Flaw Inclination Angle Research Articles

Crack coalescence and failure behaviors in slate specimens containing a circular cavity and a pre-existing flaw pair under uniaxial compression

The flaws (fractures) widely existing in rock mass pose a threat on the stability of many underground cavities. This study aims at investigating the failure process of a cavity affected by adjacent flaws. A number of slate specimens containing a circular cavity and a pre-existing flaw pair were tested under uniaxial compression. Varied flaw configurations were obtained by changing the flaw inclination angle with respect to horizontal and the spacing between flaw pair and cavity. Three main types of cracks emanated from the pre-existing flaw tips, and played a dominant role in the failure process of cavity, comprising primary wing cracks (tensile cracks) and two types of secondary cracks (quasi-coplanar shear cracks and oblique shear cracks). The initiation and propagation of these cracks were highly dependent on the flaw pair configurations. When the pre-existing flaw pairs were non-parallel to the loading direction, (1) mostly, coalescence occurred both in the tensile and compressive stress concentration regions around cavity; (2) in most cases, the quasi-coplanar and oblique shear cracks were the predominant cracks leading to the coalescence between the compressive stress concentration regions of cavity and the pre-existing flaw pair tips. When the pre-existing flaws were parallel to the loading direction, the combination of inclined shear cracks and tensile cracks or inclined shear cracks only dominated the failure of cavity. The initiation angles of wing cracks, quasi-coplanar shear cracks and oblique shear cracks agreed well with the theoretical predictions by the maximum tangential strain criterion (MTSN), Mohr-Coulomb criterion (M−C) and maximum shear stress criterion (MSS), respectively.

Cracking evolution and failure mechanism of brittle rocks containing pre-existing flaws under compression-dominating stresses: Insight from numerical approach

Comprehending the cracking evolution and failure mechanism of flawed rocks under compression-dominating stresses is essential to evaluating the stability of rock engineering. In this work, a newly developed geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) theory that can eliminate the numerical oscillation is applied to predict the development of new cracks of flawed rocks under compression-dominating stresses. The failure of bonds between particles is judged by the bond-associated stress-based fracture criteria. The cracking evolution trajectories of semi-disc and disc specimens containing flaws are traced. The effects of flaw inclination angle on the cracking trajectories are analyzed. The cracking evolution paths of rock-like specimens with two flaws under uniaxial and biaxial compression are molded. The effects of confining stress on the growth of new cracks are investigated. The confining stress restrains the propagation of tensile cracks, but it is easy to promote the growth of shear cracks. The concentration and transfer effects of stress can plainly revel the failure mechanism of flawed rocks. The present numerical method is reasonable to predict the tensile and shear failure modes of flawed specimens under compression-dominating stresses.

Crack propagation process in double-flawed granite under compression using digital image correlation method and numerical simulation

The existence of flaws seriously weakens the rock strength, directly affects the crack expansion morphology, and indirectly affects the slope stability. In this study, uniaxial compression tests were carried out on double-flawed granite to investigate the effects of flaw angle on its compressive strength and crack coalescence based on DIC technology and PFC2D numerical simulation. The result indicates that the UCS values of flawed specimens at angles of 15°, 30°, 45°, and 60° are approximately 25.5–51.7% lower than that of the intact specimen. The failure strength of the double-flawed sample increases with the increase of flaw inclination angle, and the fracture morphology shifts from no expansion to split expansion. When the flaw tip strain of each flaw sample exceeded 0.6%, the stress concentration was generated at the flaw tip, and the sample began to appear macroscopic large cracks. DIC technique can well observe the crack initiation and propagation process, recording inclined shear strain bands at flaw tips, tensile strain bands in the middle of flaws, and tensile shear O-shaped strain ring in rock bridge areas. Numerical simulations using PFC2D software were carried out and showed a good agreement with the physical results. In addition, the effect of structural inclination on specimen failure strength is clearly explained by the theory of compressive damage based on the projected size of flaws. The deformation of rock mass is not a simple material deformation but is composed of material deformation and structural deformation. These experimental and numerical results enhance our understanding of crack initiation and coalescence characteristics, aiding in the analysis of rock structure stability in scenarios such as excavated underground openings, slopes, and tunneling construction, where pre-existing cracks or step-path fractures are pivotal to structural integrity.

Dynamic fracture mechanism from a pre-existing flaw in granite: Insights from grain-based modelling

Both heterogeneity and pre-existing flaws are closely associated with the mechanical response of crystalline granite. To uncover the underlying mechanism, grain-based model (GBM) based on particle flow code (PFC), i.e., PFC-GBM, with different contacts between any two grains, was employed to carry out numerical calculations to investigate the effect of a single flaw with various inclination angles on the dynamic behavior of LdB granite. The failure pattern is identified through density and spatial distributions of microcracks, and the primary fracture directions are obtained by microcrack orientations. Microcracks are divided into inter-Grain and intra-Grain types, and these two types are further classified into more subtypes according to mineral composition. IG cracks typically form during the pre-peak stage and tend to emerge earlier than TG cracks. Conversely, TG cracks are predominantly created during the post-peak stage but constitute a significant proportion irrespective of flaw inclination angle. A novel method is also proposed to acquire high-stress particles, which promote the identification of dominant macrocrack paths. Finally, the effect of particle size is also systemically analyzed.

A hybrid finite-discrete element method for modelling cracking processes in sandy mudstone containing a single edge-flaw under cyclic dynamic loading

Rock mass deformation and failure are macroscopic manifestations of crack initiation, propagation, and coalescence. However, simulating the transition of rocks from continuous to discontinuous media under cyclic dynamic loading remains challenging. This study proposes a hybrid finite-discrete element method (HFDEM) to model crack propagation, incorporating a frequency-dependent cohesive-zone model. The mechanical properties of standard sandy mudstone under quasi-static and cyclic dynamic loading were simulated using HFDEM, and the method's reliability was verified through experimental comparison. The comparative analysis demonstrates that HFDEM successfully captures crack interaction mechanisms and accurately simulates the overall failure behavior of specimens. Additionally, the effects of pre-existing flaw inclination angle and dynamic loading frequency on rock failure mechanisms were investigated. The numerical results reveal that rock samples exhibit significantly higher compressive strength under dynamic loading compared to quasi-static loading, with compressive strength increasing with higher cyclic dynamic load frequencies. Furthermore, by analyzing the strength characteristics, crack propagation, and failure modes of the samples, insights into the failure mechanisms of rocks under different frequency loads were obtained. This study provides valuable insights into crack development and failure of rocks under seismic loads, offering guidance for engineering practices.

Investigation of the mechanical behavior of rock-like material with two flaws subjected to biaxial compression

The biaxial compression experiments of rock-like materials with two flaws are carried out under different flaw inclination angle, rock bridge ligament angle, lateral stress. The experimental studies show that crack propagation modes of rock-like material are as follows: wing crack through mode (Y mode), shear crack through mode (J mode), mixed crack through mode (wing shear JY mode), longitudinal extension of crack and transverse shear splitting. prefabricated fractured rock specimens have experienced the closing stage of prefabricated fractures, the elastic deformation stage, the generation and expansion of cracks (or plastic strengthening), and the residual loading stage. The peak strength of the specimen is increases with the increase of flaw inclination angle and lateral stress. With the increase of the rock bridge ligament angle, the failure of the rock bridge region changes from the shear crack failure to composite failure of shear crack and the wing type tensile crack failure, and then to the wing crack failure. With the increase of the lateral pressure, the failure of the specimen changes from the wing type tensile crack failure to the wing type and shear crack failure, and then to shear crack failure. The flaw inclination angle mainly changes the form of crack growth but does not effect on the failure modes. The counting number of acoustic emission events at the center of the sample is relative large, indicating that the cacks appear in the part of the rock bridge firstly. With the increasing of loads, the cracks of the rock bridge expanding constantly and connecting finally. The changes of acoustic emission event counts is consistent with the macroscopic damage form obtained from the experiments.

Investigation of mechanical properties in thin spray-on liner coated sandstone: Comparative study of unfilled and filled flaws

Thin spray-on liners (TSLs) are increasingly recognized as a potent skin support technology in underground engineering applications, particularly in mining. To better understand the coating and filling effects of TSL on the mechanical properties of the flawed specimens, a series of uniaxial compression tests were conducted on TSL-coated sandstone with unfilled and filled flaws. The experimental results showed that compared with the flawed specimen, the strength and peak strain of the TSL-coated and filled specimens increased, and the degree of improvement was more evident for the filled specimen coated with TSL. The specimens coated with TSL exhibited higher total, elastic, and dissipation energies compared to the uncoated specimens. Additionally, a greater proportion of the total input energy was transformed into dissipation energy after coating. For the filled specimens, more dissipation energy was generated during the failure process owing to the friction of the flaw surface provided by the filling effect. Moreover, the crack initiation and propagation behaviors of the flawed and filled sandstone specimens coated with TSL were analyzed by numerical simulation. For the specimens with an inclination angle of 45°, the TSL provided confinement to inhibit the initiation and propagation of tensile cracks, resulting in delayed crack initiation. The TSL filling plays a role in sharing part of the stress on the flaw surface, which weakens the stress concentration at the flaw tip. The effect of the TSL on the stress at the flaw tip was analyzed using a theoretical solution. The variation in SIF KII of the specimens with different flaw inclination angles was studied using a theoretical solution. Compared with the flawed specimens, the stress concentration in the filled flawed specimen was lower and the confinement effect could enhance the decrease in the flaw tip stress.

Experimental study of the effect of crack distribution on the failure mechanism of sandstone specimens based on inclination angles and number of parallel flaws

Discontinuous joints are prevalent in engineered rock masses and play a significant role in the stability of the rock mass. This study aims to analyze the impact of the inclination angle and number of prefabricated flaws on the crack evolution and failure pattern of sandstone specimens. Uniaxial compression tests, along with acoustic emission technology and digital image technology, were employed to monitor and analyze the effects. The findings indicate that: (1) With the increase in the flaw inclination angle, the damage mode of the specimen transitions from tensile to compressive-shear failure. The localized high-strain region on the surface of the specimen predicts the propagation path for the formation of macroscopic cracks. (2) When the number of prefabricated flaws is small, the flaws mainly expand through tensile wing cracks. As the number of flaws increases, the inner flaw tip does not produce cracks. Instead, the failure of the entire specimen occurs along the direction of the outer flaw's tensile wing crack, with the inner flaw running through it. (3) The winged tensile crack is the first crack to appear in all rock samples, regardless of the flaw initiation angles. Finally, the stress intensity factor at the crack tip under uniaxial compression conditions, without considering the closure effect, was expressed based on fracture mechanics theory. The crack initiation angle was then calculated. The results of the theoretical calculation of the initiation angle were found to be consistent with the test results. These research findings can serve as theoretical references and provide insights into the failure mechanisms of cracked rocks and the development of disaster control methods in rock engineering.

Intermediate Principal Stress Effects on the 3D Cracking Behavior of Flawed Rocks Under True Triaxial Compression

Crack initiation, growth, and coalescence in flawed rocks have been extensively studied for 2D (planar, penetrating) flaws under uniaxial/biaxial compression. However, little is known as to the mechanisms and processes of cracking from 3D flaws under true triaxial compression, where the intermediate principal stress (σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document}) is distinguished from the major and minor principal stresses. In this work, we systematically investigate the effects of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} on the 3D cracking behavior of rock specimens with preexisting flaws, through the use of mechanistic simulations of mixed-mode fracture in rocks. We explore how two characteristics of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document}, namely, (i) its orientation with respect to the flaw and (ii) its magnitude, affect two aspects of the cracking behavior, namely, (i) the cracking pattern and (ii) the peak stress. Results show that the orientation of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} exerts more control over the cracking pattern than the flaw inclination angle. The peak stress becomes highest when σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _1$$\\end{document} is parallel to the flaw, whereas it becomes lowest when σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} is parallel to the flaw. Also, the effects of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} magnitude are more significant when σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} becomes more oblique to the flaw plane. On the basis of our observations, we propose mechanisms underlying the cracking behavior of 3D flawed rocks under true triaxial compression.HighlightsThe effects of the intermediate principal stress (σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document}) on the 3D cracking behavior of flawed rocks under true triaxial compression are systematically investigated.The orientation of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} exerts more control over the cracking pattern than the flaw inclination angle.The effects of σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} magnitude become more significant when σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _2$$\\end{document} are more oblique to the flaw plane.Mechanisms underlying the cracking behavior of 3D flawed rocks under true triaxial compression are proposed based on the observations made.

Deformation localization and crack propagation of sandstone containing different flaw inclination angles under different loading rates

Defects with varying geometric distribution in the rock mass play a crucial role in determining the stability of engineered rock masses. Previous studies have primarily investigated the initiation, propagation, and coalescence behaviors of flaws within rock masses. Nevertheless, there has been limited analysis of flawed rock masses under different loading rates. In this study, we present the deformation localization and cracking process of three types of inclined flawed sandstone specimens through conducting uniaxial compression and acoustic emission tests at four different levels of loading rate. The results supported the following findings: 1) Sandstone specimens with different flaw inclination angles exhibit the loading rate strengthening effect, and the strengthening effect gradually decreases with the increase of loading rate. 2) As the loading rate increases, the type of crack emergence changes from wing cracks to anti-tensile cracks, and the time of flaw initiation is shortened. 3) The cumulative acoustic emission counts were higher for the low-loading rate specimens than for the high-loading rate specimens. 4) Tensile cracks typically occur as the initial cracks. Anti-tensile cracks often coexist with wing cracks in rock specimens that have undergone tensile damage. Coplanar secondary cracks are the primary indication of shear damage formation in rock specimens. 5) The increase in loading rate promotes the transition of rock specimens from the mixed tensile-shear damage mode to the shear damage mode. These research results are of great theoretical significance and engineering value for understanding the failure mechanism of rock mass containing flaws and proposing effective measures to prevent cracking and ensure the safety of brittle solid structures.

Experimental Investigation on the Destruction Features and Acoustic Characteristics of a Brittle Rock Sample Containing Both 2D and 3D Preset Flaws

Original fracture structures always present discontinuity in the real rock mass, and many invisible fractures hide inside the rock mass, which may cause serious engineering safety issues. To mimic the true 3D fracture structures through the experimental method, the gypsum rock-like samples containing both 2D through-type and 3D internal-type preset flaws are prepared, and multiple sets of inclination angles of the twin parallel flaws are set in the test. By applying the AE and DIC monitoring technologies during the uniaxial compression tests, the main results are as follows: (1) The flaw inclination angle presents a direct influence on the surface cracks distribution, maximum principal strain field, and the density of secondary failure in the middle rock; (2) AE events initially distribute around the internal 3D preset flaw, while the gradient inclination angle shows a slight impact on the events’ location before reaching the UCS status of samples; (3) mutations in b-values and S values can serve as evidence for predicting local damage, and the final failures quickly form at various scales and energy levels; (4) when the statistical analysis grid is divided sufficiently, the data window width and moving step length have little impact on the evaluation results, while the recommended bin width of event magnitude is 0.5 or 1.0.

Numerical modeling of crack propagation from open and closed flaws in rock

The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (KII) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of KII can be effectively eliminated when the non-singular stress (T-stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T-stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions.

Experimental Investigation of Pre-Flawed Rocks under Dynamic Loading: Insights from Fracturing Characteristics and Energy Evolution.

Different fractures exist widely in rock mass and play a significant role in their deformation and strength properties. Crack rocks are often subjected to dynamic disturbances, which exist in many fields of geotechnical engineering practices. In this study, dynamic compression tests were carried out on rock specimens with parallel cracks using a split hopkinson pressure bar apparatus. Tests determined the effects of strain rate and crack intensity on dynamic responses, including progressive failure behavior, rock fragmentation characteristics, and energy dissipation. Based on the crack classification method, tensile-shear mixed cracking dominates the failure of rock specimens under the action of impact loading. Increasing the flaw inclination angle from 0°-90° changes the predominant cracking mechanism from tensile cracking to mixed tensile-shear cracking. The larger the loading rate, the more obvious the cracking mechanism, which indicates that the loading rate can promote the cracking failure of rock specimens. The fragmentation analysis shows that rock samples are significantly broken at higher loading rates, and higher loading rates lead to smaller average fragment sizes; therefore, the larger the fractal dimension is, the more uniform the broken fragments of smaller sizes are. Energy utilization efficiency decreases while energy dissipation density increases with increasing strain rate. For a given loading rate, the energy absorption density and energy utilization efficiency first decrease and then increase with increasing flaw inclination, while the rockburst tendency of rock decreases initially and then increases. We also find that the elastic-plastic strain energy density increases linearly with the total input energy density, confirming that the linear energy property of granite has not been altered by the loading rate. According to this inherent property, the peak elastic strain energy of the crack specimen can be calculated accurately. On this basis, the rockburst proneness of granite can be determined quantitatively using the residual elastic energy index, and the result is consistent with the intensity of actual rockburst for the specimens.

Crack Coalescence Behavior of Rock-Like Specimens Containing Two Circular Embedded Flaws

Abstract Experimental research on the growth of internal flaws has rarely been reported due to the fact that it is difficult to cut internal flaws in specimens and cannot capture the initiation and propagation processes of internal flaws through direct observations. This paper proposed a method for creating internal flaws in specimens by utilizing the volatilization of camphor. A series of compression tests were performed on rock-like specimens including two embedded circular flaws, and CT techniques were used to investigate the internal damage behavior of flawed specimens. Experimental results illustrate that the strength and deformation properties of flawed specimens increase nonlinearly with the confining pressure as well as flaw inclination angle. Crack coalescence patterns and failure modes of flawed specimens depend on not only the confining pressure but also the flaw inclination angle. The crack coalescence pattern varies from wing crack coalescence to mixed tension-shear crack coalescence and then to the shear crack coalescence as the crack inclination angle increases. Confining pressure contributes to shear crack growth and has an inhibiting effect on the propagation of tension cracks. For specimens with the same flaw inclination angle, the failure mode changed from tension failure to mixed shear-tension failure or from mixed shear-tension failure to pure shear failure with the increase of confining pressure.

Experimental investigation on the effect of preexisting orthogonal cross flaws on cracking behaviors and acoustic emission characteristics of red sandstone

Uniaxial compression tests with combined acoustic emission (AE) technique and camera monitoring were conducted to investigate the influence of orthogonal cross flaws on the mechanical properties, cracking behaviors and AE characteristics of red sandstone. The effect of the primary flaw inclination angle α on the main mechanical parameters, crack initiation and propagation characteristics and failure modes were analyzed. The experimental results demonstrate that (1) The peak strength and elastic modulus of the specimens rise as α increases; the peak strain (the axial strain corresponding to the peak strength) εp increases initially and subsequently declines with increasing α, and reaches its maximum value at α = 45°. (2) The location of crack initiation is closely related to α. The new crack first initiates from the tip of the secondary flaw at the condition of α = 0°, 30° and 90°; However, when α is 45° and 60°, the new cracks first initiate from the primary flaw tip. (3) The ultimate failure mode of specimens is affected by α. When α is less than 45°, the primary flaw controls the specimen's failure mode and the specimen mainly shows shear failure; When α is greater than 45°, the secondary flaw plays a major role in controlling specimen's failure mode and the specimen shows tensile-shear mixed failure characteristics. (4) Propagation of anti-wing crack initiated from the primary flaw leads to coalescence behavior between the primary and secondary flaws under the condition of α = 30°, 45° and 60°. (5) When α is 30°, the cumulated AE counts and cumulated AE energy are the lowest, and the AE overall b-value is the highest. (6) Based on the analysis of AF value (average frequency) and RA value (the ratio of rise time to amplitude), tensile and shear cracks are classified during the loading process. The number of tensile cracks is substantially higher than that of shear cracks and α has no obvious effect on the proportion of the two types of cracks.

Simulation Study on Crack Initiation and Energy Mechanisms of Rock-like Samples with Non-Parallel Overlapping Flaws under Uniaxial Compression

Non-parallel overlapping flaws widely exist in engineering rock mass. Understanding their crack initiation and energy evolution characteristics is of great significance to ensure the stability of rock engineering. Based on the existing experiments, the influence of flaw inclination angles (β) on the crack initiation and energy evolution characteristics of rock samples with non-parallel overlapping flaws was studied by numerical simulation. The results show that (1) the uniaxial compressive strength, elastic modulus and crack initiation stress increase with the increase of flaw angle. (2) The boundary energy, strain energy and dissipated energy under peak stress increase with the increase of flaw angle; the dissipated energy increases the most. (3) With the increase of flaw angle, the tension stress zone is transferred to the flaw tip, and the zone is reduced gradually; the maximum tensile stress and the tension stress concentration decrease. (4) In the crack initiation stage, the influence of a lower flaw inclination angle (β ≤ 60°) on the lateral displacement field of the sample is higher than that of a high flaw inclination angle (β = 75°).

Dynamic fracture analysis of sandstone specimens containing different inclusions

Infilling materials are commonly distributed in natural rocks, which play a key role in the stability of rock engineering. To reveal the enhancing mechanism of inclusions, dynamic uniaxial compressive tests were carried out on sandstone specimens containing double elliptical flaws using a split Hopkinson pressure bar (SHPB) system and the digital image correlation (DIC) technique, and three inclusion conditions (R1, R2 and R3) and three flaw inclination angles (0°, 45° and 90°) were taken into consideration. The results indicate that the inclusions (R2 and R3) with a similar wave impedance to sandstone matrix can maximally enhance the dynamic strength of flawed specimens by 46.82% and 42.83%, respectively. The crack initiation and propagation behavior were significantly changed after the flaws were filled with different types of inclusions. The dominant crack in the bridge area can be identified by strain histories and stress intensity factors (SIFs) at the inner inclusion tips. The findings are projected to deepen the understanding of interaction mechanism of rock matrix and inclusions.

Dynamic progressive fracture behavior of axially confined sandstone specimens containing a single flaw

Rock masses are frequently subjected to dynamic disturbance in addition to pre-stress, which plays a key role in the stability and safety of underground projects. In this paper, the effects of flaw inclination angle and pre-stress on the mechanical properties and fracture behavior of sandstone specimens under repetitive impact loadings were investigated through a series of laboratory tests using a modified split Hopkinson pressure bar (SHPB) system. The results show that the dynamic strength decreases gradually with the increasing repetitive impact number. A larger flaw inclination angle produces fewer repetitive impacts for a given axial pre-stress. The repetitive impact counts and the cumulative absorbed energy peak at an axial pre-stress of 20–40 MPa. By the digital image correlation (DIC) technique, high strain localizations around the flaw periphery can be observed after the application of pre-stress. During the repetitive impact loadings, wing and anti-wing cracks occupy the dominant position. Compressive cracks also contribute to the ultimate failure if the specimen is subjected to solely repetitive impacts. Except for 90° specimens, shear cracks make a difference as well in the cracking process as the pre-stress increases.

Dynamic mechanical behavior of rocks containing double elliptical inclusions at various inclination angles

Inclusions embedded in rock materials highly affect their mechanical response and fracture behavior under external loadings. In this study, dynamic uniaxial compressive tests were performed on sandstone specimens containing double elliptical inclusions with various inclination angles to investigate the effects of inclusion conditions on the dynamic mechanical properties and failure mechanism of rock specimens using a split Hopkinson pressure bar (SHPB) system and the digital image correlation (DIC) technique. The results reveal that the inclusions effectively enhance the dynamic strength of flawed specimens, but its variation trend versus the flaw inclination angle is similar to that of unfilled specimens. Remarkable transformations were observed in the initiation position and propagation path of cracks after filling the flaw, which can be represented by the vertical displacement distribution along the inclusion periphery. The interaction mechanism between the double inclusions was dominated by a shear slip crack at the flaw inclination angle of 45° and tensile cracks at the flaw inclination angles of 0° and 90°. The effect of inclusions on the final failure pattern becomes slight with the increasing flaw inclination angle.

Discrete element study on the mechanical behavior of flawed rocks under dynamic compression

Pre-existing discontinuities in rock engineering significantly affect the entire structural stability, especially when subjected to dynamic loads. To deepen the understanding of fracture mechanism of flawed rock specimens, a numerical study based on the discrete element model was conducted to investigate the effects of flaw geometry and strain rate. The results indicate that the dynamic strength is sensitive to the flaw length, flaw inclination angle and strain rate. Their effects on the fracture process and failure pattern were also numerically revealed by acoustic emission and micro crack monitoring. The numerical results well reproduce the experimental results. A method combining displacement vector field, micro crack distribution and force chain pattern was proposed and it can effectively identify the crack type from both macro and micro perspectives. In accordance with the particle velocity difference, it is found that the crack initiation position moves from the flaw center to flaw tips with the inclination angle increasing, and only the flaw length longer than the critical value can affect the fracture behavior. In addition, the cumulative microcrack length can somewhat represent the fragmentation of the flawed specimen after final failure.