Coplanar Flaws Research Articles

Experimental and numerical investigation of the fracture behavior in granite specimens with two co-planar side flaws under biaxial loading

It is well known that the structural plane plays a decisive role in the mechanical properties of rock mass. To better understand the cracking mechanism and stress characteristics of co-planar intermittent double-flawed granite specimens with various dip angles (Abbreviated as flawed specimens), two co-planar flaws were prefabricated on both sides of the granite, and biaxial compression tests were conducted. The failure characteristics and local microstrain were recorded by the camera and strain acquisition instrument. The evolution law of mechanical parameters of flawed specimens was analyzed. Simultaneously, a two-dimensional particle flow code (PFC2D) was used to establish a biaxial compression model of flawed specimens. The crack initiation and propagation of the specimens were explained by the crack hot spot, the evolution law of crack, and the evolution law of the number of microcracks. It is found that (a) as flaw dip angle (α) increases, peak strength and elastic modulus initially decrease and then increase, with reductions ranging from 17.6% to 46.1% and 15.6% to 48.2%, respectively. (b) Increasing lateral stress (σ2) triggers a shift in failure mode from a tensile-shear mixed failure to a shear failure. The cohesion (c) and friction angle (φ) of flawed specimens were notably smaller compared to those of intact specimens, with reductions correlating with the α. (c) Flawed specimens exhibit pronounced contact force concentration and stress concentration at the flaw tip. The analysis of the microstrain confirms stress concentration at the flaw tip, leading to failure. However, various σ2 induces the differences in the magnitude and extent of tip stress.

Failure behaviour of frozen rock with double ice-filled flaws under Brazilian splitting tension

Geotechnical engineering in cold regions frequently involves dealing with frozen fractured rock masses, particularly in the activities of strip mining and tunnel support design, where tensile failure predominates as the main failure mode in stress-driven failures. Seasonal freezing can adversely affect the performance of rock masses. To investigate the tensile characteristics of frozen rock masses, marble specimens with double parallel ice-filled flaws were artificially frozen and subjected to Brazilian splitting experiments at a loading rate of 0.001 mm/s. The influence of the angle of the double coplanar flaws and the rock bridge angle of ice-filled flaws on the tensile behaviours were numerically studied by RFPA3D (3D Rock Failure Process Analysis), a finite element method specifically developed for simulating rock failure. Results showed that as the angle of the double parallel ice-filled flaws increases, tensile strength initially decreases and then increases. Furthermore, in specimens with the double coplanar ice-filled flaws, an increase in the angles of the flaws and rock bridge leads to a gradual decrease in tensile strength. The spatial distribution of ice-filled flaws is a crucial factor that influences the failure mode after split cracking occurs. The ice filling and bonding mechanism controls the tensile strength and cracking behaviour of frozen rock masses. The findings of this study provide valuable insights and serve as a theoretical foundation for designing blasting parameters and disaster prevention in strip mines located in cold regions.

Interaction between flaws and failure characteristics of red sandstone containing double flaws under compressive-shear loading

The failure characteristics of the fractured rock mass and the interaction between flaws were significantly affected by the flaw configurations. This study quantitatively investigated the effect of flaw geometries on the interaction between flaws under compressive-shear loading. The evolution of the surface strain field was recorded and analyzed using digital image correlation (DIC) technology, enabling the localization of crack paths and the determination of crack initiation mechanisms. Combined with DIC and scanning electron microscopy, both the macroscopic and microscopic failure characteristics of specimens with double flaws subjected to compressive-shear loading were comprehensively investigated. The results showed that the axial peak force of flawed specimen was sensitive to the flaw configuration, and the axial peak forces of flawed specimens with parallel flaws were greater than those with coplanar ones. The tensile strain was the primary factor dominating the initiation and propagation of cracks from flaw tips, whereas the cracking mechanism of edge cracks was a combination of tensile and shear strains. In addition, two novel parameters, namely independent parameter Ri and reinforced parameter Rr, were proposed to quantitatively characterize the independent effect discovered between coplanar flaws and the reinforced effect between parallel flaws, respectively. Besides, it was observed that the flaw configuration has a significant effect on rock failure characteristics, and three typical crack coalescent modes were found. The findings of this paper could facilitate a better understanding of the interaction between flaws and rock failure characteristics subjected to compressive-shear loading conditions.

Numerical simulation the fracture of rock in the framework of plastic-bond-based SPH and its applications

In this paper, a two-dimensional numerical approach named plastic-bond-based smoothed particle hydrodynamics (PB-SPH) is proposed to simulate the fracture of rock with pre-existing flaws. Under the PB-SPH framework, interaction particles are interconnected through bonds. The Drucker–Prager criterion of a tensile zone cut-off coupled maximum tensile stress criterion is applied to judge shear failure and tensile failure. To verify the capability of the PB-SPH method in simulating rock fracture behavior, two-dimensional numerical simulations of a single flaw, two coplanar flaws, and multiple flaws of uniaxial compression are carried out. Compared with previous experimental and numerical results, the present numerical results show good agreements on crack initiation positions, crack morphology and crack patterns. The numerical simulation of the progressive failure process of rock slope with multiple flaws is carried out, which shows that the PB-SPH method can be well applied to rock mechanics engineering. The present results show that the PB-SPH method has a certain reference in the study of rock fracture mechanics and the application of rock mechanics engineering.

A Study On Effects of Flaw Shape Idealization On the Interaction of Co-Planar Surface Flaws Subjected to Tension Load

Abstract Engineering Critical Assessment (ECA) guidelines contain rules to assess flaw interaction. Major flaw dimensions (depth or height and length) are typically characterized assuming the flaws to be contained entirely within a bounding rectangle through a procedure known as flaw idealization. In fracture mechanics based calculations, flaws are often assumed to be (semi-)elliptical when evaluating possible interaction. This paper investigates the implication of this simplification for the specific case of two identical co-planar surface breaking flaws. Two flaw shapes are considered and compared: semi-elliptical and canoe-shaped (quarter-circular ends with constant depth elsewhere). Especially for long and shallow flaws, the canoe-shaped configuration best approximates the bounding rectangle, whereas the semi-elliptical shape only touches the bounding rectangle at three points (deepest point and two points at the surface). Several flaw dimensions and spacing distances are studied through an extensive parametric study comprising both linear elastic and elastic-plastic finite element simulations. The results, evaluated in terms of stress intensity factor (SIF) and J-integral, show that the flaw shape idealization, particularly for long and shallow flaws, can significantly affect the degree of interaction between identical co-planar flaws. The inconsistency between semi-elliptical and canoe-shaped flaw shapes is observed in a linear elastic analysis and becomes more pronounced at higher loading levels evaluated in elastic-plastic analyses

Researches on Crack Propagation of the Two Filled Noncoalescent Coplanar Flaws under the High Strain Rate Loading by means of AUTODYN-Based Simulation

To study the influence of fillings on rock failure. By turning to the Drucker-Prager strength model and cumulative damage criteria, investigations are made, with the nonlinear AUTODYN software, into crack propagation behaviors in crack-filled and unfilled specimens under uniaxial dynamic loading. Under investigations are crack initiation position, sequence and angle, and coalescence mode. According to the mode of propagation and coalescence, cracks are divided into three types, i.e., the tensile wing, the antiwing, and the horsetail. The simulation results show that under uniaxial dynamic loading, differences are found in initiation position, angle, and coalescence mode for specimens with cracks filled or otherwise. However, filling does not affect crack initiation sequence. Under the same loading, the damage to filled specimen is less severe than that to the unfilled specimen.

A comparative study on the crack development in rock-like specimens containing unfilled and filled flaws

Rock masses consist of various discontinuities that significantly affect the crack development patterns which dominates the ultimate failure of geostructures. The interaction of the pre-existing flaws with each other and with the newly formed cracks is complicated and demands a comprehensive investigation. This paper couples the 3D printing technology with the digital image correlation (DIC) and the bonded particle model (BPM) to study failure of rock-like specimens with pre-existing flaws. Systematic flaws configurations are considered including single, coplanar, partially overlapped and fully overlapped arrangements. The flaws are considered to be unfilled and filled with a weak material. The DIC strain and BPM displacement vectors analysis indicate the strong effects of the filling material on the deformation behaviour of the 3D printed specimens. The failure pattern of the single filled flaws is transformation from compressive failure (0°) to shear failure (15°–60°) and to tensile failure (75°–90°). However, in the coplanar flaws failure is transformation from compressive (0°) to mixed-mode compressive shear (15°-30°), then to shear (45°), to mixed-mode tensile-shear (60°–75°) and then to pure tensile (90°). However, the partially coplanar filled flaws all (except 0° which is compressive failure) exhibit mixed-mode failure in the order of compressive-shear (15°–30°) and transformation to the tensile-shear (45°–90°). BPM displacement vectors revealed five crack types in the specimens by the analysis of the relative movement of the vectors in some critical locations such as flaws tips, rock bridge and coalescence zone. Moreover, a new coalescence type was identified in the 15° flaw (either unfilled or filed) which is named Type X and is a mixed-mode shear tensile crack with a coplanar secondary shear crack. Furthermore, it is observed that the peak load of the filled specimens are much higher than that of the unfilled ones because the filling material requires extra energy to fracture and thus the filled specimens can carry larger load before fail.

Numerical Analysis of Fracture Behaviour on Marble Samples Containing Two Flaws

Uniaxial compression tests were conducted on marble specimens containing two flaws. There are coplanar flaws and noncoplanar flaws. The inclination angle and spacing of flaws were considered of the coplanar flaws model, and the step angle and spacing of flaws were considered of the noncoplanar flaws model. Strength failure and crack coalescence behaviour were analysed in the paper. The crack evolution process containing microcrack initiation, coalescence, and failure is focused on the rock bridge coalescence and the extent of the pre‐existing flaws. There are four forms of rock bridge coalescence: tensile crack coalescence, shear crack coalescence, mixed tensile and shear crack coalescence, and no coalescence. Also, there are four forms of the rock failure mode: tensile failure, shear failure, mixed tensile and shear failure, and split fracture. The outer end of the critical stress values were used to compare with the crack initiation strengths, and the crack initiation strengths were slightly larger than the critical stress. In addition, energy dissipation laws were analysed during the model fracturing process. The crack evolution mechanisms around the pre‐existing flaw in the model were revealed by the distribution of microcrack and energy dissipation.

DEM modeling of crack coalescence between two parallel flaws in SiC ceramics

Abstract A discrete element model (DEM) of SiC ceramics containing two parallel flaws was used to study crack coalescence under uniaxial compression with different flaw inclination angles, ligament lengths, and ligament angles. A relationship is proposed between coalescence stress state, flaw inclination angle, and horizontal component of the ligament length during the failure process. The effects of coplanar flaws on various characteristics of the specimen, viz. compressive strength, Young's modulus, crack initiation stress, and Poisson's ratio, were studied. Coalescence modes between two parallel flaws observed in the DEM model were in good agreement with nine crack coalescence categories summarized in experimental studies. Meanwhile, the corresponding stress state at the moment of coalescence can be classified into three types – pre-peak, mid-peak, and post-peak. The results also showed that the horizontal component d of the ligament length of parallel flaws significantly influences the coalescence stress state. When parallel flaws overlap in the loading direction (d

Flaw interaction rules given in BS 7910:2013 – The history and the way forward

Information on flaw size, shape, location and interaction with the neighbouring flaws is essential to the fitness for service assessment or engineering critical assessments of components with crack-like flaws. In 2013 edition of BS 7910 the flaw interaction criteria was systematically decoupled into alignment of non co-planar flaws and combination of co-planar flaws. The alignment criteria is unchanged from the earlier edition of the BS 7910 and is based on comparing the crack tip separation with the average flaw heights. The criteria for combination of two in-plane co-planar flaws has been updated for fracture driven modes such that interacting flaws are no longer allowed to touch and are now based on the flaw height for the long shallow (a/c < 1) flaws, where a is flaw height and c is half flaw length The paper summarises the background to the flaw interaction rules, the rationale behind the updated criteria for flaw interaction and charts the way forward for further developments in flaw interaction criteria.

Numerical simulation of shear mechanism of concrete specimens containing two coplanar flaws under biaxial loading

In this paper, the effect of non-persistent joints was determined on the behavior of concrete specimens subjected to biaxial loading through numerical modeling using particle flow code in two dimensions (PFC2D). Firstly, a numerical model was calibrated by uniaxial, Brazilian and triaxial experimental results to ensure the conformity of the simulated numerical model\'s response. Secondly, sixteen rectangular models with dimension of 100 mm by 100 mm were developed. Each model contains two non-persistent joints with lengths of 40 mm and 20 mm, respectively. The angularity of the larger joint changes from 30 to 90. In each configuration, the small joint angularity changes from 0 to 90 in 30 increments. All of the models were under confining stress of 1 MPa. By using of the biaxial test configuration, the failure process was visually observed. Discrete element simulations demonstrated that macro shear fractures in models are because of microscopic tensile breakage of a large number of bonded discs. The failure pattern in Rock Bridge is mostly affected by joint overlapping whereas the biaxial strength is closely related to the failure pattern.

Mechanical and cracking behavior of granite containing two coplanar flaws under conventional triaxial compression

Flaws widely exist in rock mass, which significantly influences the strength and failure behavior of rock. The study of the flaw effect on the mechanical and cracking behavior is important to predict the unstable failure of fractured rock engineering. However, three-dimensional crack propagation behavior of real rock containing preexisting flaws under triaxial compression has been rarely studied. To increase the understanding of crack coalescence behavior, a series of laboratory conventional triaxial compression experiments were carried out on granite specimens containing two coplanar three-dimensional flaws. On the basis of experimental results, the effects of flaw angle and confining pressure on the strength properties of granite specimens were analyzed. As the flaw angle increased from 30° to 60° and the confining pressure increased from 0 to 30 MPa, the triaxial compressive strength and crack damage threshold of granite specimen increased. The cohesion and internal friction angle of preflawed granite specimen increased with increasing flaw angle. And then, X-ray micro-CT scanning technique was used to investigate the internal fracture characteristic of granite specimen. Four typical crack coalescence modes were identified in this experiment, i.e. no coalescence, two types of indirect coalescence, and shear coalescence. Under uniaxial compression, cracks from the tips of the flaws led to the specimen failure under tension, while under higher confining pressure, shear cracks and antiwing cracks were dominant.

A combination rule for multiple surface cracks based on fatigue crack growth life

A plate under cyclic loading, containing two coplanar surface flaws with both identical and dissimilar sizes, is considered in the present study. By conducting detailed step-by-step finite element analyses, the conservatism contained in different combination rules for multiple coplanar flaws provided by fitness-for-service codes (ASME, BS7910, API579 and GB/T19624) have been quantitatively assessed for the fatigue failure mode. The findings show that the re-characterization guideline provided by ASME and BS7910 may cause non-conservative estimations when two crack sizes are similar, whereas API579 and GB/T19624 lead to excessively pessimistic predictions for almost all the cases. Based on the fatigue crack growth life, we suggest a new combination rule and conclude that it always yields a reasonable estimation with necessary conservatism, for various initial crack depths, material constants and relative sizes of two cracks.

Strength, fragmentation and fractal properties of mixed flaws

Experiments on Portland cement samples containing mixed flaws are conducted to investigate the strength, fragmentation and fractal properties. Flaw geometry is a new combination of two edge-notched flaws and an imbedded flaw, which is different from those in the previous studies, where parallel or coplanar flaws are used. The physical implications of the shear-box test applied to result to rock slopes are studied. The physical and analytical fragmentation characteristics of preflawed samples are analyzed through the sieve test and fractal theory, respectively. Three different patterns of tensile cracks and shear cracks are observed. A sliding crack model is presented to elucidate the brittle failure flaws. In all of the cases of the shear-box tests, the coalescence is produced by the linkage of shear cracks, and two types of coalescence (Type C1 and Type C2) have been classified, which tend to confirm the observations from the numerical model and field of jointed rock slopes. The shear strength is a function of the flaw geometry and the shear–normal stress ratio. The result of sieve tests indicates that the fragment size distribution of fragments has the fractal property, providing a physical understanding of the fragmentation mechanism. The fragments under the shear-box test have fractal dimensions between 2.2 and 2.6, which are larger than those under the compression test but similar to those in the fault cores. The fragmentation in the case of Type C2 has a smaller fractal dimension, corresponding to a larger shear strength.

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β⩽30°). When the pre-existing flaws are steep (such as β⩾75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L⩽2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L⩽a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L⩾2a).

A numerical analysis on the interaction of twin coplanar flaws

In several practical situations, structural components present more than one crack. Such multiple cracks should be considered simultaneously since the interaction phenomenon could produce higher stress-intensity factor (SIF) values with respect to the case of a single crack. In the present paper, the influence of two identical coplanar semi-elliptical surface flaws in a plate with finite width and thickness under various stress distributions perpendicular to the crack faces is numerically analysed. Then the results for such elementary stresses are used to obtain the SIFs for real load cases. Due to the interaction effect, the SIF distribution along the crack front is asymmetric and dependent on the distance δ between the two surface cracks. The distance of non-interaction is evaluated as a function of the crack shape and the crack depth.