Influence of flaw inclination angle and loading condition on crack initiation and propagation

With reference to the experimental observation of crack initiation and propagation from pre-existing flaws in rock specimens under compression, the influences of pre-existing flaw inclination angle on the cracking processes were analyzed by means of finite element method (FEM) and non-linear dynamics method. FEM analysis on the stress field distribution induced by the presence of a pre-existing flaw provided better understanding for the influence of flaw inclination angle on the initiation position and initiation angle of the potential cracks. Numerical analysis based on the non-linear dynamics method was performed to simulate the cracking processes. The resultant crack types, crack initiation sequences and the overall crack pattern were different under different loading conditions. Under a relatively low loading rate or a small magnitude of maximum loading pressure, tensile cracks would tend to initiate prior to shear cracks. In contrast, under a relatively high loading rate and a large magnitude of maximum loading pressure, shear cracks would tend to initiate prior to tensile cracks instead.     

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.     

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.     

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β ? 30°). When the pre-existing flaws are steep (such as β ? 75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L ? 2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L ? a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L ? 2a).     

基于数字图像的不同倾角节理灰岩破裂模式及细观尺度破裂过程研究

为研究节理倾角对灰岩破裂模式及破裂过程的影响,使用数字图像对灰岩的细观非均匀性进行表征,采用岩石破裂过程分析系统(RFPA2D-DIP)对不同倾角节理灰岩的细观破裂过程及宏观破坏模式进行了研究。结果表明,细观结构对各倾角节理试样的力学特性和最终破坏模式有重要影响,含节理灰岩的弹性模量及抗压强度具有明显的各向异性,随着节理倾角的增大均呈U型变化;含节理灰岩在单轴压缩条件下以拉伸破坏为主并伴随少量剪切破坏,细观拉伸破裂的聚集导致了宏观剪切带的形成;含节理灰岩的最终破坏模式随着方位角α的不同表现出6种形式:直线形(α=45°,α=75°);N形(α=60°);斜Z形(α=0°);斜N形(α=90°);M形(α=15°);V形(α=30°)。     

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.     

有腹筋混凝土梁的剪切刚度分析模型

钢筋混凝土梁的挠度计算通常不计入剪切变形的贡献,然而对于斜向开裂的有腹筋混凝土梁,斜裂缝会显著降低梁体的有效剪切刚度,导致剪切变形值显著增大,因此在验算评估时应予以考虑.为评价钢筋混凝土梁斜向开裂后的有效剪切刚度,首先,基于变角桁架模型推导了钢筋混凝土梁在箍筋屈服状态下的有效剪切刚度;与弹性剪切刚度比较发现,剪切刚度退化系数的主要影响因素为材料弹模比、配箍率和斜压杆倾角.其次,基于试验剪切变形曲线表现出的刚度退化规律,提出了可用于不同开裂程度下剪切刚度计算的恒定切线刚度退化模式,并采用开裂后的剪力增量作为反映开裂程度的定量指标.最后,根据最小能量原理得到了剪切刚度退化中两个关键参数:斜压杆倾角和剪切刚度退化系数的解析公式.通过2根薄腹混凝土梁剪切变形试验以及收集的15个受剪梁段的剪切变形数据对模型有效性进行了验证,验证结果表明:有腹筋混凝土梁剪切刚度分析模型能较为准确地预测箍筋屈服状态的剪切刚度,并能反映不同开裂程度下的剪切刚度退化规律.     

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.     

压剪联合冲击下K9玻璃中的失效波

对K9玻璃进行了冲击速度为150~400 m/s,倾斜角为10、15的纵剖试样斜撞击实验。结果表明，在加载剪切横波(S+)和卸载纵波(P-)之间有波速超过了纵波波速的波阵面存在，此波的存在对卸载纵波和卸载横波的幅值有一定的影响。由于失效波的产生与材料的表面性质密切相关，为消除纵剖试样中间界面的影响，模拟VISAR的实验条件，进行了冲击速度为70~300 m/s、倾斜角为10的横剖试样斜撞击实验。可以确定在此冲击范围失效波的波速在0.98~1.4 km/s，产生失效波的临界状态为:压应力0.86~1.01 GPa，对应剪应力0.053~0.071 GPa。表明剪应力的存在极大降低了失效波产生的阈值。在此基础上初步分析了撞击面的动摩擦因数和相对滑移速度。