Analysis of fracture process zone in brittle rock subjected to shear-compressive loading

An analytical expression for the prediction of shear-compressive fracture process zone(SCFPZ) is derived by using a proposed local strain energy density criterion, in which the strain energy density is separated into the dilatational and distortional strain energy density, only the former is considered to contribute to the brittle fracture of rock in different loading cases. The theoretical prediction by this criterion shows that the SCFPZ is of asymmetric mulberry leaf in shape, which forms a shear-compression fracture kern. Dilatational strain energy density along the boundary of SCFPZ reaches its maximum value. The dimension of SCFPZ is governed by the ratio of K_Ⅱ to (K_Ⅰ.) The analytical results are then compared with those from literatures and the tests conducted on double edge cracked Brazilian disk subjected to diametrical compression. The obtained results are useful to the prediction of crack extension and to nonlinear analysis of shear-compressive fracture of brittle rock.

STUDY ON THE FRACTURE PROCESS OF AN AS CAST Zn 27WT% Al ALLOY

Thefracture processof an ascast ZA27 alloy under thetensiletest atthe room temperature wasstudied. Theresultsshow thatthecracksof ZA27 alloy form at(α+ η)eutectic phaseand develop bypropagatingalongthe(α+ η) phaseandcuttingthroughthe dendriteαphaseand εphase. Theinfluenceof every phasein ZA27 on thestrength and ductility was ana lyzed.

ROCK FRACTURE PROCESS ZONE AND ITS INFLUENCE ON MODEⅡFRACTURE BEHAVIOR

On the basis of that rock material usually has a larger fracture process zone,a new fracture criterion which is different from that of linear elastic fracture theory was presented.On this basis,the fracture behavior and influencing factors under modeⅡor compressive shear loading were investigated.

Management and classification of the fracture of lateral process of talus:An overview and literature update

Fracture of the lateral process of the talus(FLPT)is uncommon in clinical practice and can be easily missed or misdiagnosed.In recent years,as researchers from all over the world have further deepened their research on FLPT,there has been a breakthrough in the classification,and the methods and principles of clinical management have changed accordingly;however,there is still no standardized guideline for the diagnosis and management of FLPT,and there have been few relevant literature review articles related to this kind of fracture in the past at least 5 years.In this article,we review the clinical classification,classification-based therapeutic recommendations,and prognosis of FLPT,with the aim of providing a reference for the clinical diagnosis and management of this infrequent fracture.

A fracture model for assessing tensile mode crack growth resistance of rocks

Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering.This investigation developed a brittle fracture model to predict tensile mode(mode I)failure loads of cracked rocks.The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone(FPZ)based on the maximum normal strain(MNSN)ahead of the crack tip,and then use the effective crack to calculate the fracture toughness.We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN.In this way,the FPZ,non-singular terms and the biaxial stress state at the crack tip are simul-taneously considered.The principle of the model is explicit and easy to apply.To verify the proposed model,laboratory experiments were performed on a rock material using six groups of specimens.The model predicted the specimen geometry dependence of the measured fracture toughness well.More-over,the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature.The model was demonstrated su-perior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.

Assessment of fracture process in forta and polypropylene fiber-reinforced concrete using experimental analysis and digital image correlation

This paper aims to characterize the evolution of the fracture process and the cracking behavior in fortaferro(FF)and polypropylene(PP)fiber-reinforced concrete under the uniaxial compressive loading using experimental analysis and digital image correlation(DIC)on the surface displacement.For this purpose,6 mix designs,including two FF volume fractions of 0.10%,and 0.20%and three PP volume fractions of 0.20%,0.30%,and 0.40%,in addition to a control mix were evaluated according to compressive strength,modulus of elasticity,toughness index,and stress–strain curves.The influence of fibers on the microstructural texture of specimens was analyzed by scanning electron microscope(SEM)imaging.Results show that FF fiber-reinforced concrete specimens demonstrated increased ductility and strength compared to PP fiber.DIC results revealed that the major crack and fracture appeared at the peak load of the control specimen due to brittleness and sudden gain of large lateral strain,while a gradual increase in micro-crack quantity at 75%of peak load was observed in the fiber specimens,which thenbegan to connect with each other up to the final fracture.The accuracy of the results supports DIC as a reliable alternative for the characterization of the fracture process in fiber-reinforced concrete.

FRACTURE LIMIT LOAD OF CONE SHAPE PART IN DRAWING PROCESS

The deformation characters and load status of the blank＇s potential fracture zone are analyzed at the moment when blank is approaching to punch comer in drawing process of cone shape part. Based on tension instability theory, the formula for calculating fracture limit load of cone shape part in drawing process is derived. Also, the formula is analyzed and verified by experiment.

Transfer learning framework for multi-scale crack type classification with sparse microseismic networks

Rock fracture mechanisms can be inferred from moment tensors(MT)inverted from microseismic events.However,MT can only be inverted for events whose waveforms are acquired across a network of sensors.This is limiting for underground mines where the microseismic stations often lack azimuthal coverage.Thus,there is a need for a method to invert fracture mechanisms using waveforms acquired by a sparse microseismic network.Here,we present a novel,multi-scale framework to classify whether a rock crack contracts or dilates based on a single waveform.The framework consists of a deep learning model that is initially trained on 2400000+manually labelled field-scale seismic and microseismic waveforms acquired across 692 stations.Transfer learning is then applied to fine-tune the model on 300000+MT-labelled labscale acoustic emission waveforms from 39 individual experiments instrumented with different sensor layouts,loading,and rock types in training.The optimal model achieves over 86%F-score on unseen waveforms at both the lab-and field-scale.This model outperforms existing empirical methods in classification of rock fracture mechanisms monitored by a sparse microseismic network.This facilitates rapid assessment of,and early warning against,various rock engineering hazard such as induced earthquakes and rock bursts.

Investigation of FRP and SFRC Technologies for Efficient Tunnel Reinforcement Using the Cohesive Zone Model

Amid urbanization and the continuous expansion of transportation networks,the necessity for tunnel construction and maintenance has become paramount.Addressing this need requires the investigation of efficient,economical,and robust tunnel reinforcement techniques.This paper explores fiber reinforced polymer(FRP)and steel fiber reinforced concrete(SFRC)technologies,which have emerged as viable solutions for enhancing tunnel structures.FRP is celebrated for its lightweight and high-strength attributes,effectively augmenting load-bearing capacity and seismic resistance,while SFRC’s notable crack resistance and longevity potentially enhance the performance of tunnel segments.Nonetheless,current research predominantly focuses on experimental analysis,lacking comprehensive theoretical models.To bridge this gap,the cohesive zone model(CZM),which utilizes cohesive elements to characterize the potential fracture surfaces of concrete/SFRC,the rebar-concrete interface,and the FRP-concrete interface,was employed.A modeling approach was subsequently proposed to construct a tunnel segment model reinforced with either SFRC or FRP.Moreover,the corresponding mixed-mode constitutive models,considering interfacial friction,were integrated into the proposed model.Experimental validation and numerical simulations corroborated the accuracy of the proposed model.Additionally,this study examined the reinforcement design of tunnel segments.Through a numerical evaluation,the effectiveness of innovative reinforcement schemes,such as substituting concrete with SFRC and externally bonding FRP sheets,was assessed utilizing a case study from the Fuzhou Metro Shield Tunnel Construction Project.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste,understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities.The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure.This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions.To investigate the mechanism of microscale mode-I ruptures,it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework.In this contribution,we derive the model from microstructures that contain periodically distributed microcracks within a porous material.The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical(HM)anisotropy at the microscale.The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation.Verification examples are presented to validate the developed model step by step.An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate,initial damage,and applied stress,on the gas migration process.Numerical examples of direct tension tests are used to demonstrate the model’s efficacy in describing localized failure characteristics.Finally,the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks.The model successfully captures the common behaviors observed in laboratory experiments,such as a sudden drop in gas injection pressure,rapid build-up of downstream gas pressure,and steady-state gas flow following gas breakthrough.

Cracking process of rock mass models under uniaxial compression

Anisotropic strength and deformability of the rock mass with non-persistent joints are governed by cracking process of the rock bridges. The dependence of cracking process of jointed rock masses on the two important geometrical parameters, joint orientation and joint persistence, was studied systematically by carrying out a series of uniaxial compression tests on gypsum specimens with regularly arranged multiple parallel pre-existing joints. According to crack position, mechanism and temporal sequence, seven types of crack initiations and sixteen types of crack coalescences, were identified. It was observed that both tensile cracks and shear cracks can emanate from the pre-existing joints as well as the matrix. Vertical joints were included and coplanar tensile cracks initiation and coalescence were observed accordingly. For specimen with joint inclination angle ,8=75~, it was found that collinear joints can be linked not only by coplanar shear cracks but also by mixed tensile-shear cracks, and that a pair of them can form a small rotation block. Seven failure modes, including axial cleavage, crushing, crushing and rotation of new blocks, stepped failure, stepped failure and rotation of new blocks, shear failure along a single plane and shear failure along multiple planes, were observed. These modes shift gradually in accordance with the combined variation of joint orientation and joint persistence. It is concluded that cracking process and failure modes are more strongly affected by joint orientation than by joint persistence, especially when joint inclination angle is larger than 45~. Finally, variations of macroscopic mechanical behaviors with the two geometrical parameters, such as patterns of the complete axial stress-axial strain curves, peak strength and elastic modulus, are summarized and their mechanisms are successfully explained according to their different cracking process.

Experimental study of ultralong wave band for electro－magnetic signals and acoustic emission during rock fracture

The electro-magnetic (EM) and acoustic emission (AE) in the fracture process of both dry and wet rock samples including gabbro, granite, sandstone and marble are studied in the experiment in the laboratory under uniaxial pressure. Signals during the test are detected in ultralow frequency band. The experimental results may be outlined as follows: original waveforms of the electro-magnetic radiation (EMR) and AE in the range of 0-20 kHz frequencies are obtained; the EMR's intensity in fracture process is related to some factors as rock type, content of water, fracture intensity of rocks, loading rates and fracture state etc.; the EMR'S rate is proportional to that of AE during fracture statistically. About 70% of maximum values of EMR rate and AE rate are corresponded with each other; furthermore, the EM signals (EMS) are generally more developed and longer duration than AE signals; the principal energy of EMS detected by copper coin antenna as sensor in power spectra are distributed in frequencies lower than 6 kHz and otherwise those detected by EMinduction coil are at about 10 kHz, and in contrast the major energies of AE are in frequencies less than3 kHz; another notable phenomenon is that distinct electro-magnetic signals are detected before AE occurrence. Since EMR and AE signals obtained in the process of rock fracture are better corresponded to eachother, therefore it'S reasonable to propose that the EMR anormalies observed prior to some earthquakes aremainly produced by fractures of rock in source region, as for the EMS occurred before AE may be related topiezoelectric and piezomagnetic effects.

Impacts of Disk Rock Sample Geometric Dimensions on Shear Fracture Behavior in a Punch Shear Test

Punch shear tests have been widely used to determine rock shear mechanical properties but without a standard sample geometric dimension suggestion.To investigate the impacts of sample geometric dimensions on shear behaviors in a punch shear test,simulations using Particle Flow Code were carried out.The effects of three geometric dimensions(i.e.,disk diameter,ratio of shear surface diameter to disk diameter,and ratio of disk height to shear surface diameter)were discussed.Variations of shear strength,shear stiffness,and shear dilatancy angles were studied,and the fracture processes and patterns of samples were investigated.Then,normal stress on the shear surface during test was analyzed and a suggested disk geometric dimension was given.Simulation results show that when the ratio of the shear surface diameter to the disk diameter and the ratio of disk height to the shear surface diameter is small enough,the shear strength,shear stiffness,and shear dilatancy angles are extremely sensitive to the three geometric parameters.If the ratio of surface diameter to disk diameter is too large or the ratio of disk height to surface diameter is too small,a part of the sample within the shear surface will fail due to macro tensile cracks,which is characterized by break off.Samples with a greater ratio of disk height to shear surface diameter,namely when the sample is relatively thick,crack from one end to the other while others crack from both ends towards the middle.During test,the actual normal stress on the shear surface is greater than the target value because of the extra compressive stress from the part of sample outside shear surface.

Low-cycle Fatigue Behavior of Ni-based Superalloy GH586 with Laser Shock Processing

Low-cycle fatigue behavior of Ni-based superalloy GH586 with laser shock processing（LSP） was investigated. The residual stress of the specimens treated with LSP was assessed by X-ray diffraction method. The microstructure and fracture morphology were characterized by using an optical microscope（OM）, a scanning electron microscope（SEM）, and a transmission electron microscope（TEM）. The results indicated that the maximum residual compressive stress was at about 1 mm from the shocking spot center, where the residual compressive stress was slightly lower. High density tangling dislocations, dislocation walls, and dislocation cells in the microstructure of the specimens treated with LSP effectively prevented fatigue cracks propagation. The fatigue life was roughly twice as long as that of the specimens without LSP. The fatigue crack initiation（FCI） in specimens treated with LSP was observed in the lateral section and the subsurface simultaneously. The fatigue striation in the fracture treated with LSP was narrower than that in the untreated specimens. Moreover, dimples with tear ridges were found in the fatigued zones of the LSP treated specimens, which would be caused by severe plastic deformation.

Microscale crack propagation in shale samples using focused ion beam scanning electron microscopy and three-dimensional numerical modeling

Reliable prediction of the shale fracturing process is a challenging problem in exploiting deep shale oil and gas resources.Complex fracture networks need to be artificially created to employ deep shale oil and gas reserves.Randomly distributed minerals and heterogeneities in shales significantly affect mechanical properties and fracturing behaviors in oil and gas exploitation.Describing the actual microstructure and associated heterogeneities in shales constitutes a significant challenge.The RFPA3D(rock failure process analysis parallel computing program)-based modeling approach is a promising numerical technique due to its unique capability to simulate the fracturing behavior of rocks.To improve traditional numerical technology and study crack propagation in shale on the microscopic scale,a combination of high-precision internal structure detection technology with the RFPA^(3D) numerical simulation method was developed to construct a real mineral structure-based modeling method.First,an improved digital image processing technique was developed to incorporate actual shale microstructures(focused ion beam scanning electron microscopy was used to capture shale microstructure images that reflect the distri-butions of different minerals)into the numerical model.Second,the effect of mineral inhomogeneity was considered by integrating the mineral statistical model obtained from the mineral nanoindentation experiments into the numerical model.By simulating a shale numerical model in which pyrite particles are wrapped by organic matter,the effects of shale microstructure and applied stress state on microcrack behavior and mechanical properties were investigated and analyzed.In this study,the effect of pyrite particles on fracture propagation was systematically analyzed and summarized for the first time.The results indicate that the distribution of minerals and initial defects dominated the fracture evolution and the failure mode.Cracks are generally initiated and propagated along the boundaries of hard mineral particles such as pyrite or in soft minerals such as organic matter.Locations with collections of hard minerals are more likely to produce complex fractures.This study provides a valuable method for un-derstanding the microfracture behavior of shales.

Experimental study on strain field evolution around a simulated thrust fault

Earthquakes result from continuous geodynamic processes.A topic of significant interest for the scientific community is to elaborate on the phenomena governing the faulting and fracturing of crustal rocks.Therefore,in this study,uniaxial compressive shear failure experiments were conducted on Fangshan marble rock samples with a prefabricated slot to simulate thrust faulting.The center of each marble plate(105 mm × 80 mm × 5 mm) was engraved with a 30-mm long double-sided nonpenetrating slot(depth:2 mm,width:0.5 mm).The deformation and destruction processes of the rock surface were recorded using a high-speed camera.The digital image correlation method was used to calculate the displacement and strain distribution and variation at different loading stages.The accumulative and incremental displacement fields u and v,strain field exand e_(y),and shear strain e_(xy) were analyzed.When the loading level reached its ultimate value,the strain field was concentrated around the prefabricated slot.The concentration reached a maximum at the ends of the prefabricated slot.The magnitude of shear strain reached 0.1.This experiment contributes to our understanding of the dynamic process of active faulting.

Statistical damage model for quasi-brittle materials under uniaxial tension

Based on the parallel bar system, combining with the synergetic method, the catastrophe theory and the acoustic emission test, a new motivated statistical damage model for quasi-brittle solid was developed. Taking concrete for instances, the rationality and the flexibility of this model and its parameters-determining method were identified by the comparative analyses between theoretical and experimental curves. The results show that the model can simulate the whole damage and fracture process in the fracture process zone of material when the materials arc exposed to quasi-static uniaxial tensile traction. The influence of the mesoscopic damage mechanism on the macroscopic mechanical properties of quasi-brittle materials is summarized into two aspects, rupture damage and yield damage. The whole damage course is divided into the statistical even damage phase and the local breach phase, corresponding to the two stages described by the catastrophe theory. The two characteristic states, the peak nominal stress state and the critical state are distinguished, and the critical state plays a key role during the whole damage evolution course.

An experimental investigation of the fracturing behaviour of rock-like materials containing two V-shaped parallelogram flaws

The distribution characteristics and evolution law of rock mass fissures induced by mining are a key scientific issue in the study of deep rock mechanics.In this study,a series of uniaxial compression experiments was conducted on rock-like specimens containing double V-shaped prefabricated fissures at dip angles ofα=β=45°,α=45°<b=60°,α=β=60°,andα=60°<β=75°with a rock mechanics servocontrolled testing system.According to the experimental results,the effects of the dip angles of the double V-shaped prefabricated flaws with the same area on the mechanical parameters and fracturing process of the specimens were analysed in detail.Additionally,the crack initiation stress presented a nearly linear growth trend,which is generally similar to that of the crack peak stress with increasing flaw dip angle.By applying photographic monitoring to the crack initiation,propagation,coalescence,and failure modes in rock-like specimens,it was easily seen that the V-shaped flaw properties slightly influence the crack initiation positions but significantly influence the crack trajectories.The crack failure modes can be summarized into two distinct types.The study reported herein can provide a better understanding of the evolution of double V-shaped prefabricated fissures induced by coal mining.

A two－dimensional earthquake fault modeling with fractal structure strength distribution

In this paper a two dimensional (2 D) model of earthquake fault rupturing was presented. It was estabilished on the basis of 1 D spring block model. Using this model, we studied the dynamical plane strain fracture problem, modeled the whole dynamical process of nucleating, expanding and propagating of fracture on a 2 D fault with homogeneous or inhomogeneous rupture strength distribution. Our studies show that under homogeneous prestress condition, the fault will gain enough momentum to tear strong obstacles in their propagating path. The rupturing fronts can also propagate forth around the isolated barriers. It is shown that the stopping conditions for rupturing processes play an important role in modeling whole earthquake process. We also studied the dynamical rupturing problems of the fault on which the rupture strength distribution is inhomogeneous, and modeled the earthquake sequence generated on a 2 D fault with the strength distribution of fractal structure. It possesses some similar features as a seismic sequence in the nature. These features mainly depend on the distribution of rupture strength on the fault plane and the level of initial stress drop. The modeling studies which were established on the basis of experiments and observations provided the physical basis for explaining some statistical rules of seismicity.

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon,in order to promote the versatility of gas/oil reservoirs.A numerical simulation of proppants transport at both hydraulic fracture(HF)and natural fracture(NF)intersection is performed to provide a better understand-ing of key factors which cause,or contribute to proppants transport in HF-NF intersection.Computational fluid dynamics(CFD)in association with discrete element method(DEM)is used to model the complex interactions between proppant particles,host fluid medium and fractured walls.The effect of non-spherical geometry of particles is considered in this model,using the multi-sphere method.All interaction forces between fluid flow and particles are considered in the computational model.Moreover,the inter-actions of particle-particle and particle-wall are taken into account via Hertz-Mindlin model.The results of the CFD-DEM simulations are compared to the experimental data.It is found that the CFD-DEM sim-ulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data.The results indicate that the HF-NF intersection type,fluid velocity and NF aperture affect the quality of blockage occurrence,presenting a new index,called the blockage coefficient which indicates the severity of the blockage.