A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.

Effects of pre-existing cracks and infillings on strength of natural rocks--Cases of sandstone, argillite and basalt

This study aims to examine the influence of pre-existing discontinuities on the strengths of four natural rocks of different origins.A series of unconfined compression tests was performed on specimens of two types of sandstones,argillite and basalt that contain open and filled cracks.It was found that the presence of cracks tends to decrease the overall strength for all studied rocks;however,the magnitude of strength reduction is related to the property of rock.The larger strength decrease was observed for the relatively harder argillite and basalt,compared to the softer sandstone.It was also found that the infill material could increase the strength of rock specimens,while the obtained strength depended on the characteristics of the fill material.

Damage and failure characteristics of rock similar materials with pre-existing cracks

In order to further study the damage and failure mechanism for rock similar materials,this study investigated the mechanical properties and failure characteristics,law of damage space development,and damage evolution characteristics for rock similar materials with pre-existing cracks of varying length under uniaxial compression load.The equipment used in this study is the self-developed YYW-Ⅱ strain controlled unconfined compression apparatus and the PCIE-8 acoustic emission monitoring system.Results show that,as the length of pre-existing crack increases:(1) the peak and residual strength reduces,and the peak axial strain and the strain during the initial compression phase increases;(2) the major failure mode is changed from shear failure to tensile failure along a vertical plane that passes the middle of the pre-existing crack;(3) The damage increases during the stable and accelerated development stage,and the effect of the pre-existing cracks is more during the accelerated development stage than the stable development stage.

Plastic deformation mechanism transition of Ti/Ni nanolaminate with pre-existing crack:Molecular dynamics study

Tensile behaviors of Ti/Ni nanolaminate with model-I crack are investigated by molecular dynamics simulations.The Ti/Ni nanolaminates with center crack either in Ti layer or in Ni layer under different loading directions are utilized to systematically study the mechanical performance of the cracked material.The results indicate that pre-existing crack dramatically changes the plastic deformation mechanism of the Ti/Ni nanolaminate.Unlike the initial plastic deformation originating from the interface or weak Ti layer of the crack-free samples,the plastic behavior of cracked Ti/Ni nanolaminate first occurs at the crack tip due to the local stress concentration.Subsequent plastic deformation is dominated by the interaction between the crack and interface.The Ti/Ni interface not only impedes the movement of the initial plastic deformation carriers(dislocation,slip band,and deformation twinning)from the crack tip,but also promotes the movement of interfacial dislocations in the tension process.Microstructure evolution analysis further confirms that the plastic deformation mechanism transition is ascribed to the orientation-dependent tensile behavior at the crack tip,which is intrinsically attributed to the anisotropy of the certain crystal structure and loading direction of the cracked Ti/Ni nanolaminate.In addition,by analyzing the effects of different plastic deformation carriers on crack propagation in specific crystal,it can be discovered that the interfacial dislocations moving towards the crack tip can further promote the crack growth.

Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression

The mechanism of cracks propagation and cracks coalescence due to compressive loading of the brittle substances containing pre-existing cracks(flaws)was modeled experimentally using specially made rock-like specimens from Portland Pozzolana Cement(PPC).The breakage process of the specimens was studied by inserting single and double flaws with different inclination angles at the center and applying uniaxial compressive stress at both ends of the specimen.The first crack was oriented at 50° from the horizontal direction and kept constant throughout the analysis while the orientation of the second crack was changed.It is experimentally observed that the wing cracks are produced at the first stage of loading and start their propagation toward the direction of uniaxial compressive loading.The secondary cracks may also be produced in form of quasi-coplanar and/or oblique cracks in a stable manner.The secondary cracks may eventually continue their propagation in the direction of maximum principle stress.These experimental works were also simulated numerically by a modified higher order displacement discontinuity method and the cracks propagation and cracks coalescence were studied based on Mode I and Mode II stress intensity factors(SIFs).It is concluded that the wing cracks initiation stresses for the specimens change from 11.3 to 14.1 MPa in the case of numerical simulations and from 7.3 to 13.8 MPa in the case of experimental works.It is observed that cracks coalescence stresses change from 21.8 to 25.3 MPa and from 19.5 to 21.8 MPa in the numerical and experimental analyses,respectively.Comparing some of the numerical and experimental results with those recently cited in the literature validates the results obtained by the proposed study.Finally,a numerical simulation was accomplished to study the effect of confining pressure on the crack propagation process,showing that the SIFs increase and the crack initiation angles change in this case.

Recent research progress in the mechanism and suppression of fusion welding-induced liquation cracking of nickel based superalloys

Nickel-based superalloys are extensively used in the crucial hot-section components of industrial gas turbines,aeronautics,and astronautics because of their excellent mechanical properties and corrosion resistance at high temperatures.Fusion welding serves as an effective means for joining and repairing these alloys;however,fusion welding-induced liquation cracking has been a challenging issue.This paper comprehensively reviewed recent liquation cracking,discussing the formation mechanisms,cracking criteria,and remedies.In recent investigations,regulating material composition,changing the preweld heat treatment of the base metal,optimizing the welding process parameters,and applying auxiliary control methods are effective strategies for mitigating cracks.To promote the application of nickel-based superalloys,further research on the combination impact of multiple elements on cracking prevention and specific quantitative criteria for liquation cracking is necessary.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Effects of orientation on the fatigue crack growth behaviors of the ZK60 magnesium alloy in air and PBS

Strong anisotropic corrosion and mechanical properties caused by specimen orientations greatly limit the applications of wrought magnesium alloys.To investigate the influences of specimen orientation,the corrosion tests and(corrosion)fatigue crack growth tests were conducted.The rolled and transverse surfaces of the materials show distinct corrosion rate differences in the stable corrosion stage,but the truth is the opposite for the initial stage of corrosion.In air,specimen orientations have a significant influence on the plastic deformation mechanisms near the crack tip,which results in different fatigue fracture surfaces and cracking paths.Compared with R-T specimens,N-T specimens show a slower fatigue crack growth(FCG)rate in air,which can be attributed to crack closure effects and deformation twinning near the crack tip.The corrosion environment will not significantly change the main plastic deformation mechanisms for the same type of specimen.However,the FCG rate in phosphate buffer saline(PBS)is one order of magnitude higher than that in air,which is caused by the combined effects of hydrogen-induced cracking and anodic dissolution.Owing to the similar corrosion rates at crack tips,the specimens with different orientations display close FCG rates in PBS.

Unraveling engineering disturbance effects on deformation in red-bed mudstone railway cuttings:incorporating crack-facilitated moisture diffusion

Red-bed mudstone, prevalent in southwest China, poses a formidable challenge due to its hydrophilic clay minerals, resulting in expansion, deformation, and cracking upon exposure to moisture. This study addresses uplift deformation disasters in high-speed railways by employing a moisture diffusion-deformation-fracture coupling model based on the finite-discrete element method(FDEM). The model integrates the influence of cracks on moisture diffusion. The investigation into various excavation depths reveals a direct correlation between depth and the formation of tensile cracks at the bottom of the railway cutting. These cracks expedite moisture migration, significantly impacting the temporal and spatial evolution of the moisture field. Additionally, crack expansion dominates hygroscopic deformation, with the lateral coordinate of the crack zone determining peak vertical displacement. Furthermore, key factors influencing deformation in railway cuttings, including the swelling factor and initial moisture content at the bottom of the cutting, are explored. The number of tensile and shear cracks increases with greater excavation depth, particularly concerning shear cracks. Higher swelling factors and initial moisture contents result in an increased total number of cracks, predominantly shear cracks. Numerical calculations provide valuable insights, offering a scientific foundation and directional guidance for the precise prevention, control, prediction, and comprehensive treatment of mudstone-related issues in high-speed railways.

HZSM-5 zeolites undergoing the high-temperature process for boosting the bimolecular reaction in n-heptane catalytic cracking

High-temperature treatment is key to the preparation of zeolite catalysts.Herein,the effects of hightemperature treatment on the property and performance of HZSM-5 zeolites were studied in this work.X-Ray diffraction,N2physisorption,27Al magic angle spinning nuclear magnetic resonance(MAS NMR),and temperature-programmed desorption of ammonia results indicated that the hightemperature treatment at 650℃ hardly affected the inherent crystal and texture of HZSM-5zeolites but facilitated the conversion of framework Al to extra-framework Al,reducing the acid site and enhancing the acid strength.Moreover,the high-temperature treatment improved the performance of HZSM-5 zeolites in n-heptane catalytic cracking,promoting the conversion and light olefins yield while inhibiting coke formation.Based on the kinetic and mechanism analysis,the improvement of HZSM-5 performance caused by high-temperature treatment has been attributed to the formation of extra-framework Al,which enhanced the acid strength,facilitated the bimolecular reaction,and promoted the entropy change to overcome a higher energy barrier in n-heptane catalytic cracking.

Evolution model and failure mechanisms of rainfall-induced cracked red clay slopes:insights from Xinshao County,China

Red clay landslides are widely distributed worldwide,resulting in severe loss of life and property.Although rainfall-induced red clay slopes have received extensive attention,the role of cracks in the evolutionary process of red clay slopes and their connection to failure mechanisms is still poorly understood.A comprehensive approach integrating field investigation,laboratory tests,and numerical simulations was conducted to study the 168 red clay landslides in Xinshao County,China.The results show that red clay is prone to forming cracks at high moisture content due to its low swelling and high shrinkage properties.The failure mode of red clay slopes can be summarized in three stages:crack generation,slope excavation,and slope failure.Furthermore,the retrospective analysis and numerical simulations of the typical landslide in Guanchong indicated that intense rainfall primarily impacts the shallow layer of soil within approximately 0.5 m on the intact slope.However,cracks change the pattern of rainfall infiltration in the slope.Rainwater infiltrates rapidly through the preferential channels induced by the cracks rather than uniformly and slowly from the slope surface.This results in a significant increase in both the depth of infiltration and the saturated zone area of the cracked slope,reaching 3.8 m and 36.2 m^(2),respectively.Consequently,the factor of safety of the slope decreases by 13.4%compared to the intact slope,ultimately triggering landslides.This study can provide valuable insights into understanding the failure mechanisms of red clay slopes in China and other regions with similar geological settings.

Effect of icosahedral phase formation on the stress corrosion cracking(SCC)behaviors of the as-cast Mg-8%Li(in wt.%)based alloys

Through exploring the stress corrosion cracking(SCC)behaviors of the as-cast Mg-8%Li and Mg-8%Li-6%Zn-1.2%Y alloys in a 0.1 M NaCl solution,it revealed that the SCC susceptibility index(I_(SCC))of the Mg-8%Li alloy was 47%,whilst the I_(SCC)of the Mg-8%Li-6%Zn-1.2%Y alloy was 68%.Surface,cross-sectional and fractography observations indicated that for the Mg-8%Li alloy,theα-Mg/β-Li interfaces acted as the preferential crack initiation sites and propagation paths during the SCC process.With regard to the Mg-8%Li-6%Zn-1.2%Y alloy,the crack initiation sites included the I-phase and the interfaces of I-phase/β-Li andα-Mg/β-Li,and the preferential propagation paths were the I-phase/β-Li andα-Mg/β-Li interfaces.Moreover,the SCC of the two alloys was concerned with hydrogen embrittlement(HE)mechanism.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Simulation of Corrosion-Induced Cracking of Reinforced Concrete Based on Fracture Phase Field Method

Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.

Detection of internal crack growth in polyethylene pipe using guided wave ultrasonic testing

Despite the success of guided wave ultrasonic inspection for internal defect detection in steel pipes,its application on polyethylene(PE)pipe remains relatively unexplored.The growth of internal cracks in PE pipe severely affects its pressure-holding capacity,hence the early detection of internal cracks is crucial for effective pipeline maintenance strategies.This study extends the scope of guided wave-based ultrasonic testing to detect the growth of internal cracks in a natural gas distribution PE pipe.Laboratory experiments and a finite element model were planned to study the wave-crack interaction at different stages of axially oriented internal crack growth with a piezoceramic transducer-based setup arranged in a pitch-catch configuration.Mode dispersion analysis supplemented with preliminary experiments was performed to isolate the optimal inspection frequency,leading to the selection of the T(0,1)mode at 50-kHz for the investigation.A transmission index based on the energy of the T(0,1)mode was developed to trace the extent of simulated crack growth.The findings revealed an inverse linear correlation between the transmission index and the crack depth for crack growth beyond 20%crack depth.