Discrete element model for quasi‐brittle rupture under tensile and compressive loading

In the absence of initial cracks, the material behavior is limited by its strength, usually defined in homogeneous conditions (of stress and strain). Beyond this limit, in quasi‐brittle case, cracks may propagate and the material behavior tends to be well described by fracture mechanics. Discrete element approaches show consistent results dealing with this transition during rupture. However, the calibration of the parameters of the numerical models (i.e., stiffness, strength, and toughness) may be quite complex and sometimes only approximative. Based on a brittle rupture criterion, we analyze the biaxial response of uncracked samples. Thus, tensile and compressive strengths are analytically identified and become direct parameters of our discrete model. Furthermore, a physically reliable crack initiation (and subsequent propagation) is shown to be induced during rupture and verified by the simulation of three‐point bending and diametral compression tests. Copyright © 2016 John Wiley & Sons, Ltd.     

A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model

Numerical models based on the discrete element method are used to study the fracturing process in brittle rock‐like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads.     

岩石材料裂纹扩展的改进近场动力学方法模拟

在传统键基近场动力学模型的基础上,提出可以反映岩石类材料应力-应变变化特点的改进型模型,弥补了传统近场动力学模型在模拟岩石类材料时无法反映岩石内应力随应变先增加再减小最后破坏这一特性的不足。运用改进型模型,对含有单裂纹试件在不同预制裂纹角度及拉伸荷载条件下的裂纹扩展过程进行了数值模拟,分析了开裂角度在不同预制裂纹角度及拉伸荷载条件下的变化。结果表明：预制角度及拉伸荷载对开裂角度都有影响,在试件周围拉荷载接近的情况下会获得较小的开裂角,并且在拉荷载一定的条件下开裂角会有先增加后减少的规律。同时模拟了含裂纹岩石在单轴压缩条件下的裂纹扩展情况,将数值模拟的结果与室内试验的结果对比,验证了所提出新模型的有效性。所提出的新模型可以较好地模拟岩石类材料在拉荷载条件下的力学特性,在岩石数值模拟方面有着较为广泛的应用前景。     

正交各向异性岩体裂纹扩展的扩展有限元方法研究

石油开采和非常规天然气开采等领域经常遇到页岩、砂岩等沉积岩,这类岩石材料往往具有正交各向异性特征。采用扩展有限元方法研究了正交各向异性岩体裂纹扩展问题,并基于Matlab平台编写了数值计算程序Betaxfem2D。将由复变函数法得到的裂纹尖端渐进位移场作为裂尖位移增强函数,用相互作用积分法计算混合模式应力强度因子,采用修改后的最大周向拉应力扩展准则确定裂纹扩展方向。与传统有限元方法的对比表明,扩展有限元方法达到相同计算精度需要的自由度少,节省计算机时。分别采用扩展有限元程序和传统有限元程序模拟了岩石试件4点弯曲试验,二者所得结果一致。数值试验表明：随着正交材料坐标系与空间坐标系夹角α的增大,裂纹扩展方向角? 按照周期为? 的近似正弦函数的规律变化;保持剪切模量和泊松比不变时,正弦函数的值域随着弹性模量比值E1 /E2的减小而缩小,但相位基本保持不变;研究沉积岩断裂力学问题时,岩石的正交各向异性特征不可忽略。     

基于3D-ILC含内裂纹孔口脆性固体断裂特性试验

孔口问题为力学领域中经典问题之一,也是岩土如隧洞、巷道等工程领域重要的问题之一。随断裂力学的发展,对含裂纹孔口问题的研究也不断深入。但是,以往研究多集中在二维问题或者含表面裂纹的孔口问题,含纯内裂纹的孔口问题研究报道较少。基于3D-ILC技术（对表面无任何影响的情况下,凭空生成任意参数的深埋内裂纹）,在含有孔口的脆性材料中生成内裂纹,开展单轴压缩试验,与无裂纹完整孔口试样试验结果及已有文献进行对比,并开展理论与数值模拟研究。结果表明：（1）3D-ILC与传统方法相比,裂纹特征更为真实,为解决断裂力学中的三维内裂纹问题奠定了基础;（2）完整孔口试样裂纹形态主要有主裂纹与八字形裂纹;（3）含内裂纹试样裂纹形态以内裂纹扩展为主,主要有翼裂纹、次生裂纹、反翼裂纹、反向次生裂纹、竖向扭曲裂纹与主裂纹6种;（4）含裂纹孔口试样最终的破坏荷载比无裂纹孔口试样平均低76.49%,起裂应力较无裂纹孔口试样平均低96.72%;（5）通过数值模拟对完整孔口试样、含主裂纹孔口试样、含内裂纹孔口试样的裂纹扩展进行定性分析,与试验结论一致。该研究结果为含三维内裂纹的孔口脆性材料的断裂理论研究提供了物理试验基础。     

石材亚临界裂纹扩展量测研究

在试验室进行裂纹稳定扩展及非稳定扩展的研究,其试验基座以楔形劈裂试验为基础改良而成,考虑材料的均质性,试验试体采用供铺设地板或建筑用外墙之天然石材。试验过程中利用裂缝应变片即时记录系统求出试体在稳定扩展及非稳定扩展下的裂纹扩展速度及其分形特性。结果表明,稳定扩展速度范围约在0.113～313.043 cm/s;非稳定扩展速度范围约在0.094～2 489.816 cm/s;亚临界分形维数范围约在0.994 3～1.036 6;起裂断裂韧性范围约在1.891 5～3.500 1 MPa?m1/2;分形亞臨界斷裂韌性范围约在2.063 6～3.712 8 MPa?m1/2。     

Modeling crack propagation path of anisotropic rocks using boundary element method

In a cracked material, the stress intensity factors (SIFs) at the crack tips, which govern the crack propagation and are associated with the strength of the material, are strongly affected by the crack inclination angle and the orientation with respect to the principal direction of anisotropy. In this paper, a formulation of the boundary element method (BEM), based on the relative displacements of the crack tip, is used to determine the mixed‐mode SIFs of isotropic and anisotropic rocks. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, and degree of material anisotropy are presented. Furthermore, the BEM formulation combined with the maximum circumferential stress criterion is adopted to predict the crack initiation angles and simulate the crack propagation paths. The propagation path in cracked straight through Brazilian disc specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Copyright © 2008 John Wiley & Sons, Ltd.     

含预制裂纹脆性岩石破坏数值模拟研究

岩石是经过变形、遭受过破坏的地质体。在外界荷载条件下岩石内部缺陷引起的渐进性破坏,这个过程与材料本身存在的缺陷有着密切的关系。应用数值模拟方法对含有预制裂纹的脆性岩石的破坏规律进行了初步的研究,分析了裂纹的存在对岩石破坏的影响机制。研究发现,在对带有预制裂纹的岩石试件进行加载试验过程中,预制裂纹的存在成为了影响岩石破裂方式的主要因素。与之相比,由材料非均质性所造成的影响便成了次要因素,而对于含有双预制裂纹的岩石试件裂纹的间距是影响岩石破坏型式的重要因素。     

3D polycrystalline discrete element method (3PDEM) for simulation of crack initiation and propagation in granular rock

A three-dimensional Voronoi tessellation model based on the distinct element method (DEM) is proposed to model the representative part of the microstructures of granular brittle rocks. Regularization is employed to decrease the frequency of polyhedrons with large edge ratio and contributes to a higher efficiency for element meshing. Sensitivity analyses are performed for a series of micro contact parameters in accordance with the macro responses observed in laboratory experiments (e.g. the uniaxial compression test, the Brazilian disc test and the triaxial compression test). Verifications by simulating the spalling test and plate impact test indicate that the 3D polycrystalline discrete element method (3PDEM) can be employed for efficiently simulating nonlinear mechanical behaviors, large deformation, strain softening and rock dynamics.     

模拟岩石破裂过程的块体单元离散弹簧模型

在变形体离散元的基础上建立块体单元离散弹簧模型,并应用于岩石破裂过程的数值模拟研究。该模型以连续介质力学理论为基础,将块体单元离散为具有明确物理意义的弹簧系统,通过对弹簧系统的能量泛函求变分获得各弹簧的刚度系数,进而可以直接利用弹簧刚度求解单元的变形和应力,提高计算效率。以重力作用下的岩质边坡计算为例,通过与传统的有限元进行对比,验证该模型弹性计算结果的正确性。在该基础上,引入Mohr-Coulomb与最大拉应力的复合破坏准则,判断单元的破坏状态及破裂方向。当单元的内部破坏面确定后,则通过块体切割的方式实现单元破坏,并建立单元边界和单元内部的双重破裂机制,实现块体由连续到非连续的破裂过程,进而显示的模拟裂纹的形成和扩展。最后,以巴西圆盘劈裂、单轴压缩破裂以及三点弯曲梁等典型算例验证该方法,结果表明该方法可以较好地模拟拉伸、压剪等应力状态下裂纹的形成和扩展,从而可模拟岩石介质由连续到非连续的破裂过程。     

锦屏深埋大理岩破裂扩展的时间效应试验及特征研究

脆性岩石破裂扩展的时间效应与地下工程的长期稳定性密切相关。针对锦屏深埋大理岩易受高应力卸荷而产生初始损伤的特点,首先利用无损取样技术获得无损岩样,并利用声发射对无损岩样进行初始损伤检测,剔除初始损伤对试验结果的影响。之后利用获得的无损岩样进行一系列的长期加载的静态疲劳试验验证锦屏大理岩强度的时效特性。结果显示,锦屏大理岩表现出强度随时间衰减的特性,当应力驱动比较低时,需要的时间也相应增加,最后得到静态疲劳极限为0.48。分析证明,脆性岩石在稳定荷载作用下蠕变曲线也分为3个阶段,同时应变率也表现出相应的变化趋势,利用扩容指标阐述了岩样在静态疲劳试验中的变形特征和破坏模式。最后,利用FLAC3D计算了开挖引起的应力松弛区和应力集中区,说明了埋深对试验结果的影响。针对试验中出现的含节理岩样强度较低的问题,借助颗粒流程序PFC中的光滑节理模型进行了数值试验,结果显示,节理的存在极大地影响了岩样的整体强度,并且在加载初期,存在压缩紧密,而在残余阶段,存在一定的强化效应和延性特征。     

Discrete fracture model for simulating waterflooding processes under fracturing conditions

In our study, we develop a model for simulating fracturing processes in a poroelastic medium. The proposed approach combines the discrete fracture model enriched with contact plane mechanics. The model captures mechanical interactions of fractures and a deformable medium, fluid, and heat transfer in fractures and in a porous medium. Both effects of poroelasticity and thermoelasticity are accounted in our model. Mass and heat conservation equations are approximated by the finite volume method, and mechanical equilibrium equations are discretized by means of the Galerkin finite element approach. Two‐dimensional grid facets between 3‐dimensional finite elements are considered as possible fracture surfaces. Most of these facets are inactive from the beginning and are activated throughout the simulation. A fracture propagation criterion, based on Irwin's approach, is verified on each nonlinear iteration. When the criterion is satisfied, additional contact elements are added into finite element and discrete fracture model formulations respectively. The proposed approach allows modeling of existing natural and artificially created fractures within one framework. The model is tested on single‐ and multiple‐phase fluid flow examples for both isothermal and thermal conditions and verified against existing semianalytical solutions. The applicability of the approach is demonstrated on an example of practical interests where a sector model of an oil reservoir is simulated with different injection and production regimes.     

Granular element method for three‐dimensional discrete element calculations

This paper endows the recently‐proposed granular element method (GEM) with the ability to perform 3D discrete element calculations. By using non‐uniform rational B‐Splines to accurately represent complex grain geometries, we proposed an alternative approach to clustering‐based and polyhedra‐based discrete element methods whereby the need for complicated and ad hoc approaches to construct 3D grain geometries is entirely bypassed. We demonstrate the ability of GEM in capturing arbitrary‐shaped 3D grains with great ease, flexibility, and without excessive geometric information. Furthermore, the applicability of GEM is enhanced by its tight integration with existing non‐uniform rational B‐Splines modeling tools and ability to provide a seamless transition from binary images of real grain shapes (e.g., from 3D X‐ray CT) to modeling and discrete mechanics computations.Copyright © 2013 John Wiley & Sons, Ltd.     

岩石类材料振动裂隙扩展试验和数值分析

岩性体振动裂隙扩展是路基、桥梁、振动施工和防震等领域共同关注的问题。通过自制惯性加载装置联合振动实验台,对12组含边中穿透裂隙的板状相似岩样进行振动加载试验,观测裂隙扩展和贯通规律,并利用PFC颗粒流软件建立试验对应模型,进一步分析裂隙扩展的控制机制。结果表明,不同区域振动变形的相位差会促进裂隙的扩展行为;边裂隙的起裂方向与振动方向夹角较小,约在±10°以内,且与振向相同的边裂隙最容易扩展,与振向相同的边—中裂隙对最容易贯通;破坏频率与裂隙间距呈正相关性,并且随着裂隙倾角和振向夹角的增大,裂隙扩展越来越困难,垂直振向的裂隙最难扩展;振动裂隙扩展路径为裂尖最近路线,符合能量最小原理。     

含裂隙岩体单轴压缩裂纹扩展机制离散元分析

将由室内试验总结得到的岩石微观胶结模型嵌入离散元软件,对Lac du Bonnet花岗岩石进行预制单裂隙单轴压缩试验DEM数值模拟,分析了压缩过程中裂隙试样中应力的分布,并与理论计算结果进行对比分析,同时对各种断裂判据中裂纹起裂角的预测值进行了适用性的对比分析。结果表明,离散元模拟试样破坏形态与试验结果相近;离散元分析得到的应力分布与理论解在定性上相似;当预制角度较小时,侧向应力都处于拉压状态;由于裂隙左右两端压应变的集中造成了裂隙上下面拉应变的产生,造成了裂隙周围特殊的应力分布;当裂隙角度较大时,应力集中现象已不明显,因而,理论值与试验值有偏差;在断裂判据中最大周应力准则和最大能量释放率准则得到的裂纹扩展角与室内试验与DEM结果中的数值较为吻合。     

A mixed mode rock fracture model for the prediction of crack path

Crack propagation in rocks is simulated by using a displacement substitution method based on a mixed mode fracture criterion. The main advantage of this model is that it can distinguish between mode I and mode II stress intensity factors simultaneously. A typical finite element program is used to compute displacements adjacent to the crack tip. The maximum circumferential tensile stress is adopted as a ‘yield surface’ for the calculation of the load factor in each crack increment. Pure mode I and mixed mode examples have been analysed to validate the capability of the model. Copyright © 1999 John Wiley & Sons, Ltd.     

An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete element modelling of creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the discrete element model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013). The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution.