Crack Coalescence Modes Research Articles

A study on three coalescence modes of non-collinear parallel elliptical double cracks

Based on the Gurson-Tvergaard-Needleman (GTN) damage model, this study focused on the coalescence modes of non-collinear parallel elliptical double cracks in a homogeneous plate, and the coalescence modes of elliptical double cracks under different horizontal distances and vertical distances were investigated. The ratio of horizontal distance s to crack length a was taken as the horizontal axis, the ratio of vertical distance h to crack length a was taken as the vertical axis to plot the graph, then the coalescence modes were summarized and compared with the coalescence modes of linear double cracks. It was found that the non-collinear parallel elliptical double cracks exhibited three coalescence modes: crack tip to crack tip coalescing, crack interval to crack interval coalescing, and crack tip to crack interval coalescing. Each coalescence mode had its own characteristics. The three coalescence modes were distributed regularly in three regions in the graph with s/a and h/a as coordinates. When the horizontal distance s and the vertical distance h between the double cracks were equal respectively, there were significant differences in the crack propagation process and coalescence modes between elliptical double cracks and linear double cracks.

Mechanical properties and failure behaviour of anchored granite containing two filled edge-notched fissures in triaxial compression

High in-situ stress commonly exists in deep rock engineering and causes great difficulties in underground mining support systems. To elucidate the relationship between the anchoring effect of bolts and confining pressures, triaxial compression tests were performed to study the deformation characteristics, mechanical properties, and failure behaviour of anchored granite with two pre-existing fissures. The results demonstrated that the deformation characteristics or mechanical properties of anchored granite, including triaxial compressive strength, elastic modulus, and stored or dissipated energy, increased with increasing confining pressure under low confining pressures. Rockbolt boreholes significantly weaken the mechanical properties and failure behaviour under high confining pressures and have a negative impact on the peak axial strength and stored or dissipated energy of the anchored granite. The fissure angle and confining pressure have a direct impact on the failure mode of anchored granite. With increasing confining pressures or fissure angles, shear cracks and anti-wing cracks instead of tensile wing cracks are more likely to cause ultimate failure. In addition, four modes of crack coalescence were identified: no coalescence, two types of direct crack coalescence, and indirect crack coalescence.

Numerical study on cracking behavior and fracture failure mechanism of flawed rock materials under uniaxial compression

AbstractThe numerical approach is a vital means for evaluating the stability of flawed rocks. In this paper, the extended non‐ordinary state‐based peridynamics (NOSB‐PD) theory is employed to simulate the fracture process of rocks containing two pre‐existing flaws. Two stress criteria, including the maximum tensile stress criterion and the Mohr–Coulomb criterion, are implemented into the NOSB‐PD numerical method to respectively judge the tensile and shear failure of rock materials. The effects of inclination angles and ligament angles on the crack initiation and coalescence modes for flawed rocks are investigated based on the numerical results. The numerical results are in good agreement with the previous experimental results. The fracture mechanism of flawed rocks is revealed based on the evolutionary distribution characteristics of the maximum principal stress field and shear stress field obtained by the extended NOSB‐PD theory.

Experimental investigation on the mechanical properties of thermally damaged granite specimens containing pre‐existing holes

AbstractA comprehensive understanding of the mechanical behavior of thermally damaged rock is crucial for the design, prediction, and stability control of rock engineering. However, the strength and fracture characteristics of rock containing pre‐existing flaws have not been studied systematically. Therefore, in this study, uniaxial compression tests were conducted on preholed granite specimens using MTS816 rock mechanics testing and acoustic emission (AE) monitoring systems. The mechanical properties, AE characteristics, and failure patterns of thermally damaged granite specimens were analyzed, and the alteration of the mechanical behavior was explained by the P‐wave velocity, effective porosity, mineral components, and thermal cracking. The results show that the peak strength and elastic modulus of preholed granite specimens first increased and then decreased with the increasingly high temperature. Cracks were always initiated from the left and right perimeters of the pre‐existing hole, and the crack coalescence modes between the two pre‐existing holes were independent of the high temperature. After 150°C treatment, thermal cracks were observed, and the complexity and interconnectivity of the fracture surface increased with temperature. The variations of the mineral component and crystal structure induced by increasing the high temperature contributed to the thermal damage of the granite. The experimental results are expected to enhance the understanding of the macromechanical and mesomechanical behaviors of rock with respect to high temperature.

Fatigue failure identification using deformation and energy rate for hole‐fissure contained granite under freeze–thaw and variable‐frequency–variable‐amplitude cyclic loads

AbstractThis work conducted laboratory tests considering the coupled freeze–thaw (FT) and variable‐frequency–variable‐amplitude cyclic loads on granite containing two fissures and a circular hole. The analysis is dedicated to reveal the deformation and energy rate characteristics. Testing results show that increasing FT cycle and loading level both accelerate rock damage. The rock subjecting to high FT cycle behaves much larger damage rate in terms of volumetric strain and dissipated energy. The warning strength is defined according to the volumetric strain rate and dissipated energy rate which can early issue a warning than the crack damage stress point. In addition, the rock instability precursor is proposed by monitoring the incremental rate of the radial strain and volumetric strain; drastic damage occurs when the volumetric rate exceeds the radial rate. Three typical crack coalescence modes of double shear coalescence, single shear coalescence, and single tensile coalescence were revealed.

Biaxial Shear Crack Propagation Modes of Rock-Like Specimens with Prefabricated Fissures and Their Strength Characteristics

A biaxial shear test is performed on prefabricated, single-fissure type, cubic rock-like specimens by using the TZW-500 rock direct shear apparatus to study the shear strength characteristics, crack coalescence, and propagation modes of the specimens with different geometric parameters. Results show that the crack coalescence and propagation modes of the rock-like specimens with prefabricated fissures can be divided into four types, namely, single main shear crack coalescence mode, main shear crack coalescence and secondary tensile-shear crack propagation mode, main shear crack coalescence and secondary shear crack propagation mode, and main shear crack coalescence and secondary tensile crack propagation mode. All modes are affected by the dip angle α and length l of the prefabricated fissure. When the dip angle of the prefabricated fissure is α∈[0°, 20°) or (70°, 90°], the cracks center on shear failure, and most shear cracks propagate along one end of the prefabricated fissure. At α∈(30°, 50°), the cracks bear the tensile-shear combined action, and the shear cracks propagate along the two ends of the prefabricated fissure. The peak shear strength of the rock-like specimens with prefabricated fissures is also closely related to the dip angle α and length l of the fissure. With the increase in dip angle α of the prefabricated fissure, the peak shear strength of each rock-like specimen decreases initially then increases, and the peak shear strength curve presents a similar “U” shape. At α∈[30°, 60°], the peak shear strength is within the peak-valley interval. When the length l of the prefabricated fissure is increased, the peak shear strength experiences a gradual reduction. When l > 20 mm, the peak shear strength is greatly influenced by l, but the influence is minimal when l ≥ 20 mm. At the same dip angle α and fissure length of l ≥ 20 mm, the correlation between peak shear strength and fissure width b is low.

Experimental and numerical simulation study of crack coalescence modes and microcrack propagation law of fissured sandstone under uniaxial compression

Fissured rock mass is the most common construction object in geotechnical engineering and its mechanical properties are closely related to the stability of geotechnical engineering. A laboratory uniaxial compression test and a numerical simulation test were separately carried out on the fissured sandstone samples. Based on parameters, such as crack coalescence modes, the ratio of rise time to amplitude (RA) and the ratio of acoustic emission (AE) counts to duration (AF) of AE signals and spatial distribution of microcracks, failure modes and microcrack propagation laws of fissured sandstone were studied. The results demonstrate that the failure mode of fissured sandstone changes from being dominated by tensile failure into by shear failure with the increase of the dip angle of prefabricated fissures. The results of RA and AF of AE signals illustrate that it is difficult to produce tensile microcracks, but easy to generate shear microcracks in the samples with the rise of the dip angle of prefabricated fissures. In the numerical simulation test, when the dip angle of prefabricated fissures is small (θ ≤ 60°), microcracks initiate near the tip of prefabricated fissures. However, if the dip angle is large (θ ≥ 75°), the initiation location of microcrack is slightly affected by prefabricated fissures. In addition, the method for determining tensile and shear cracks was proposed based on the velocity field of particles. The results show that as the dip angle of prefabricated fissures increases, there are increasingly less tensile macrocracks, but increasingly more shear cracks at failure of the samples, which is basically consistent with conclusions obtained in the laboratory test of rock mechanics.

Experimental study of energy dissipation characteristics and crack coalescence modes of cracked sandstone under different cyclic loading paths

Experimental study of energy dissipation characteristics and crack coalescence modes of cracked sandstone under different cyclic loading paths

The crack coalescence mode and physical field evolutionary characteristics of a brittle material containing two 3-D parallel embedded flaws

This research presents the crack coalescence mode and physical field evolution characteristics of a brittle material containing two 3-D parallel embedded flaws. A numerical model based on the flat-joint model is established and validated by laboratory experiments. The crack coalescence modes of two 3-D parallel flaws with different geometries are summarized. The physical field evolution characteristics during the cracking process are investigated. The mechanisms of wing crack initiation and propagation are effectively reflected by the physical fields. Moreover, the impacts of the interactions between the two flaws on the crack coalescence mode and physical fields are analysed. The simulation results indicate that the flat-joint model is appropriate for simulating the cracking process of two 3-D flaws in a brittle material. The flaw dislocation O can reflect the interaction strength. A strong interaction promotes the earlier fracture of the rock bridge, which also significantly weakens the mechanical properties of the specimen. In general, the mechanism of wing crack initiation is tensile, and stable propagation occurs by mixed tension and shear. However, strong interactions between flaws have significant impacts on the physical fields within the rock bridge and concentrate the tensile and shear forces, which may induce wing crack initiation as mixed tensile and shear cracks.

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.

An experimental investigation of the fracturing behaviour of rock-like materials containing two V-shaped parallelogram flaws

The distribution characteristics and evolution law of rock mass fissures induced by mining are a key scientific issue in the study of deep rock mechanics. In this study, a series of uniaxial compression experiments was conducted on rock-like specimens containing double V-shaped prefabricated fissures at dip angles of α = β = 45°, α = 45°<β = 60°, α = β = 60°, and α = 60°<β = 75° with a rock mechanics servo-controlled testing system. According to the experimental results, the effects of the dip angles of the double V-shaped prefabricated flaws with the same area on the mechanical parameters and fracturing process of the specimens were analysed in detail. Additionally, the crack initiation stress presented a nearly linear growth trend, which is generally similar to that of the crack peak stress with increasing flaw dip angle. By applying photographic monitoring to the crack initiation, propagation, coalescence, and failure modes in rock-like specimens, it was easily seen that the V-shaped flaw properties slightly influence the crack initiation positions but significantly influence the crack trajectories. The crack failure modes can be summarized into two distinct types. The study reported herein can provide a better understanding of the evolution of double V-shaped prefabricated fissures induced by coal mining.

Deformation localization and cracking processes of sandstone containing two flaws of different geometric arrangements

AbstractWe present deformation localization and cracking process of sandstone with two flaws of different geometric configurations in uniaxial compression. The full field strain and progressive cracking processes are quantitatively monitored using three‐dimensional digital image correlation and acoustic emission techniques. The results show that peak strength and elastic modulus show a first decrease and then increase trend with regard to ligament angle under the same flaw geometry, achieving the minimum at the ligament angle 60°. The tensile strain develops at low stress level and then increases significantly. However, the shear strain only tends to be obvious while approaching peak stress. With the ligament angle increasing, the crack coalescence mode transfers from indirect to direct coalescence. In addition, the complete cracking processes of sandstone can be divided into six stages, together with six crack coalescence modes.

Experimental study of failure characteristics and fissure propagation in hydrous siltstone

The seepage-control design and evaluation of underground water conservancy projects need to consider the effects of water and original fissures on rock mechanical properties and fissure evolution laws. In this paper, uniaxial compression test was conducted on siltstone samples containing prefabricated fissures with different moisture contents to investigate the effects of fissure angle, ligament angle, and moisture contents on the mechanical properties and crack propagation. The results show that the peak stress, elastic modulus, and peak strain of rock are positively correlated with fissure angle and negatively correlated with the ligament angle. With increasing moisture content, the effects of fissure angle and ligament angle on rock mechanical properties gradually decrease, and the peak stress and elastic modulus are negatively linearly correlated with moisture content. The acoustic emission (AE) and photographic monitoring techniques were adopted to analyze the dynamic evolution laws of micro-crack propagation, and seven types of crack initiation and seven kinds of crack coalescence modes were summarized. The failure characteristics and crack coalescence of rock are controlled by fissure angle and ligament angle, and water content has an impact on the whole crack evolution process. This study provides a significant understanding of the instability and failure of underground rock engineering.

Stability analysis of flawed rock slope by using virtual-bond-based general particles dynamics

General particle dynamics code (GPD) with a virtual bond model is adopted to investigate the stability of rock slopes subjected to gravity. The natural discontinuities are represented by straight flaws in the numerical model. The failure process of rock samples containing three pre-existing and four pre-existing flaws subjected to uniaxial compression is simulated. The numerical failure processes of rock samples are in good agreement with the experimental observations as well as the complete stress–strain curves. Moreover, six en-echelon flaw arrays including collinear flaw array, en-echelon flaw array with bridge angle of 90°, en-echelon flaw array with bridge angle more than 90°, en-echelon flaw array with bridge angle less than 90°, multiple rows of en-echelon flaws with doubly periodic rectangular array, multiple rows of en-echelon flaws with diamond-shaped array in rock slope are studied. The crack initiation, propagation and coalescence process in rock slopes with six en-echelon flaw arrays subjected to gravity are analyzed. Two crack initiation modes including primary crack and secondary crack are found as well as nine crack coalescence modes. The stress distributions as well as displacement fields are investigated during the crack evolution. The gravity increase method is implemented into the VB-GPD to obtain the safety factor of rock slopes. The proposed method was then verified by the case study of the Xingluokeng mine in China. The results indicate a good accordance between simulation and field monitoring. This study reveals that the proposed method can tackle flawed rock slope failure problems.

Mechanical behavior around double circular openings in a jointed rock mass under uniaxial compression

To better understand the mechanical behavior in a jointed rock mass, a series of uniaxial compression tests were conducted on non-persistently jointed rock specimens with double circular holes. Acoustic emission (AE) and digital image correlation (DIC) techniques were applied to capture micro-crack events and real-time strain field evolution in the specimens. The results indicate that the existence of non-persistent joints has a significant influence on the strength characteristics of the specimens. Specifically, peak strength decreases at first and reaches a minimum at 30° then increases with increase in the joint dip angle. DIC technology has successfully monitored the development of surface strain fields. The fracture evolution process is comprehensively understood. Every sudden change in a strain field is usually accompanied by apparent AE events and stress–strain curves take the form of oscillations. The crack coalescence modes among joints can be summarized as six types and the crack coalescence patterns around holes and joints can be divided into three categories. These results are helpful to understanding further the mechanical properties and fracture mechanism of openings in non-persistently jointed rock masses.

Peridynamic simulation on fracture mechanical behavior of granite containing a single fissure after thermal cycling treatment

Abstract In this study, the thermal-mechanical fracturing behaviors of granite after thermal cycling treatment are investigated using the fully coupled ordinary state-based peridynamic method. First, two benchmark examples: transient heat conduction and crack propagation, are conducted to test the numerical convergence and calibrate the simulation parameters. Then, a new method for accurately reflecting the mineral compositions and the corresponding characteristics is proposed to simulate the heterogeneity property of rock materials. Based on the latter, the thermal microcracking behaviors of granite induced by the incompatible expansion between different minerals under thermal cycling treatment (infrared-radiation-heating stage, constant-temperature stage and natural-cooling stage) are simulated. Finally, the numerical specimens of a granite material containing a single pre-existing fissure with various fissure inclination angles under uniaxial compression after thermal cycling treatment are modeled. Correspondingly, the methods for reducing the unexpected failure caused by a thermal shock are discussed. The combination effect of the temperature and fissure inclination angle on the stress-strain response as well as the crack evolution processes is also systematically investigated, and the corresponding characteristics of crack initiation, propagation, and coalescence modes are discussed and summarized.

Effects of Flaw Geometry on the Fracturing Behavior of Rock‐Like Materials Containing Two Arch‐Like Parallelogram Flaws

To increase understanding of the strength and failure mechanism of rocks with arch‐like fractures generated in the overlying strata above a gob during coal mining, a series of uniaxial compression tests on rock‐like specimens containing two preexisting parallelogram flaws at inclination angles varying from 45° to 75° were made using a rock mechanics servocontrolled testing system. Based on the experimental results, the effects of the inclination angles of two flaws having the same area on the mechanical parameters and fracturing process of the specimens were analyzed in detail. By adopting photographic monitoring, the crack initiation, propagation, coalescence, and failure modes in rock‐like specimens were observed and characterized. The crack initiation stress and the second initiation stress were distinctly related to the flaw inclination angles, although the crack initiation stress presented a change trend generally similar to that of the crack second initiation stress with increasing flaw angle. Four modes of ultimate macroscopic failure morphology and the crack coalescence and failure modes of three types could be summarized. The research reported here could provide some theoretical support for the arch‐like fracture evolution in the overburden during the excavation in underground engineering, especially in coal mining engineering.

Failure Behaviour of Sandstone with a Preexisting Joint under Stepped Excavation

Much geotechnical construction needs to be carried out under the condition of stepped excavation. However, there is still a lack of research on crack coalescence and failure modes of jointed rock mass under stepped excavation conditions. In order to simulate the stepped excavation test of the real project, the polylactic acid (PLA) material is selected as the filler for the excavation area. The stepped excavation tests are performed on sandstone specimens containing a preexisting joint under different normal load conditions. The dynamic stepped excavation of simulating excavate rock engineering is realised. The constant normal loads during the excavation process are determined to be 80 kN and 100 kN. The influence of the joint inclination on the failure characteristics of the excavation process is analysed. Four typical failure modes are summarised: (a) Mode I: crack coalescence of tensile failure; (b) Mode II: crack coalescence of mixed failure; (c) Mode III: without crack coalescence of mixed failure; (d) Mode IV: without crack coalescence of shear failure. Furthermore, the failure characteristics of the area above the excavation hole and the preexisting joint are analysed. The results show that there are three failure modes: (a) Type I: spalling failure; (b) Type II: shear slip failure; (c) Type III: shear slip and spalling mixed failure.

An experimental study of the mechanical and fracturing behavior in PMMA specimen containing multiple 3D embedded flaws under uniaxial compression

This paper studies the mechanical and fracture behavior of poly methyl methacrylate (PMMA) specimens containing multiple embedded flaws, under uniaxial compression. The initiation, propagation, coalescence of cracks, and failure of specimens are captured by a high-speed digital video camera system. Six types of cracks and three modes of crack coalescence are captured in the PMMA specimens. The experimental observations show that the effects of the flaw angle on crack propagation and coalescence are stronger than the non-overlapping length. Furthermore, the peak strength and crack initiation stress show regular change with increasing in the flaw angle and the non-overlapping length.

Fracture Processes of Rock-Like Specimens Containing Nonpersistent Fissures under Uniaxial Compression

Many rock engineering accidents have proven that the coalescence of discontinuities in surrounding rock can have a major impact on the security and stable operation of energy infrastructure. To give an insight into the understanding of the crack propagation and coalescence in fissured rock masses, a series of uniaxial compression experiments were conducted on rock-like specimens containing nonpersistent fissures. The digital speckle correlation method (DSCM) and the acoustic emission (AE) monitoring system were adopted to capture the real-time strain field on the specimens’ surfaces and microfracturing events within specimens, respectively. The experimental results indicated that the strength and deformation modulus of specimens were significantly affected by fissure inclination. The damage process showed obvious progressive stain localization failure characteristics. The clear and intuitive full-field strain field development was successfully monitored by the DSCM technique. The real-time strain accumulation, crack initiation, propagation, and coalescence were also analyzed. Each time, the saltation of the strain field was usually accompanied by the fluctuation of the stress curve and obvious AE events. Crack coalescence modes between fissures changed from tension coalescence mode to mixed tension-shear coalescence mode, then to shear coalescence mode with an increase in fissure inclination. Five basic failure modes were identified from the experimental results: Tensile failure across the fissure planes, rotation failure of newly generated blocks, mixed failure mode, shear failure, and splitting failure. An investigation of the fracture processes of rock-like specimens containing nonpersistent fissures using these methods can enhance understanding of the fracture behavior of jointed rocks.