Crack Coalescence Behavior Research Articles

Crack coalescence and failure behaviors in slate specimens containing a circular cavity and a pre-existing flaw pair under uniaxial compression

The flaws (fractures) widely existing in rock mass pose a threat on the stability of many underground cavities. This study aims at investigating the failure process of a cavity affected by adjacent flaws. A number of slate specimens containing a circular cavity and a pre-existing flaw pair were tested under uniaxial compression. Varied flaw configurations were obtained by changing the flaw inclination angle with respect to horizontal and the spacing between flaw pair and cavity. Three main types of cracks emanated from the pre-existing flaw tips, and played a dominant role in the failure process of cavity, comprising primary wing cracks (tensile cracks) and two types of secondary cracks (quasi-coplanar shear cracks and oblique shear cracks). The initiation and propagation of these cracks were highly dependent on the flaw pair configurations. When the pre-existing flaw pairs were non-parallel to the loading direction, (1) mostly, coalescence occurred both in the tensile and compressive stress concentration regions around cavity; (2) in most cases, the quasi-coplanar and oblique shear cracks were the predominant cracks leading to the coalescence between the compressive stress concentration regions of cavity and the pre-existing flaw pair tips. When the pre-existing flaws were parallel to the loading direction, the combination of inclined shear cracks and tensile cracks or inclined shear cracks only dominated the failure of cavity. The initiation angles of wing cracks, quasi-coplanar shear cracks and oblique shear cracks agreed well with the theoretical predictions by the maximum tangential strain criterion (MTSN), Mohr-Coulomb criterion (M−C) and maximum shear stress criterion (MSS), respectively.

Macro-micro failure and crack coalescence behavior of soft-hard composite rock with three parallel joints under uniaxial compression

Jointed soft-hard composite rock mass is very common in engineering. The existence of joint and the uncoordinated deformation of soft-hard layer make the failure behavior more complicated. In this study, soft-hard composite rock with three parallel joints (two coplanar joints and one out-of-plane parallel joint) were fabricated to carry out uniaxial compression experiment. With the aid of digital imagine correlation (DIC) and acoustic emission (AE) technology, the influence of joint angle, ligament angle and the location of out-of-plane joint on crack propagation behavior of specimen is analyzed. The results show that when the hard layer contains more joints, the rock mass presents more obvious brittleness. The variation of peak strength with ligament angle also depends on the rock layer where the out-of-plane crack is located. Three failure modes and ten crack coalescence modes are summarized, which are affected by joint angle and ligament angle. The transition of crack coalescence between adjacent rock layer is mainly influenced by the space of wing cracks at joint tips. The coalescence of rock bridge in the layer with double joints is affected by ligament angle and the relative strength of layer. When the out-of-plane joint is in the hard layer, the coalescence possibility is greatly reduced.

A fully coupled thermo-mechanical peridynamic model for cracking analysis of frozen rocks

In cold regions, the crack propagation and coalescence behaviors of frozen rocks with ice-filled flaws are very complex. Research on the failure mechanisms of such rock masses is essential to ensure the structural safety of geological engineering in low-temperature environments. Therefore, a fully coupled thermo-mechanical model considering the frost heave effect was constructed using the ordinary state-based peridynamic (OSBPD) theory, and the cracking characteristics of frozen rocks were analyzed. The constitutive equations of the OSBPD model were modified by introducing the coupling term for the thermal-structural interaction and an equivalent pressure density term for frost heave. An improved global convergence criterion was also proposed to achieve a fast convergence to the numerical solution. The correctness and validity of the proposed coupling model were confirmed using several numerical examples. Additionally, the effect of frost heave pressure on the cracking behavior and mechanical properties of frozen rocks was thoroughly discussed. The results show that (a) the frost heave pressure drives the rock to crack along the direction of prefabricated flaws, and (b) the ultimate compressive strength of frozen rocks exhibits a decreasing trend with an increase in frost heave pressure.

Fatigue Crack Coalescence Behavior of Stainless Steel Plate with Multiple Cracks

Fatigue Crack Coalescence Behavior of Stainless Steel Plate with Multiple Cracks

Evolution Characteristics and Instability Analysis of Stratified Roof Structure in Roadway with Different Stress Levels.

With the extension of mines to deep mining, horizontal stress has become an important factor in the stability of the roadway surrounding rock, and the influence of horizontal stress on the structure of a layered roof is more complex. The simulation test of a layered roof of a roadway under different lateral pressure coefficients was carried out by using a self-designed test device and discrete element simulation software. The crack coalescence behavior of a layered roof in a roadway was analyzed, and the critical stress of rock beam failure in each layer was determined. The results show that the larger the stress levels, the larger the number and height of cracks in the layered roof were, and the relationship between them can be characterized by a quadratic polynomial. With the increase of stress levels, the layered roof was damaged gradually from the bottom to the top along the bedding plane. The maximum height of the roof caving was 9, 23, 31, and 39 mm, respectively. The width of the upper roof caving was 72, 35, 31, and 27 mm in turn. The left angle of the caving range had little change (about 60°). With the increase of stress level, the maximum caving height of the layered roof tended to increase, while the width of the top surface tended to decrease. The relationship between the stress level and the height and width can be represented by a quadratic polynomial and exponential function. According to the stability theory of the compression bar, the critical stress of failure and the decrease of the span of the rock beam in each layer were determined respectively, and the reasons for the instability of the layered roof caving are explained.

Study of the coupling effect of elliptical cavities and cracks on tunnel stability under dynamic loads

This study to explore the coupling effect of elliptical cavities and cracks on the dynamic stability and failure modes of tunnels. A series of dynamic numerical simulations and model tests were conducted by using AUTODYN code and a modified drop hammer impact test device. A cracked tunnel model with an elliptical cavity was proposed in this study. The crack coalescence behaviour, crack initiation time and stress field around the elliptical cavity and the crack tips were calculated by using numerical simulation, and the dynamic initiation fracture toughness (DIFT) was also determined according to experimental and numerical results. According to these results, we conclude that the long and short axes of the elliptical cavity have a great influence on the crack coalescence behaviour and the stress field, and the long axis of the elliptical cavity has a greater influence than the short axis. When the inclination angle θ of the elliptical cavity is 90°, the stability of the crack is lowest, and when the inclination angle θ of the elliptical cavity is 45°, the effect of the elliptical cavity on the crack initiation behaviour is largest. DIFT was calculated and indicated that when the inclination angle of the elliptical cavity shows its smallest value, 90°, the cracked tunnel stability is lowest.

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.

On fracture and damage evolution modelling of fissure‐hole containing granite induced by multistage constant‐amplitude variable‐frequency cyclic loads

AbstractThis work aims to reveal the fracture the damage evolution characteristics of fissure‐holes containing rock under multistage constant‐amplitude variable‐frequency cyclic loads. Testing results show that the peak strength and fatigue lifetime both increase as the fissure angle increases from 10° to 70°. However, the volumetric deformation, AE activities, and crack network scale get to a maximum for a sample having a 50° fissure angle. More small‐sized cracks were formed for rock having a high fissure angle, and the proportion of low‐frequency signal is relatively high. A damage evolution model was proposed based on AE rate, and an inverted “S”‐shaped curve reflects the damage propagation of the experimental data. Additionally, the highlighted internal crack network reveals the crack coalescence and hole spalling behaviors; three types of rock bridge coalescence modes of single tensile coalescence, double‐tensile coalescence, and double shear coalescence were identified.

Fracture Strength and Crack Coalescence Behavior of SUS304 Plate with Multiple Cracks

Tensile tests were conducted at room and high temperature to clarify the fracture strength and crack coalescence behavior of multiple cracks in SUS304 flat plates. The shape of the specimen is a plate, and electrical discharge machined (EDM) notches were introduced on both sides of the central smooth part. Then, a fatigue pre-crack was generated at the tip of the notch. The position of the crack was expressed by the distance between the crack surfaces and the distance between the crack tips. As a result of the tensile test at room temperature, when the distance between the crack surfaces was shorter than about 8 mm, the cracks coalesced. On the other hand, when the distance between the crack surfaces was about 10 mm, no crack coalescence was observed, and there was a change point in the crack coalescence behavior. As a result of the high temperature test, crack coalescence was observed when the distance between the crack planes was about 8 mm, but the change point of the crack coalescence behavior is unknown because there is no data. It was found that the change points of the coalescence behavior of the cracks obtained in the experiment satisfy codes for nuclear power generation facilities (JSME S NA1-2019).

Coalescence Behavior of Multiple Cracks in SUS304 Plate with under Creep Rupture Conditions

A creep test was conducted to clarify the coalescence behavior of cracks in a SUS304 flat plate with multiple cracks on different planes. The test temperature is 600 degrees. The shape of the specimen is a plate, and electrical discharge machined (EDM) notches were introduced on both sides of the central smooth part. Then, a fatigue pre-crack was generated at the tip of the notch. The position of the crack was expressed by the distance between the crack surfaces and the distance between the crack tips. As a result of the experiment, the cracks coalesced when the distance between the crack planes was shorter than about 3 mm. On the other hand, when the distance between the crack surfaces was about 7 mm, no crack coalescence was observed, and there was a change point in the crack coalescence behavior. It was found that the change point of the coalescence behavior of the crack obtained in the creep test satisfied codes for nuclear power generation facilities (JSME S NA1-2019). As a result of fracture surface observation, it was found that the crack growth from the fatigue pre-crack due to creep is due to grain boundary rupture regardless of the presence or absence of crack coalescence.

Effect of a large population of seeded alumina inclusions on crack initiation and small crack fatigue crack growth in Udimet 720 nickel-base disk superalloy

Crack initiation, crack coalescence and small crack growth behavior were monitored for over 400 seeded inclusions during interrupted low cycle fatigue testing conducted on the P/M Udimet 720 nickel disk alloy at 650 °C. Two types of seeded alumina inclusions with average sizes of 54 µm and 122 µm were used in the study performed at varying loading conditions resulting in LCF lives ranging from 2,000 cycles to over 1,000,000 cycles. The fatigue behavior was sub-categorized into four groups. Visual maps detailing inclusion size/cycle history were developed. The effect of surface residual stresses on the fatigue life was also investigated.

Rock bridge fracturing characteristics in granite induced by freeze-thaw and uniaxial deformation revealed by AE monitoring and post-test CT scanning

This work presents the impacts of freeze-thaw (F-T) fatigue damage on the crack coalescence behaviors at the rock bridge segment for granite samples containing two unparallel flaws. The pre-existing flaw geometry in the rock was a combination of a horizontal flaw and an upper inclined flaw forming a rock bridge structure. In-situ acoustic emission (AE) detection technique and post-test X-ray computed tomography (CT) scanning were used to reveal the rock bridge fracturing characteristics during the whole deformation. Results show that both the F-T cycle and flaw inclined angle influence the crack propagation path, sample strength, deformation and AE pattern and the rock bridge fracture behavior. The AE counts and energy curves present skip phenomenon and are in consistent with the stress drop points on the macroscopic stress-strain curves. The accumulative AE energy and count decrease with increasing F-T cycles. In addition, the cracks during sample failure can be classified into six types by AE spectral frequency analysis, and the high amplitude - low frequency signal was good evident to predict the brittle fracture of the rock bridge. By the post-test CT scanning visualization of the internal crack coalescence pattern at the rock bridge segment, the most striking finding is that the rock bridge structure easily deteriorates for rock subjected to high F-T damage, which suggests that repeated F-T damage drives the crack propagation at the flaw tip and can accelerate the communication of the pre-existing flaws. The testing results are expected to enhance the understanding of the F-T fatigue damage effect on the rock bridge fracturing and can be favorable for predicting the stability of rock structures and rock mass in cold regions.

Experimental study on fracture behaviour of three‐flawed sandstone specimens after high‐temperature treatments

AbstractThe crack coalescence of rocks significantly affects the stability of rock engineering, and extensive studies have been performed on preflawed rock specimens without thermal treatment. However, the fracturing behaviour of preflawed specimens after thermal treatment has not been investigated comprehensively. In this study, three‐flawed sandstone specimens with different flaw inclinations after high‐temperature treatments were tested under uniaxial compression. Photographic, acoustic emission and digital image correlation techniques were used to investigate the crack initiation, propagation and coalescence behaviour. Experimental results show that the peak strength, elastic modulus and peak strain of the three‐flawed specimens were lower than those of intact specimens and that they gradually recovered with increasing flaw angle. The peak strength and elastic modulus first increased and then decreased, whereas the peak strain increased with temperature. Noncoalescence, indirect coalescence and direct coalescence were three patterns observed between the two adjacent pre‐existing flaws. Finally, the mechanism of high temperature in alteration of the mechanical properties of sandstone was revealed through microobservations.

Experiment and peridynamic simulation on cracking behavior of red sandstone containing a single non-straight fissure under uniaxial compression

It is widely accepted that the strength, deformability, and failure behaviors of rock material are strongly influenced by widespread natural fissures. Research focusing on the crack initiation, propagation, and coalescence behavior in fissured rock material is important to ensure the reliability and predictability of rock engineering. However, the types and forms of pre-existing fissures are complex and variable; thus, mechanical experiments have rarely been conducted on rock samples containing non-straight prefabricated open fissures. In this research, the strength, deformability, and failure behaviors of sandstone samples containing a single non-straight fissure were systematically investigated by a series of uniaxial compression experiments and numerical simulations. First, the influence of the fissure angle (α) on the strength and deformation characteristics of red sandstone containing a single non-straight fissure was evaluated. Then, the ordinary state-based peridynamics model was used to investigate the fracture behavior of red sandstone specimens with respect to various α values. The results indicate that for α = 0°–15° and 75°–90°, tensile cracks first initiated from the convex points of the prefabricated fissure, and the crack initiation position transferred from the convex point to the tip of the prefabricated fissure for α = 30°–60°. In addition, for the α = 0°–90°, the cracks initiated in the form of tensile cracks, and the ultimate failure modes were mixed tensile and shear failure. Secondary cracks always appeared in the form of shear crack. Moreover, for α ≥ 75°, fewer cracks were initiated before the peak strength was reached; afterward, the crack initiations were more prolific, and more acoustic emission counts were observed.

Investigation on Crack Coalescence Behaviors for Granite Containing Two Flaws Induced by Cyclic Freeze-Thaw and Uniaxial Deformation in Beizhan Iron Mining, Xinjing, China

This work is aimed at investigating the effect of freeze-thaw (F-T) cycle on the crack coalescence behavior for granite samples containing two unparallel flaws under uniaxial compression. The flaw geometry in the samples was a combination of an upper inclined flaw with a horizontal flaw underneath. After the uniaxial compression experiments, macroscopic crack pattern description and the mesoscopic posttest CT imaging were used to reveal the effects of F-T cycle on the crack coalescence morphology at the rock bridge area. Results show that the stress–strain curves present a fluctuating growth trend and stress drop phenomenon becomes weaker with increasing F-T cycles. In addition, three different kinds of cracks (tensile-wing cracks, oblique shear cracks, and antiwing cracks) were observed, and the crack coalescence pattern was influenced by the F-T cycles and approach angle. A mix of tensile and shear failure occurs for the sample subjected to weak F-T treatment, and simple tensile failure occurs for the sample subjected to high F-T treatment. Moreover, CT imaging reveals a crack network pattern at the rock bridge area, and it is found that the fracture degree deceases with increasing F-T cycles and increases with the increasing approach angle. It suggests that the rock bridge area can be easily fractured for the sample subjected to high F-T cycles. Results of this study can provide theoretical foundation for the instability predication of fractured rock structures in cold regions.

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.

Crack coalescence behavior of sandstone specimen containing two pre-existing flaws under different confining pressures

Flaws widely exist in engineering rock masses, which significantly influence the overall mechanical behaviors (strength, elastic modulus and failure, etc.) of rock masses. The study of crack coalescence behavior of rock specimen containing pre-existing flaws enhances the understanding of failure mechanism of rock. In this study, a series of PFC3D simulations on numerical specimens were carried out to investigate the crack initiation, propagation and coalescence process under conventional triaxial compression. First, numerical model for cylindrical sandstone specimen was constructed and a set of micro-parameters were calibrated by comparing with the experimental results of intact sandstone with different confining pressures. Then, two pre-existing open flaws which were the same as the tested sandstone were created by deleting balls. Triaxial compression simulations were conducted on pre-flawed specimens for a range of confining pressures (10–40 MPa). The numerically simulated results were compared with the experimental results, which showed that the simulations were in agreement with the laboratory tests. The processes of crack initiation, propagation and coalescence for pre-flawed specimens were investigated by program in PFC3D. The relationships among the cracking process, stress-strain curve and number of micro-crack were analyzed in detail. Finally, the internal crack patterns in pre-flawed specimens were revealed by analyzing the cross-sections from X-ray CT scanning and PFC3D.

Dynamic Mechanical Properties and Fracturing Behavior of Marble Specimens Containing Single and Double Flaws in SHPB Tests

Dynamic impact tests were conducted on rectangular marble specimens with flaws to investigate the effect of the flaw angles and ligament angles on the rock dynamic mechanical properties, fracturing behavior, and energy evolution characteristics. A 75-mm diameter split Hopkinson pressure bar (SHPB) device was used in the tests. The experimental results show that the flaw geometries have a strong effect on the dynamic mechanical properties and fracturing behavior of rocks. In general, the effects of the flaw angle and flaw number on the dynamic strength are more significant than the effect of the ligament angle. A high-speed camera was used to monitor and record the crack initiation and coalescence and the failure processes of the marble specimens in real-time. The crack propagation can be divided into two major stages, i.e., the formation of white patches and the generation of macrocracks. The white patches usually appear prior to the peak stress of the specimen. The shear cracks usually initiate at or near the flaw tips and propagate to form X or half-X shear belts that dominate the macroscopic failure under impact loading. Nine types of crack coalescence behaviors are identified for the marble specimens with double flaws, and the macro failure modes of the specimens is usually combined by some of them. The energy absorption properties of the marble specimen are also significantly affected by the pre-existing flaws. The energy absorption ratio can be maximized by setting a certain number of pre-existing flaws with an appropriate inclination angle and a proper ligament angle to effectively improve the fragmentation efficiency of rocks.

Experimental study on crack coalescence behavior of double unparallel fissure-contained sandstone specimens subjected to freeze-thaw cycles under uniaxial compression

To study the rock fracturing characteristics in cold-region engineering, uniaxial compression tests are conducted on double unparallel fissure-contained sandstone specimens subjected to freeze-thaw (FT) cycles. First, the effects of FT cycles on the water absorption, peak strength, initiation stress and deformation behavior of flawed sandstone specimens are investigated. The water absorption, uniaxial compressive strength, initiation stress, elastic modulus and deformation modulus of flawed sandstone specimens decrease with an increase in the number of FT cycles. However, the peak strain of flawed sandstone specimens increases with an increase in the number of FT cycles. Second, the cracking processes of flawed sandstone specimens are investigated in detail via images captured by a high-speed digital video camera system. The relationship between the real-time crack coalescence and the axial stress-strain curve of flawed specimens, which evaluates the macroscopic deformation characteristics of precracked rock subjected to FT cycles well, is considered. Third, the interaction mechanism of fissures in rock specimens is discussed. Fourth, the influence of water and temperature on the rock-weakening process is discussed. In this study, during the rock FT cycle weakening process, the effect of water, including the dissolution effect and the stress effect, is analyzed, whereas temperature damages the rock by means of different temperature gradients and the phase transition of water. Finally, the local strong fatigue-damaged zones around the fissure tips of sandstone specimens are also analyzed. These experimental results are helpful to improve the understanding of fracture mechanisms of a rock mass in cold-region engineering.

In Vivo X-ray Computed Tomography Investigations of Crack Damage Evolution of Cemented Waste Rock Backfills (CWRB) under Uniaxial Deformation

Cemented waste rock backfill (CWRB), which is a mixture of tailings, waste rock, cement, and water, is subjected to combination actions in underground mining operations and has been widely used in deep resource mining. While the strength requirement and macroscopic deformation behaviors of CWRB have been well studied, the mesoscopic damage evolution mechanisms are still not well understood. In this work, a CWRB sample with a waste rock proportion of 30% was studied with a uniaxial compression test under tomographic monitoring, using a 450 kV industrial X-ray computed tomography (CT). Clear CT images, CT value analysis, crack identification, and extraction reveal that CWRB damage evolution is extremely inhomogeneous and affected by the waste rock size, shape, and distribution. Furthermore, the crack initiation, propagation, and coalescence behaviors are limited to the existing waste rocks. When deformation grows to a certain extent, the cracks demonstrate an interlocking phenomenon and their propagation paths are affected by the waste rocks, which may improve the ability to resist compressive deformation. Volumetric dilatancy caused by the damage and cracking behavior has closed a link with the meso-structural changes, which are controlled by the interactions between the waste rocks and the cemented tailing paste.