Single Flaw Research Articles

Experimental investigation of the coupled effects of bedding planes and flaws on fracture evolution of soft bedded rocks based on 3D printing and DIC technologies

Bedded rocks are a typical geological formation with significant implications for understanding tectonic evolution, rock engineering, and geological hazard mitigation. This study introduces a novel method for fabricating bedded rocks using 3D printing (3DP) technology. By comparing the mechanical anisotropic properties and failure modes of 3DP bedded rocks with natural bedded rocks, we validate the feasibility of this approach. Compression tests are conducted on 3DP bedded rocks containing a single flaw to investigate the coupled effects of bedding planes and flaws on the mechanical properties. Digital image correlation (DIC) is employed for full-field deformation measurement during loading, enabling the study of deformation and crack evolution patterns. The results indicate that bedding planes dominate the brittleness of 3DP bedded rocks containing a single flaw. Significant plastic characteristics and prolonged nonlinear deformation stages are observed when the bedding angle (α) is between 0° and 45°, while brittleness becomes apparent beyond 45°. Both strength and elastic modulus are decided by bedding planes and initial flaws. By comparing stress–strain curves and rate of effective variance change (REVC)-strain curves, crack initiation can be quantitatively identified, revealing a linear correlation between strength and stress values at crack initiation points. The bedding plane also dominates crack propagation and failure modes: when α ≤ 30°, cracks propagate through the bedding, indicating tensile failure; when 45° ≤ α＜90°, cracks propagate along the bedding, indicating tensile-shear or shear failure; and when α = 90°, cracks propagate along bedding planes, indicating tensile failure. The findings of this study provide insights for explaining and predicting failure modes in engineering projects involving bedded rock formations, such as slopes, tunnels, and coal mines.

Dynamic fracture mechanism from a pre-existing flaw in granite: Insights from grain-based modelling

Both heterogeneity and pre-existing flaws are closely associated with the mechanical response of crystalline granite. To uncover the underlying mechanism, grain-based model (GBM) based on particle flow code (PFC), i.e., PFC-GBM, with different contacts between any two grains, was employed to carry out numerical calculations to investigate the effect of a single flaw with various inclination angles on the dynamic behavior of LdB granite. The failure pattern is identified through density and spatial distributions of microcracks, and the primary fracture directions are obtained by microcrack orientations. Microcracks are divided into inter-Grain and intra-Grain types, and these two types are further classified into more subtypes according to mineral composition. IG cracks typically form during the pre-peak stage and tend to emerge earlier than TG cracks. Conversely, TG cracks are predominantly created during the post-peak stage but constitute a significant proportion irrespective of flaw inclination angle. A novel method is also proposed to acquire high-stress particles, which promote the identification of dominant macrocrack paths. Finally, the effect of particle size is also systemically analyzed.

Experimental and numerical study on the damage evolution and acoustic emission multi-parameter responses of single flaw sandstone under uniaxial compression

Cracks are generally the weakest position in engineering rock mass. It is of great practical significance to study the influence of cracks on the fracture process of rock mass and the precursor criterion of failure for disaster prevention and mitigation projects. In this paper, particle flow program (PFC2D) is used to analyze the mechanical strength and damage evolution of fractured rock. The multi-parameter stage characteristics of acoustic emission (AE) and the difference of fracture precursor information of fractured rock mass under uniaxial compression (UC) are explored. The results are as follows: (1) The strength and modulus of elasticity of fractured rock samples are smaller than that of intact rock mass, and increase in quadratic function with the increase of fracture angle, and the strength of B-90 sample is closest to intact rock samples; (2) The PFC analysis shows that the cracks in the defective rock samples all originate from the tip of the prefabricated crack, and the crack initiation angle is basically in the range of 60°∼90°. The loading process mainly produces tensile damage, and the number of tensile cracks are far more than that of shear cracks. Compressive stress and tensile stress increase with the increase of load, but the force chain of failure surface is the smallest after complete failure of rock; (3) The acoustic emission ringing number, RA/AF value, b value and entropy value of sandstone have obvious stage characteristics, the main frequency signal is mainly low frequency signal, and large-scale cracks are mainly produced in the failure process. The sudden increase point of AE ringing times and RA/AF value accumulation curve can be used as critical failure point. The fluctuation of B value and entropy value reflects the instability of fracture development, and “cliff-like” descending point and ascending point can be regarded as the precursor of critical failure of rock; (4) The failure precursor of acoustic emission parameters of sandstone appears in the peak load period of 85 %–98 %. The order of response time of different parameters is: cumulative RA/AF value, cumulative event number, entropy value, B value. The response time of B-45 and B-15 is earlier, while that of B-60 and B-30 is later. The research results are expected to deepen the understanding of the relevant standards of damage evolution and failure precursors of defective rocks in engineering applications.

Revealing crack initiation and extension of brittle rock via time-lapse acoustic attenuation: Insights from active ultrasonic experiments

Predicting brittle rock failure is essential for rock mechanics research and early disaster alerts in deep rock engineering. Successful prediction relies on identifying crack initiation and extension. However, currently, there is no universally accepted method for accurately identifying and tracking crack evolution to predict brittle failure of the surrounding rock. In this study, the propagation parameters of transmission ultrasonic waves were used to characterize crack behaviors at the laboratory scale. The differential acoustic attenuation term was proposed by modifying the spectral ratio method to evaluate the dissipation capability of the corresponding medium to the transmitted ultrasonic waves. In addition to acoustic attenuation, velocity and amplitude attenuation were introduced to characterize the damage evolution during brittle failure. The indicators were analyzed by conducting a uniaxial compression test on a sandstone sample with a single flaw. During compression, active ultrasonic surveys were conducted to attain the propagation parameters. The two-dimensional digital image correlation method was simultaneously applied to capture the full-field strain on the front surface of the sample. The shear and tensile strain profiles indicated that the shear damage initially accumulated at the tips of the flaw, causing a reduction in the velocity and amplitude of the transmitted ultrasonic waves. The acoustic attenuation indicator in the flaw-tip regions increased before the shear strain began. As the damage developed further, the acoustic attenuation increased overall, with numerous local fluctuations in the flaw-tip regions due to stress rearrangement and damage development, while the velocity and amplitude remained consistently low. In contrast, intact regions that were far away from the tips of the flaw exhibited different characteristics. The velocity and amplitude variations were more staged, while the acoustic attenuation changed gradually. The results indicated that the variations in the propagation parameters exhibited specific patterns before the damage was initiated, offering a potential for predicting crack initiation. The variations in the acoustic attenuation, velocity, and amplitude attenuation allow for tracking the crack propagation.

Quantitative Analysis and 3D Visualization of Crack Behavior in 3D-Printed Rock-Like Specimens with Single Flaw Using In-Situ Micro-CT Imaging

3D printing technology allows for precise control of preparing complex geometries and internal defects in printed rock analogs, while in-situ Micro-CT imaging enables real-time observation of crack behavior. The combination of these technologies offers a new research approach for studying rock crack behavior. In this study, 3D-printed rock-like specimens containing a pre-existing flaw were prepared using a gypsum powder-based 3D printer. An advanced in-situ Micro-CT system equipped with a loading device was used to quantitatively and visually investigate the crack behavior in 3D-printed specimens under uniaxial compression testing. 2D CT images obtained from in-situ compression testing at different deformations could be used to reconstruct a 3D model and visually identify the crack patterns of the extracted cracks in 3D-printed specimens. The initiation angle of cracks, volume of the pre-existing flaw, volume of newly formed cracks, and damage value with respect to strains were analyzed to quantitatively investigate crack behavior. The results indicated that within the 3D-printed specimens, tensile cracks were first initiated near the internal flaw, followed by the occurrence of shear cracks or tensile-shear mixed cracks at the flaw tips. Additionally, there was a negative linear correlation between the initiation angle of newly formed cracks and the initial flaw angle. For flaw angles in the range of 0° ≤ α ≤ 45°, a higher number of newly formed cracks were observed in the 3D-printed specimens, and the rates of increase in crack volume and damage values with strain were faster. However, for flaw angles in the range of 45° < α ≤ 90°, the results showed the opposite trend. Furthermore, through comparison with the crack behavior of natural rocks containing a single flaw, it was found that the failure modes and crack behavior of the 3D-printed specimens exhibit certain similarities with natural rocks.

Dynamic Mechanical Responses and Freezing Strengthening Mechanism of Frozen Sandstone with Single Flaw: Insights from Drop Weight Tests and Numerical Simulation

Dynamic Mechanical Responses and Freezing Strengthening Mechanism of Frozen Sandstone with Single Flaw: Insights from Drop Weight Tests and Numerical Simulation

Numerical modeling of crack propagation from open and closed flaws in rock

The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (KII) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of KII can be effectively eliminated when the non-singular stress (T-stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T-stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions.

Experimental investigation of damage evolution and fracture mechanism in rocks with a single flaw under stepwise cyclic compression

Experimental investigation of damage evolution and fracture mechanism in rocks with a single flaw under stepwise cyclic compression

An extended peridynamic model equipped with a new bond-breakage criterion for mixed-mode fracture in rock-like materials

This paper develops a numerical model based on two-parameter extended bond-based peridynamics with a new bond-breakage criterion to simulate mixed-mode fracture in rock-like materials. This model requires only four basic parameters: Young’s modulus, Poisson’s ratio, and Mode-I and Mode-II energy release rates. Tensile and shear cracks can be distinguished explicitly from mixed-mode fracture phenomena by decomposing the bond potential into dilatational and deviatoric terms. The m- and δ-convergence studies are first performed on the gypsum specimen with a single flaw subjected to uniaxial compression. The initialization and propagation of wing cracks (tensile cracks), quasi-coplanar and oblique secondary cracks (shear cracks) are successfully captured. As an example application, the crack initiation, propagation and coalescence processes of gypsum specimens with various double-flaw configurations are investigated. Under uniaxial compression, three typical types of crack coalescence patterns characterized by shear cracking or mixed tensile-shear cracking are obtained. In all cases, the numerical results predicted by the developed approach agree well with the experimental observations, both qualitatively and quantitatively.

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.

Flaws in advance directives that request withdrawing assisted feeding in late-stage dementia may cause premature or prolonged dying

BackgroundThe terminal illness of late-stage (advanced) Alzheimer’s and related dementias is progressively cruel, burdensome, and can last years if caregivers assist oral feeding and hydrating. Options to avoid prolonged dying are limited since advanced dementia patients cannot qualify for Medical Aid in Dying. Physicians and judges can insist on clear and convincing evidence that the patient wants to die—which many advance directives cannot provide. Proxies/agents’ substituted judgment may not be concordant with patients’ requests. While advance directives can be patients’ last resort to attain a peaceful and timely dying consistent with their lifelong values, success depends on their being effective and acceptable. A single flaw can provide opponents justification to refuse the directive’s requests to cease assisted feeding.AimThis article considers 24 common advance directive flaws in four categories. Process flaws focus on how patients express their end-of-life wishes. Content flaws reflect drafters’ selection of conditions and interventions, and how they are described. Inherent flaws can make advance directives unacceptable to authorities concerned about premature dying. Strategies are needed to compel physicians to write needed orders and to prevent third parties from sabotaging these orders after they are implemented. The article includes excerpts from “dementia-specific” directives or supplements that exemplify each flaw—mostly from the US and Europe. No directive critiqued here included an effective strategy to resolve this long-debated bioethical conflict: the past directive requests “Cease assisted feeding” but the incapacitated patient apparently expresses the desire to “Continue assisted feeding.” Some opponents to the controversial request, cease assisted feeding, use this conflict as a conceptual wedge to practice hard paternalism. This article proposes a protocol to prevent this conflict from emerging. These strategies may prevent authorities from requiring patients to fulfill authorities’ additional clinical criteria as a prerequisite to honor the requests in patients directives.ConclusionThis critique of flaws may serve as a guide to drafting and to selecting effective and acceptable advance directives for dementia. It also poses several bioethical and clinical questions to those in authority: Does your paternalistic refusal to honor patients’ wishes respect their self-determination? Protect vulnerable patients from harm? Force patients to endure prolonged suffering? Violate the principles of bioethics? Violate the very foundation of patient-centered care?

A Numerical Study of Wave Propagation and Cracking Processes in Rock-Like Material under Seismic Loading Based on the Bonded-Particle Model Approach

An earthquake is usually followed by a considerable number of aftershocks that play a significant role in earthquake-induced landslides. During the aftershock, the cracking process in rocks becomes more complex because of the formation of faults. In order to investigate the effects of seismic loading on the cracking processes in a specimen containing a single flaw, a numerical approach based on the bonded-particle model (BPM) was adopted to study the seismic loading applied in two orthogonal directions. The results reveal that no transmission and reflection phenomena were observable in the small specimens (76 mm × 152 mm) because they were considerably smaller than the wavelength of the P-wave. Furthermore, under seismic loading, the induced crack was solely tensile in nature. Repeated axial seismic loading did not induce crack propagation after the first axial seismic loading. Cracks began to propagate only when the seismic loading direction was changed from axial to lateral, and then back to axial, ultimately resulting in the failure of the specimen.

Dynamic progressive fracture behavior of axially confined sandstone specimens containing a single flaw

Rock masses are frequently subjected to dynamic disturbance in addition to pre-stress, which plays a key role in the stability and safety of underground projects. In this paper, the effects of flaw inclination angle and pre-stress on the mechanical properties and fracture behavior of sandstone specimens under repetitive impact loadings were investigated through a series of laboratory tests using a modified split Hopkinson pressure bar (SHPB) system. The results show that the dynamic strength decreases gradually with the increasing repetitive impact number. A larger flaw inclination angle produces fewer repetitive impacts for a given axial pre-stress. The repetitive impact counts and the cumulative absorbed energy peak at an axial pre-stress of 20–40 MPa. By the digital image correlation (DIC) technique, high strain localizations around the flaw periphery can be observed after the application of pre-stress. During the repetitive impact loadings, wing and anti-wing cracks occupy the dominant position. Compressive cracks also contribute to the ultimate failure if the specimen is subjected to solely repetitive impacts. Except for 90° specimens, shear cracks make a difference as well in the cracking process as the pre-stress increases.

DVTChain: A blockchain-based decentralized mechanism to ensure the security of digital voting system voting system

Voting is a fundamental democratic activity. Many experts believe that paper balloting is the only appropriate method to ensure everyone’s right to vote. But this method is prone to errors and abuse. Many nations utilize digital voting methods to solve the difficulties of paper balloting. A single flaw in digital voting may lead to massive vote-rigging. Election voting methods must be legal, accurate, safe, and convenient. However, issues with digital voting methods may restrict acceptance. Due to its end-to-end verification capabilities, blockchain technology was developed to address these problems. To guarantee We have used blockchain technology anonymity, privacy, verifiability, mobility, integrity, security, and fairness in voting. By using blockchain our proposed system ensures security, privacy, and integrity. This system provides voter anonymity by keeping the voter information as a hash in the blockchain. It also provides fairness by keeping the casted vote encrypted till the ending time of the election. After ending time, the voter can verify their casted vote, ensuring verifiability. To test our protocol, we put it on Ethereum 2.0, a blockchain platform that uses Solidity as a programming language to create smart contracts. The adoption of smart contracts provides a safe means for performing voter verification, ensuring the correctness of voting results, making the counting system public, and protecting against fraudulent activities. We analyzed the system’s performance based on security and gas costs. It improves in terms of security characteristics and the related cost for the necessary infrastructure.

Rotation and deflection of 3D principal stress axes induced by a prefabricated single flaw in sandstone: A numerical investigation based on DEM

Fracture structure in the rock mass is an enduring research interest because of its negative impacts on the strength and safety of rocks. Therefore, a series of DEM simulations of two types of fractured sandstones are conducted based on the former published experimental test. It is proved that different fracture structures have various influences on the mechanical properties and failure patterns of sandstone samples, which lead to the redistribution of principal stress in surrounding rock. The main results and conclusions are as follows: 1) fractured sample without filler shows a relatively lower uniaxial compressive strength and a larger elastic modulus, and the flaw free surfaces make the secondary crack band illustrate a typical arc-shape distribution. 2) maximum principal stress concentrations in the open-type flawed sample occur at the left and right flaw tips, the corresponding axes show progressive deflection in the vertical direction, and the intermediate and minimum principal stress axes demonstrate various rotations as the positions move away from the flaw tip. 3) maximum principal stress axes in the cement-filled fractured sample are basically parallel to the external loading direction, the largest deflection occurs in the cement filler material, and the intermediate principal stress axes near the flaw tip are consistently vertical to the flaw strike direction. 4) initiation positions of tensile and shear cracks in the open-type flaw sample are different because of the non-negligible flaw thickness, while all secondary cracks start from the top and bottom tips of the cement-filled flaw.

Fractal Study on the Failure Evolution of Concrete Material with Single Flaw Based on DIP Technique

Crack inclination and material heterogeneity have important effects on the meso-mechanical mechanism and macroscopic mechanical behavior of rock-like materials. In order to study the failure characteristics of shotcrete body during the process of using shotcrete bolt mesh support in the deep fractured rock mass of Lannigou Gold Mine, this paper combined the Digital Image Processing Technique (DIP) and RFPA2D (Rock Failure Process Analysis System) to establish a real meso-structure numerical model of concrete with different inclination angle cracks, simulating its crack propagation law and failure process, and studied the influence of crack geometry distribution and meso-heterogeneity on the effect of concrete structure. The findings reveal that the crack inclination angle has a substantial impact on concrete materials' compressive strength and elastic modulus, and both of them all show a nonlinear increase with the increase of crack angle; Because of the inhomogeneity of the materials, the inclination and propagation pathways of wing cracks are random, and the aggregate inhibits crack initiation and propagation. The wing crack's initiation position moves closer to the tip as the crack inclination angle increases, and the length gets shorter; Acoustic emission(AE) evolution characteristics are similar in samples with varying dip angles. In the early stages of loading, the AE energy is minimal, and increases rapidly when approaching the peak stress. The fractal dimension was used to describe the damage evolution process inside the material, and a damage variable index (ω) based on the fractal theory was proposed. The more the ω, the greater the material's degree of degradation. The proposed index provided a new method for quantitative study of the damage evolution characteristics of rock-like materials. It has guiding significance for the research on the stability of wet shotcrete in the deep fractured rock mass of Lannigou Gold Mine.

Numerical analysis of mechanical behavior of stratified rocks containing a single flaw by utilizing the particle flow code

The evaluation of the mechanical properties of stratified rock masses with flaws is of great significance to geological engineering problems such as underground project and slope stability, etc. To investigate the mechanical properties of fractured stratified rock, the two-dimensional particle flow code (PFC2D) was used to conduct uniaxial compression simulation tests on stratified rock model containing a single flaw. To study the failure mechanism of the specimen, the stress-strain curve, acoustic emission events, mechanical parameters and cracking mode were recorded and analyzed. The simulation results showed that the stress-strain curves and AE events of specimens with different arrangements of flaw and stratification can be divided into three types, namely multi-peak type, pre-peak wave type and single peak with few fluctuations type. Inclined stratification caused the cracks to gradually propagate along the bedding planes, which weakened the strength and dominated the failure modes of the specimen. The flaw affected the stress distribution and played a role in connecting micro-cracks. The combined effect of stratification and flaw depended on the relative relationship between the stratification and the flaw, which determined the cracking path and failure modes.

Demultiplexer based on one-dimensional chalcogenide photonic crystal

This research utilised a one-dimensional chalcogenide photonic crystal to create a four-channel optical demultiplexer (DMUX). We have used four one-dimensional As2Se3/air multilayered structures in the suggested construction. By replacing the As2Se3 layer in each structure with As2S3, a single flaw of varying thickness is established. The transmission spectra are calculated using the transfer matrix method (TMM). The thickness of a defect layer can alter mode frequencies. As a result, by altering the thickness of the defect layer in the structure, we may extract any desired wavelength. This property may be utilised to create a DWDM optical communication wavelength demultiplexer.

Experimental investigation on the strain energy evolution mechanism of granite specimens with a single flaw

Damage and fracture of rocks is a comprehensive result of strain energy dissipation and release. In order to study the energy evolution mechanism of hard brittle rock masses during failure process, uniaxial compression tests on the granite specimens with a single pre-existing flaw are carried out with digital image correlation method (DIC). The results indicate that: (1) The stress fluctuation before structural failure corresponds to the sudden increase of the dissipated energy, the essence is that rock masses occur obviously damage and cracking. (2) For medium flaw dip angles, the stress fluctuation occurs repeatedly in stages, whose strain energy is dissipated gradually; for large or small dip angles, the stress fluctuation is almost not appeared, and the energy dissipation is insignificant. (3) With the increase of flaw dip angles, the dissipated energy ratio at the peak stress first increases and then decreases showing an inverted U-shaped, resulting in a similar law of rock damage but a contrary law of strength; the corresponding elastic energy ratio is U-shaped of decreasing first and then increasing, causing the structural failure changes from dynamic to static and then to dynamic again. The results can provide theoretical references for the formation mechanism and prevention method of dynamic disasters of rock underground engineering.

Multiscale damage constitutive model of jointed rock masses based on the influence of crack initiation

A rock mass has a large number of macroscopic and microscopic defects, such as joint cracks and microcracks, which greatly affect its physical and mechanical properties. In this study, a multiscale elastoplastic damage model was proposed to describe the influence of the existence and evolution of two types of cracks on rocks. The macroscopic damage variable expressed by the stress intensity factor was derived on the basis of damage mechanics and fracture mechanics and regarded as a piecewise function with initiation stress as the dividing point. The rock was divided into two parts based on micromechanics: matrix and microcracks. The macroscopic damage was considered the deterioration of the mechanical properties of the rock matrix. Under the framework of thermodynamics, a constitutive model that could reflect the growth of macrocracks and the friction–damage coupling of microcracks was constructed. This model could reflect the physical mechanism of macroscopic and microscopic damage of jointed rock masses, so the physical parameters of the model had clear meanings. Lastly, the rationality of the model was verified via uniaxial compression tests of rock-like materials with a single flaw of different inclination angles.