Types Of Crack Coalescence Research Articles

Study on mechanical and fracture characteristics of rock-like specimens with rough non-persistent joints by YADE DEM simulation

Rough non-persistent joints exist widely in natural rock mass. The roughness of joints influences its mechanical and fracture characteristics. However, the research on rough non-persistent jointed rock mass is inadequate. To investigate the effects of joint angle, rock bridge angle and roughness of rough non-persistent joints, the rough non-persistent joints were truncated and their JRC was calibrated based on the Barton typical roughness profiles. A series of DEM numerical uniaxial compression tests were conducted based on the laboratory tests of rock-like specimens with 3D printed non-persistent joints. By the investigation of mechanical behaviour, crack coalescence types, crack evolution law, fracture modes presented by the strain field, and micro-fracture mechanism revealed by the displacement vectors, it was verified that YADE is suitable to simulate the fracture of rough non-persistent jointed specimens; the six types of coalescence of rough non-persistent joints were concluded, and the relation between micro-crack and macro-fracture was established by the four types of micro-cracks causing macro-fractures.

Experimental study on the fracture and fatigue behaviors of flawed sandstone under coupled freeze–thaw and cyclic loads

This paper investigates the effects of coupled freeze–thaw (FT) cycles and cyclic loads on the mechanical properties, cracking behaviors and fatigue damage mechanism of flawed rocks. The digital image correlation technology is used to monitor the real-time cracking process and to analyze the evolution characteristics of deformation fields for tested samples. The effects of FT cycles and ligament angles on the mechanical evolution properties of flawed rocks subjected to cyclic loads are first analyzed. Secondly, the cracking processes of flawed rocks with different ligament angles subjected to FT cycles are studied in detail. Seven types of cracks including anti-wing crack, wing crack, oblique secondary crack, far-field crack, out-of-plane shear crack, out-of-plane tensile crack and quasi-coplanar secondary crack are observed. Two crack initiation modes including wing crack initiation and anti-wing crack initiation are registered, and seven crack coalescence types in tested samples are discriminated. The apparent displacement fields can be employed to reveal the fracture mechanism of flawed rocks under coupled FT cycles and cyclic loads. Finally, the fatigue damage mechanism of FT cycles coupling with cyclic loading and unloading is discussed in detail. The experimental results are very meaningful to evaluate the safety and stability of rock engineering in cold regions.

Material point method for the propagation of multiple branched cracks based on classical fracture mechanics

The material point method (MPM) combines the advantages of both mesh-free and grid-based methods for simulating complex cracking problems without the limitations of the grid. However, the conventional MPM cannot deal with cracks directly because of the continuous nodal velocity field. Therefore, in this study, the conventional MPM is improved using three new algorithms to simulate the propagation of multiple branched cracks. The first proposed algorithm is the phantom node method using a particle cutting technique, which allows discontinuity of the velocity field around arbitrary cracks, and the second one is the multi-crack contact algorithm to deal with the contact problem between multiple objects cut by multiple cracks, avoiding crack penetration. The last one is particle interaction integral method based on classical fracture mechanics to get the dynamic stress intensity factors (DSIF) and realize the crack propagation. And all algorithms are validated by comparing with the extended finite element method. Subsequently, uniaxial compression tests of three rock samples with different pre-existing cracks are simulated using the extended MPM. Three types of crack coalescence are found, and the simulated results agree with the previous experimental results, which demonstrate the feasibility and flexibility of the proposed extended MPM for simulating the propagation of multiple branched cracks.

Mechanical behaviour of a jointed rock mass with a circular hole under compression-shear loading: Experimental and numerical studies

The tunnels excavated in a mountain body interact with the jointed rock mass under compression-shear and present a complex stress state. The joints often have a significant influence on the possible damage points of tunnels. However, the failure behaviour of jointed rock mass with a hole under the compression-shear condition is still unclear. The crack coalescence mechanism needs to be further explored. In this study, compression-shear tests were carried out on jointed rock-like specimens containing a circular hole. The corresponding numerical model was established by the discrete element method (DEM) modelling. The results show that with the increase in joint inclination, the peak load first increases and decreases. Four types of crack coalescence among joints and three kinds between joint and hole were found. The crack coalesces with the hole easily occur on both sides of the hole. When the joint inclination is small, the crack coalesces through the shear slip. However, the tensile crack coalesces with the joints and hole when the joint inclination is large. Finally, the failure behaviour of the specimen was further analysed based on the displacement field. The experimental results also verify the above analysis and agree well with simulation results.

Crack coalescence in rock-like specimens with two dissimilar layers and pre-existing double parallel joints under uniaxial compression

Layered rock masses with joints are widely found in nature. Their mechanical behavior plays a key role in rock engineering applications. However, previous studies have concentrated on the single lithologic layer, and few studies have reported the crack coalescence mechanism in layered rock masses with joints. In this study, uniaxial compression tests were performed on jointed rock-like specimens with two dissimilar layers. The acoustic emission (AE) and the digital image correlation (DIC) techniques are employed to investigate the crack coalescence process of specimens with two dissimilar layers. The influence of the joint angle and rock bridge angle on the mechanical behavior and failure processes in layered rock masses is investigated. The results show that the peak strength is associated with the joint angle and the rock bridge angle. Seven types of crack coalescence have been identified in the specimens, which are not only related to the joint angle and the rock bridge angle but also influenced by the rock layers. Cracks easily coalesce when the joint angle and the rock bridge angle are small. However, when the joint angle and the rock bridge angle are larger, it is difficult for cracks to initiate and propagate in the layer with higher strength. The failure mechanism of the specimens is primarily caused by crack propagation in the layer with lower strength.

Experimental Study on Anchorage Mechanical Behavior and Surface Cracking Characteristics of a Non-persistent Jointed Rock Mass

It is significant to conduct anchorage on the non-persistent jointed rock mass by bolts to inhabit the unstable fracture evolution of rock engineering. In this research, a series of experiments are done on 70 specimens to investigate the effect of anchorage method on strength and deformation behavior of a non-persistent jointed rock mass. First, based on the stress–strain curves of anchorage jointed specimens, the effect of anchorage method on the peak strength and elastic modulus of non-persistent jointed rock mass is investigated. The experimental results show that the peak strength and elastic modulus of jointed specimens changes with anchorage method for the same joint angle, while first decreases and then increases from 0° to 90° for the same anchorage method. Second, the effect of pretightening force on the strength and deformation behavior of anchorage jointed specimens is analyzed. The axial stress-axial strain curves of anchorage jointed specimens with various pretightening forces can be characterized into five types: (I) strain softening after the specimen drops to yield platform from peak strength; (II) strain hardening after the specimen drops to yield platform from peak strength; (III) strain hardening after the specimen yields; (IV) stepwise strain softening after the peak strength; (V) single stress drop after the peak strength. The peak strength and elastic modulus of jointed specimens for the same dip angle all increases nonlinearly with the pretightening force. And then, based on a series of surface failure mode of non-persistent jointed rock specimen, it can be seen that the initiation, propagation and coalescence of surface cracks depend on not only the joint angle, but also the magnitude of pretightening force. Twelve crack coalescence types are identified to analyze the surface crack mode of anchorage non-persistent jointed rock specimens. Finally, the effect of pretightening force on brittleness index of non-persistent jointed rock mass is made a discussion.

Cracking behaviours of rock‐like materials containing three preexisting flaws after high‐temperature treatments

AbstractThe mechanical properties and cracking behaviours of rock‐like materials containing three preexisting flaws after high‐temperature treatments are studied. The temperature variations of 25°C, 70°C and 140°C are chosen to explore the influence of temperature, and the ligament angle variations of 75°, 90° and 105° are chosen to explore the effect of preexisting flaws. The crack initiation and coalescence modes and specimen failure after high‐temperature treatments are recorded by a high‐speed dynamic analysis system. Seven modes of crack initiation and ten types of crack coalescence are recorded in the rock‐like specimens. With an increase in temperature and ligament angle, the mechanical properties such as peak strength, peak strain and crack initiation stress change regularly. Furthermore, the experimental results demonstrate that the temperature has a significant impact on the complete stress–strain curves and cracking behaviours of flawed rock‐like materials.

Strength and failure characteristics of jointed rock mass with double circular holes under uniaxial compression: Insights from discrete element method modelling

Underground projects are typically performed in nonpersistent jointed rock masses. Excavation of tunnels or chambers causes crack initiation, propagation and coalescence, resulting in the instability and destruction of surrounding rocks. The failure behaviour of rocks is complicated owing to the interaction between holes and joints. Therefore, understanding the failure characteristics of holes in jointed rock masses is essential. In this paper, the mechanical characteristics of a jointed rock mass with double circular holes under uniaxial loading was investigated using the discrete element method. The effects of different joint parameters on the strength and failure behaviour of the jointed rock mass with double circular holes were studied. The results show that the existence of joints degrades the mechanical behaviour of the rock mass. Specifically, the peak strength and elastic modulus of the specimens show a “U” shape change with the joint dip angle and reach the minimum value when the angle is 30°. With an increase in joint spacing, the peak strength and elastic modulus increase gradually. An investigation of the crack coalescence process and displacement field of the specimens reveal the crack propagation mechanism based on the interaction between holes and joints under uniaxial loading. Five types of crack coalescence among the holes and adjacent joints were summarized. Four typical failure modes were observed: tensile failure across joints, block rotation failure around holes, shear failure through joint planes and tensile–shear mixed failure through holes.

Effects of Brittleness on Crack Behaviors in Rock-Like Materials

Abstract The principal objective of this work is to understand the effects of brittleness on crack behaviors in rock, rock-like materials, and the underlying fracturing mechanisms. Brittleness, as one of the critical parameters of rock, significantly affects mechanical properties and fracturing behaviors. A better understanding of the effects of the brittleness on fracturing behaviors can lead to a more satisfactory characterization and assessment of the overall behaviors and performances of rock mass. In this study, experiments on rock-like materials with two parallel preexisting flaws are conducted to study the effects of brittleness, as well as the mechanical properties, crack initiation modes, crack coalescence types, and ultimate failure modes, on cracking behaviors of rock-like materials. We find that the content of the adhesive material’s polyamide and epoxy have a significant effect on the brittleness of rock-like materials that consist of sand, barite, epoxy, polyamide, and alcohol at different mass ratios. The brittleness of specimens decreases with increasing content of the cementing agents epoxy and polyamide. Seven types of crack initiation—wing crack, antiwing crack, coplanar secondary crack, oblique secondary crack, out-of-plane tensile crack, out-of-plane shear crack, and far-field crack—are observed in high-speed images of the ultimate failure crack morphology. Four types of crack coalescence are also identified: tension coalescence mode, shear coalescence mode, and the mixed mode including tension-shear coalescence mode and tension-shear-tension coalescence mode. A primary observation was that the ultimate failure mode is a transition from tension failure mode to tension-shear failure mode and shear failure mode, in sequence, and the rupture angle increases gradually with decreasing brittleness. Finally, the effects of the brittleness on the mechanical properties of rock-like materials, including the complete axial stress-strain curves, crack initiation stress ratio, and residual stress, are investigated in detail.

3-D Numerical Study on Progressive Failure Characteristics of Marbles under Unloading Conditions

3-D particle-based discrete element method (PB-DEM) was employed to numerically study the mechanical and progressive failure characteristics of pre-fissured marble specimens under conventional triaxial unloading conditions. The microscopic parameters of PB-DEM for marble materials were calibrated using comparison with the previous experimental data. To systematically investigate the mechanical properties and the progressive failure characteristics of pre-fissured marble specimens under the unloading conditions, a series of numerical specimens were simulated. The effects of fissure geometric conditions, initial confining pressures, and unloading rates on the mechanical and failure behaviors were explored via simulations. The present numerical results indicate that peak strength increased as the initial confining pressures increased or the unloading rate decreased. Crack coalescence types and the ultimate failure modes in the pre-fissured marble specimens were significantly affected by the unloading stress paths. The present numerical results provide a better understanding of unloading mechanical and failure characteristics to scientists and engineers in rock mechanics and rock engineering.

Failure behavior and crack evolution mechanism of a non-persistent jointed rock mass containing a circular hole

In natural rock masses, joints or flaws usually occur in sets that are more or less parallel and regularly spaced. Many problems occurred in tunnel engineering mainly result from the failure of joints or faults because they are weaker compared with the rock matrix. Therefore, it is important to study the interaction of joints with the tunnel, as well as the interactions between themselves. In this research, rock-like specimens of non-persistent jointed rock masses containing a circular hole are prepared and tested under uniaxial compression. The test results show that the peak strength and elastic modulus of the non-persistent jointed rock specimens display a “U” type variation with respect to the joint inclination. The multiple joints can be simplified and regarded as a combination of three types of two-joints relative location, and the crack coalescence types and failure modes are in accordance with the classic crack coalescence types of the two joints. The crack coalescence between the joints and a circular hole can be categorized into three modes with respect to the joint inclination. The Discrete Element Method (DEM) model of the jointed rock specimen that contains a circular hole is established in particle flow code 2D (PFC2D). The simulation results show a good agreement with the experiment results. Furthermore, the displacement fields at the crack zones reveal that the coalescence of joints is mainly caused by tensile cracks and that shear slipping cracks easily occur at the sidewalls of the circular hole. By comparing the parallel-bond force fields in jointed models containing a circular hole with no a circular hole, it is shown that the circular hole can change the stress state at the top and bottom. The joints at a joint inclination of 90° have the smallest effect on the mechanical behavior of the rock specimen.

Understanding the fracture behavior of brittle and ductile multi-flawed rocks by uniaxial loading by digital image correlation

Fracturing behavior of ductile multi-flawed rock mass is very different from those of brittle multi-flawed rock mass. However, there is a very vague distinction of the fracture mechanism of ductile multi-flawed rock mass from that of brittle multi-flawed rock mass due to the absence of quality experimental data. To evaluate the fracturing behavior and further reveal the failure mechanism of brittle and ductile multi-flawed rock masses, a comparison study on brittle and ductile laboratory rock-like specimens that contain nine pre-existing flaws subjected to uniaxial compression is conducted. The advanced optical technique, Digital Image Correlation (DIC), is adopted to capture the real-time displacement and strain fields on the surface of the rock-like specimens. The fractal dimension estimation method is introduced to quantitatively track the fracture process. The fracture process, the crack coalescence mode and the fracturing mechanism are obtained as well as the stress-strain response. For ductile multi-flawed rock-like specimens, four crack initiation modes and nine types of crack coalescence are observed. For brittle multi-flawed rock like specimens, four crack initiation modes and eight types of crack coalescence are observed. Comparison of fracturing behavior indicates that crack initiation mode transforms from shear crack to tensile crack as the brittleness index increases; the coalescence mode transforms from shear crack coalescence to the coalescence of tensile crack and shear crack; then to the tensile crack coalescence as the brittleness index increases. Observations on the ultimate failure modes indicate that the failure mode transforms from shear failure to the mixed tension-shear failure, then to splitting failure as the brittleness index increases. Most macrocracks in brittle multi-flawed rock-like specimens develop from crack coalescence occurring in a “columnar” pattern, while most macrocracks in ductile multi-flawed rock-like specimens develop from shear cracks. Moreover, the effects of the brittleness index on the complete stress-strain curve, the crack initiation stress and the peak strength are also investigated in detail.

A modification of the phase-field model for mixed mode crack propagation in rock-like materials

The critical energy release rates for mode I and II fracture for rock-like materials are usually different. In this paper, a modified phase-field model is proposed for simulating mixed mode crack propagation. The model can distinguish between the critical energy release rates for mode I and mode II cracks. For the purpose of validation, rock-like materials with a single flaw or double flaws under compression are studied. The simulated results are compared to experimental data, both qualitatively and quantitatively. It is shown that the proposed model is able to capture the commonly observed propagation pattern of wing crack emergence followed by secondary cracks. Additionally, the typical types of crack coalescence observed in experimental tests are successfully reproduced, including the critical loads at which crack coalescence occurs.

The Effects of Crack Openings on Crack Initiation, Propagation and Coalescence Behavior in Rock-Like Materials Under Uniaxial Compression

This paper experimentally investigates the cracking behavior of rock-like specimens containing artificial open flaws under uniaxial compressive loads. The present experiments mainly focus on the effects of crack openings on crack propagation and coalescence behavior in rock-like materials under uniaxial compression. The real-time crack coalescence processes in the specimens with different crack openings are analyzed. The experimental results show that the crack openings significantly affect the crack initiation stresses and the crack initiation modes. The initiation stresses of wing cracks and coplanar secondary cracks decrease with increasing crack openings. However, the initiation stress of anti-wing cracks increases with increasing crack openings. Moreover, five types of crack coalescence in the specimens containing three pre-existing open flaws under uniaxial compression are observed. The effects of crack openings on the mechanical properties of rock-like materials, which include the complete axial stress–strain curves, peak stresses, peak strains and initiation stresses, are investigated in detail.

An Experimental Study of Crack Coalescence Behaviour in Rock-Like Materials Containing Multiple Flaws Under Uniaxial Compression

Experiments on man-made flawed rock-like materials are applied extensively to study the mechanical behaviour of rock masses as well as crack initiation modes and crack coalescence types. A large number of experiments on specimens containing two or three pre-existing flaws were previously conducted. In the present work, experiments on rock-like materials (formed from a mixture of sand, plaster, limestone and water at mass ratio of 126:9:9:16) containing multiple flaws subjected to uniaxial compression were conducted to further research the effects of the layout of pre-existing flaws on mechanical properties, crack initiation modes and crack coalescence types. Compared with previous experiments in which only three types of cracks were found, the present experiments on specimens containing multiple flaws under uniaxial compression revealed five types of cracks, including wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane tensile cracks and out-of-plane shear cracks. Ten types of crack coalescence occurred through linkage among wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane shear cracks and out-of-plane tensile cracks. Moreover, the effects of the non-overlapping length and flaw angle on the complete stress–strain curves, the stress of crack initiation, the peak strength, the peak strain and the elastic modulus were also investigated in detail.

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.