Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.     

DEM analysis of the effect of joint geometry on the shear behavior of rocks

In order to comprehensively investigate the effect of different joint geometries on the shear behavior of rocks, the Distinct Element Method (DEM) was utilized with a new bond contact model. A series of direct shear tests on coplanar and non-coplanar jointed rocks was simulated using the PFC2D software, which incorporates our bond contact model. Both coplanar jointed rocks with different joint persistence and non-coplanar ones with different joint inclinations were simulated and investigated numerically. The numerical results were compared and discussed with relevant laboratory tests as well as some reported numerical works. The results show that for coplanar jointed rocks, the peak shear stress decreases nonlinearly with the joint persistence, and the failure process can be divided into four stages: elastic shearing phase, crack propagation, failure of rock bridges, and residual phase. For non-coplanar jointed rocks, as the absolute value of the inclination angle of the rock joints increases, its shear strength increases, changing the failure patterns and the length of new fractures between existing cracks. When the absolute value increases from 15° to 30°, the average shear capacity increases the most as 39%, while the shear capacity increases the least as 2.9% when the absolute value changes from 45° to 60°. There is a good consistency of the failure patterns obtained from experiments and numerical tests. All these demonstrate that the DEM can be further applied to rock mechanics and practical rock engineering with confidence in the future.     

压缩-剪切复合应力下PMMA材料的静态力学特性研究

通过压缩具有一定倾斜角(0°,10°,15°,20°和25°)试件和双剪切模型试件,实现了单轴压缩、压缩-剪切复合应力以及纯剪切三种应力状态,得到PMMA(聚甲基丙烯酸甲酯)在相应应力状态下的应力-应变曲线,同时对不同应力状态下试件的破坏模式进行了分析。结果表明:在不同受力环境中材料的强度和破坏的机理不同;同单轴压缩状态下相比,材料在压缩-剪切复合应力状态下屈服极限、强度极限以及破坏应变均不同程度的增大,呈现明显的"剪切增强"现象。单轴压缩与压缩-剪切应力状态下试件的破坏模式均为在试件短对角面上出现明显的剪切屈服带,由应力分析得出试件剪应力在短对角面上达到最大,引起在此平面上分子链间滑动从而产生应变软化形成剪切屈服带;双剪切试件的破坏模式为与剪切面呈45°的斜面。     

Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression

Fractures in natural rocks have an important effect on the strength and failure behavior of rock mass, which are often evaluated in rock engineering practice. The theoretical evaluation of mechanical behavior of fractured rock mass has no satisfactory answer due to the role of confining pressure and crack geometry. Therefore, in this paper, conventional triaxial compression experiments were carried out to study the strength and failure behavior of marble samples with two pre-existing closed cracks in non-overlapping geometry. Based on the experimental results of a number of triaxial compression tests, the effect of crack coalescence on the axial supporting capacity and deformation property were investigated with different confining pressures. The results show that intact samples and flawed samples (marble with pre-existing cracks) have different deformation properties after peak stress, which change from brittleness to plasticity and ductility with the increase of confining pressure. The peak strength and failure mode are found depending not only on the geometry of flaw, but also on the confining pressure. The strength of flawed samples shows distinct non-linear behavior, which is in a better agreement with non-linear Hoek–Brown criterion than linear Mohr–Coulomb criterion. For a kind of rock that has been evaluated as a Hoek–Brown material, a new evaluation criterion is put forward by adopting optimal approximation polynomial theory, which can be used to confirm more precisely the strength parameters (cohesion and internal friction angle) of flawed samples. For intact samples, the marble leads to typical shear failure mode with a single fracture surface under different confining pressures, while for flawed samples, under uniaxial compression and a lower confining pressure (σ₃ = 10 MPa), tests for coarse and medium marble (the coarse and medium refer to the grain size) exhibit three basic failure modes, i.e., tensile mode, shear mode, and mixed mode (tensile and shear). Shear mode is associated with lower strength behavior. However, under higher confining pressures (σ₃ = 30 MPa), for coarse marble, the axial supporting capacity is not related to the geometry of flaw. The friction among crystal grains determines the strength behavior of coarse marble. For medium marble, the failure mode and deformation behavior are dependent on the crack coalescence in the sample. The present research provides increased understanding of the fundamental nature of rock failure under conventional triaxial compression.     

不同围压下含天然贯通节理岩石卸载破坏机理研究

二郎山特长高速公路隧道断裂带较多,受此影响,隧道开挖后岩爆灾害十分严重．从此隧道中取样制备成含天然贯通节理试件,进行常规单轴压缩室内试验,获取基本力学参数和破坏模式．本文以室内实验结果为依据,确定数值试验时所采用的岩石和节理的力学参数,利用RFPA软件开展数值试验,研究了不同围压同轴向荷载下卸掉围压诱发岩石失稳破坏机理．试验结果表明,五种不同围压(5、10、15、20、25 MPa)卸载后应力-应变曲线均呈“断崖式”跌落,试样均突然破坏,与现场岩爆情况吻合;受贯通节理影响,不同围压试样的具体破坏形态、声发射数量最大值出现时刻有所差异;在卸载阶段五种试样声发射累积数量都突然急剧增大．     

Loading rate and confining pressure effect on dilatancy,acoustic emission,and failure characteristics of fissured rock with two pre-existing flaws

Investigating the dilatancy, acoustic emission and failure characteristics of fissured rock are significant to ensure their geotechnical stability. In this paper, the uniaxial and triaxial compression experiments with AE monitoring under different loading rates were carried out on fissured rock specimens with the same geometrical distribution of two pre-existing flaws. The dilatancy and AE activity of these specimens were discussed, and the effects of the confining pressure and loading rate on the mechanical parameters and failure characteristics were analyzed. The results show that the exponential strength criterion is more suitable than the Mohr–Coulomb strength criterion to characterize the strength characteristics of fissured rock. The crack evolution and failure characteristics of fissured rock specimens are more complicated than those of intact rock specimens. The failure characteristics of the fissured rock follow the tensile shear coalescence model, crack branching occurs with increasing the loading rate, and the multi-section coalescence model is verified with increasing the confining pressure. The phenomena of stress drop and yield platform usually occur after the dilatancy onset, the specimen does not fail instantaneously, and the propagation and coalescence of cracks cause a sharp increase in the AE signals, circumferential strain, and volumetric strain.     

不同节理角度和地应力条件下岩石双孔爆破的数值模拟

在采矿工程、地下交通工程和水利水电工程等岩体开挖工程中,爆破法仍是一种主要的破岩方法. 实际天然岩体中存在的裂隙、节理等不连续面和所处的地应力场环境,都会对爆破荷载传播过程和最终的破碎效果产生重要影响. 本文把岩石爆破视为爆炸应力波动态作用和爆生气体压力准静态作用两个独立的先后作用过程,同时考虑初始应力场的静态作用,建立岩石爆破的力学模型. 基于渗流方程描述爆生气体在爆生裂纹中的传播过程,进而基于流固耦合理论实现爆生气体准静态压力对裂纹尖端的力学作用. 爆炸应力波主要在孔周引起压碎区和径向微裂纹区,随后爆生气体压力楔入径向裂纹尖端,促使裂纹进一步扩展,形成径向主裂纹. 数值模型可以再现孔周压碎区、径向微裂纹区、径向主裂纹区萌生、扩展的完整演化过程. 针对不同节理角度和地应力条件下岩石双孔爆破过程的数值模拟结果表明,初始地应力场的压应力作用不利于爆生裂纹的萌生与扩展,但节理的存在对裂纹的扩展具有明显的导向和促进作用,有利于爆生裂纹沿节理面方向的扩展.      

三轴压缩岩石细观损伤扩展特性CT实时检测

利用作者最新研制的与CT（computerized tomography)机配套的专用加载设备,完成了三轴压缩荷载作用下岩石破坏全过程的细观损伤扩展规律的实时CT检测试验。得到了在不同荷载作用下岩石中微孔洞被压密、微裂纹萌生、分叉、发展、断裂、破坏、卸载等各个阶段清晰的CT图像。对得到的CT数、CT图像等数据进行了分析,引入了初始损伤影响因子和闭合影响系数,定义了一个基于CT数的损伤变量,基于岩石细观损伤演化CT试验的结果,给出了岩石应力损伤门槛值,将岩石应力应变全过程曲线分为5段,得到了岩石损伤扩展的初步规律。     

Study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads

It is of important significance to study the coalescence mechanism of splitting failure of crack-weakened rock masses under compressive loads. In this paper, a simplified mechanism of crack propagation, in which the crack grows along the direction of maximum principal compressive stress, is proposed. Thus, only mode I is taken into account in the formulation and solution. On the basis of the near crack line analysis method, the elastic–plastic stress field near the crack line is analyzed, and the law that the length of the plastic zone along the crack line is varied with an external loads have been established by the matching condition of the elastic- plastic fields on the boundary, the coalescence stress and the strength properties of rock masses have been determined. The solution is a function of the geometry of the crack array. The results show that the crack coalescence depends on the crack interface friction coefficient, the sliding crack spacing, orientation of the cracks, and the crack half-length. The conclusions are of important significance for rock mass engineering.     

On the axial propagation of kink bands in fiber composites : Part i experiments

In many fiber composites, longitudinal compressive failure leads to the formation of kink bands. It has been found that these kink bands, once formed, can be made to propagate (broaden) in a steady-state manner at a constant stress level called the propagation stress (σ_P) . This is a characteristic stress of the material which, for the AS4⧹PEEK composite used in the study reported here, is approximately 40% of its compressive strength. This phenomenon is investigated experimentally using a special confining set-up that allows direct observation of the propagation process. For the composite studied, the kink bands have a repeatable inclination (β) of approximately 15°, and the fibers within the bands are rotated to about 30° in the absence of a load. When loaded to σ_P, however, they are found to rotate further to 40°, that is, substantially greater than the 2β reported elsewhere. The mechanism of propagation is found to be a bend-break-rotate sequence undergone by short segments of fibers at the edge of the kink band. It is well known that polymeric matrix composites such as the one used in this study exhibit rate-dependent behavior. Experimental results are presented which show that the kink band propagation stress is also rate dependent.     

基于数字图像处理的含缺陷花岗岩破裂力学分析1）

在细观尺度上,采用数字图像处理技术研究花岗岩中由石英、长石和云母等材料的形状、大小及分布对花岗岩材料造成的非均匀性,结合RFPA-DIP 程序建立了能准确反映材料真实细观结构的含缺陷花岗岩数值模型,并进行了常规单轴压缩模拟试验,研究不同矿物颗粒结构与缺陷对其细观破裂力学行为的影响,再现了外载荷作用下不同数值模型的真实破裂过程与最终破坏模式. 试验结果表明:缺陷对试样强度的影响比改变矿物颗粒的形态构造对其强度的影响更加显著,缺陷的存在削弱了颗粒形态对花岗岩强度影响的能力;缺陷及矿物颗粒的形态构造对试样裂纹的萌生、扩展以及最终破坏模式有直接影响,缺陷与矿物颗粒的空间结构关系是导致岩石形成各种复杂破坏模式的主要因素. 起裂应力水平受试样内部细观介质构造和缺陷的影响,而缺陷的存在对起裂应力的影响更加显著.     

预制裂缝宽度对HCFBD试件确定岩石断裂韧度的影响

为了考察人工预制裂缝宽度对确定岩石断裂韧度的影响,采用大理岩制作了含有不同预制裂缝宽度的中心圆孔裂缝平台巴西圆盘试件(hole-cracked flattened Brazilian disc, HCFBD),在RMT150B试验机上进行试验,对不同预制裂缝宽度圆盘的应力强度因子进行有限元计算,并对测试方法进行了研究。结果表明,采用将预制裂缝宽度视作零宽度裂缝方法确定的断裂韧度值偏低,给出了一种采用最小载荷和最大无量纲应力强度因子确定岩石断裂韧度的新方法,该方法能够消除预制裂缝宽度对圆盘试件测定岩石断裂韧度的影响。     

Analysis of elastic crack bridging in ceramic matrix composites

A micromechanics analytical model based on the consistent shear lag theory is developed for predicting the failure modes in fiber reinforced unidirectional stiff matrix composites. The model accounts for a relatively large matrix stiffness and hence its load carrying capacity. The fiber and matrix stresses are established as functions of the applied stress, crack geometry, and the microstructural properties of the constituents. From the predicted stresses, the mode of failure is established based on a point stress failure criterion. The role of the microstructural parameters of the constituents on the failure modes such as self-similar continuous cracking, crack bridging and debonding parallel to the fibers is assessed.     

The three-dimension model for the rock-breaking mechanism of disc cutter and analysis of rock-breaking forces

To study the rock deformation with threedimensional model under rolling forces of disc cutter,by carrying out the circular-grooving test with disc cutter rollingaround on the rock,the rock mechanical behavior underrolling disc cutter is studied,the mechanical model of disccutter rolling around the groove is established,and the theory of single-point and double-angle variables is proposed.Based on this theory,the physics equations and geometricequations of rock mechanical behavior under disc cutters oftunnel boring machine(TBM) are studied,and then the balance equations of interactive forces between disc cutter androck are established.Accordingly,formulas about normalforce,rolling force and side force of a disc cutter are derived,and their validity is studied by tests.Therefore,a newmethod and theory is proposed to study rock-breaking mechanism of disc cutters.     

Cracking simulation of a tubesheet under different loadings

For shell-and-tube heat exchangers, tubesheet cracking is a major failure form. Owing to complicated structures, loadings and environments, mechanisms for the crack nucleation and propagation often puzzle engineers and as a result, it is hard to take effective measures to prevent this kind of failure from happening again. In this paper, three dimensional finite element models were established to investigate a real tubesheet cracking with the emphasis on the driving forces for the crack propagation from a fracture mechanics point of view. Three different loadings, namely residual expansion stress, crack face pressure and transverse pressure, and three crack growth patterns were considered. In order to obtain the residual stresses, the hydraulic expanding process of tube-to-tubesheet joint was simulated. Residual contact pressures between the tube and tubesheet and the induced residual stress distributions in the tubesheet were computed. The possibility for crack propagation in the tubesheet under the action of the different loadings was investigated in terms of the strain energy density factor. Results show that surface crack propagation may be driven by all the three loadings especially the transverse pressure. But when surface cracks come into the interior of the tubesheet along the thickness, as acted along the whole tubesheet thickness, the residual expansion stress would play key roles in crack propagation.     

Experimental investigation on the propagation of fatigue cracks emanating from sharp notches

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches is investigated by means of an experimental campaign performed on Al-7075-T651 specimens carrying notches with opening angles of 45°, 90°, and 135°. The samples were tested using a servohydraulic machine under different loading directions and at several loading levels. The crack deflection induced by the variation in loading direction was determined my measuring the kinking angle and by studying the crack propagation plane through fractographic analysis. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. The influence of K _II on the crack propagation was discussed on the basis of theoretical and semi empirical models.     

基于GMTS准则的岩石复合型断裂机理研究

使用国际岩石力学协会规定的半圆盘岩石试件,加工不同倾角的直裂纹试样,通过三点弯曲加载试验得到不同I-II复合比断裂的断裂韧性和初始断裂角．传统裂纹扩展准则忽视了常数项即T应力及更高阶项的影响,导致该扩展准则的理论预测结果存在较大缺陷,本文通过考虑常数项,建立广义最大周向应力准则(GMTS)．在此基础上,分别采用传统的裂纹扩展准则和考虑T应力的裂纹扩展准则预测不同复合比裂纹的断裂韧性和初始扩展角,然后对比理论预测结果和实验结果．分析可得：常数项即T应力对断裂的临界应力强度因子和初始断裂角的影响是不可忽略的,且II型断裂占比较大时影响更大,广义最大周向应力准则预测值与实验测试结果之间的误差最小．     

动力荷载对围压卸载下岩石动态变形模量的影响

利用SHPB岩石动静组合加载实验系统,研究在不同轴压水平下围压以1 MPa/s速率卸载至预加值50%时矽卡岩受频繁冲击作用的动态变形模量变化规律。实验结果表明:高轴压促使岩石内部微裂纹萌发与扩展,降低了岩石抵抗外部冲击的能力。围压的侧向约束阻碍岩石内部裂纹的横向扩展,但在围压卸载时会加剧岩石内部的损伤,这是由于高轴压下,围压卸载导致岩石内部应力重新分布。轴压与围压卸载共同影响着冲击作用下的岩石动态变形模量,通过岩样在冲击荷载下的能量耗散分析岩石动态变形模量的变化规律,有助于了解深部岩体开挖的破坏机制。