A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation

In nature, there exist several forms of anisotropy in rock masses due to the presence of bedding planes, joints, and weak layers. It is well understood that the anisotropic properties of jointed rock masses significantly affect the stability of surface and underground excavations. However, these critical anisotropic characteristics are often ignored in existing uniaxial dynamic failure criteria. This study investigates the effect of a pre-existing persistent joint on the rate-dependent mechanical behaviours of a rock mass using a particle mechanics approach, namely, bonded particle model (BPM), to realistically replicate the mechanical response of the rock mass. Firstly, in order to capture the rate-dependent response of the jointed rock mass, the BPM model is validated using published experimental data. Then, a dynamic strength model is proposed based on the Jaeger criterion and simulation results. To further investigate the dynamic behaviours, the dynamic uniaxial compressive strength (UCS) for anisotropic rock masses with various joint orientations is investigated by subjecting the BPM models to uniaxial compression numerical tests with various strain rate. The proposed dynamic strength model is validated based on numerical simulation results. Finally, the fragmentation characteristics of the jointed rock masses are analysed, which demonstrate that the failure mode affects the dynamic UCS. This is further confirmed by the analysis of the orientations of microscopic cracks generated by the compression loading.     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。     

Analysis of Critical Excavation Depth for a Jointed Rock Slope Using a Face-to-Face Discrete Element Method

Summary The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D _s and the natural slope angle α, the joint inclination angle θ as well as the strength parameters of the joints c _r ,φ _r is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.     

含两组交叉贯通节理岩体的强度及破坏特征分析

天然岩体中常含有多组相互交叉的贯通节理,它们的存在极大地削弱了岩体的力学性质。为了研究含两组交叉贯通节理岩体的强度及破坏特征,基于弹塑性数值流形方法,对不同应力状态下,节理倾角和节理间距不同的岩体压缩试验进行数值模拟。结果表明：岩体强度随节理倾角的变化曲线呈现出多波峰、多波谷特点,岩体强度随节理间距变化曲线符合负指数函数形式。根据节理状态,两组节理岩体的破坏模式可以分为3种：岩块破坏、沿一组节理滑移和沿两组节理滑移。两组节理均会影响岩体强度,一组起主要作用,另一组起次要作用,并且节理组之间存在相互影响。通过对数值计算结果进行回归分析,基于一组节理岩体强度预测模型,量化节理组之间的相互影响,提出适用于含两组交叉贯通节理岩体的强度预测模型。模型形式简单,使用方便,可为实际工程中正确评估岩体强度提供指导性意见。     

逆层岩质边坡地震动力破坏过程FLAC/PFC耦合数值模拟分析

建立含有非贯通层面和正交次级节理的逆层岩质边坡FLAC/PFC2D耦合计算模型,进行地震动力破坏过程模拟试验,研究了逆层岩质边坡地震动力破坏机理。试验结果证明,在地震动力破坏过程中,边坡内部层面主要产生剪切破坏,少量张拉破坏集中于逆层边坡顶部位置并且总是发生在坡体已经产生动力失稳之后,因此层面的抗拉强度并不影响逆层边坡的地震动力稳定性。坡顶正交次级节理只能产生张拉破坏,形成宏观的岩层倾倒趋势,而坡底的正交次级节理既会产生张拉破坏,也会产生剪切破坏,破坏面滑动趋势明显。动力响应坡顶放大效应和破坏面发育位置深度导致坡顶岩体的张拉倾倒早于坡底岩体的剪切滑动,与逆层边坡静力倾倒破坏顺序相反。     

Failure Characteristics of Complicated Random Jointed Rock Mass Under Compressive-Shear Loading

Most natural rock masses contain a large number of random joints and fissures, and most of the rock masses at the rock engineering are commonly in both compression and shear stress environment. However, the research on the failure characteristics of complex random jointed rock mass under compressive-shear loading is still limited. To address this gap, this paper uses the particle flow code 2D to establish a discrete fractured rock mass model and carry out a series of numerical tests with different compressive-shear angles (α) and different joint geometric parameters. The effects of compressive-shear angle and joint geometric parameters on the strength and failure characteristics of fractured rock masses are studied. The results indicate that with the increase of α, the peak strength of the specimen decreases gradually, and the failure mode changes from the composite shear failure mode (Mode-I) to a plane shear failure mode (Mode-II) and then to intact shear failure mode (Mode-III). Specifically, the three failure modes occur in the specimens with α?=?15°, 30° or 45°, 60°, respectively. The existence of joints affects stress distribution on rock mass during the loading process. Furthermore, the stress at the joint tip is relatively concentrated, while on both sides of the joint is smaller. Three kinds of crack coalescence patterns are observed: tensile, shear, and tensile-shear mixed coalescence. The inclination angle of the rock bridge between adjacent joints affects the specific type of coalescence.

     

含顺层断续节理岩质边坡地震作用下的破坏模式与动力响应研究

基于二维颗粒流软件PFC2D的人工合成岩体技术（SRM）,研究了岩桥倾角和节理间距不同组合形式的含顺层断续节理岩质边坡在地震作用下的破坏模式与动力响应规律。研究结果显示：在地震动力作用下,含单潜在滑动面的顺层断续节理岩质边坡呈现出滑移-倾倒的混合破坏特征,含多潜在滑动面的顺层断续节理岩质边坡则主要发生倾倒破坏;由顺层断续节理以及岩桥交替连接所组成的潜在滑动面是控制边坡动力稳定性的关键因素。在地震动力作用下,最靠近坡脚的岩桥段首先萌生翼裂纹,使得拉应力得到释放,随后各节理相继萌生裂纹并扩展、贯通,最终导致坡体发生阶梯状整体失稳。裂纹扩展受顺层断续节理控制,萌生裂纹中以张拉裂纹为主,且裂纹数量与输入地震波的加速度曲线具有同步性。另一方面,节理面的存在对边坡动力响应产生明显影响,沿坡表以及沿水平方向上的峰值速度、峰值位移随着岩桥倾角的增大、节理间距的减小而增大,同时节理间距和岩桥倾角对于峰值加速度（PGA）放大系数的影响范围主要集中在坡表、坡肩;沿竖直方向上,峰值位移随着岩桥倾角、节理间距的增大而减小,PGA放大系数曲线随高程变化总体呈现U型分布特征。     

Anisotropic Deformation of a Circular Tunnel Excavated in a Rock Mass Containing Sets of Ubiquitous Joints: Theory Analysis and Numerical Modeling

Determining anisotropic deformation surrounding underground excavations for tunnels is an intuitional task that involves many difficulties due to the inherent anisotropies in the strength and deformability of natural rocks. This study investigates joint-induced anisotropic deformation surrounding a tunnel via a numerical simulation that accounts for the mechanical behavior of intact rock, the orientations of joint sets, and the mechanical behavior of joint planes; this numerical simulation can model the complete stress–strain relationship with anisotropic rock mass characteristics. Simulation results demonstrate that the well-known excavation-induced stress variation–decrease in the radial component and increase in the tangential component–decrease shear strength and increase shear stress for the joint plane tangential to the tunnel wall, resulting in joint sliding failure and considerable shear deformation. This joint sliding failure and significant shear deformation account for the joint-induced anisotropic deformation surrounding a tunnel. When a rock mass has two joint sets with unfavorable joint orientations, the area with joint sliding failure can deteriorate mutually, resulting in large anisotropic deformation. Additionally, for a rock mass containing three joint sets with well-distributed orientations, joint sliding in various joint sets and associated stress variations can counter balance each other, resulting in less anisotropic deformation than those of rock masses containing one or two joint sets.     

On the role of joint roughness on the micromechanics of rock fracturing process: a numerical study

The deformation process and failure mechanism of rock mass with increased joint roughness subjected to unconfined compression are investigated in this study using discrete element method. A numerical model is developed using soft-bonded particle and validated to realistically replicate the mechanical response of the rock mass. The micro-parameters of the rock material are first determined, and the effects of the joint roughness on the macromechanical response and fracture growth mechanism are then investigated. Analyses are also performed to examine the tensile and shear crack distributions, acoustic emission (AE) characteristics, coordination number, and crack anisotropy to advance the current understanding of the role of joint roughness on the mechanical behavior and deformability of rock mass. The results show that strength and deformability of the jointed rocks are highly dependent on the joint orientation and roughness. Joint roughness is found to restrain the propagation and coalescence of microcracks and AE events from the interlocking of asperities. In addition, the spatial distribution of the contact forces allows for better understanding of the effect of joint inclination angle on the response of the investigated rock samples.

     

锚固的贯通节理岩体剪切破坏特性分析

为了研究节理对锚固岩体力学特征和失稳损伤演化的影响,采用对锚固贯通节理岩体进行室内剪切试验和PFC2D数值模拟的方法,研究不同节理倾角下锚固贯通节理岩体剪切性能的作用机制和破坏模式,研究结果表明:（1）随着节理倾角变化,贯通节理岩体呈现出不同的破坏形式,锚固贯通节理岩体的抗剪强度与剪切位移曲线并不是呈线性增长,而是呈"双驼峰"趋势。（2）锚固体系在剪切试验的过程中,节理面颗粒的接触方位角会发生一定程度的改变,主要集中在锚杆和节理倾角附近。（3）锚固体系在剪切试验的过程中,会因为颗粒间黏结键的断裂生成裂纹,裂纹数生成的越少,其抗剪强度越高,裂纹分为张拉裂纹和剪切裂纹,并且张拉裂纹的数量要远远大于剪切裂纹的数量。研究结论可用于实际工程破坏模式的预测和岩体工程稳定性评价。     

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

TBM滚刀破岩的广义粒子动力学数值模拟

提出了一种新的无网格数值模拟计算方法--广义粒子动力学法(GPD),并在GPD算法中引入了粒子损伤理论。运用GPD方法,建立了TBM单滚刀、双滚刀作用下的完整岩体破岩模型,成功模拟了TBM滚刀破岩过程。通过与数值模拟结果及室内试验结果的对比分析,验证了GPD法模拟TBM滚刀破岩过程的有效性。同时,运用GPD方法建立了含节理岩体及高围压条件下岩体的TBM滚刀破岩模型,研究了节理及围压条件下TBM滚动破岩过程。得到了节理对TBM滚刀破岩效率的影响,既可能是促进作用又可能是抑制作用,高围压对TBM滚刀破岩过程中裂纹的起裂及扩展和破岩深度有较大的影响。     

Anisotropic mechanical properties and brittleness evaluation of layered phylliteEI北大核心

为了研究层状千枚岩的力学特性与各向异性特征,开展了不同层理倾角与不同围压下的千枚岩力学试验。对比分析了千枚岩试样强度、变形、脆性与破坏模式等各向异性特征。结果表明:(1)随着层理倾角β增加,岩样的强度、变形特征曲线形状呈U型;随围压增加,岩样强度及塑性增强,各向异性度逐渐减弱稳定。(2)采用多种强度准则描述岩样强度各向异性,其中Saeidi准则和改进Ramamurthy准则能很好地预测岩样在不同层理倾角下的抗压强度。(3)基于岩样峰前应力-应变曲线与能量特征提出了综合脆性评价指标,在层理倾角β=45°左右时,岩样脆性指标较低,更易发生剪切滑移破坏,得出脆性下降顺序为:沿层理面拉伸劈裂>穿层理面拉伸劈裂>沿层理面剪切>穿层理面剪切。(4)千枚岩的破坏模式与层理倾角和围压有关,单轴条件下,岩样劈裂破坏后易形成复杂裂纹网络;高围压下,岩样破裂后多形成单一的沿层理面或贯穿多层理面的剪切破坏。     

Numerical Simulation of the Process of Fracture of Echelon Rock Joints

The effect of joint overlap on the full failure behavior of a rock bridge in the shear-box test was numerically investigated by means of the particle flow code in two dimensions (PFC2D). Initially, the PFC2D was calibrated by use of data obtained from experimental laboratory tests to ensure the conformity of the simulated numerical model’s response. Furthermore, validation of the simulated models was cross-checked with the results from direct shear tests performed on non-persistent jointed physical models. By use of numerical direct shear tests, the failure process was visually observed and the failure patterns were seen to be in reasonable accordance with experimental results. Discrete element simulations demonstrated that macro shear fractures in rock bridges are because of microscopic tensile breakage of a large number of bonded discs. The failure pattern is mostly affected by joint overlap whereas the shear strength is closely related to the failure pattern. The results show that non-overlapping joints lost their loading capacity when nearly 50 % of total cracks developed within the rock bridge whereas the overlapping joints lost their loading capacity as soon as cracks initiated from the joint walls. Furthermore, progressive failure or stable crack growth was seen to develop for non-overlapped joints whereas brittle failure or unstable crack growth was seen to develop in overlapped joints.     

基于有限元修正节理岩质边坡稳定性计算的解析解

采用有限元方法探讨在人工开挖或自然侵蚀环境下,岩质边坡体内应力场的变化及节理发育形成机理,并采用有限元强度折减法对后缘具有张节理边坡的稳定性影响因素进行敏感性对比分析,进而得出具有非贯通节理边坡稳定性计算的修正解析解。结果表明：卸荷及风化作用导致边坡体由表及里出现应力重分布及应力集中的现象,使边坡后缘由顶部向下发育一簇竖直向下或略向临空面倾斜的张节理,当张节理与下部的缓倾剪节理贯通时,边坡发生破坏;边坡稳定性最敏感的影响因素为受剪节理的倾角及贯通度,其次是节理的强度参数;可将工程中较难调查的节理贯通度转化为节理的强度参数来等效表达,并根据Mohr-Coulomb强度准则推导得到适用于具有非贯通节理的岩质边坡稳定性的修正解析解。     

不规则柱状节理岩体力学特性模型试验研究

结合Voronoi图随机模拟和3D打印技术制备不规则柱状节理网络模型,采用白水泥浆类岩石相似模型材料浇筑模型并拆模,然后分别采用白乳胶和502胶水作为黏结剂黏结柱体得到两组不规则柱状节理岩体试件,通过对其进行室内单轴压缩试验研究不规则柱状节理岩体强度特性和破坏模式。试验结果表明：不规则柱状节理岩体试件单轴抗压强度随柱体倾角的变化曲线呈现近似“J”型,表现出显著各向异性特征;不规则柱状节理岩体试件典型破坏模式包括沿柱状节理面的劈裂破坏、沿柱状节理面的剪切破坏和沿柱体的压裂破坏等3种,其部分破坏形态有异于规则柱状节理岩体试件。同时,通过与采用净水泥浆作为黏结剂的柱状节理岩体试验结果进行比较,结果表明：采用白乳胶和502胶水作为黏结剂时柱体间黏结强度更低,能够较好反映柱状节理面的弱化效应,试件力学响应与真实柱状节理岩体更为一致。     

Three-Dimensional Numerical Investigations of the Failure Mechanism of a Rock Disc with a Central or Eccentric Hole

The diametrical compression of a circular disc (Brazilian test) or cylinder with a small eccentric hole is a simple but important test to determine the tensile strength of rocks. This paper studies the failure mechanism of circular disc with an eccentric hole by a 3D numerical model (RFPA3D). A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. First, numerically simulated Brazilian tests are compared with experimental results. Special attention is given to the effect of the thickness to radius ratio on the failure modes and the peak stress of specimens. The effects of the compressive strength to tensile strength ratio (C/T), the loading arc angle (2α), and the homogeneity index (m) are also studied in the numerical simulations. Secondly, the failure process of a rock disc with a central hole is studied. The effects of the ratio of the internal hole radius (r) to the radius of the rock disc (R) on the failure mode and the peak stress are investigated. Thirdly, the influence of the vertical and horizontal eccentricity of an internal hole on the initiation and propagation of cracks inside a specimen are simulated. The effect of the radius of the eccentric hole and the homogeneity index (m) are also investigated.     

On the role of pre-existing discontinuities on the micromechanical behavior of confined rock samples: a numerical study

The deformation process and failure mechanism of rock mass with increased density of initial joints subjected to confined stress state are investigated in this study using discrete element method (DEM). A numerical model of standard size granite samples is developed and validated using experimental data for both intact and jointed rocks. The micro-parameters of the rock material are first determined, and the effects of the rock discontinuity on strength, deformability, stress–strain relationship, and failure modes are then investigated at the macro-scale level. Analyses are also performed to examine the tensile and shear crack distributions, fragmentation characteristics, particle kinematics, and energy dissipation to advance the current understanding of the deformation processes and failure mechanisms of jointed rock masses. The microscopic evolutions in the fabric and force anisotropy during loading and distributions of contact forces provide insights into the influence of increasing initial jointing on the macroscopic deformational behavior of the rock. The results show how the deceleration in the growth of fabric and contact force anisotropies develops and confirms that the increase in initial jointing and the associated changes in microstructure can restrain the development of anisotropy, thereby reducing significantly the strength of the rock samples.

     

基于RJM断续节理岩体强度与破坏特征的数值模拟研究

裂隙结构的存在对于工程岩体的强度和稳定性具有重要影响,岩石宏观裂隙的产生源自于微破裂的积累。针对岩体裂隙的粗糙特性,通过Matlab建立考虑粗糙度的节理模型（Roughness Joint Model）,采用简化的正弦曲线来表示粗糙节理,并将其导入到颗粒流试验模型中进行单轴压缩试验。对比完整岩体、直线型裂隙岩体、RJM岩体三者破坏的应力-应变曲线,改变裂隙倾角（与水平方向夹角）α,岩桥倾角β,裂隙密度γ,建立不同裂隙分布的断续节理岩体数值试样,开展一系列数值模拟试验。研究结果发现:（1）裂隙的存在明显降低了岩体的抗压强度,RJM模型峰值强度和峰值应变均高于直线型裂隙岩体;（2）岩体抗压强度总体上随裂隙倾角增大而增加,随裂隙密度增加而减小,但随岩桥倾角的改变呈非线性变化,岩桥倾角45°时峰值强度最低,峰值应变最小;（3）裂隙分布会影响岩体的破裂模式,微裂隙的扩展反映了岩体力学性质的各向异性;（4）不同倾角下增加裂隙密度,岩体强度下降程度不同,倾角75°时密度对强度影响最小,30°和60°时影响最大。     

多尺度节理岩体力学特性的颗粒流分析

以白云鄂博露天铁矿东矿岩质高边坡为工程背景,结合现场地质调查、室内岩石和节理力学试验等数据,采用等效岩体技术,构建能充分反映节理分布特征的实验室、现场原位试验和工程尺度等多尺度等效岩体模型。通过对各类等效岩体模型进行单轴压缩试验,研究岩体单轴抗压强度、弹性模量等力学特性的尺寸效应和各向异性。研究表明：节理的存在使岩体表现出尺寸效应和各向异性,且随着尺寸的增大,这种特性基本呈逐渐减弱的趋势;研究区域岩体的表征单元体积、单轴抗压强度和弹性模量分别为20 m×10 m×10 m、1.46 MPa和3.91 GPa;岩体单轴抗压强度、弹性模量与轴向尺寸的关系,近似符合渐进式指数函数关系,且该函数能直观地给出工程尺度岩体的力学特性。