Single Pre-existing Flaw Research Articles

Strength Properties and Damage Evolution Mechanism of Single-Flawed Brazilian Discs: An Experimental Study and Particle Flow Simulation

Understanding the tensile strength properties and damage evolution mechanism in fissured rock is very important to fundamental research and engineering design. The effects of flaw dip angle on the tensile strength, macroscopic crack propagation and failure mode of symmetrical Brazilian discs of rock-like materials were investigated. A parallel bonding model was proposed to examine the damage of pre-flawed discs under splitting the load. The microscopic parameters of particles and bonds in the model that can characterize rock-like materials’ mechanical and deformation properties were obtained by calibrating against the laboratory test results. The crack development, energy evolution and damage characteristics of Brazil discs containing a single pre-existing flaw were studied at the microscopic scale. The results show that the flaw significantly weakens the strength of the Brazilian disc, and both the peak load and the initial cracking load decrease with increasing flaw angle. The failure modes of the rock-like specimens are mainly divided into three types: wing crack penetration damage mode, tensile-shear penetration damage mode and radial penetration failure mode. Except for the flaw dip angle 0°, the wing cracks generally sprouted at the tip of the pre-flaw, and the wing cracks at both tips of the pre-flaw are centrosymmetric. Crack coalescence was concentrated in the post-peak stage. Based on the particle flow code (PFC) energy partitions, the damage variables characterized by dissipation energy were proposed. The disc specimen’s pre-peak damage variables and peak damage variables decreased with increasing flaw angle, and the damage was concentrated in the post-peak phase.

Creep Behavior and Associated Acoustic Characteristics of Heterogeneous Granite Containing a Single Pre-existing Flaw Using a Grain-Based Parallel-Bonded Stress Corrosion Model

Creep Behavior and Associated Acoustic Characteristics of Heterogeneous Granite Containing a Single Pre-existing Flaw Using a Grain-Based Parallel-Bonded Stress Corrosion Model

Identification of crack initiation and damage thresholds in sandstone using 3D digital image correlation

In this study, a non-contact image correlation measurement technique, Three-Dimensional Digital Image Correlation (3D-DIC), is employed to identify and quantify the evolution of rock crack initiation and propagation. With the aim of carefully investigating the cracking progress, a uniaxial compression test was conducted on sandstone specimens with a single pre-existing flaw. The surface and internal micro-fracture characteristics of the sandstone specimen were detected by combining 3D-DIC and acoustic emission techniques from both optical and acoustic perspectives. On the basis of the full-field deformation data derived by 3D-DIC, a method for determining the principal strain of cracks was defined, which aids in identifying the spatial propagation characteristics of rock cracks. Additionally, the crack principal strain method (CPSM) was proposed for determining the characteristic stress threshold of rocks based on the crack principal strain. Then, the results obtained from CPSM are compared to the conventional acoustic emission method (AEM) and axial stiffness method (ASM) tests. The research results suggest that AEM is suitable for identifying crack closure stress and crack initiation stress, whereas ASM and CPSM are superior for identifying damage stress. This work provides a novel method and concept for the measurement of non-contact characteristic stress thresholds, as well as has an insight into the detection and evaluation of the evolutionary process of rock damage and fracture.

Improved peridynamic model and its application to crack propagation in rocks.

The conventional bond-based peridynamics (BB-PD) model is suitable for simulating the failure mode of homogeneous elastic-brittle materials. However, the strain hardening and subsequent strain softening characteristics of rocks under loading cannot be reflected. In addition, the fracture mechanisms of rock materials under tension and compression are completely different. To solve these problems, this paper proposes an improved BB-PD model using different fracture criteria in the tensile and compression stages of the bond based on previous improved models, and a critical failure condition obeying the Weibull distribution is introduced to reflect the heterogeneity of the rock. The crack propagation processes of an intact rock specimen, rock specimen with a single pre-existing flaw and rock specimens with two and three pre-existing flaws under compressive loading are simulated using the model, and its feasibility is verified by comparing with the results of previous laboratory tests. Next, the effects of the inclination angle and length on the wing crack propagation length are studied. Finally, the changes in the crack aggregation modes under different rock bridge inclination angles are simulated. Eight types of crack aggregation modes are found, and the conditions under which they may occur are analysed. The improved model proposed can effectively simulate the crack propagation and coalescing processes and has a wide application prospect for rock fracture simulations.

Fracture behavior and damage evolution model of sandstone containing a single pre-existing flaw under discontinuous fatigue loading

The process of disaster incubating in deep rock mass engineering is mainly related to the fracture behavior and damage mechanism of the rock mass. This paper proposes a new damage model based on Lemaitre's equivalent strain hypothesis with improved Harris distribution and laboratory discontinuous fatigue loading test (DFLT). Firstly, discontinuous fatigue loading tests were carried out on the jointed sandstone specimens and acoustic emission (AE) was used as a research tool. Based on the b-value and AF-RA theory, the failure mode of specimens was further explored in terms of the crack evolution process and crack classification. Meanwhile, digital image correlation (DIC) techniques were used to analyze the evolution of the deformation field on the surface of the specimen. Subsequently, the fracture morphological characteristics of the rock masses were analyzed from a microscopic perspective by scanning electron microscopy (SEM) techniques. The investigations found that in a short time, the low-level constant load will lead to the interlocking of particles inside the rock mass, reduced incremental coupled damage, and enhanced plasticity “with” reducing the coupled damage increment and enhancing the plasticity, thereby inhibiting the damage growth rate. In addition, as the stress level increases, the friction between the grains intensifies, the cuttings and roughness of the fracture surface increase, the fatigue softening effect is enhanced, and the specimen gradually transforms from brittle failure to ductile failure. At the same time, the proportion of stress-induced tensile cracks and shear cracks gradually increased, resulting in the specimen finally presenting tensile-shear composite failure.

Evolution of tensile and shear cracking in crystalline rocks under compression

We performed laboratory-scale unconfined compression experiments on Barre granite specimen with a single pre-existing flaw to study the evolution of tensile and shear cracking that occurs during different stress levels. Moment tensor inversion of acoustic emission (AE) events in combination with the nonelastic strain component obtained through the 2D digital image correlation (DIC) technique are used to track the changes in the source mechanisms of the stress-induced cracks. The mode of deformation computed from the image based strain profiles, enables visual comparison of the nucleation, growth and interaction of the tensile and shear cracks with the microseismic source mechanism observed by moment tensor inversion of the AE events. Comparing the results obtained from the two techniques on the same dataset demonstrates a quantitative correlation between the acoustic and visual observations in terms of the cracking mechanisms obtained at different stages of cracking from crack initiation at the flaw tips to the failure of the rock specimen.

Cracking Behavior and Acoustic Emission Characteristics of Rock Containing a Single Preexisting Flaw

The existence of flaws in brittle rocks or rock-like materials has an obvious influence on the material mechanical properties and cracking behavior of civil engineering projects. In this work, the two-dimensional particle flow code PFC2D was used to study the deformation and strength properties, failure processes, and acoustic emission (AE) characteristics of mudstone with a single preexisting flaw. First, the procedure to construct a parallel bond model is introduced. The Weibull distribution is used to reflect the mechanical heterogeneity of rocks. Then, the microscopic parameters used in PFC2D are calibrated to the macroproperties of mudstone obtained from laboratory tests under the uniaxial compression. The results indicate that the increases of the flaw inclination lead to the increasing uniaxial compressive strength and elastic modulus. In terms of microcrack evolution, the initiation, propagation, and coalescence of microcracks are closely related to the force chain. Specifically, an “X” shaped tension force chain concentrated area around the preexisting flaw is founded, which is the most prone area for microcracks to initiate. With an increase in flaw inclination, the b value of AE also shows an increasing trend. By incorporating the AE event numbers into a damage variable, this paper derives a constitutive model, which is verified by numerical results on brittle rocks with a single preexisting flaw under uniaxial compression.

Modeling crack propagation in heterogeneous granite using grain-based phase field method

The cracking behavior and mechanical properties of brittle rocks is controlled by its microstructure. In this work, an extended grain-based phase field method (GB-PFM) based on Voronoi tessellation technology is proposed to investigate the mechanical properties and crack propagation in heterogeneous brittle rocks by considering material heterogeneities and microstructure heterogeneities at the grain scale. Then, a trial and error calibration procedure is developed after comprehensive study of uncertain parameters such as grain boundaries thickness and critical energy release rate. It is shown that greater grain boundaries thickness results in a lower tensile strength and lower Young’s modulus, and greater number of intergrain cracks. Then, a group of models with single pre-existing flaw (flaw inclination angles: 0°, 30°, 45°, 60°, 90°) are built according to calibration parameters to study the mechanical properties and cracking behavior of heterogeneous granite under direct tension. The path of the macrocracks obtained from GB-PFM shows a more noticeable tortuous nature as compared with that results by others phase field methods. The variation of flaw inclination has an obviously influence on crack propagation. Failure patterns obtained by GB-PFM revealing the macrocracks are composed of intragrain and intergrain cracks at the microscopic view. Moreover, the stress field distribution obtained by GB-PFM is agree well with the theoretical analyses and other numerical simulations. The above simulated results prove that the GB-PFM provides an applicable numerical method for efficiently reproducing the microstructure and the related crack propagation of brittle crystalline rocks, which greatly expand the application of the phase field methods.

Experimental investigation on the strain energy evolution mechanism of granite specimens with a single flaw

Damage and fracture of rocks is a comprehensive result of strain energy dissipation and release. In order to study the energy evolution mechanism of hard brittle rock masses during failure process, uniaxial compression tests on the granite specimens with a single pre-existing flaw are carried out with digital image correlation method (DIC). The results indicate that: (1) The stress fluctuation before structural failure corresponds to the sudden increase of the dissipated energy, the essence is that rock masses occur obviously damage and cracking. (2) For medium flaw dip angles, the stress fluctuation occurs repeatedly in stages, whose strain energy is dissipated gradually; for large or small dip angles, the stress fluctuation is almost not appeared, and the energy dissipation is insignificant. (3) With the increase of flaw dip angles, the dissipated energy ratio at the peak stress first increases and then decreases showing an inverted U-shaped, resulting in a similar law of rock damage but a contrary law of strength; the corresponding elastic energy ratio is U-shaped of decreasing first and then increasing, causing the structural failure changes from dynamic to static and then to dynamic again. The results can provide theoretical references for the formation mechanism and prevention method of dynamic disasters of rock underground engineering.

A comprehensive study of single-flawed granite hydraulically fracturing with laboratory experiments and flat-jointed bonded particle modeling

Understanding the mechanisms of crack initiation and development is important for utilizing the hydraulic fracturing in practical engineering applications. In this study, hydraulic fracturing experiments were conducted on granite specimens containing a single pre-existing flaw, and the failure processes were analyzed using the digital image correlation method. A flat-jointed bonded particle model was built with a modified fluid flow algorithm to better understand the fracture behavior under the experimental conditions. Combining the DIC strain fields and the simulated displacement fields, we found that shear behavior with a small value also emerges ahead of the tips of the microcracks and was covered by the subsequent tensile behavior, as a result, shear strain could not be observed in the experiments. A comparison between the strain localization and the microcracks revealed that the fracturing process observed in the experiments had two stages: the isolated strain localization formed during Stage I, mainly resulting from the increase in microcracks, and the continuous high tensile strain path formed during Stage II. Additionally, the effect of the different flaw inclination angles was discussed from two perspectives: the different types of macrocracks and the change in the fracturing liquid pressure.

Effects of bedding planes on mechanical characteristics and crack evolution of rocks containing a single pre-existing flaw

The existence of bedding planes in rock materials has an obvious impact on the material mechanical properties and the failure process of engineering projects. In this study, a series of pre-cracked models with different bedding plane properties (i.e., strength reduction factor, bedding plane angle and spacing) were established and simulated to fail under the uniaxial compression. The results indicate that the increases of the strength reduction factor and the bedding plane spacing lead to the increasing peak strength, the change of peak strength regarding the bedding plane angle presents a concave upward trend. In terms of crack evolution, the proportion of cracks formed in rock matrix increases concerning the increasing strength reduction factor and bedding plane spacing, the abovementioned crack proportion in models with increasing bedding plane angles firstly decreases and then increases. The rock matrix has higher mechanical characteristics than bedding planes, the change of crack proportion can account for the changing peak strength from the microscopic viewpoint. By summarizing the failure patterns, the failure of models with the 45° ~ 75° bedding plane angle is induced by cracks formed in bedding planes, which can be depicted and discussed by the plane of weakness model. The above results imply that the rock slope stability can be evaluated by analyzing bedding plane properties in the field.

Investigation of the correlation between crack propagation process and the peak strength for the specimen containing a single pre-existing flaw made of rock-like material

This paper investigated the relationship between the strength of fractured rock and the crack propagation process. A series of uniaxial compression tests were carried out on the rock-like material specimens with single pre-fabricated flaw. Moreover, DIC (digital image correlation) technology was utilized to monitor and analyze the failure process of specimens. The initiation of each crack was defined as a key event, and the relationship between several key events and the axial load of the specimen during the crack propagation was quantitatively analyzed. The time-sequence analysis of crack propagation was also conducted by selecting benchmark points on the both sides of major cracks. It can be found that only the wing crack propagation occurs and there is no obvious shear crack before the peak strength. When the first secondary crack initiated, the specimen reached its peak strength and the wing crack just reached its critical length. Beyond the peak strength, secondary cracks initiated and coalesced rapidly, which leads to the sudden failure of fractured rock. Therefore, the peak strength of the specimen can be assessed by taking the critical length of the steadily propagating wing crack as the condition which determines whether the specimen reaches the peak strength. Furthermore, the discrete element numerical simulation was also implemented to confirm the experimental results.

Simulation on heterogeneous rocks with a flaw using grain-based discrete-element method

To take into consideration the effect of mineral microstructure on crack growth and mechanical properties of heterogeneous rocks containing a single pre-existing flaw under uniaxial compression, th...

Peridynamic micro-elastoplastic constitutive model and its application in the failure analysis of rock masses

In the process of compression, rock exhibits post-peak strength, which means that the failure criterion of traditional bond-based peridynamics is not suitable for rock materials. The peridynamic constitutive function is mainly for homogeneous materials and functional materials, which cannot reflect the characteristics of the post-peak strength of the rock. Therefore, based on peridynamic theory, a micro-elastoplastic constitutive model considering the post-peak stage of rock mass under compression loading is proposed, and the loading-unloading path in the post-peak stage of the rock is considered. This model makes up for the disadvantage that the traditional peridynamics model cannot reflect the post-peak strength of rock. Considering that the nonlinearity of the mechanical properties is caused by the heterogeneity of rock materials, the nonuniform discrete method is used in the model, which further improves the accuracy of the numerical simulation. Using the micro-elastoplastic model, the rock specimens were numerically simulated in uniaxial compression tests and uniaxial cyclic load tests, while the flaw propagation of a single pre-existing flaw with different inclination angles under uniaxial compression was analysed. The numerical simulation results are in good agreement with experimental results, which verifies the accuracy and superiority of the new model.

Acoustic Emission Characteristics and Joint Nonlinear Mechanical Response of Rock Masses under Uniaxial Compression

The joint arrangement in rock masses is the critical factor controlling the stability of rock structures in underground geotechnical engineering. In this study, the influence of the joint inclination angle on the mechanical behavior of jointed rock masses under uniaxial compression was investigated. Physical model laboratory experiments were conducted on jointed specimens with a single pre-existing flaw inclined at 0°, 30°, 45°, 60°, and 90° and on intact specimens. The acoustic emission (AE) signals were monitored during the loading process, which revealed that there is a correlation between the AE characteristics and the failure modes of the jointed specimens with different inclination angles. In addition, particle flow code (PFC) modeling was carried out to reproduce the phenomena observed in the physical experiments. According to the numerical results, the AE phenomenon was basically the same as that observed in the physical experiments. The response of the pre-existing joint mainly involved three stages: (I) the closing of the joint; (II) the strength mobilization of the joint; and (III) the reopening of the joint. Moreover, the response of the pre-existing joint was closely related to the joint’s inclination. As the joint inclination angle increased, the strength mobilization stage of the joint gradually shifted from the pre-peak stage of the stress–strain curve to the post-peak stage. In addition, the instantaneous drop in the average joint system aperture (aave) in the specimens with medium and high inclination angles corresponded to a rapid increase in the form of the pulse of the AE activity during the strength mobilization stage.

Underlying Mechanisms of Crack Initiation for Granitic Rocks Containing a Single Pre-existing Flaw: Insights From Digital Image Correlation (DIC) Analysis

Determination on underlying mechanisms of crack initiation is of vital importance to understand the failure processes of geomaterials in practical engineering. In this study, uniaxial compression experiments of granitic samples containing a single pre-existing flaw were conducted and the failure processes were recorded by using the high-speed camera. To quantitatively determine the crack initiation mechanism, a novel method was first proposed based on digital image correlation (DIC) analysis and then its validity was confirmed. By utilizing this method, three types of cracks with different initiation mechanisms were identified and the effect of flaw inclination angle on crack initiation mechanisms was discussed from the viewpoint of theoretical analysis. With the increase of inclination angles, wing cracks change from mixed mode I/II cracks to mode I cracks, while anti-wing cracks have no evident changes and are dominated by mode II cracks. Under compressive pressure, the upper and bottom surfaces of pre-existing flaw deform to each other and the distributions of full-field tangential stress around flaw are different, which might induce the variation of crack initiation mechanisms with regard to the inclination angle.

Experimental study on the mechanical properties and damage evolution of red sandstone containing a single ice-filled flaw under triaxial compression

To better understand the mechanical properties and damage evolution of ice-filled preflawed rock, a series of triaxial compression tests on frozen red sandstone specimens containing a single preexisting flaw were carried out with a self-developed DRTS-500 subzero rock triaxial testing system. According to the experimental results, the influences of the confining pressure and flaw dip angle on the strength, deformation, damage evolution behavior, and failure mode of the specimens were analyzed in detail. The confining pressure increased the strength and enhanced the plastic characteristics of red sandstone with a single ice-filled flaw. The peak strength, elastic modulus, internal friction angle, and cohesion were distinctly related to the flaw dip angle, whereas the peak strain and Poisson’s ratio were not obviously dependent on the flaw dip angle. The red sandstone specimens containing a preexisting ice-filled flaw exhibited shear failure under low confining pressure conditions. The failure mode of the specimens was greatly affected by the dip angle of the preexisting flaw under high confining pressure conditions. The acoustic emission (AE) events that occurred during the whole specimen damage process had different features in different loading stages. The damage evolution process of the specimens was analyzed by using a damage model based on AE counts, and the degree of damage of the specimen was the largest when the flaw dip angle was close to 45~60°.

Full-field strain evolution and characteristic stress levels of rocks containing a single pre-existing flaw under uniaxial compression

In this study, full-field strain evolution and characteristic stress levels of marble samples containing a single pre-existing flaw were comprehensively studied. The full-field strain was performed by digital image correlation (DIC) method, and the variations of characteristic stress levels with respect to inclination angle were discussed. To compare the experimental results, discrete element method was adopted, and the full-field stress evolution was reproduced to reappraise the localization zones. The results indicate that the presence of pre-existing flaws induces strain localization and degradation of mechanical properties for pre-cracked samples. When the strain localization firstly appeared surrounding pre-existing flaws, the axial stress levels at this moment increase with regard to inclination angle, leading to the increase of peak strength, crack initiation stress, crack damage stress, and normalized crack initiation stress. The normalized crack damage stress obtained by experiments shows flaw independency, and the results were verified by simulation results. Based on the full-field stress evolution, the tensile stress in x direction concentrates around pre-existing flaw and its location moves towards flaw tips with the increase of inclination angle. The compressive stress in y direction around pre-existing flaw is lower than other zones, revealing the upper and bottom surfaces of pre-existing flaw deform to each other. When the numerical models are subjected to same axial loading, the full-field stress around pre-existing flaw decrease as the inclination angle increases, which confirmed the results of full-field strain evolution and elucidated the pre-existing flaw with large inclination angle has less effect on degrading the mechanical properties.

Numerical investigation of dynamic fracture in rock specimens containing a pre-existing surface flaw with different dip angles

Numerically simulated specimens with a three-dimensional pre-existing surface flaw are subjected to stress waves until failure via finite element analysis. Different types of cracks are reproduced, including wing cracks, anti-wing cracks, shell-like cracks and spalling fractures. The effects of different flaw dip angles on the initiation and propagation of wing cracks, anti-wing cracks and shell-like cracks are analysed under dynamic loading conditions. The numerical simulation results indicate that the dip angle of the flaw plays an important role in the crack behaviour and failure patterns of flawed specimens under dynamic loading. Wing cracks and anti-wing cracks emerge and present similar crack propagation patterns on the surface of the specimen when the pre-existing flaw dip angle is less than 60°. In contrast, only wing cracks appear in specimens with flaw dip angles of 75° and 90°. Shell-like cracks are reproduced inside of the specimens in all cases except the specimen with a flaw dip angle of 90°. In addition, the further propagation of shell-like cracks proceeds after the wing and anti-wing cracks stop propagating. Meanwhile, the numerical simulation also identifies the acoustic emission (AE) counts and energy of the specimen, which are closely related to the flaw dip angle during the dynamic failure process. The flaw dip angle has a slight effect on the dynamic strength of the specimens. Furthermore, the cracking patterns of specimens with a single pre-existing flaw under dynamic and static loading conditions are compared based on numerical investigations. Dynamic loading can produce more cracks and lead to more complex cracking behaviour. Moreover, loading rates can significantly influence crack propagation patterns and AE characteristics of rock specimens. Under high loading rates, the specimens fragment more efficiently. In addition, for specimens subjected to high loading rates, the more shear fractures occur, the greater the cumulative AE energy and the fewer the AE counts. Finally, heterogeneity also plays an important role in the distribution of micro-cracks in the material and the crack propagation patterns. Crack branching occurs in relatively heterogeneous rocks, which affects the further propagation of cracks initiated early. The stress concentration zone is not the only decisive factor and may be replaced by the degree of heterogeneity to determine the crack initiation and propagation. The results of this study can provide a valuable reference for studies on the failure process of heterogeneous brittle materials under dynamic loading.

Experimental Study on Rock-Like Specimens with Single Flaw under Hydro-Mechanical Coupling

In order to study the mechanical characteristics and cracking behavior of jointed rock mass under hydro-mechanical coupling, a series of uniaxial compression tests and triaxial compression tests were carried out on cylinder gypsum specimens with a single pre-existing flaw. Under different confining pressures, water pressure was injected on the pre-existing flaw surface through a water injection channel. The geometrical morphology and tensile or shear properties of the cracks were determined by X-ray computed tomography (CT) and scanning electron microscope (SEM). Based on the macro and micro observation, nine types of cracks that caused the specimen failure are summarized. The results of mechanical properties and crack behavior showed that the confining pressure inhibited the tensile cracks, and shear failure occurred under high confining pressure. The water pressure facilitated the initiation and extension of tensile crack, which made the specimens prone to tensile failure. However, under the condition of high confining pressure and low water pressure, the lubrication effect had a significant effect on the failure pattern, under which the specimens were prone to shear failure. This experimental research on mechanical properties and cracking behavior under hydro-mechanical coupling is expected to increase its fundamental understanding.