Wing Cracks Research Articles

The effects of carbonaceous inclusions and their distributions on dynamic failure processes in boron carbide ceramics

AbstractCommercially available boron carbide ceramics typically have heterogeneous microstructures that contain distributions of processing‐induced inclusions. The inclusions that are rich in carbon (i.e., carbonaceous) govern the underlying mechanisms of brittle fracture through wing crack formation, and thus dictate the mechanical response of the ceramic. In this study, we investigate the dynamic failure of five boron carbide ceramic materials with different inclusion populations. All of the materials were prepared by hot‐pressing; four of these boron carbides contained different sizes and concentrations of carbonaceous inclusions, while one contained no carbonaceous inclusions. The heterogeneity distributions were characterized in some detail for statistical analysis using scanning electron microscopy and quantitative image analysis. A modified compression Kolsky bar setup with in situ ultra‐high‐speed microscopic imaging (10 million frames per second) was then used to study the influence of the inclusion distributions on the dynamic failure processes in these materials, at nominal high strain rates of 102–103 s−1. The in situ ultra‐high‐speed microscopy highlighted the link between micro and macroscale failure processes and demonstrated that the carbonaceous inclusions are indeed the preferential sites for nucleation of wing cracks, as previously hypothesized based on post‐mortem observations. The relative orientation of an inclusion with respect to the compression axis was shown to affect the likelihood that it would participate in crack nucleation. All of the ceramics were also found to have orientation‐dependent peak compressive stress, regardless of the presence of carbonaceous inclusions, suggesting that grain orientation distributions are also important.

Study on the global stress field of the rock mass under compression and shear considering three kinds of crack parameters

AbstractThe mechanical behavior of the cracked rock mass is controlled by the crack initiation and propagation under compression and shear. The key to predicting the wing crack initiation angle is to correctly describe the distribution of the stress field at the crack tip. First, the previous studies are reviewed, and their inadequacies are discussed in detail. Next, according to the experimental results, three kinds of crack parameters (i.e., geometry, strength, and deformation) are introduced, and a stress transfer model on the crack face under compression and shear considering crack parameters is proposed. Then, the relevant formulae of stress intensity factors (KI and KII) and non‐singular term (T‐stress) at the crack tip are obtained. Finally, the proposed model is verified by other researchers' test results, and the effects of three kinds of crack parameters and the rock property on the distribution of tangential stress at the crack tip are discussed.

Influence of polymeric resin-infilling on onset and fracture growth along wing trajectory in open-flawed sandstone specimen

Onset and growth of wing fracture in open/resin-infilled sandstone specimens are primarily investigated. Stress/LEFM-based VCCT embedded fracture analysis is carried out through three-dimensional FEM, experimentally validated with wing crack initiation points/extension angles. Principal-stress/SERR-based G/F-criteria are used for numerical estimation of onset points/extension angles. Griffith (G)-criteria predicts extension angle for open flaw but fails for infilled case, whereas F-Criteria distinguishing unequal contribution of fracture modes fits. Tensile Stress Concentration (TSC) at flaw-resin interface is reduced through significant reduction of in-plane stresses (σx, σy, τxy) over out-of-plane (σz, τyz, τxz) components. Shifting of TSC/Wing Trajectory (WT) alternation in resin-infilled case is due to through-the-thickness variation of out-of-plane stresses. Curve-fitted experimental WT profile inducted; realistic FE-simulation technique is implemented for fracture growth investigation. Both open/infilled flaws undergo Mode-I-dominated wing fracture growth with least dominance of Mode-II/III. Resin infilling causes significant reduction/slight improvisation of Mode-I/Mode-II SERRs, respectively, leading to self-similar, delayed, thin wing fractures compared to visible wing fractures in open flaw cases. As the wing fracture grows, propensity towards Mode-I fracture is reduced in absence/presence of resin infill. However, the tendency for Mode-II is increased for open flaw and reduced for infilled-flaw cases.

Crack Initiation and Propagation of Embedded Three-Dimensional Parallel Cracks in Transparent Rock-Like Material

Abstract In order to understand the initiation and propagation of three-dimensional (3D) embedded parallel cracks in brittle rock under uniaxial and biaxial compression, a preparation method of a transparent rock-like material was proposed in order to observe the propagation process of cracks in brittle rock. Uniaxial and biaxial compression tests were carried out on the transparent rock-like samples containing two embedded 3D parallel cracks. Four types of crack propagation modes were observed: wing crack, petaloid crack, flat-wing crack, and ring-like crack. It is also found that the direction of lateral pressure relative to the strike of the embedded crack has a significant effect on the propagation direction of new generated cracks: a lateral pressure parallel to the strike of the embedded cracks promotes crack propagation in the direction of the maximum principal stress; on the other hand, a lateral pressure normal to the strike of the embedded cracks promotes cracks propagation around the embedded crack at an angle of 30°–60°, forming ring-like cracks, which is similar to the zonal disintegration phenomenon monitored around deep underground excavations.

Experimental study on 3D internal penny‐shaped crack propagation in brittle materials under uniaxial compression

AbstractFractures are widely present in geomaterials of civil engineering and deep underground engineering. Given that geomaterials are usually brittle, the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure. However, the crack initiation and propagation in brittle materials under composite loading remain unknown so far. In this study, a three‐dimensional internal laser‐engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces. The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear. The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack, which is a mixed‐Mode I–II–III fracture; in contrast, Mode I fracture is present in the specimen with a vertical internal crack. The fractography characteristics of Mode III fracture display a lance‐like pattern. The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure. The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model, a three-dimensional strength criterion for hard rock was developed in detail in this paper. Although the basic expression is derived from initiation and propagation of a single crack, it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic. Besides, it can be derived as Hoek–Brown criterion when the intermediate principal stress σ2 is equal to the minimum principal stress σ3. In addition, the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient, which could be described by an empirical function and verified by 10 kinds of hard rocks. Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level. As the effects of these two factors on the strength are opposite, the intermediate principal stress effect is induced.

Experimental and numerical research of the behavior of 3D internal cracks under uniaxial compression using 3D-ILC technology

Uniaxial compression tests are one of the classic tests of solid mechanics. However, there remain some unsolved problems involving the test methods and numerical simulation. In the present study, in view of the difficulties in the manufacture of real internal cracks, glass, a classical material whose brittleness is quite close to that of natural rock material, is selected to generate pure closed internal cracks using 3D Internal Laser-Engraved Crack (3D-ILC) technology. Through the uniaxial compression test, we observe that the failure of specimens originates from the pre-existing internal crack. First, wing cracks are generated around it, which then propagate. As the load reaches the maximum bearing capacity, the later tensile crack eventually leads to the failure of the specimen. This test method can be used to observe and study the crack propagation process, failure law, failure mode and characteristic load of brittle materials. In the numerical analysis, adaptive grid method is used for grid division and update. The distribution of KI, KII, and KIII at the crack tip is obtained by M-Integral, and the crack propagation is simulated in combination with the maximum tensile stress (MTS) criterion. In terms of numerical simulation, the mode I/II/III propagation simulation of 3D internal crack is successfully realized, which is of great significance. At present, the research of 3D crack propagation and internal crack propagation has encountered bottlenecks in theory, experiment and numerical simulation. It is hoped that the experimental and numerical simulation methods in this paper can provide some reference.

The effect of flaw geometry and infilling on crack initiation, propagation, and coalescence of a parallel flaw pair in marble

A series of uniaxial compression tests were conducted on unfilled or filled marble specimens with a parallel flaw pair to study the effect of the flaw geometry and infilling on the crack coalescence pattern. Special attention was paid to the crack initiation, propagation, and coalescence processes, which were traced by the CCD camera and digital image correlation (DIC) technique. The experimental results have shown that the appearance of the white patch and strain localization band precedes the initiation of macroscopic crack. The tensile crack evolves from a narrow strain band or white patches with clear boundaries, while the shear crack evolves from a wider strain band or white patch with blurry boundaries. The high-strength fillers suppress the initiation and propagation of the tensile cracks (i.e., T1, T2, and T3) and promote the appearance of the coplanar shear cracks and mixed tensile-shear cracks (i.e., M1, M2, and S1). The variation in the infilling condition leads to the difference in the fundamental crack types, hence resulting in different coalescence patterns for a given flaw geometry. For small rock bridge angles (i.e., β = 30°, 45°), no coalescence and indirect coalescence tends to occur between the open and gypsum-filled flaws, while shear coalescence is prone to occur between the cement- and resin-filled flaws. The coalescence patterns are dominated by the flaw geometry for medium rock bridge angles (i.e., β = 60°, 90°), but the crack coalescence stress and peak strength of specimens are greatly affected by the infilling conditions. For large rock bridge angle (i.e., β = 120°), the increase in the strength of the filler tends to generate straighter wing cracks for the tensile coalescence at the rock bridge and promotes the initiation of mixed tensile-shear cracks for additional coalescence outside the rock bridge.

An Extended Hydro-Mechanical Coupling Model Based on Smoothed Particle Hydrodynamics for Simulating Crack Propagation in Rocks under Hydraulic and Compressive Loads

A seepage model based on smoothed particle hydrodynamics (SPH) was developed for the seepage simulation of pore water in porous rock mass media. Then, the effectiveness of the seepage model was proved by a two-dimensional seepage benchmark example. Under the framework of SPH based on the total Lagrangian formula, an extended hydro-mechanical coupling model (EHM-TLF-SPH) was proposed to simulate the crack propagation and coalescence process of rock samples with prefabricated flaws under hydraulic and compressive loads. In the SPH program, the Lagrangian kernel was used to approximate the equations of motion of particles. Then, the influence of flaw water pressure on crack propagation and coalescence models of rock samples with single or two parallel prefabricated flaws was studied by two numerical examples. The simulation results agreed well with the test results, verifying the validity and accuracy of the EHM-TLF-SPH model. The results showed that with the increase in flaw water pressure, the crack initiation angle and stress of the wing crack decreased gradually. The crack initiation location of the wing crack moved to the prefabricated flaw tip, while the crack initiation location of the shear crack was far away from the prefabricated flaw tip. In addition, the influence of the permeability coefficient and flaw water pressure on the osmotic pressure was also investigated, which revealed the fracturing mechanism of hydraulic cracking engineering.

Study on the creep properties and crack propagation behavior of single-fissure sandstone based on the damage bond model

As geotechnical engineering expands to deeper formations, the creep behavior of surrounding rock becomes more significant. To better understand the creep deformation and creep propagation of fissured rocks, this study conducts triaxial compression tests and triaxial creep tests of sandstone samples containing a single fissure. The experimental results show that fissured sandstone has a time-dependent failure mode, and creep loading not only causes the crack that dominates the failure of the fissured sandstone to change from a wing crack to an anti-wing crack but also produces more secondary cracks, which are obvious in samples with a low-angle fissure. The steady-creep rate of fissured samples is higher than that of intact samples and first increases and then decreases with increasing fissure angle. The sample with a 45° fissure produces the maximum axial deformation before entering the accelerated creep stage. The theory of the damage bond model (DBM) applied in Particle Flow Code software is proposed, combining the Kachanov damage theory and linear parallel bond model. The DBM effectively simulates the creep deformation and crack propagation process of sandstone in all creep stages, and the failure mode is consistent with the test results. During the initial and steady-state creep stages, the number of microcracks slowly increases, generating a dispersed distribution that rarely exhibits coalescence. Then, the microcracks propagate unstably and coalesce macroscopic cracks, and the accelerated creep stage starts, which is both stress- and time-dependent. Under the same deviatoric stress, the creep simulation samples generate more microcracks than the triaxial compression samples and exhibit a greater reduction in the width of the preexisting fissure after failure. Creep damage accumulation with time significantly affects the evolution of contact forces and displacement vectors. A stress concentration is more likely to occur along the propagation path of an anti-wing crack in creep samples, and the anti-wing cracks present a trend of shear failure. This study plays an important role in predicting the deformation of fissured surrounding rock in underground engineering and explaining the mechanisms of catastrophic events due to the evolution of damage.

Influences of the number of non-consecutive joints on the dynamic mechanical properties and failure characteristics of a rock-like material

The dynamic mechanical properties and failure characteristics of jointed rocks are the focus of research in rock engineering. In this study, cement mortar specimens with 0–4 parallel non-consecutive joints were prepared. The split Hopkinson pressure bar (SHPB) was used for dynamic impact testing of prepared specimens. Nuclear magnetic resonance (NMR) was used to detect the pore structure deterioration of the specimens after impact. Finally, the failure characteristics of the specimens were studied by extracting the surface cracks of the specimens. The results show that the number of non-consecutive joints have a significant effect on the dynamic mechanical properties of cement mortar specimens. The increased number of joints will change the stress–strain curve from a single-peak shape to a multi-peak shape and enhance the ductility. The dynamic peak strengths and the proportion of dissipated energy of the specimens decrease with the increase of number of joints, but the magnitude of change decreases gradually. NMR analysis reveals the pore structure alterations of the specimens. After being impacted, the internal pores of the specimens increase significantly, especially the macro-pores and micro-pores. Some micro-pores become meso-pores and macro-pores, and some pores are connected. These changes of microscopic pore structure lead to macroscopic failure of specimens. A quantitative analysis of the porosity of the specimens shows that the rate of change in porosity is in direct proportion to the number of joints, which means that the greater the number of joints, the larger the damage degree of the specimens. The failure characteristics of the specimens indicate that tensile stress mainly dominates the fracture behavior of the specimens, while shear stress has limited damage to the specimens. After the tensile wing cracks start from both tips of the joint, they extend along the rock bridge to the adjacent joint or the end of the specimen. After the wing cracks coalesce, they form a rectangular failure zone. In addition, axial tensile cracks will start near the middle of the first joint and the middle of the last joint, extending to the top and bottom of the specimen, respectively. Slight shear cracks only develop at the joint ends.

Mechanical properties and failure law of composite rock containing two coplanar fractures

Composite rocks comprise the rock structures that are commonly used in geotechnical engineering. The fracture configuration has a substantial influence on the mechanical behavior, failure mode, and crack propagation of composite rocks. In this study, we considered a composite rock with two prefabricated coplanar fractures. Through laboratory uniaxial compression tests and using a digital image acquisition system, we systematically studied the effects of different fracture lengths and inclination angles on the mechanical properties and failure characteristics of the rocks. We obtained the following results: 1) during the loading deformation of the rock sample, the peak stress and elastic modulus increased with an increase in the fracture inclination angle and decreased with an increase in the fracture length. The deterioration coefficient k (the ratio of the difference between the peak strength of intact and fractured rock sample to that of intact rock sample) decreased with an increase in the fracture inclination angle and increased with an increase in the fracture length. 2) The failure type of the rock samples was primarily controlled by the fracture inclination angle and material of the two rock types, and the fragmentation degree was primarily controlled by the fracture length. With an increase in the fracture inclination angle, the failure mode of rock sample exhibited the following order of changes leading to failure: a double-Y type (trwo wing and one antiwing cracks appeared on each prefabricated fracture) → double-Z type (two wing cracks appeared on each prefabricated fracture) → Z type (one wing crack appeared on each prefabricated fracture). 3) The type of coalescence of the rock bridge was controlled by the fracture inclination angle and structural plane. The crack positions were primarily affected by the fracture length. 4) At a low fracture inclination angle (α ≤ 30°), the propagation of the microcracks showed aggregated band formation. Above moderate fracture inclination angles (α > 30°), the microcrack aggregation band gradually weakened and expanded in the direction of dispersion.

Time-dependent cracking and brittle creep in macrofractured sandstone

Time-dependent cracking and brittle creep of rock is fundamental to understanding the long-term evolution and dynamic failure in underground rock engineering. In the present paper, we present a systematic laboratory investigation into the control of single open macrofractures of differing orientations on time-dependent cracking and brittle creep in sandstone using digital image correlation (DIC). For a given macrofracture inclination angle β, we find that the failure of macrofractured sandstone under a constant stress is accompanied by the generation of more tensile fractures (wing cracks and secondary cracks) than in our constant strain rate experiments. This result differs from experiments performed on intact sandstones, for which macroscopic failure under a constant stress and constant strain rate were essentially identical. The nucleation site for the wing cracks is β-dependent. As β is increased, the crack nucleation position gradually moves from the center of the fracture towards the fracture tip with a decreasing speed. The kink angle of the secondary crack (k1) increases quasi-linearly with the increase of fracture angle γ. With the increase of the secondary crack angle θ, the kink angle of the tail crack (k2) shows different increasing trends for the left-lateral and right-lateral shear. The secondary crack could be inclined at a maximum of 26° (θ) to the maximum principal stress direction. Creep bursts—transient accelerations in deformation—are more easily triggered in macrofractured rock than in initially intact rock, and coincide in time with the coalescence of secondary cracks. The likelihood of occurrence of a creep burst was found to be higher for lower values of β. Finally, we present a secondary crack location map that defines the swing interval and identifies the fracture mechanism. The influence of a macrofracture, and its orientation, on damage evolution and the likelihood of creep bursts during interseismic periods provides crucial information for those tasked with monitoring hazards associated with the dynamic failure of crustal rocks.

Fracture Process and Failure Mode of Brazilian Discs with Cracks of Different Angles: A Numerical Study

In order to determine the effect of internal cracks on the tensile failure of materials, a hybrid finite–discrete element method was used to analyze the Brazilian disc test with cracks of different angles. When the pre-crack angle is between 0° and 60°, the wing crack is initiated from the pre-crack end. When the pre-crack is 90°, the crack initiated from the pre-crack center. When the pre-crack angle is between 0° and 60°, the maximum principal stress and plastic strain are concentrated at the pre-crack end. When the pre-crack angle is 90°, the maximum principal stress and plastic strain are concentrated in the pre-crack center. As the crack angle increased from 0° to 90°, the failure mode of Brazilian discs with cracks transits from splitting into two parts to splitting into four parts. The influence of crack length is further studied. When the crack length is less than 5 mm, the crack angle has little influence on the disc failure mode; Brazilian discs with cracks of different angles undergoes splitting failure along the loading axis. When the crack length is larger than 5 mm, the crack angle has a great effect on the disc failure mode.

Two-level simulation of injection-induced fracture slip and wing-crack propagation in poroelastic media

In fractured poroelastic media under high differential stress, the shearing of pre-existing fractures and faults and propagation of wing cracks can be induced by fluid injection. This paper presents a two-dimensional mathematical model and a numerical solution approach for coupling fluid flow with fracture shearing and propagation under hydraulic stimulation by fluid injection. Numerical challenges are related to the strong coupling between hydraulic and mechanical processes, the material discontinuity the fractures represent in the medium, and the strong effect that fracture deformation and propagation have on the physical processes. The solution approach is based on a two-level strategy that is classified into the coarse and fine levels. In the coarse level, flow in and poroelastic deformation of the matrix are coupled with the flow in the fractures and fracture contact mechanics, allowing fractures to frictionally slide. Fracture propagation is handled at the fine level, where the maximum tangential stress criterion triggers the propagation of fractures, and Paris' law governs the fracture growth processes. Simulations show how the shearing of a fracture due to fluid injection is linked to fracture propagation, including cases with hydraulically and mechanically interacting fractures. • Wing-crack propagation caused by injection-induced slip of fractures and faults. • Modeling of fracture slip, deformation and propagation in poroelastic media. • Two-scale solution strategy with local adaptive remeshing on fine-level and coarse-level grids. • Open-source 2D implementation combining finite volume and finite element methods. • Simulation results on hydromechanical coupling in fracture slip and propagation.

Mechanical behavior of anchored rock with an infilled joint under uniaxial loading revealed by AE and DIC monitoring

The progressive failure of fractured rock affects the stability and safety of rock engineering and has always been a key issue in rock engineering field. As the most common support way, the addition of bolt will change the stress distribution and further effect the failure characteristics of fractured rock. It is of significance to study the failure characteristics of anchored fractured rock for the relevant projects. In this study, digital image correlation (DIC) and acoustic emission (AE) technology were used to study the influence of bolt on fracture behavior of infilled jointed rock under uniaxial loading. The results show that the addition of bolt makes the pre-peak ductility more obvious. The enhancement degree of bolt on mechanical parameters decreases with the variation of joint angle. The principal strain field shows that the addition of bolt can effectively inhibit the propagation of wing crack and anti-wing crack, which leads to the failure of anchored specimen tends to shear failure. The RA-AF distribution of anchored specimens also shows that the scattered points shift to the shear signal area in the plastic stage and post-peak stage. In addition, for anchored specimens, b-value corresponding to the peak stress is higher than b-value corresponding to the initial loading, indicating that there exists an obvious anchoring effect of the bolt in the plastic stage and post-peak stage.

Micromechanics of rock damage and its recovery in cyclic loading conditions

SUMMARY Under compressive stress, rock ‘damage’ in the form of tensile microcracks is coupled to internal slip on microscopic interfaces, such as pre-existing cracks and grain boundaries. In order to characterize the contribution of slip to the overall damage process, we conduct triaxial cyclic loading experiments on Westerly granite, and monitor volumetric strain and elastic wave velocity and anisotropy. Cyclic loading tests show large hysteresis in axial stress–strain behaviour that can be explained entirely by slip. Elastic wave velocity variations are observed only past a yield point, and show hysteresis with incomplete reversibility upon unloading. Irrecoverable volumetric strain and elastic wave velocity drop and anisotropy increase with increasing maximum stress, are amplified during hydrostatic decompression, and decrease logarithmically with time during hydrostatic hold periods after deformation cycles. The mechanical data and change in elastic properties are used to determine the proportion of mechanical work required to generate tensile cracks, which increases as the rock approaches failure but remains small, up to around 10 per cent of the net dissipated work per cycle. The pre-rupture deformation behaviour of rocks is qualitatively compatible with the mechanics of wing cracks. While tensile cracks are the source of large changes in rock physical properties, they are not systematically associated with significant energy dissipation and their aperture and growth is primarily controlled by friction, which exerts a dominant control on rock rheology in the brittle regime. Time-dependent friction along pre-existing shear interfaces explains how tensile cracks can close under static conditions and produce recovery of elastic wave velocities over time.

Numerical investigation and experimental study on fracture processes of central flawed sandstone Brazilian discs

The propagations and connections of rock mass fissures are direct factors that lead to failure of rock engineering structures. Based on this, the traditional kernel function in the smoothed particle hydrodynamics (SPH) method was improved, which could simulate the progressive propagation processes of rock fissures. Brazilian disc samples of red sandstone with different fissure angles were prepared, and experiments on the crack propagations of Brazilian discs under uniaxial compression were carried out combined with digital image correlation technology. The results show that when the inclination angle of the prefabricated fissure is 0°, cracks initiate from the middle of the fissure and propagate along the loading direction; “Wing cracks” occur at prefabricated fissure inclination angles of 30°∼60°; when the inclination angle is 90°, cracks propagate along the direction of the prefabricated fissure. The peak load of the samples first decreases and then increases with increasing inclination angle, and was minimum when the angle was 60°. An improved SPH algorithm was used to simulate the crack growth of Brazilian discs with different fissure angles, and the simulation results are consistent with the experimental results, which verifies the rationality of the proposed method. However, most rock engineering problems are three-dimensional, so future research directions should focus on the development of 3D SPH parallel programs.

Application of the 3D DEM in the modelling of fractures in pre-flawed marble specimens during uniaxial compression

The results of modelling fractures in pre-flawed marble cylinder specimens under uniaxial compression are presented in this study. The discrete element method (DEM) was used to investigate crack propagation and coalescence in marble specimens with pre-existing open cracks at various angles to the horizontal. The results of numerical three-dimensional (3D) simulations were directly compared to laboratory investigations. Pure spheres and clumps composed of spheres mimicking marble were used in mesoscopic fracture estimates. The formation of wing and secondary cracks under load were studied. The influence of smaller grains and the ratio between contact cohesion and contact normal strength were investigated. The geometric qualities of the initial faults and the interlocking effect influenced the strength, post-peak response, and crack propagation patterns in the marble specimens. The computational and experimental results were found to be in satisfactory agreement. The DEM simulations showed that the results were significantly influenced by the ratio of cohesive to tensile normal contact stress. The results also showed a correlation with the particle shape (spheres versus clumps).

Influence of the Preexisting Fracture Network on the Mechanical Properties of Rock Mass and the Secondary Crack Propagation

Preexisting fracture network (PFN) is ubiquitous in natural rock mass and is one of the key factors affecting the mechanical properties of rock mass. This research employed a combined approach of theoretical analysis and finite element numerical simulation to investigate the mechanical behavior of PFN-containing rock mass. Based on the sliding crack model and fracture mechanics theory, the initiation mechanism of closed and open cracks driven by compressive and shear stress was theoretically analyzed. Rock mass models with different inclination angles (β) of PFN were built in Fast Lagrangian Analysis of Continua in 3 Dimensions. The complete stress–strain curves of rock mass and the secondary crack propagation were obtained. Results indicated that the increase of β reduced the strength and elastic modulus of rock mass. When β is less than 45°, this influence is more prominent. Based on the load-bearing capacity of PFN-containing rock mass, the stress–strain curves can be classified into two types: type I curve has multipeak and is strain-softening in the postpeak stage when β is 15°, 30°, 45°, 60°, and 90°; type II curve is unimodal and with brittle failure when β is 60° and 75°. Secondary crack propagation can be classified into four main types: type I is the coplanar crack, type II is the wing crack around PFN, type III is the near-field wing crack, and type IV is the macroscopic shear crack.