Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression

Failure of rock mass that is subjected to compres-sive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research inves-tigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the pre-existing flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: pri-mary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour.     

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.     

Uniaxial experimental study of the acoustic emission and deformation behavior of composite rock based on 3D digital image correlation (DIC)

In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3 D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the θ = 0?–45?specimens had obvious plastic deformation during loading, and the brittleness of the θ = 60?–90?specimens gradually increased during the loading process. When the anisotropic angle θincreased from 0?to 90?, the peak strength, peak strain,and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories:tensile fracture across the discontinuities(θ = 0?–30?), slid-ing failure along the discontinuities(θ = 45?–75?), and tensile-split along the discontinuities(θ = 90?). The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the θ = 0?–45?specimens and was almost the same as that of the θ = 60?–90?specimens. As for the strain localization highlighted in the maximum principal strain field, the θ = 0?–30?specimens appeared in the rock matrix approximately parallel to the loading direction,while in the θ = 45?–90?specimens it appeared at the hard and weak rock layer interface.     

A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material简

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.     

Quantitative assessment of the surface crack density in thermal barrier coatings

In this paper, a modified shear-lag model is developed to calculate the surface crack density in thermal barrier coatings（TBCs）. The mechanical properties of TBCs are also measured to quantitatively assess their surface crack density. Acoustic emission（AE） and digital image correlation methods are applied to monitor the surface cracking in TBCs under tensile loading. The results show that the calculated surface crack density from the modified model is in agreement with that obtained from experiments. The surface cracking process of TBCs can be discriminated by their AE characteristics and strain evolution. Based on the correlation of energy released from cracking and its corresponding AE signals, a linear relationship is built up between the surface crack density and AE parameters, with the slope being dependent on the mechanical properties of TBCs.     

INVESTIGATION ON COMPLIANCE ROTATION CORRECTION FOR COMPACT TENSILE SPECIMEN IN UNLOADING COMPLIANCE METHOD

The rotation correction method of unloading compliance for a compact tensile (CT) specimen in the current Jintegral resistance curves or critical Jintegral test standards was under suspicion by tracing to its source, and a new rotation correction method was proposed. The rotation center of the specimen is close to the crack tip, and the material constitutive relationship has little effect on the rotational radius R. If the formula for rotation correction recommended in current standards is used to measure the crack length of CT specimen, it will lead to larger error. A new formula with better accuracy for the crack length measurement of the CT specimen was presented.     

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE STRESS-STRAIN RELATION FOR MESOSCOPIC HETEROGENEOUS ROCK UNDER UNIAXIAL TENSILE LOADING

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.     

STRESS FIELD AT A TIP OF A PREFABRICATED SPIRAL V-NOTCH

Based on the tranditional V-notched blasting, a technique of spirally V-notched blasting to loosen earth and rock was presented. Fracture mechanics and Westergaard stress function were adopted to build a complex stress function to derive the plane stress and strain fields at one tip of the crack under a quasi-static pressure. An expression was formulated to define the stress intensity factor of spiral V-notch loosen blasting. Factors that have effects on the stress intensity factor were studied. It is demonstrated that spiral V-notch loosen blasting is an extension of vertical V-notch blasting, straight cracking, and alike theories.     

Stress field of orthotropic cylinder subjected to axial compression

Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.     

Macro and micro mechanics behavior of granite after heat treatment by cluster model in particle flow code

In this paper, a cluster model in particle flow code was used to simulate granite specimens after heat treatment under uniaxial compression. The results demonstrated that micro-cracks are randomly distributed in the specimen when the temperature is below 300?C, and have partial coalescence when the temperature is up to 450?C, then form macro-cracks when the temperature is above 600?C. There is more inter-granular cracking than intra-granular cracking, and their ratio increases with increasing temperature.The micro-cracks are almost constant when the temperature decreases from 900?C to room temperature, except for quartz α–β phase transition temperature(573?C). The fracture evolution process is obviously affected by these cracks, especially at 600–900?C. Elevated temperature leads to easily developed displacement between the grains, and the capacity to store strain energy becomes weaker, corresponding to the plasticity of granite after heat treatment.     

Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression

Based on experimental results of brittle, intact sandstone under uniaxial compression, the micro-parameters were firstly confirmed by adopting particle flow code(PFC2D). Then, the validation of the simulated models were cross checked with the experimental results of brittle sandstone containing three parallel fissures under uniaxial compression. The simulated results agreed very well with the experimental results, including the peak strength, peak axial strain, and ultimate failure mode. Using the same microparameters, the numerical models containing a new geometry of three fissures are constructed to investigate the fissure angle on the fracture mechanical behavior of brittle sandstone under uniaxial compression. The strength and deformation parameters of brittle sandstone containing new three fissures are dependent to the fissure angle. With the increase of the fissure angle, the elastic modulus, the crack damage threshold,and the peak strength of brittle sandstone containing three fissures firstly increase and secondly decrease. But the peak axial strain is nonlinearly related to the fissure angle. In the entire process of deformation, the crack initiation and propagation behavior of brittle sandstone containing three fissures under uniaxial compression are investigated with respect tothe fissure angle. Six different crack coalescence modes are identified for brittle sandstone containing three fissures under uniaxial compression. The influence of the fissure angle on the length of crack propagation and crack coalescence stress is evaluated. These investigated conclusions are very important for ensuring the stability and safety of rock engineering with intermittent structures.     

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.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

A 3-D ellipsoidal flaw model for brittle fracture in compression

Engineering materials are rarely free of flaws. Mode I cracking from pre-existing flaws is the major cause of the brittle fracture in compression of materials such as concrete and rock. A 3-D ellipsoidal flaw model is used to show the significant influence of flaw geometry on crack initiation in uniform uniaxial, biaxial and triaxial compression. The model shows that the governing criterion for crack initiation may change from energy to stress with increasing crack size, and that for voids of similar size a spherical void is the most critical shape for crack initiation. The model thus provides a basis for a better understanding of both the phenomenon and the mechanism of brittle fracture in compression.     

砂岩脆性变形破坏过程中声发射信息试验研究

针对砂岩试样进行了单轴刚性加载试验，并测试整个过程的声发射信息。根据试验情况，可将砂岩在整个变形阶段的声发射信号特征划分为压密、弹性、稳定破裂、非稳定破裂和峰后情况五个阶段。通过对稳定破裂和非稳定破裂分界点对应的临界点处的应力和应变值与峰值应力及其对应的应变比值分析发现，大部分应变比在74%与78%之间；应力比则相对具有较大的离散性，均值在73%左右。上述研究，通过对砂岩脆性破坏过程中声发射信息与应力比和应变比之间的关系分析，增进了对岩石破裂过程中生发现象的认识，为相应岩石脆性破坏导致的地质灾害分析提供了新的研究思路。     

基于声发射参量的不同深度灰岩塑性破坏识别研究

对某矿深部灰岩进行单轴压缩试验,测得试件破坏全过程的应力、应变和声发射参数。通过分析应力、应变和声发射参数之间的关系,可根据声发射振铃计数率的变化情况,将全过程分为三个阶段:第一阶段处于孔隙裂隙压密阶段,振铃计数率较多;第二阶段处于稳定变形阶段,声发射处于平静期;第三阶段岩石进入塑性变形阶段,振铃计数率明显增加。研究发现,深度越深,第一阶段终止时的应力水平越高;将声发射累计能率与累计振铃计数率的比值定义为能振比λ,λ的变化规律一定程度上反映出试件内部裂隙发展情况。研究λ的变化规律能够为识别岩体失稳提供依据,提高声发射技术监测预报的准确性。     

岩石紧凑拉伸断裂过程及其尺寸效应的三维数值模拟

采用最近开发的三维岩石破裂过程分析软件RFPA3D模拟单边裂纹紧凑拉伸断裂过程。试验中五个不同尺寸的岩样具有相同的力学性质参数分布,模拟结果得到了裂纹扩展中的应力场、位移场和声发射的空间分布以及单边裂纹扩展贯通的过程。单边裂纹拉伸断裂的路径是一个复杂的空间三维曲面,三维裂纹比二维裂纹更为复杂。分析了岩石试样的峰值强度和试样尺寸之间的关系。随着岩样尺寸的增加,峰值强度逐渐减小,并且延性破坏特征更加明显,模拟结果满足岩石的尺寸效应规律。最后模拟了三组不同均匀性的试样拉伸破坏过程,结果表明细观上的非均匀性对岩石尺寸效应有很大影响,随着非均匀性的增加,岩石宏观强度随之提高,即使在均匀材料中一样存在尺寸效应。     

类岩石材料中表面裂纹扩展模式的实验研究

采用粘贴式轴拉方法实现了类岩石材料的直接拉伸实验,通过在类岩石材料试件中预制表面裂纹研究了类岩石材料中表面裂纹的扩展模式.研究发现,粘贴式轴拉方法可以满足一般类岩石材料的直接拉伸实验;类岩石材料中表面裂纹首先从试件正面开始扩展;表面裂纹的存在极大地影响着材料的破坏模式,类岩石材料在试件的正面上会表现出明显的二维穿透性裂纹的扩展形态,但是受其影响裂纹在厚度方向扩展会发生偏转,从而使得试件背面的最终贯通方向没有与加载方向垂直,而是呈一倾角,并且和表面裂纹的倾角和深度有关.