Single Flaw Research Articles

New crack initiation model for open-flawed rock masses under compression–shear stress

Many tests and numerical calculation results have demonstrated that the relationship between the strength of a rock mass with an open single-flaw and the flaw angle (β)is not a symmetrical U-shaped distribution at β = 45°, as calculated using the slide crack model. In this study, based on a comparison between previous tests by other investigators and the slide crack model, uniaxial compression tests were conducted on sandstone specimens containing a single flaw. The peak strength (σc), initiation stress (σci), crack initiation, and failure of the specimens were analyzed in detail. In contrast to the sliding crack model, in which cracks in all the specimens initiate in the form of wing cracks, two other modes of crack initiation were observed for specimens with β = 0°–40°: the anti-wing and middle cracks. The results indicated that the compressive stress (σy) on the flaw surface contributes significantly to the crack initiation process. Therefore, a crack initiation criterion is proposed: when the sum of the I-type stress intensity factor (KI) generated by the shear stress (τ) and σy attains the fracture toughness (KIC), cracks will initiate from the tip of the pre-existing flaw (when σy > τ, crack initiation is in the form of an anti-wing crack, otherwise it is a wing crack). When the tensile stress (σt) on the flaw surface reaches the tensile strength of the rock before KI at the crack tip reaches KIC, cracks in the specimen will initiate in the form of middle cracks.

Micro- and macrocracking behaviors in granite and molded gypsum containing a single flaw

The effect of preexisting defects on fracture behaviors is significant for the stability analysis of rock engineering. To study the effect of preexisting flaws on the micro- and macrocracking behaviors of rocks, photographic monitoring together with strain field analysis, passive acoustic emission (AE) and active ultrasonic testing were carried out on gypsum and granite samples containing a single flaw. Based on coupled analysis of the acousto-optic-mechanical characteristics, it is suggested to identify micro- and macrocrack initiation by AE monitoring rather than stress–strain behaviors, photographic observation and P-wave measurement. The micro- and macrocrack initiation stresses generally increase with the flaw angle. The microcrack initiation stress ranging from 0.22σc to 0.62σc (peak strength) coincides with the onset of AE events, and the macrocrack initiation stress ranging from 0.60σc to 0.85σc coincides well with a dramatic increase in AE energy for flawed granite. The crack types are classified into nine different categories. Macrocrack coalescence is observed before reaching σc, and violent rock failure occurs seconds after σc is achieved for flawed granites, which differs from that process for gypsum samples. The cracking process of flawed granites experiences three typical stages and is highly dependent on the flaw angle. A stress drop accompanied by a significant increase in the AE energy rate appears several times. With an increasing flaw angle, the count of stress drop and the cumulative AE energy decrease, while the maximum value of the AE energy rate and the average hit energy increase gradually. The energy and stress release reduces the violent failure degree of rock. The AE energy correlated with the cracking magnitude changes more violently than the AE event before peak failure. P-wave attenuation increases sharply after macrocrack initiation. A sharp reduction in velocity is always accompanied by a significant increase in the AE rate. Compared with the global cracking damage of rock characterized by AE characteristics, the fracture identified by P-wave velocity is localized.

A New DIC-Based Method to Identify the Crack Mechanism and Applications in Fracture Analysis of Red Sandstone Containing a Single Flaw

As a representative non-interferometric optical technique, the digital image correlation (DIC) can provide full-field displacement and strain measurement for the deformed rocks. However, the standard DIC technique has a limitation in measuring the displacements at the discontinuity and cannot be directly used for identifying the crack mechanism. Thus, a new DIC-based method is proposed for automatically tracing the discontinuities and quantitatively identifying the crack mechanism, i.e. mode I, mode II, and mixed-mode I/II. The new method involves three steps, including displacement measurement from the standard DIC technique, displacement field reconstruction at the discontinuity with the modified subset splitting technique, and post-processing for crack identification and displacement jump measurement. The effectiveness and robustness of the modified subset splitting technique and post-processing method have been verified with the synthetic images and theoretical displacement fields of mode I crack and dislocation. Then, the proposed method is utilized to locate cracks and quantitatively identify the crack mechanism of the initiated cracks in red sandstone containing a single flaw under uniaxial compression. The crack development in the flawed red sandstone specimens is analyzed and the crack types are summarized, in which wing cracks are in mode I, while horsetail cracks and anti-wing cracks are identified as mixed-mode I/II crack. It is shown that the new method avoids some ambiguous identification of crack mechanism and present more objective results.

Mechanical behavior of SiC ceramics with single flaw under three-point bending

As a common defect in ceramics, the flaw-like defect will affect the fracture damage and mechanical properties of ceramics. For the current experimental equipment, it is difficult to accurately prefabricate defects in ceramics and observe the internal crack propagation when the specimen is damaged under loading, however, numerical simulation can solve this problem well. In order to explore the effect of various parameters of a single flaw on the crack evolution and bending strength of SiC ceramics under three-point bending, a SiC ceramic discrete element model with a prefabricated single-flaw defect is established and calibrated in this study, and the effects of the flaw length, inclination angle, and position on the bending strength of SiC ceramic specimens are investigated. The results show that the SiC ceramic specimen has the highest sensitivity to the existence of single-flaw defect when the flaw height ratio is 0 and inclination angle is 90°. As the height ratio of the single-flaw defect increases, the weakening effect of the flaw on the bending strength is reduced. Moreover, the influence of the flaw inclination angle on the bending strength of the specimen is weaker than that of the height ratio, but a change in the flaw inclination angle may induce the generation of secondary cracks in the specimen. In addition, the effect of the horizontal offset of the flaw on the bending strength is not obvious, but secondary cracks may also be generated in the specimen.

FracProp: Stochastic Fracture Propagation Model

This paper presents a geometric, mechanics-based, stochastic model—FracProp—that was developed to predict fracture initiation and propagation in rock. FracProp is capable of quantifying uncertainties associated with the point of fracture initiation and direction of fracture propagation. The current version of FracProp uses compounded probability distributions that are continuously fitted based on mechanical principles (stress distribution and material properties). The model assumes that fracture initiation and propagation depend on the stress profiles around the fracture (flaw) tip in a rock block subjected to vertical, horizontal, and internal loading. To develop the model, we studied the mechanics of a rock block containing one single flaw (pre-existing opening) with the Finite Element (FE) software ABAQUS. Stress profiles obtained in the modeling were used with the model’s probabilistic processes to dynamically simulate (model) crack/fracture propagation. FracProp was validated with the results of experiments under various loading conditions done at the Massachusetts Institute of Technology (MIT) geomechanics laboratory.

Crack Growth in Rocks with Preexisting Narrow Flaws under Uniaxial Compression

Crack growth in rocks with preexisting flaws is of real concern for many rock engineering applications. The present paper considers the flaw that has a narrow gap that eventually gets closed on loading. Crack growth behavior leads to different failure modes, and corresponding strength characteristics were studied with respect to flaw angle. An experimental study was carried out with gypsum specimens replicating rock, that considered single and double flaws subjected to uniaxial compression. Crack growth and stress behaviors were analyzed and compared. The study was later extended to include numerical analyses using ABAQUS that adopted the extended finite element method with a cohesive zone model to capture crack growth behavior. The numerical model successfully mimicked wing crack propagation similar to the experimental results. The appearance of shear cracks and their growth upon loading was also predicted and crack initiation stress with respect to wing- and shear cracks was investigated. No significant differences were observed for single flaw specimens. However, in the case of multiple flaws with nonparallel configurations, the effect of shielding had a significant impact on coalescence behavior.

Experimental and numerical study on crack propagation and coalescence in rock-like materials under compression

The discontinuous crack surface in a rock affects the stability of the whole rock system. The experiments in this paper were carried out by prefabricating rock-like specimens with different types of flaws, then the specimens were tested under uniaxial compression. Moreover, based on the theory of particle flow, PFC2D software was used for numerical simulation, and the comparative analysis of the experimental and simulative results was carried out to obtain the crack initiation sequence, propagation phenomenon, and failure mode of rock specimens with different flaw types. The results indicated that the wing crack started at the tip of flaw and the form of crack assumed split failure, followed by shear failure caused by the secondary crack. The tensile failure degree decreases and the influence of shear failure increases with the increase of flaw angle. The wing crack and secondary initiation stress value is 35%–55% and 85%–95% of the peak stress value. Crack coalescence appeared in adjacent flaws of rock-like specimens with multiple parallel single flaws, single-cross flaws and double-cross flaws, and the coalescence phenomenon always occurs when the stress peak value is reached. With the number of flaws increasing, the splitting failure of rock-like specimens became more and more serious, the splitting failure of double cross-flaw specimen is the most serious. As for the specimen with single-cross flaw, the wing crack would be produced at the tip of the flaw with larger obliquity. The results of this paper may offer certain reference value for the study on the mechanism of rock crack.

The Microscopic Mechanism of Crack Evolution in Brittle Material Containing 3-D Embedded Flaw

In this paper, the microscopic mechanism of crack evolution in brittle material containing 3-D embedded flaw is investigated. The crack evolution mode of 3-D flaw is summarized by the uniaxial compression experiment first. Based on experiment results, the micro-parameters in the flat-joint model are calibrated and numerical models containing 3-D embedded flaw are established in PFC3D. Then, the numerical uniaxial compression experiment is carried out to validate the effectiveness of numerical model. The simulation results indicate that the flat-joint model is appropriate to model the cracking processes of 3-D flaw. The method of particle velocity vector field is introduced to analyze crack evolution mechanism, and four types of particle velocity vector field corresponding to typical cracks are proposed. Generally, the initiation of wing crack is tensile crack and the further propagation is mixed tensile and shear crack. However, the interaction between flaws has important impacts on the crack evolution mechanism and the specimen failure mode. In the rock bridge, wing crack may initiate as mixed tensile and shear crack. The failure mode turns from burst failure to splitting failure with the condition changing from single flaw to double flaws.

Deformation characteristics of high-porosity rock mass with a single flaw under axial loading and lateral restraint

Rock-like replicas with different dip-angle flaws were tested in an apparatus with axial loading and lateral restraint to study the stress-strain characteristics of high-porosity rock with a single flaw. The results showed that a coefficient of the lateral stress could be calculated using a coefficient of the lateral frictional resistance and frictional coefficient. It was determined that the lateral stress increases linearly with axial loading. The relationship between the flaw aperture and loading can be described by an exponential function. The high-porosity rock mass with a single flaw exhibited a creep deformation, which was practically no creep deformation during an initial loading stage and then increased remarkably when the loading pressure exceeded the uniaxial compressive strength. The internal flaw affected a lateral deformation of the porous space for a high-porosity rock replica, which was limited to outside lateral deformation, and the porosity structure collapse was the main reason for the flaw closure. Elastic-plastic stage, collapse stage, and strain-hardening stage were investigated in the rock replica stress-strain process, and the strain-hardening process was generated after the flaw closure. The volumetric ratio of fracture volume to porosity was kept constant in the first loading process, and after the porosity structure collapsed, the ratio decreased quickly, and porosity deformation played a dominant role in the overall strain. This study provided a new understanding related to research of stress-strain characteristics of fractured-porous rock.

Modeling acoustic emission in the Brazilian test using moment tensor inversion

Abstract To investigate the crack propagation and failure mechanisms of brittle materials in the Brazilian tests, an acoustic emission (AE) simulation was implemented in the Discrete Element Method. AE location and magnitude were monitored during the whole process of the simulation to detailedly observe crack initiation and associated AE evolution. Moment tensors were directly calculated by the forces and motions of the particles and decomposed into isotropic and deviatoric parts. According to the decomposition results of moment tensors, AE events (microcracks) can be classified into explosive (tensile), shear and implosive sources. Explosive sources were found to dominate both the total number and energy emission, followed by shear sources and finally implosive sources. AE distributions of different AE types were compared with the stress distribution to explore the relation between failure evolution and intrinsic stress state of the Brazilian test. Furthermore, the approach was applied to the compression test with a single flaw. Comparisons with experimental results indicated that the AE simulation can overcome the shortcoming of signal missing near the peak load in experiments and is approved to be an effective and accurate way to study rock fracture mechanism.

Dynamic fracturing process of fissured rock under abrupt unloading condition: A numerical study

Unloading can cause many geotechnical disasters, e.g., the rock burst. The underlying mechanism of rock failure is the propagation and coalescence of cracks. To get insight into rock unloading failure, the discretized virtual internal bond (DVIB) model in conjunction with element partition method (EPM) is used to simulate the dynamic fracturing process under unloading conditions. At first, the samples with the single flaw are simulated under unloading conditions. It is found that the fracturing pattern exhibits the tensile-shear transition with the initial stress level increasing. When the flaw inclination is closer to 45 degree or the flaw is longer, shear cracks are more likely to occur. Then, the unloading failure process of rock with multiple flaws are simulated. It is found that the inclination of the parallel flaws has remarkable influence on the unloading failure of rock. When the inclination angle is about 45 degree, the rock is easier to fail. For the rock with multiple randomized flaws, the amount of flaws has slight influence on acoustic emission counts. However, the configuration of randomized flaws can significantly affect the fracture process and failure patterns. These findings can improve understanding of rock burst and provide valuable references for the prediction of unloading failure of rock.

冻融循环条件下单裂隙岩体损伤破坏特征研究

冻融循环条件下单裂隙岩体损伤破坏特征研究

A Numerical Study on the Crack Development Behavior of Rock-Like Material Containing Two Intersecting Flaws

It is quite often that rocks contain intersecting cracks. Therefore, crack behavior cannot be completely studied by only considering several isolated, single flaws. To investigate the crack behavior of rock or rock-like material containing intersecting flaws under uniaxial loading, numerical simulations were carried out using parallel bonded-particle models containing two intersecting flaws with different inclination angles (varying β) and different intersection angles (varying αα). The crack propagation processes are analyzed and two typical patterns of linkage are observed between two intersecting flaws: (1) One-tip-linkage that contains three subtypes: Coalescence position near the tip; coalescence position at the flaw, but far away from the tip; coalescence position outside the flaw at a certain distance from the tip; and (2) two-tip-linkage with two subtypes: Straight linkage and arc linkage. The geometries of flaws influence the coalescence type. Moreover, the effects of intersection angle α and inclination angle β on the peak stress, the stress of crack initiation, and the stress of crack coalescence are also investigated in detail.

Predicting strength distributions of MEMS structures using flaw size and spatial density

The populations of flaws in individual layers of microelectromechanical systems (MEMS) structures are determined and verified using a combination of specialized specimen geometry, recent probabilistic analysis, and topographic mapping. Strength distributions of notched and tensile bar specimens are analyzed assuming a single flaw population set by fabrication and common to both specimen geometries. Both the average spatial density of flaws and the flaw size distribution are determined and used to generate quantitative visualizations of specimens. Scanning probe-based topographic measurements are used to verify the flaw spacings determined from strength tests and support the idea that grain boundary grooves on sidewalls control MEMS failure. The findings here suggest that strength controlling features in MEMS devices increase in separation, i.e., become less spatially dense, and decrease in size, i.e., become less potent flaws, as processing proceeds up through the layer stack. The method demonstrated for flaw population determination is directly applicable to strength prediction for MEMS reliability and design.

Effect of grout in-filling, flaw thickness and inclination angle on strength and failure pattern of rock-like specimens with single flaw

The flaws that exist in rock masses may lead to crack propagation and instability of rock masses. Epoxy resin is often used to fill in flaws and to reinforce the fractured rock masses. Previous studies on the combined influence of grouting with epoxy resin and flaw geometry (flaw thickness and inclination angle) on the strength and failure pattern of rock masses are rare. In this research, rock-like specimens with an unfilled flaw having different geometries were fabricated and tested under uniaxial compressive load under both unfilled flaw and epoxy resin filled flaw conditions. The specimens had flaw thicknesses of 1 mm, 2 mm, and 3 mm and flaw inclination angles of 0°, 30°, 45°, 60°, and 90°. The experimental results reveal that for the specimens with an unfilled flaw the UCS drops in the range of 7–17% as the flaw thickness increases, but failure patterns do not change as the flaw thickness increases. UCS also dropped as the flaw inclination angle increased from 30° to 60° and then increased when the inclination angle increased from 60° to 90°. For the specimens with an unfilled flaw, the minimum UCS of about 62% of the intact UCS of the model material was obtained for 60° flaw inclination angle. For the specimens grouted with epoxy resin, as the flaw thickness increases, the UCS decreases in the range 16–21% when the flaw inclination angle is 30°, 45°, and 60°; but the UCS changes negligibly for the flaw inclination angles of 0° and 90°. For the specimens with a grouted flaw, the minimum UCS of about 74% of the intact UCS of the model material was obtained for flaw inclination angle of 60°. For grouted flaw, a maximum UCS almost equal to the intact UCS of the model material was obtained for 0° and 90°. The failure patterns of these grouted specimens are affected by both the flaw thickness and flaw inclination angle. The strengthening factor Ds is used to indicate the grouting effect; a larger Ds represents a stronger grouting effect. When α = 0° and 90°, Ds of a specimen with a larger flaw thickness is larger than that of a specimen with a smaller flaw thickness. When α = 30°, 45°, and 60°, the thickness has little influence on the Ds in this angle range. Ds of the specimens with the flaw inclination angle of 0° is much higher (22% to 43%) than that of the specimens with the flaw inclination angles of 30°, 45°, 60° and 90° (14% to 24%). For the specimens with the flaw thickness of 1 mm, 2 mm, and 3 mm, Ds increases slightly as α increases from 30° to 60°. The effect of grouting on the failure patterns and strength of the specimens has a close relationship with the flaw thickness and flaw inclination angle. The above conclusions are new findings, which can provide useful information for estimating the failure mode and grouting effect of fractured rock masses grouted with epoxy resin.

Numerical Simulations on Cracking Behavior of Rock-Like Specimens with Single Flaws under Conditions of Uniaxial and Biaxial Compressions

AbstractThe expanded distinct element method based on a strain strength criterion was applied herein with the aim of analyzing and comparing the cracking behaviors of rock-like specimens with singl...

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.

Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase‐field method

AbstractA phase‐field method (PFM) is used to investigate cracking behaviours, including crack initiation and propagation, in interlayered rocks with preexisting flaws subjected to tension. An example with a bi‐material plate with a centre flaw is used to validate the PFM. Then, numerical simulations of cracking behaviours in interlayered rocks with a single flaw and a cross‐flaw are carried out using PFM. Moreover, the load‐displacement responses are numerically investigated. The PFM numerical results show that the crack propagation trajectories and peak loads of rock specimens depend on the preexisting flaw configuration and the mechanical properties of the interlayers.

Effect of the Interaction between Cavities and Flaws on Rock Mechanical Properties under Uniaxial Compression

Cavities and flaws are common types of defects in rock specimens that have an important impact on the mechanical properties of rockmass. In this paper, cement mortar was used to prefabricate a rock-like specimen with two cavities and a single flaw, and the uniaxial compression test was carried out. The process of fracture evolution on the specimen surface was obtained by using photography technology. The evolution regularity of a fracture was monitored by utilizing acoustic emission (AE) technology during the process of the specimen failure. Moreover, three-dimensional (3D) tomograms of specimens after uniaxial compression were obtained by using computerized tomography (CT) scanning technology, investigating the development characteristics of microcracks and the distribution of the final macrofractures. The particle flow code in two dimensions (PFC2D) program was used to simulate the mechanical behavior of brittle rock combining with microcrack propagation. The calculated stress-strain curve, AE features, and fracture distribution of the specimen obtained from the PFC2D simulation were relatively consistent with the experimental results.

Comparison of crack processes in single-flawed rock-like material using two bonded–particle models under compression

The parallel bond model (PBM), one type of basic bonded particle model (BPM), has been diffusely studied in natural rock and rock-like material. It is well-known that BPMs yield unrealistically low ratios of compressive to tensile strength (UCS/TS), friction angles and linear strength envelopes. The flat-joint model (FJM) overcomes those intrinsic deficiencies with a special structure. Thus, FJM can provide satisfactory replication of the mechanical behavior of rock-like materials. In this paper, rock-like material samples containing a single flaw were constructed with flaw angles of 0°, 30°, 45°, 60°, and 90° measured from the horizontal. The PBM and FJM were used to simulate this rock-like material. The results of the numerical simulations were compared with observations from physical tests, including strength, main types of microcracks, macroscopic fracture zones, and location and sequence of the first and secondary cracks. The results demonstrate that (1) the flaw inclination angle had a significant effect on strength; (2) the FJM results showed better agreement with respect to the main types of microcracks and macroscopic fracture zones, reproducing vertical tension failure dominance over shear failure in the rock-like material, contrary to the PBM results; and (3) using the FJM to capture the initiation location, direction, and sequence of the first and secondary cracks is recommended.