanics, where problems like mining, mineral processing or rock blasting canbe solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional（2D） FDEM aiming at clusters and desktop computers is developed. Dynamic domain decompositionbased parallelization solvers covering all aspects of FDEM have been developed. These have beenimplemented into the open source Y2D software package and have been tested on a PC cluster. Theoverall performance and scalability of the parallel code have been studied using numerical examples. Theresults obtained confirm the suitability of the parallel implementation for solving large scale problems.
2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.     

Numerical modeling of thermal breakthrough induced by geothermal production in fractured granite

It is well known that the complicated channeling of fluid flow and heat transfer is strongly related with the intricate natural fracture system. However, it is still challenging to set up the fracture network model which is strong heterogeneous. Compared with other methods (e.g. equivalent continuum model (ECM), discrete fracture model (DFM), and ECM-DFM), the fracture flow module in the COMSOL Multiphysics simulator is powerful in definition of fractures as the inner flow boundary existing in the porous media. Thus it is selected to simulate the fluid flow and heat transfer in the geothermal-developed fractured granite of Sanguliu area located at Liaodong Peninsula, Eastern China. The natural faults/fractures based on field investigation combined with the discrete fracture network (DFN) generated by the MATLAB are used to represent the two-dimensional geological model. Numerical results show that early thermal breakthrough occurs at the production well caused by quick flow of cold water along the highly connected fractures. Suitable hydraulic fracturing treatments with proper injection rates, locations, etc. can efficiently hinder the thermal breakthrough time in the natural fracture system. Large well spacing helps the long-term operation of geothermal production, but it is highly dependent on the geometrical morphology of the fracture network. The enhancement of reservoir properties at the near-well regions can also increase the geothermal production efficiency. The results in this study can provide references to achieve a sustainable geothermal exploitation in fractured granitic geothermal reservoirs or hot dry rocks at depth.     

Influence of data analysis when exploiting DFN model representation in the application of rock mass classification systems

Discrete fracture network (DFN) models have been proved to be effective tools for the characterisation of rock masses by using statistical distributions to generate realistic three-dimensional (3D) representations of a natural fracture network. The quality of DFN modelling relies on the quality of the field data and their interpretation. In this context, advancements in remote data acquisition have now made it possible to acquire high-quality data potentially not accessible by conventional scanline and window mapping. This paper presents a comparison between aggregate and disaggregate approaches to define fracture sets, and their role with respect to the definition of key input parameters required to generate DFN models. The focal point of the discussion is the characterisation of in situ block size distribution (IBSD) using DFN methods. An application of IBSD is the assessment of rock mass quality through rock mass classification systems such as geological strength index (GSI). As DFN models are becoming an almost integral part of many geotechnical and mining engineering problems, the authors present a method whereby realistic representation of 3D fracture networks and block size analysis are used to estimate GSI ratings, with emphasis on the limitations that exist in rock engineering design when assigning a unique GSI value to spatially variable rock masses.     

Slope stability assessment of an open pit using lattice-spring-based synthetic rock mass (LS-SRM) modeling approach

Discontinuity waviness is one of the most important properties that influence shear strength of jointed rock masses, and it should be incorporated into numerical models for slope stability assessment. However, in most existing numerical modeling tools, discontinuities are often simplified into planar surfaces. Discrete fracture network modeling tools such as MoFrac allow the simulation of non-planar discontinuities which can be incorporated into lattice-spring-based geomechanical software such as Slope Model for slope stability assessment. In this study, the slope failure of the south wall at Cadia Hill open pit mine is simulated using the lattice-spring-based synthetic rock mass (LS-SRM) modeling approach. First, the slope model is calibrated using field displacement monitoring data, and then the influence of different discontinuity configurations on the stability of the slope is investigated. The modeling results show that the slope with non-planar discontinuities is comparatively more stable than the ones with planar discontinuities. In addition, the slope becomes increasingly unstable with the increases of discontinuity intensity and size. At greater pit depth with higher in situ stress, both the slope models with planar and non-planar discontinuities experience localized failures due to very high stress concentrations, and the slope model with planar discontinuities is more deformable and less stable than that with non-planar discontinuities.     

Overhanging rock slope by design: An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.     

Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

Seepage–stress coupled analysis on anisotropic characteristics of the fractured rock mass around roadway

Anisotropic properties of the fractured rock masses are investigated considering the coupled effect of the seepage and stress. The equivalent permeability and damage tensor of the fractured rock mass are initially examined using a series of Discrete-Fracture-Network (DFN) models with varied size and orientations from the geological investigation data of the sandstone roadway on the floor of 12# coal seam in Fangezhuang Coal Mine. A seepage–stress cross-coupling anisotropic model considering the coupled effect of the seepage and stress is described and applied to analyze the influence of the principal orientations of the joint sets on the anisotropic properties of the rock mass. It appears that the anisotropic properties of the rock mass have a great influence on the stress distribution, hydraulic conductivity coefficient and damage zone. The model may contribute to a more reasonable explanation on the dominant effect of the joint sets on deformation and failure of rock mass.     

A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.     

Nonlinear analysis of masonry-infilled steel frames with openings using discrete element method

Nonlinear numerical modeling of masonry-infilled frames is one of the most complicated problems in structural engineering field. This complexity is attributed to the existence of joints as the major source of weakness and material nonlinearities as well as the infill-frame interaction which cannot be properly modeled using the traditional finite element methods. Although there are many numerical studies available on solid masonry-infilled steel frames’ behavior, however, few researches have been conducted on infilled frames with openings. In this paper a two-dimensional numerical model using the specialized discrete element method (DEM) software UDEC (2004) is developed for the nonlinear static analysis of masonry-infilled steel frames with openings subjected to in-plane monotonic loading. In this model, large displacements and rotations between masonry blocks are taken into account. It was found that the model can be used confidently to predict collapse load, joint cracking patterns and explore the possible failure modes of masonry-infilled steel frames with a given location for openings and relative area. Results from the numerical modeling and previous experimental studies found in the literature are compared which indicate a good correlation between them. Furthermore, a nonlinear analysis was performed to investigate the effect of door frame on lateral load capacity and stiffness of infilled frames with a central opening.     

Hydraulic properties of fractured rock masses with correlated fracture length and aperture

Permeability of fractured rocks is investigated considering the correlation between distributed fracture aperture and trace length, based on a newly developed correlation equation. The influence of the second moment of the lognormal distribution of apertures on the existence of representative elementary volume (REV), and the possibility of equivalent permeability tensor of the fractured rock mass, is examined by simulating flow through a large number of stochastic discrete fracture network (DFN) models of varying sizes and varying fracture properties.The REV size of the DFN models increases with the increase of the second moment of the lognormal distribution, for both the correlated and uncorrelated cases. The variation of overall permeability between different stochastic realizations is an order of magnitude larger when the aperture and length are correlated than when they are uncorrelated. The mean square error of the directional permeability increases with increasing value of the second moment of the lognormal distribution function, and good fitting to an ellipsis of permeability tensor can only be reached with very large sizes of DFN models, compared with the case of constant fracture aperture, regardless of fracture trace length.     

土压平衡盾构掘进对上软下硬地层扰动研究

 采用Ф800 mm模型盾构开展室内掘进试验以研究土压盾构掘进对上软下硬地层的扰动特征,试验充分考虑土压盾构动态施工全过程的影响。建立与室内掘进试验对应的离散元模型定量分析软土超挖现象并挖掘其他地层扰动信息。研究结果表明：土压盾构在硬岩地层中掘进时地表沉降曲面呈现向软土侧展开的“扇面”状;进入上软下硬地层后地表沉降值与范围均急剧增加,沉降曲面呈现自上而下逐渐收缩的“漏斗”状,硬岩侧收缩速度快于软土侧;上软下硬地层地表位移小于均质软土地层,而地中沉降显著大于后者;上软下硬地层地中沉降槽宽度参数沿深度方向呈指数增加,硬岩占断面比例越小,地中沉降槽宽度参数越大。相同埋深条件下,上软下硬地层地中沉降槽宽度参数小于均质软土地层。硬岩占断面比例越大,渣土中砂土所占比例与相应理论值差异越明显。地表水平位移在竖向沉降槽曲线反弯点处最大。研究可为土压盾构在上软下硬地层施工提供参考。     

Study on the mesostructure and mesomechanical characteristics of the soil–rock mixture using digital image processing based finite element method

The soil–rock mixture (SRM) is a kind of inhomogeneous geomaterial, which poses difficulties of in situ sample acquisition and in laboratory geomaterial tests; hence, the study of the SRM's mechanical properties is still at an early stage. In this paper, the technique of digital image processing based on the finite element method (DIP-FEM) is introduced to study SRMs in the Leaping Tiger Gorge Reservoir Area, China. Based on the DIP, the mesostructural characteristics of the SRM are analyzed statistically. The mesostructural concept model of SRM that can actually represent the inhomogeneity of SRM is built. By using geometry vectorizaiton transformation, the mesostructural model of SRM in the binary image format has been translated into a vector format (such as DWG or DXF format) which can be imported into the finite element software. By using the finite element method, two large-scale direct shear tests of inhomogeneous SRM and homogeneous soil are simulated. The numerical results indicate that the existence of “rock” blocks in SRM will greatly influence the distribution and the failure models of the internal stress field. As a result, three kinds of failure models of the SRM are put forward.     

A discrete model for prediction of radon flux from fractured rocks

Prediction of radon flux from the fractured zone of a propagating cave mine is basically associated with uncertainty and complexity. For instance, there is restricted access to these zones for field measurements, and it is quite difficult to replicate the complex nature of both natural and induced fractures in these zones in laboratory studies. Hence, a technique for predicting radon flux from a fractured rock using a discrete fracture network (DFN) model is developed to address these difficulties. This model quantifies the contribution of fractures to the total radon flux, and estimates the fracture density from a measured radon flux considering the effects of advection, diffusion, as well as radon generation and decay. Radon generation and decay are classified as reaction processes. Therefore, the equation solved is termed as the advection-diffusion-reaction equation (ADRE). Peclet number (Pe), a conventional dimensionless parameter that indicates the ratio of mass transport by advection to diffusion, is used to classify the transport regimes. The results show that the proposed model effectively predicts radon flux from a fractured rock. An increase in fracture density for a rock sample with uniformly distributed radon generation rate can elevate radon flux significantly compared with another rock sample with an equivalent increase in radon generation rate. In addition to Pe, two other independent dimensionless parameters (derived for radon transport through fractures) significantly affect radon dimensionless flux. Findings provide insight into radon transport through fractured rocks and can be used to improve radon control measures for proactive mitigation.     

Comparison of undrained behaviors of granular media using fluid-coupled discrete element method and constant volume method

The fluid-coupled discrete element method (DEM) and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials, have been discussed by many researchers. The fluid-coupled DEM, which couples the motions of discrete particles with pore fluid movements, is theoretically robust although it requires a large amount of computation time. As a substitution for the complex fluid-coupled DEM, the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles; hence, the validity of its results is questionable. In this paper, the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared. Based on a comparison of both macroscopic and microscopic responses given by the two methods, it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains, which has a high permeability, and thus a rapid pore pressure equalization. However, it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores. With regard to the dense material adopted, similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.