Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

Fractured reservoir modeling by discrete fracture network and seismic modeling in the Tarim Basin,China

Fractured reservoirs are an important target for oil and gas exploration in the Tarim Basin and the prediction of this type of reservoir is challenging.Due to the complicated fracture system in the Tarim Basin,the conventional AVO inversion method based on HTI theory to predict fracture development will result in some errors.Thus,an integrated research concept for fractured reservoir prediction is put forward in this paper.Seismic modeling plays a bridging role in this concept,and the establishment of an anisotropic fracture model by Discrete Fracture Network （DFN） is the key part.Because the fracture system in the Tarim Basin shows complex anisotropic characteristics,it is vital to build an effective anisotropic model.Based on geological,well logging and seismic data,an effective anisotropic model of complex fracture systems can be set up with the DFN method.The effective elastic coefficients,and the input data for seismic modeling can be calculated.Then seismic modeling based on this model is performed,and the seismic response characteristics are analyzed.The modeling results can be used in the following AVO inversion for fracture detection.

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 measure- ments, 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.

Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information

The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。

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 Modeling of Natural Fracture Distributions in Shale

The production efficiency of shale gas is affected by the interaction between hydraulic and natural fractures.This study presents a simulation of natural fractures in shale reservoirs,based on a discrete fracture network(DFN)method for hydraulic fracturing engineering.Fracture properties of the model are calculated from core fracture data,according to statistical mathematical analysis.The calculation results make full use of the quantitative information of core fracture orientation,density,opening and length,which constitute the direct and extensive data of mining engineering.The reliability and applicability of the model are analyzed with regard to model size and density,a calculation method for dominant size and density being proposed.Then,finite element analysis is applied to a hydraulic fracturing numerical simulation of a shale fractured reservoir in southeastern Chongqing.The hydraulic pressure distribution,fracture propagation,acoustic emission information and in situ stress changes during fracturing are analyzed.The results show the application of fracture statistics in fracture modeling and the influence of fracture distribution on hydraulic fracturing engineering.The present analysis may provide a reference for shale gas exploitation.

Multi-dimensional size effects and representative elements for nonpersistent fractured rock masses: A perspective of geometric parameter distribution

This study takes a fractured rock mass in the Datengxia Hydropower Station,China as an example to analyze the size effects and determine the representative elementary sizes.A novel method considering geometric parameter distributions is proposed in this work.The proposed method can quickly and simply determine the size effects and representative elementary sizes.Specifically,geometric parameter distributions,including fracture frequency,size and orientation,are generated on the basis of the Bernoulli trial and Monte Carlo simulation.The distributions are assessed using the coefficient of variation(CV),and the acceptable variations for CV(5%,10%and 20%)are used to determine representative elementary sizes.Generally,the representative element of rock masses is the representative elementary volume(REV).The present study extends the representative element to other dimensions,i.e.representative elementary length(REL)and representative elementary area(REA)for one and two dimensions,respectively.REL and REA are useful in studying the size effects of one-(1D)and twodimensional(2D)characteristics of rock masses.The relationships among multi-dimensional representative elementary sizes are established.The representative elementary sizes reduce with the increase in the dimensions,and REA and REV can be deduced by REL.Therefore,the proposed method can quickly and simply determine REL and further estimate REA and REV,which considerably improves the efficiency of rock mass analysis.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

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.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su^zestions for future study are also oresented.

深层页岩气储层水力压裂裂缝扩展影响机理

现有中浅层页岩气压裂取得的认识难以解释深层页岩气储层压裂过程中水力裂缝扩展的影响机理。为了研究四川盆地深层页岩气储层水力压裂裂缝扩展机理,文中以泸州深层页岩气区LS1平台为研究对象,进行基于地质-工程一体化的水力压裂裂缝扩展数值模拟与分析。首先,根据泸州区块目标井区储层的地质概况,建立地质模型,明确地质力学属性;然后,基于微地震和蚂蚁体数据,建立符合真实储层构造特性的离散天然裂缝网络;在此基础上,根据现场实际施工数据,建立了基于DFN的水力压裂复杂裂缝扩展模型,并基于微地震监测结果对模型进行了验证;最后,还研究了4个单因素对储层改造体积的影响特点。研究结果对深层页岩气储层水力压裂复杂缝网研究有一定的指导作用。

Productivity analysis of a fractured horizontal well in a shale gas reservoir based on discrete fracture network model

The treatment of horizontal wells with massive hydraulic fracturing technology is important for the economical development of shale gas reservoirs, but sometimes is complex because of the induced fractures during the fracturing process. The studies of the fluid flow characteristics in such formations are rare. In this study, a numerical method based on a finite element method (FEM) is developed for the productivity analysis of a horizontal well in a shale gas reservoir with complex fractures. The proposed method takes into account the adsorbed gas and the complex hydraulic fracture branches. To make the problem more tractable, the dimension of the fracture system is reduced from 2-D to 1-D based on the discrete fracture network (DFN) model. The accuracy of the new method is verified by comparing its results with those obtained by the Saphir commercial software. Finally, the productivity of the fractured horizontal wells in shale gas reservoirs with complex fractures systems is evaluated and analyzed. Results show that if a well is produced with a constant bottomhole pressure, the well productivity is much increased due to the existence of fracture branches that can increase the stimulated reservoir volume (SRV). In addition, the number of hydraulic fractures (Nf) and the fracture halMengths (Lf) have an important influence on the well's productivity. The larger the values of Nf,Lf,the greater the well productivity will be. The existence of adsorbed gas can markedly improve the well productivity, and the greater the Langmuir volume, the greater the productivity will be. The conclusions drawn by this study can provide a guidance for the development of unconventional shale gas reservoirs.

基于分形几何理论的DFN模型构建方法研究

以重庆梁-忠(梁平县-忠县)高速公路礼让隧道为工程研究背景,通过测线法调查现场节理,获得了节理产状分布概率密度函数,并从分形几何学的角度分析了节理间距及迹长的分形分布规律,推导出能反映节理间距及迹长分布状态的分形维数D及分形分布概率密度函数。在该基础上采用Matlab软件以及Monte-Carlo随机分析方法,产生节理参数随机数,结合3DEC中最新模块离散裂隙网络(DFN)技术,建立了能反映节理裂隙分布特征的离散裂隙网络模型并验证了模型的有效性,结果表明,分形分布比负指数分布包含更多的间距、迹长分布信息,更接近于实际分布;分形维数D反映了节理间距、迹长在其变化范围内的分布特征,分形维数的大小取决于小间距、小迹长部分数量在总节理数量中的比例,为节理裂隙岩体网络模型构建提供了一种新方法。

DFN模型裂缝建模新技术

DFN模型是目前世界上描述裂缝的一项先进技术,它通过展布于三维空间中的各类裂缝片组成的裂缝网络集团来构建整体的裂缝模型,实现了对裂缝系统从几何形态到其渗流行为的逼真细致的有效描述,吉林油田晴子井油田采用这一技术很好地解决了油田开发的诸多问题。

应用DFN方法建立下寺湾地区长7陆相页岩气藏裂缝模型

目前,页岩气藏的数值模拟主要采用等效连续模型,但陆相页岩气藏的裂缝具有强非均质性,等效连续模型对裂缝非均质性过度简化,不再适用于陆相页岩气藏;为了实现陆相页岩气藏天然裂缝系统的模拟,采用离散裂缝网络(DFN)建模方法建立陆相页岩气藏天然裂缝模型。通过岩心描述、成像测井分析、常规测井分析得到裂缝信息,并与DFN随机建模方法有机结合,建立可靠的裂缝模型;裂缝方位采用多峰分布函数模拟,裂缝大小(长度、开度)采用分数维与裂缝大小的函数模拟;在此基础上,通过裂缝密度的约束来建立页岩气藏离散裂缝网络模型,并以鄂尔多斯盆地中生界延长组长7张家滩泥页岩为研究对象,建立泥页岩裂缝系统的离散裂缝网络模型。采用微地震资料对所建DFN模型进行检验,证实所建立的DFN模型符合真实泥页岩天然裂缝系统。

A three-dimensional feature extraction-based method for coal cleat characterization using X-ray μCT and its application to a Bowen Basin coal specimen

Cleats are the dominant micro-fracture network controlling the macro-mechanical behavior of coal.Improved understanding of the spatial characteristics of cleat networks is therefore important to the coal mining industry.Discrete fracture networks(DFNs)are increasingly used in engineering analyses to spatially model fractures at various scales.The reliability of coal DFNs largely depends on the confidence in the input cleat statistics.Estimates of these parameters can be made from image-based three-dimensional(3D)characterization of coal cleats using X-ray micro-computed tomography(m CT).One key step in this process,after cleat extraction,is the separation of individual cleats,without which the cleats are a connected network and statistics for different cleat sets cannot be measured.In this paper,a feature extraction-based image processing method is introduced to identify and separate distinct cleat groups from 3D X-ray m CT images.Kernels(filters)representing explicit cleat features of coal are built and cleat separation is successfully achieved by convolutional operations on 3D coal images.The new method is applied to a coal specimen with 80 mm in diameter and 100 mm in length acquired from an Anglo American Steelmaking Coal mine in the Bowen Basin,Queensland,Australia.It is demonstrated that the new method produces reliable cleat separation capable of defining individual cleats and preserving 3D topology after separation.Bedding-parallel fractures are also identified and separated,which has his-torically been challenging to delineate and rarely reported.A variety of cleat/fracture statistics is measured which not only can quantitatively characterize the cleat/fracture system but also can be used for DFN modeling.Finally,variability and heterogeneity with respect to the core axis are investigated.Significant heterogeneity is observed and suggests that the representative elementary volume(REV)of the cleat groups for engineering purposes may be a complex problem requiring careful consideration.

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.

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(3 D) 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 3 D 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.

利用热-孔隙流体耦合有限元数值模拟研究干热岩开发温度下降过程——以青海共和盆地恰卜恰地区干热岩开发为例

水力压裂是干热岩(HDR)开发最常用到的压裂方式,水力压裂形成的裂缝网络为增强地热系统的运行(EGS)提供了高渗透率的人工储层.本文在系统总结前人关于共和盆地水力压裂实验、数值模拟资料和现场水力压裂监测结果的基础上,引入了离散裂缝网络(DFN),利用多物理场模拟软件COMSOL Multiphysics建立了共和盆地恰卜恰地区干热岩开采过程中的二维裂缝-基质热-孔隙流体耦合模型,并讨论了裂缝开度和基质渗透率对干热岩开采温度下降过程的影响.结果表明,裂缝网络是流体运移的主要通道.温度下降和早期压力变化范围沿着裂缝延伸,并向周围被裂缝分割的基质扩展.裂缝开度和基质渗透率是影响干热岩地热开采过程中温度下降的重要因素.当裂缝开度越大时,流体运移范围就越大,储层温度和产出水温下降就越快,储层下降范围就越广,热突破时间和运行寿命就越短.当基质渗透率越大时,越有利于流体进入基质进行热量交换,越容易从干热岩中提取热量,产出水温下降越快,运行寿命越短.

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.