Flaw Inclination Angle Research Articles

Study on Freezing-Thawing damage mechanism and evolution model of concrete

Freezing-thawing (F-T) cycle is one of the main reason of concrete damage in cold regions. F-T cycle mainly lead to degradation of macroscopic mechanical properties of concrete by changing the number of micropores, mesopores and macropores, and causing severely damage to its internal texture. The variations of the physical and mechanical properties of concrete sample with different inclination angle of internal flaw exposed to different F-T cycles (0, 10, 30 and 50 cycles) under unconfined compression condition was deeply investigated based on the acoustic emission (AE) and nuclear magnetic resonance (NMR) technology. The evolution of the internal cracks are tracked in real-time by AE monitoring systems during the entire test process. Meanwhile, the micro-structure of the concrete sample after F-T cycle treatment is microscopically observed with T2 distribution by low-field nuclear magnetic resonance. The results show that the peak strength of concrete decreases with the increasing F-T cycles and increases as the increasing inclination angle of prefabricated flaw. The elastic modulus decreased gradually with the increase of F-T cycles. The elastic modulus of the sample without F-T cycles treatment increases with the increase of inclination angle of prefabricated flaw. As the flaw inclination angle increases from 0° to 90°, the F-T cycles increases from 0 to 50, the peak strain shows an obvious discreteness without monotone change. When the number of F-T cycle reaches 50, concrete blocks fall off from the sample surface. A continuum damage model considering F-T damage from different pore size is finally introduced to describe the damage evolution of concrete during compression test. The research results can be used to quantitatively evaluate the strength of concrete samples treated by F-T cycle without mechanical tests.

Experimental study on the dynamic behavior of sandstone with coplanar elliptical flaws from macro, meso, and micro viewpoints

A series of dynamic tests were performed using a split Hopkinson pressure bar device to investigate the effect of coplanar elliptical flaws with a range of inclination angles on the dynamic behavior of sandstone specimens. The fracturing process was studied from macro, meso, and micro perspectives using a combination of strain gauge (SG), digital image correlation (DIC), and scanning electron microscope (SEM) techniques, respectively. The results show that the dynamic compressive strength and Young’s modulus negatively correlate with the flaw inclination angle. The dominant diagonal shear cracks penetrating the entire specimen ultimately led to slippage along the long axis for small inclination angles (30°, 45°), whereas tensile cracks dominated the macroscopic collapse for specimens with inclination angles larger than 45°. Shear and tensile cracks were effectively identified by DIC and their microscopic surface morphologies by SEM. The strain energy release path was also sensitively related to the flaw inclination angle.

Crack propagation mechanism of rock-like specimens containing non-parallel flaws subjected to internal hydraulic pressure and shear loading

The rock masses with existing discontinuous joints are more prone to failure under the combination of fissure water and shear loading. Therefore, combining laboratory experiments with discrete element simulation, the mechanism of crack initiation, propagation, and coalescence in rock-like specimens (a type of high brittle cement mortar material) with non-parallel flaws under shear loading and internal water pressure is investigated. 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. When the flaw inclination angle reaches −30°, the cracks initiated near pre-existing flaw tips are the result of the combined effects of fluid pressure and compressive stress fields. Compared with the hydraulic fracturing curve, both plateau period and water pressure fluctuations appear in the selected domain near the crack propagation paths, which can demonstrate that the evolution of water pressure is extremely complex due to the constant crack healing and opening. With the increase of water pressure, the global stress field becomes more uniform, and the stress concentration near pre-existing flaw tips is weakened, indicating that water pressure can lead to local stress redistribution. Ultimately, the work is expected to provide guidance to the safe construction of tunnel excavation under complex geological conditions.

Strength and the cracking behavior of frozen sandstone containing ice‐filled flaws under uniaxial compression

AbstractUnderstanding the mechanical properties of frozen flawed rock masses is fundamental to conducting safe rock engineering in frozen rock strata. However, there has been scarce research in this area, especially on key issues such as the strength and deformability of frozen flawed rock masses and failure processes under load. In this paper, frozen flawed sandstone was subjected to uniaxial compression and the cracking process was observed. The influences of flaw inclination angle and freezing temperature on the strength and cracking behavior of frozen flawed sandstone under load were determined. The results show that: (a) the strength of frozen flawed sandstone increases with increases in flaw inclination and decreases in temperature; (b) the flaw inclination has a dramatic influence on both the crack coalescence behavior and the final failure form of frozen flawed samples under compression; and (c) the significant influence of freezing temperature on the cracking behavior of frozen flawed sandstone is caused by the interaction between flaw ice and its surrounding rock. Strengthening of flawed sandstone by freezing results because (i) pore ice provides support and cohesion at the pore scale, while (ii) at the crack scale ice can support the flaw and resist its deformation during compression, and cementation of the ice–rock interface provides normal and tangential cracking resistance.

Dynamic Mechanical Response, Cracking Behavior, and Stress Intensity Factors of Cement Mortar Specimens with Open and Closed Flaws

Major civil and military infrastructures are usually located in mountainous areas with complex geological structures. When subjected to impact loads caused by operational blasting or seismic activities, the inherent flaws or joints in the hosting rock mass may grow irreversibly and eventually and cause the entire structure to collapse. It is, therefore, desirable to understand the mechanical and cracking behaviors of flawed rock structures under dynamic loads. In this work, the cement mortar is used to make the plate specimens, and two different types of flaws, i.e., the open and the closed (resin-filled) flaws, with different inclination angles from 0° to 90° with respect to the loading direction are prefabricated. The nominal strength, crack initiation, and failure characteristics of the specimens under different loading rates are investigated using the split Hopkinson bar (SHPB) system in conjunction with the digital image correlation (DIC) technique. The results indicate that the dynamic nominal strength of both two types of specimens shows similar loading rate and flaw angle dependency, specifically, monotonically increasing with the increase of the loading rate while increasing first and then decreasing with increasing the flaw inclination angle. The strength of specimens with an open flaw is obviously lower than that of the specimens with a closed flaw at a similar loading rate. Besides, the failure mode of specimens with an open flaw is mainly an X-shaped tensile or tensile-shear mixed form regardless of the flaw inclination, whereas the resin-filled flawed specimens always fail in the form of an atypical X-shaped shear pattern with obvious randomness. Moreover, the stress field around the crack tip is carefully extracted based on the obtained displacement field from DIC analysis; the stress intensity factors at crack initiation onset also show flaw inclination- and loading rate-dependent behavior. The strength, cracking behavior, and stress field around the tip during the dynamic loading are closely related to the friction effect between the flaw surfaces. The findings in this work provide some basic insights into the cracking mechanism of rock with open and closed flaws under dynamic loading conditions.

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.

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.

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.

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.

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.

Mechanical properties and reinforcement effect of jointed rock mass with pre-stressed bolt

Pre-stressed bolt anchorage is the key technology for jointed rock masses in rock tunnelling, slope treatment and mining engineering. To investigate the mechanical properties and reinforcement effect of jointed rock masses with pre-stressed bolts, in this study, uniaxial compression tests were conducted on specimens with different anchoring types and flaw inclination angles. ABAQUS software was used to verify and supplement the laboratory tests. The laws of the uniaxial compressive strength (UCS) obtained from the numerical simulations and laboratory tests were consistent. The results showed that under the same flaw angle, both the UCS and elastic modulus of the bolted specimens were improved compared with those of the specimens without bolts and the improvements increased with an increase in the bolt pre-stress. Under the same anchoring type, the UCS and elastic modulus of the jointed specimens increased with an increase in the flaw angle. The pre-stressed bolt could not only restrain the slip of the specimens along the flaw surface but also change the propagation mode of the secondary cracks and limit the initiation of cracks. In addition, the plot contours of the maximum principal strain and the Tresca stress of the numerical models were influenced by the anchoring type, flaw angle, anchoring angle and bolt position.

Modelling micro-cracking behaviour of granite during direct tensile test using cohesive GBM approach

We employed a cohesive grain-based model (GBM) to investigate the mechanical behaviour and micro-cracking response of Neuhauser granite under direct tensile loading. The microstructural properties of Neuhauser granite were incorporated into the numerical model, and hourglass-shaped specimens were generated based on the geometrical configuration of specimens. We proposed an alternative calibration procedure, and the numerical observations revealed that the cohesive GBM could accurately reproduce the failure behaviour of physical specimen. At the same time, the conventional GBM failed to return a reliable output. The calibration procedure was augmented by examining the impacts of the random distribution of minerals and tensile loading rate on the fracture behaviour of GBM specimens. Besides, pre-cracked granite was generated to investigate the influence of pre-existing cracks on mechanical and fracture behaviour. By increasing the flaw inclination angle, the peak tensile strength of both single and double flaw specimens was increased. The micro-cracks initiated from flaw tips and extended horizontally towards the side of specimens. At low flaw inclination angles, the macroscopic tensile fracture was almost identical to that of intact rock while the fracture pattern was different at high flaw angles.

Mechanical behavior and failure analysis of fracture-filled gneissic granite

Grouting reinforcement is a common way to strengthen fractured rock mass in rock engineering, which will transform the natural open flaws in rock mass into filled flaws. The existence of fillers will change the stress state of the flaws, thus affecting the mechanical properties and cracking behavior of fractured rock mass. In this paper, uniaxial compression experiments were carried out on granite specimens in four different filling states to study the effects of different filling materials on the strength, fracture behavior and strain state of flawed rock specimen. The experimental results show that compared with the unfilled specimen, the fillers can improve the strength of the specimen, delay the crack initiation and reduce the strain at the flaw tip, but these effects will weaken with the increase of the flaw inclination angle. In addition, the effect of fillers varies with different filling materials, and the effect of resin and gypsum fillers is significantly greater than that of silicone filler. Moreover, the mechanism of the interaction between filler and rock specimen is analyzed. The results reveal that the fillers can reduce the flaw tip stress, which is related to filling material parameters. This reduction of flaw tip stress will be more significant with the increase of the elastic modulus of the filling material, the friction angle and cohesion of the interface between rock and filling material.

Experimental Investigation of Dynamic Fracture Patterns of 3D Printed Rock-like Material Under Impact with Digital Image Correlation

This paper presents the results of an experimental study on the dynamic fracture behaviour of 3D printed rock-like disc specimens with various pre-existing flaw configurations under high strain rate loading. The 3D printing technology is utilized to prepare disc specimens containing a single or a pair of unfilled or filled flaws. A split Hopkinson pressure bar is employed to generate high rate loading on the specimens, while the digital image correlation (DIC) technique is adopted to determine the type of new cracks, and their initiation, propagation paths and coalescence types. The results show that the dynamic strengths of the 3D printed specimens are higher than the quasi-static ones. When under high strain rate loading, not only can the specimens with filled flaws carry more load than the corresponding specimens with an unfilled flaw, but also their cracking pattern is different as compared to the unfilled flaw counterpart. It is interesting to note that the dynamic peak loads are not dependent on the flaw inclination angle, while the quasi-static peak loads show obvious flaw inclination angle dependence. Moreover, DIC results reveal that under some specific flaw configurations, the filling material undergoes shear strain concentration and a shear band develops inside the filled flaws. Overall this study confirms the strong effects of the flaw configurations and filling material on the deformation and crack patterns of the 3D printed rock-like materials under impact loading.