Study On Laws Of Crack Initiation, Extension And Failure In Rock Masses Under Compression

It is an important subject of rock fracture mechanics to study the law of the flaw initiation, propagation and failure in rock masses under compression. Numerous studies indicate that growth of wing cracks(I mode crack) is main reason for rock masses with the single crack or multiple cracks under uniaxial compression or under biaxial compression with low confining pressure. So laws of the wing crack initiation, propagation and failure have important significance for the study on the failure mode and failure mechanism of the rock masses with crack under compression. In this paper, the theoretical method, numerical methods and testing methods are combined to study the initiation, propagation and failure laws of the wing cracks for both open cracks and closing cracks under compression, besides the closing law for open crack and the effect of crack closing in the open crack initiation are also included. And the detail researches are explained as followings:(I)Study on the closing law and initiation characteristics of open crack under compression.1. The law of the deformation of the open crack surface under compression is studied. In the paper the methods of complex function and conformal transformation are combined to construct the parameter function, and the parameters of the function are solved. Through the parameter function, the geometry shapes of the deforming crack surface under compression can be described easily.2. Based on the study about deformation of the open crack surface under compression, the geometric model for analysis of the open crack closure is established. Through the geometric model, two conclusions are drawn as follows: First the closing law of the open crack is obtained which agrees with the general viewpoints of rock mechanics - an open crack exists either completely closed or completely open under compressive loading in rock masses. Next the criterion for a crack closure is defined which is expressed by the deformation parameters. By use of this criterion the critical closing stress of an open crack can be determined by a simple quadratic equation easily. Besides this criterion doesn't deal with the assumption of the load pattern, so it can be applied under any compressive loads, which extends the applied range of the traditional closing criterions of the open crack. At the same time, it is very convenient to be applied because of its simple mathematical form and definite physical meanings of its unknown parameters.3. Based on the simplified hypotheses that the thickness of open cracks is far smaller than their length, a simplified formula is established to determine closing stress of an open crack. Comparisons between the results calculated by the simplified formula and original theory are made. It shows that only small error happens by using the simplified formula, consequently, the simplified formula is feasible.4. Referring to the experiments data, the finite element method (ABAQUS) is used to simulate the closing process of the open crack under compression. It reveals that the numerical results support the theoretical viewpoints: an open crack exists only in the state of completely closed or completely open under compressive loading. Through the analysis on the displacement curves of the nodes of the finite element model, a new numerical method is presented to determine the closing stress of an open crack. Finally, the closing stresses solved separately by the numerical method, the previous theoretical formula and the simplified formula are compared, showing that the results obtained by three methods are identical, which approve the validity of the proposed conclusion in the paper.5. Base on the closing law of open crack under compression, the further study on the effect of the open crack closure in the initiation characters of the open crack. Before the analysis of the initiation of the open crack under compression, it is pre-requisite to ensure if the open crack is closed before its initiation. Therefore, a closure criterion of an open crack is established to determine existence state of crack before initiation. If the crack is closed before initiation, the closed crack model must be chosen and the interaction force along the crack surface should be considered for the fracture analysis. If the crack keeps open before initiation, the open model should be used, and deformation of the open crack should be considered. Based on the above study on the deformation and closing law of open crack, the traditional SIFs are modified in order to reflect the impact of the deformation or closure of the crack on the initiation characters of the open crack.6. Considering the effect of the open crack's geometric shape in the crack initiation, Chenchi crack model is used in the study of the crack fracture in the rock masses under compression. Then the methods of complex function and conformal transformation are combined to construct the stress distribution around crack surface. Based on the above conclusion the stress intensity factor of crack is calculated, and the fracture criterion of the crack model is built to analyze the initiation compression stress and angle of crack which agree with the experiments. The Further comparison between the results of the ellipse model and the Chenchi model is done, and the results show the Chenchi model can reflect the initiation property of the crack open more accurately. (II)Study on growth and failure characters of the wing cracks from open crack1. The second development of ABAQUS is implemented to automaticly remesh the finite element meshes. Besides the maximum circumferential stress fracture criterion is used for the second development of ABAQUS to determine the cracking directions of wing cracks. Then the wing crack growth is simulated by the finite element method, by which the propagation paths and the mixed-mode stress-intensity factors of wing cracks were also obtained.2. The asymptotic failure characteristics of the wing cracks are studied by the combination of the testing method and the numerical simulation method, it is found that under compression, the wing cracks of the open main flaws start from the tip of the main crack and grow along the curve path. With the length increasing, the wing crack gradually approximate to the line which passes the middle point of the main crack and is parallel to the direction of maximum main stress. It is the important geometric feature of the wing crack paths. According to the geometric characteristics of the wing crack paths, a hyperbolic equation is set up to describe the curve paths of wing cracks approximately. In the equation, the unknown parameters are determined by the crack initial angle, the crack length and the angle between the direction of the maximum main stress and the crack surface. This equation of wing cracks is simple and its physical meaning is clear which is convenient for application.3. According to Geometric Characteristics of the wing crack paths, the cure wing crack model- hyperbolic-wing crack model is built to analyze the extension and failure laws of wing crack from the open crack under compression. In the paper, the comparative analysis on the paths by the hyperbolic equation, numerical simulation and the experiments is made, and the results show the paths by the hyperbolic equation are in concordance with those by experiments, which prove that the hyperbolic equation in the paper can be used to describe the propagation paths of wing cracks under compression. Furthermore, the stress intensity factors along the hyperbolic path are calculated by ABAQUS, and the extending loads of the wing cracks are analyzed. Through comparing with the experiment results and numerical simulation results, it is found that the extending loads by the hyperbolic wing cracks in the paper fit better with by the experiments and numerical simulation, which shows validity of the results in the paper.4. The effect of the boundary size on the extending characteristics of wing cracks under uniaxial compression. In general, the boundary size of the infinite plate has little effect on the wing crack paths, but has great impact on the extension loads (SIFs) along the wing crack path. For a crack in a finite plate, its SIFs along the wing crack path tend to a fixed positive value which depends on the size of the infinite plate. But for a crack in an infinite plate, its SIFs along the wing crack path will tend to zero value. That's to say, for a crack in an infinite plate, its wing crack will extend stably for ever with the load increase. However for a crack in a finite plate, its wing crack will extend unstably and the crack will burst when the load arrives at a certain value which can be observed in testing. So for the wing cracking in an infinite plate, it is notable that the boundary effect should be considered for the mixed-mode stress-intensity factors of the wing cracks.(III)Study on growth and failure characters of the wing cracks from closing crack1. The numerical simulation is implemented to study laws of the wing crack extension from the closing crack by the second development of ABAQUS. The asymptotic behaviors of the wing crack paths of the closing cracks are also found: the wing cracks of the open main flaws start from the tip of the main crack and grow along the curve path. With the length increasing, the wing crack gradually approximate to the line which passes a certain point of the main crack and is parallel to the direction of maximum main stress. The asymptotic lines of cure wing cracks of the closing crack are determined by theoretical analysis method. Compared with the wing crack of the open crack, the asymptotic lines of the wing crack of the closing crack don't always pass through the center point of the main crack.2. According to the geometric characteristics of the wing crack paths, a hyperbolic equation is set up to describe the curve paths of wing cracks approximately. In the equation, the unknown parameters are determined by the initial crack angle, the initial crack length, the friction coefficient of the initial crack surfaces, and the angle between the direction of the maximum main stress and the crack surface. This equation of wing cracks is simple and its physical meaning is clear which is convenient for application. According to Geometric Characteristics of the wing crack paths, the cure wing crack model- hyperbolic-wing crack model is built to analyze the extension and failure laws of wing crack from the closing crack under compression. In the paper, the stress intensity factors along the hyperbolic path are calculated by ABAQUS, and the extending loads of the wing cracks are analyzed. Through comparing with the experiment results and numerical simulation results, it is found that the extending loads by the hyperbolic wing cracks in the paper fit better with by the experiments and numerical simulation, which shows validity of the results in the paper.3. In order to show validity of the cure wing crack model in the paper, a comparative Analysis of the cure wing crack model and the traditional linear wing crack model is made. First the analysis of the extension loads of the wing crack in the testing is done respectively by the above two models. Then analysis results respectively by the above two models are compared with the testing result and the numerical computation results, and the comparison results show: the extension loads determined by the curve wing crack model coincide well with the results from the testing and numerical computation, but the extension loads determined by the traditional linear wing crack model have larger difference from the ones by the testing and numerical computation. The above comparative analysis results support the validity of the curve wing crack model proposed by the paper.4. In order to show the difference between the 'initial open flaw-curve wing crack model' and the 'initial closing flaw-curve wing crack model' proposed in the paper, a comparative Analysis of the two models is made. According to the initial open flaw and the initial closing flaw, though they have the same flaw angle, the same flaw length and the same friction coefficients, the paths of their wing cracks make a great difference, so do the extending loads for their wing cracks. Therefore, before the study of the extending law of the initial flaw under compression, it is needed to distinguish the initial closing flaw and the initial open flaw by use of the closing law proposed in the paper, which shows the necessity of the closing law for the open crack.