Flaw Inclination Research Articles

Experimental study on the shear mechanical behaviour of rock-like materials containing one embedded flaw under unloading normal stress conditions

It is difficult to cut internal defects, and capture the initiation and propagation of internal defects by direct observation in actual rocks. This article presents a new method to create internal defect samples by volatilisation of camphor. Then, in order to better understand the influence of unloading normal stress on shear mechanical behaviour, laboratory tests are carried out on rock-like samples containing one embedded penny shape flaw with constant shear stress and unloading normal stress under different stress paths and shear directions conditions. The failure pattern and fracture morphologies of rock-like samples with different shear paths, flaw inclination and shear direction are analyzed. The strength and deformation behaviour are investigated also. Results show that the degree of fracture surface of direct shear tests and linear normal unloading shear tests are smaller than that of the complex normal unloading shear tests. The normal unloading amount determines the failure mode of rock-like samples. The failure pattern transforms from tensile failure to shear failure when the normal unloading amount gradually decreases. Although normal unloading deformation plays an important role in rock failure, shear deformation has little effect on fracture mode.

Numerical study on full-field stress evolution and acoustic emission characteristics of rocks containing three parallel pre-existing flaws under uniaxial compression

A linear parallel bond model combined with Weibull distribution to take into account the mechanical heterogeneity of brittle rocks is used to investigate the cracking behavior, acoustic emission (AE) characteristics and full-field stress evolution of rocks containing three parallel pre-existing flaws under uniaxial compression. The intact model is calibrated to the macro mechanical properties of rocks obtained from laboratory tests. The numerical results indicate that the presence of three parallel pre-existing flaws weakens the mechanical properties of rocks. As the flaw inclination increases, uniaxial compression strength shows a trend of first decreasing and then increasing, and the elastic modulus and Poisson's ratio are roughly increasing. The displacement localization zones chronologically formed around pre-existing flaws can interact with each other, and the damage or fracture processes of pre-cracked samples are complicated. And the tensile stress in x direction concentrates around pre-existing flaws. As the flaw inclination increases, the tensile stress concentration area at the end of the pre-existing flaws in the x direction also changes, at the same time, the area of the tensile stress concentration area in the y direction gradually decreases. And AE events with high fracture intensity are located in the macroscopic shear zone or split zone.

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

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

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

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

Combined numerical and experimental studies on the dynamic and quasi-static failure modes of brittle rock

Loading rate affects not only the mechanical properties of rock but also the cracking behaviour or the failure mode. Firstly, experimental studies on the mechanical properties and the related cracking behaviour are studied based on the Carrara marble specimens containing a preexisting flaw under different loading rates. The result shows that both the compressive and tensile strengths are rate-dependent but with different sensitivities to strain rate. Meanwhile, the cracking processes of the single-flawed specimens are also found to be rate-dependent with the aid of an ultra-high-speed video system. Secondly, to investigate the mechanism behind the experimental phenomena, a material model based on the experimental strength data is proposed and applied to the numerical model. The influence of the rate-dependent strength on the cracking behaviour is studied comprehensively by using the 2D and 3D explicit dynamic FEM code. The numerical results reveal how the rate-dependent strength affect fracturing behaviour, as well as the failure stress of the single-flawed specimen. The plastic zones do not equal the damaged zone or the cracks. The dynamic loadings lead to the “X” shaped failure mode of the single-flawed specimen regardless of the flaw inclination angle. In contrast, the quasi-static loadings lead to the diagonal failure mode. It indicates that shear displacement dominates the whole cracking process under dynamic loadings, while it only dominates the failure period under quasi-static loadings.

Crack propagation mechanism in rock-like specimens containing intermittent flaws under shear loading

The rock masses, especially with existing discontinuous joints, are prone to shear failure when subjected to constant changing stress in the direction perpendicular to the free face, which may result in tunnel collapse and slope slip instability in the processes of rock engineering construction. To better understand the effect of various joint geometries on the shear behavior of rocks, the mechanism of crack initiation, propagation, and coalescence in rock-like materials (a kind of cement mortar) with intermittent flaws under shear loading is investigated using both laboratory experiments and numerical simulations. The component of moment tensor is utilized to investigate the temporal and spatial evolution of acoustic emission events and determine the geometry state of the cracks. The major principal stress and velocity field are presented to distinguish crack types and study the stress evolution associated with crack propagation. The results reveal that for specimens with various flaw dip angles the propagation direction of all newly generated cracks is basically parallel to the shearing loading, and the failure patterns of specimens are mainly controlled by tensile fractures. When the flaw inclination angle reaches 45°, the evolution of the thickness of newly generated micro cracks is controlled by the type of stress field, and after peak strength its variation mainly occurs near the tips of the pre-existing flaws. The secondary cracks obtained from the velocity field analysis mainly include tensile, compressive-shear, tensile-shear and pure shear cracks rather than simple tensile cracks, and the secondary cracks appear instantly and abundantly on both sides of the specimen. The work may shed light on the mechanism of slope slip, and provide guidance to the safe construction of engineering projects.

Full-field quantification of time-dependent and -independent deformation and fracturing of double-notch flawed rock using digital image correlation

The quantitative characterization of time-dependent and -independent deformation and fracturing of rock is crucial to reveal the short-term and long-term instability mechanisms of structural rocks. In the present paper, we conduct uniaxial constant strain rate and stress-stepping creep tests on double-notched sandstone samples with different rock bridge and flaw inclination angles. Full-field measurements of strain and crack evolution by using digital image correlation (DIC) are presented to understand time-dependent and -independent deformation, fracturing and associated crack types and failure modes of cracked rock. Results from uniaxial and creep experiments show that the flaw inclination, rock bridge inclination and time significantly affect the evolution of the strain field, and in turn change the crack propagation behaviour, and the final strength and failure mode of the rock. The vertical maximum principal stress direction is often in compression near the flaw tips, and as it moves away from the tip, the compression gradually changes to tension, while the parallel maximum principal stress direction is often in tension. Compared with short-term loading, tensile cracks such as wing cracks and far-field cracks, are prominent under creep loading conditions and can be fully developed and characterized by a longer expanded trajectory. Highlights 1. Full-field measurements of strains and crack evolution in rock with three flaw configurations by the DIC. 2. Comparative analysis of time-dependent and -independent crack types and failure modes. 3. Tensile cracks are prominent under creep loading conditions and can be fully developed.

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

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

Experimental study and particle flow modeling on 3D cracking behavior of rock-like samples with an embedded flaw

Cracking behavior of surface cracks in rock materials is extensively studied, while studies on cracking behavior of internal cracks are very limited. In this study, a new method for preparing rock-like materials containing embedded flaws is proposed using camphor sheets. A series of laboratory uniaxial and triaxial compression experiments were carried out on rock-like samples containing internal flaws. The experimental results demonstrate that the existence of an internal flaw results in a large reduction of the sample peak strength and elastic modulus. As the flaw inclination angle increases, the peak strength of flawed sample decreases, and the failure mode varies from the combined shear-tension failure to shear failure and then to splitting failure. Three 3D wing cracking patterns, which mainly occur in small flaw inclination angles, and one 3D shear cracking pattern, which mainly occurs in larger flaw inclination angles, are identified in the experiment. And then PFC3D was used to simulate cracking behavior of rock-like samples with internal flaws, and the simulated results (including stress–strain curve and failure modes) are in good agreement with the experimental results. The crack evolution mechanism in rock-like samples containing internal flaws is revealed by analyzing micro-crack propagation, contact force chain, and displacement field.

Shaking Table Test on the Tunnel Dynamic Response under Different Fault Dip Angles

Fault-crossing tunnels are often severely damaged under seismic dynamics. Study of the dynamic response characteristics of tunnels crossing faults is thus of great engineering significance. Here, the Xianglushan Tunnel of the Central Yunnan Water Diversion Project was studied. A shaking table experimental device was used, and four sets of dynamic model tests of deep-buried tunnels with different fault inclination angles were conducted. Test schemes of model similarity ratio, similar material selection, model box design, and sine wave loading were introduced. The acceleration and strain data of the tunnel lining were monitored. Analysis of the acceleration data showed that when the input PGA was 0.6 g, compared with the ordinary tunnel, the acceleration increases by 117% when the inclination angle was 75°, 127% when the inclination angle was 45°, and 144% when the inclination angle was 30°. This indicates that the dynamic response of the cross-fault tunnel structure was stronger than that of the ordinary tunnel, and the effect was more obvious as the fault dip angle decreased. Analysis of the strain data showed that the strain response of the fault-crossing tunnels was more sensitive to the fault dip. The peak strain and increase in fault-crossing tunnels were much larger than those of ordinary tunnels, and smaller fault dips led to larger increases in the strain peak; consequently, the tunnel would reach the ultimate strain and break down when the input PGA was smaller. Generally, the influence of fault inclination on the dynamic response of the tunnel lining should receive increased consideration in the seismic design of tunnels.

Dynamic model to predict vibration characteristics of rolling element bearings with inclined surface fault

The dynamic behavior of rolling element bearings has been a complex phenomenon in high speed rotating machinery. Consistent fluctuations in load and speed lead to induct faults on the bearing surface. This work investigates the effect of inclined surface faults on the dynamic response of rolling element bearings. The dynamic model for the rotor-bearing system is derived using Dimensional analysis considering the angle of inclined surface faults, rotor speed, load, and significant bearing parameters. Vibration responses of double row spherical roller bearing are experimentally investigated to analyse the effects of size and slope angle of the artificially developed inclined surface faults. The results indicate that increasing surface fault inclination angle significantly decreases the relative vibration amplitude under diverse rotor speed but rises with increasing fault depth. This empirically obtained variation in the vibration amplitude helps to predict the bearing surface fault inclination. This dynamic model to predict the effect of inclined surface faults using the Dimension principle found efficient and contributed to the condition monitoring in process industries.

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.

Numerical assessment of the rate-dependent cracking behaviours of single-flawed rocks in split Hopkinson pressure bar tests

This paper numerically investigated the rate-dependent progressive cracking behaviours of single-flawed rock specimens in split Hopkinson pressure bar (SHPB) tests. First, a 3D numerical SHPB system is established based on the discrete element method (DEM). By comparing with our laboratory experiments, micro-parameters of the DEM model are calibrated, which guarantees the reliability of the numerical simulations results. Via slice-cutting view, the inner and surface progressive cracking processes are explicitly revealed and compared, which compensates some defects in laboratory tests. Our numerical simulation results show that the progressive cracking behaviours of the single-flawed rock specimens exhibit evident rate dependence. Under low strain rates, tensile wing cracks dominate the entire cracking process, and only a few shear cracks appear during the post-peak stage. In contrast, under high strain rates, tensile wing racks are significantly suppressed, while anti-wing cracks and shear cracks are fully developed, leading to the final X-shaped failure modes. In addition, progressive cracking behaviours of the single-flawed rock specimens with different flaw inclination angles are assessed. Via stress field visualization and theoretical analysis, the different initiation locations of tensile wing cracks are explained. Furthermore, based on the generalized maximal tangential stress (GMTS) criteria, the fracture initiation angles of tensile wing cracks are predicted. The results show that the fracture initiation angles and the fracture process zone (FPZ) are significantly affected by the strain rate. The length of FPZ under dynamic loads is evidently longer than that under static loads, and the length of FPZ generally increases with an increasing strain rate, exhibiting evident rate dependence.

Experimental and Theoretical Study of Failure Characteristics of Rock Containing Single 3D Internal Open-Type Flaws

A 3D internal open-type flaw inside gypsum rock-like specimens is prepared using a volume-loss method. It has three types of flaw inclinations and four types of flaw strike lengths. Uniaxial compression and acoustic emission monitoring tests show a small range of secondary local failures are initially distributed near the internal flaw. The area of these secondary failures remains stable and does not extend to other positions until the uniaxial compression strength status of specimens is reached. To explain the special test results, which have rarely been seen in previous 2D fractured rock studies, the surrounding rock of the internal open-type fracture is simplified as a rectangular board model with fixed boundary conditions on four sides. Theoretical calculations prove that a Destruction Region (secondary tensile failures) occurs in the central parts of the internal free surface as built from the internal flaw and is surrounded by a circular Anti-destruction Region. (The rock is under triaxial compression, and tensile failure cannot develop.) Once rock in the Anti-destruction Region reaches its triaxial compressive strength, the constraining effects on the secondary tensile failures disappear. These theoretical analysis results are consistent with experimental phenomena and provide an important reference for geotechnical engineering under similar conditions.

Mechanical properties and fracture behavior of flawed granite under dynamic loading

The dynamic mechanical properties and fracture process of rock materials with pre-existing flaws are crucial for explaining the failure mechanisms of deeply buried constructions. To investigate the mechanical properties and fracture behavior of flawed granite subjected to dynamic loading, dynamic experiments were conducted on granite specimens by using a split-Hopkinson pressure bar test system. The effects of strain rate and flaw inclination angle on granite strength and deformation properties were investigated. The white patch initiation, micro-crack propagation, and failure mode were analyzed using a high-speed camera and digital image correlation technology. The fracture mechanism was revealed by quantitatively analyzing the localized strain field and fractal features. The results demonstrated that the dynamic strength and deformation of the flawed specimen compared to an intact specimen had more obvious strain rate effects. The development of white patches determined the direction and path of crack propagation. The fracture process and shear-tensile failure mode were closely correlated with the evolution of the strain field. Furthermore, the fractal characteristics indicated that a larger fractal dimension resulted in a more complex fracture distribution and mixed failure modes. These results provide a reference for the construction design and safety control of deep rock engineering.

Compressive strength of flawed cylindrical specimens subjected to axial loading

Discontinuities are known to have a significant impact on the engineering characteristics of the rock masses, governing their potential failure pattern, increasing their deformation, and reducing their strength. In particular, the impact of non-persistent joints on the strength and failure mechanism of rock mass needs to be investigated further. The impact of different flaw geometrical characteristics such as flaw inclination, flaw length, flaw aperture, and flaw filling on uniaxial compressive strength of specimens has not been investigated thoroughly. In this paper, a series of uniaxial compression tests were conducted on cylindrical specimens containing an open central flaw. The effect of different parameters such as flaw inclination, flaw length, flaw aperture, and filling on the uniaxial compressive strength of specimens have been investigated through laboratory experiments. Response Surface Methodology (RSM) is adopted to analyze the impact of flaw parameters on the compressive strength of the constructed samples. The results of the experiments show that flaw inclination and flaw length have a significant impact on the peak strength of the samples, meaning that strength increases by growing of flaw angle and decreases by increasing of flaw length. In addition, at a low flaw length, aperture affects the UCS significantly, while by increasing flaw length, its effect decreases dramatically, and strength drops at a flaw inclination of 45 degrees. Conversely, at a higher flaw length, by increasing flaw inclination, the UCS increases constantly. It also has been observed that changing the flaw aperture had no important effect on the peak strength.

Numerical Analyses of Fracturing Behavior and Strength of Specimens with Two Parallel Infilled Flaws under Uniaxial Compression

Grouting is a common method used to fill rock joints to improve the stability and integrity of rock mass in geotechnical engineering, and the filling has been observed to have an effect on crack behavior and mechanical property. To investigate this topic, a numerical study of crack behavior and mechanical property of rock samples with two parallel open flaws or infilled flaws under uniaxial compression was conducted in this research. The smooth joint model was proved to be suitable to simulate the interface between rock material and grout material. The occurrence of shear cracks at the interface between rock material and grout material as well as the occurrence of tensile cracks in the grouting material has been successfully simulated in this research. Numerical results indicate that grouting can reduce the tensile force near the flaws, suppress the generation of tensile cracks, and improve the initiation stress of the sample. The tensile force in the specimens with infilled flaws is smaller than that with open flaws, which lead to the improvement of the peak strength of the sample. Moreover, crack development and mechanical properties of samples are affected by bridge inclination angle and flaw inclination angle.

Reverse migratory behaviour of the earthquakes aftershock sequences along Himalayan Seismic Belt, Northwest Himalaya

The Anderson's theory (Anderson, 1951) can be utilized to understand the allocation of principal stresses. For various tectonic regimes, the global seismicity trend for crustal earthquakes of less than 20 km depth suggests that the source fault inclination also plays a critical part in the propagation of the aftershocks in the subsurface rupture with respect to the mainshock earthquake. It has also been observed that majority of the compression earthquakes that display upward seismicity migration typically occur along steep faults. However, in the context of Himalaya seismicity, the opposite migratory behaviour of the aftershock sequence is observed even along the gentle dipping source faulting. The failure envelope Mohr's diagram is used to understand the alteration in the dynamics of the subsurface locked zone of Himalayan Seismic Belt (HSB). This study discusses the alteration in the effective strength of the rock mass which imply the variation in the crustal hydrostatic fluid pressure at shallow depth (0–15 km). Different earthquakes and their aftershocks sequence of Himalayan terrain have been incorporated to corroborate the role of orientation of tectonic principal stresses, subsurface morphology and fluids/partial melts if present. In addition, topography contributes to the vertical loads and development of the subsurface geometry, therefore its role and its influence on seismicity has been discussed. This study highlights the controlling factors and the trend of the principal applied stresses and subsurface fluids in the distribution of aftershock sequences along tectonic regime of the Himalayan arc.

Strain localization and cracking behavior of sandstone with two gypsum-infilled parallel flaws

The infilled flaws within rocks significantly influence the mechanical behavior of non-through flawed rocks. To investigate the influence of infilling on strain localization in the pre-cracking, cracking and cracking coalesce stages, experimental and numerical investigations were conducted on sandstone containing two gypsum-infilled parallel flaws, but of different flaw geometric configurations. The full-field strain evolution and progressive cracking process are analyzed using the acoustic-optical-mechanical methods, while the stress evolution and stress transfer by infilling were studied by the particle flow code modeling. The results show that the major principal strain of flawed sandstone with infilling changes from the diffused ellipse to highly localized linear strip with the increase of loading level, while the shear strain keeps a diffused ellipse shape invariable. The shear strain localization of infillings with a large flaw inclination initiates at a lower loading level than that of small one. The peak strength and Young’s modulus of flawed sandstone show a first decrease, then increase and finally decrease trend with the ligament angle increasing from 0° to 150°, and both achieve their minimums at 60°. Ten types of cracks were observed, and four patterns of crack coalescence were identified. By comparison with sandstone of open flaws, the flaw infilling simplifies the geometric pattern of produced crack networks, which is quantitatively characterized by fractal dimension analysis. The numerical modeling shows that the infilling enlarges the compressive bond force zone and decreases the tensile bond force zone in the surrounding areas of pre-existing flaw, thus increasing the reinforcement coefficient. Moreover, the flaw geometric configuration has a significant influence on the reinforcement coefficient. It is also found that the increment of reinforcement coefficient defined by crack initiation stress is greater than those defined by either crack coalescence or peak stresses.

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

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