Using fracture mechanics method to analyze the failure mechanism and equilibrium equation of interfacial loess-mudstone landslides

Loess-mudstone landslides are common in the Loess Plateau.Investigations into the mechanical theory of loess-mudstone landslides have become a challenging undertaking due to the distinctive interfacial properties of loess-mudstone and the unique water sensitivity characteristics of mudstone.Hence,it is imperative to develop innovative mechanical models and mathematical equations specifically tailored to loess-mudstone landslides.In this study,we analyze the fracture mechanism of the loess-mudstone sliding zone using plastic fracture mechanics and develop a unique fracture yield model.To calculate the energy release rate during the expansion of the loess-mudstone interface tip region,the shear fracture energy G is applied,which reflects both the yield failure criterion and the fracture failure criterion.To better understand the instability mechanism of loess-mudstone landslides,equilibrium equations based on G are established for tractive,compressive,and tensile loess-mudstone landslides.Based on the equilibrium equation,the critical length Lc of the sliding zone can be used for the safety evaluation of loess-mudstone landslides.In this way,this study proposes a new method for determining the failure mechanism and equilibrium equation of loessmudstone landslides,which resolves their starting mechanism,mechanical equilibrium equations,and safety evaluation indicators,thus justifying the scientific significance and practical value of this research.

Integrity and Failure Analysis of Cement Sheath Subjected to Coalbed Methane Fracturing

Perforation and fracturing are typically associated with the development of coalbed methane wells.As the cement sheath is prone to failure during this process,in this work,the effects of the casing pressure,elastic modulus of the cement,elastic modulus of the formation,and casing eccentricity on the resulting stresses are analyzed in the frame of a finite element method.Subsequently,sensitivity response curves of the cement sheath stress are plotted by normalizing all factors.The results show that the maximum circumferential stress and Mises stress of the cement sheath increase with the casing internal pressure,elastic modulus of the cement and casing eccentricity.As the elastic modulus of the formation increases,the maximum circumferential stress of the cement sheath decreases,and its maximum Mises stress increases slightly.The cement sheath undergoes tensile failure during coalbed methane fracturing.The stress sensitivity of the cement sheath to the influential parameters is in the following order:casing internal pressure>elastic modulus of cement sheath>casing eccentricity>elastic modulus of formation.

Modelling fracture propagation and failure in a rock pillar under mechanical and thermal loadings

The Aspoe Pillar Stability Experiment （APSE） was conducted to study the rock mass response in a heated rock pillar between two large boreholes. This paper summarizes the back calculations of the APSE using a two-dimensional （2D） fracture propagation code FRACOD. To be able to model all the loading phases of the APSE, including the thermal loading, the code was improved in several ways. A sequential excavation function was developed to model promptly the stepwise changing loading geometry. Prior to the mod- elling, short-term compressive strength test models were set up aiming to reproduce the stress-strain behaviour observed for the Aspoe diorite in laboratory. These models simulate both the axial and lateral strains of radial-controlled laboratory tests, The volumetric strain was calculated from the simulations and compared with the laboratory results, The pillar models include vertical and horizontal 2D models from where the stress in the pillar wall was investigated, The vertical model assesses the stability of the experimental rock volume and suggests the resultant stress below the tunnel floor in the pillar area. The horizontal model considers cross-sections of the pillar between the two large boreholes. The horizon- tal model is used to simulate the evolution of the stress in the rock mass during the excavation of the boreholes and during and the heating phase to give an estimation of the spalling strength. The modelling results suggest that the excavation-induced stresses will cause slight fracturing in the pillar walls, if the strength of the APSE pillar is set to about 123 MPa. Fracture propagation driven by thermal loading leads to minor spalling. The thermal evolution, elastic behaviour and brittle failure observed in the experiment are well reflected by the models.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n)) ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.As σ_(n) increases,the peak stress shows an increasing trend,with correlation coefficients R² ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,as σ_(n) increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

Implications for fault reactivation and seismicity induced by hydraulic fracturing

Evaluating the physical mechanisms that link hydraulic fracturing(HF) operations to induced earthquakes and the anticipated form of the resulting events is significant in informing subsurface fluid injection operations. Current understanding supports the overriding role of the effective stress magnitude in triggering earthquakes, while the impact of change rate of effective stress has not been systematically addressed. In this work, a modified critical stiffness was brought up to investigate the likelihood, impact,and mitigation of induced seismicity during and after hydraulic fracturing by developing a poroelastic model based on rate-and-state fraction law and linear stability analysis. In the new criterion, the change rate of effective stress was considered a key variable to explore the evolution of this criterion and hence the likelihood of instability slip of fault. A coupled fluid flow-deformation model was used to represent the entire hydraulic fracturing process in COMSOL Multiphysics. The possibility of triggering an earthquake throughout the entire hydraulic fracturing process, from fracturing to cessation, was investigated considering different fault locations, orientations, and positions along the fault. The competition between the effects of the magnitude and change rate of effective stress was notable at each fracturing stage. The effective stress magnitude is a significant controlling factor during fracturing events, with the change rate dominating when fracturing is suddenly started or stopped. Instability dominates when the magnitude of the effective stress increases(constant injection at each fracturing stage) and the change rate of effective stress decreases(the injection process is suddenly stopped). Fracturing with a high injection rate, a fault adjacent to the hydraulic fracturing location and the position of the junction between the reservoir and fault are important to reduce the Coulomb failure stress(CFS) and enhance the critical stiffness as the significant disturbance of stresses at these positions in the coupled process. Therefore,notable attention should be given to the injection rate during fracturing, fault position, and position along faults as important considerations to help reduce the potential for induced seismicity. Our model was verified and confirmed using the case of the Longmaxi Formation in the Sichuan Basin, China, in which the reported microseismic data were correlated with high critical stiffness values. This work supplies new thoughts of the seismic risk associated with HF engineering.

A comparison of electromigration failure of metal lines with fracture mechanics

Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to characterize the electromigration failure, a comparison study is carded out with some typical phenomena treated by fracture mechanics for thin and large structures. An example of thin structures, which have been treated by fracture mechanics, is silica opti- cal fibers for communication systems. The damage growth in a metal line by electromigration is characterized in compar- ison with the crack growth in a silica optical fiber subjected to static fatigue. Also a brief comparison is made between the electromigration failure and some fracture phenomena in large structures.

Mechanical properties and failure characteristics of fractured sandstone with grouting and anchorage

Based on uniaxial compression experimental results on fractured sandstone with grouting and anchorage, we studied the strength and deformation properties, the failure model, crack formation and evolution laws of fractured sandstone under different conditions of anchorage. The experimental results show that the strength and elastic modulus of fractured sandstone with different fracture angles are significantly lower than those of intact sandstone. Compared with the fractured samples without anchorage,the peak strength, residual strength, peak and ultimate axial strain of fractured sandstone under different anchorage increase by 64.5–320.0%, 62.8–493.0%, and 31.6–181.4%, respectively. The number of bolts and degree of pre-stress has certain effects on the peak strength and failure model of fractured sandstone. The peak strength of fractured sandstone under different anchorage increases to some extent, and the failure model of fractured sandstone also transforms from tensile failure to tensile–shear mixed failure with the number of bolts. The pre-stress can restrain the formation and evolution process of tensile cracks, delay the failure process of fractured sandstone under anchorage and impel the transformation of failure model from brittle failure to plastic failure.

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and. nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.

Investigation on Effects of Mooring Line Fractures and Connector Failures for A Hybrid Modular Floating Structure System

The present work reports a Hybrid Modular Floating Structure(HMFS)system with typical malfunction conditions.The effects of both fractured mooring lines and failed connectors on main hydrodynamic responses(mooring line tensions,module motions,connector loads and wave power production)of the HMFS system under typical sea con-ditions are comparatively investigated.The results indicate that the mooring tension distribution,certain module motions(surge,sway and yaw)and connector loads(Mz)are significantly influenced by mooring line fractures.The adjacent mooring line of the fractured line on the upstream side suffers the largest tension among the remaining mooring lines,and the case with two fractured mooring lines in the same group on the upstream side is the most dangerous among all cases of two-line failures in view of mooring line tensions,module motions and connector loads.There-fore,one emergency strategy with appropriate relaxation of a proper mooring line has been proposed and proved effective to reduce the risk of more progressive mooring line fractures.In addition,connector failures substantially affect certain module motions(heave and pitch),certain connector loads(Fz and My)and wave power production.The present work can be helpful and instructive for studies on malfunction conditions of modular floating structure(MFS)systems.

Particle simulation of the failure process of brittle rock under triaxial compression

In order to investigate the failure process of brittle rock under triaxial compression through both experimental and numerical approaches, the particle simulation method was used in numerical simulations and the simulated results were compared with those of the experiment. The numerical simulation results, such as fracture propagation, microcrack distribution, stress-strain response, and damage patterns, were discussed in detail. The simulated results under various confining pressures （0-60 MPa） are in good agreement with the experimental results. The simulated results reveal that rock failure is caused by axial splitting under uniaxial compression. As the confining pressure increases, rock failure occurs in a few localized shear planes and the rock mechanical behavior is changed from brittle to ductile. Consequently, the peak failure strength, microcrack numbers, and the shear plane angle increase, but the ratio of tensile to shear microcracks decreases. The damage formation during the compression simulations indicates that the particle simulation method can produce similar behaviors as those observed through laboratory compression tests.

Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method (FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory (URL) Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks (DFNs) of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.

Improved Reliability Analysis Method Based on the Failure Assessment Diagram

With the uncertainties related to operating conditions,in-service non-destructive testing（NDT） measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram（FAD） approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics（PFM） assessment method is proposed.By integrating 2D kernel density estimation（KDE） technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.

Experimental and numerical study of failure behavior and mechanism of coal under dynamic compressive loads

A comprehensive understanding of the failure behavior and mechanism of coal is a prerequisite for dealing with dynamic problems in mining space.In this study,the failure behavior and mechanism of coal under uniaxial dynamic compressive loads were experimentally and numerically investigated.The experiments were conducted using a split Hopkinson pressure bar(SHPB)system.The results indicated that the typical failure of coal is lateral and axial at lower loading rates and totally smashed at higher loading rates.The further fractography analysis of lateral and axial fracture fragments indicated that the coal failure under dynamic compressive load is caused by tensile brittle fracture.In addition,the typical failure modes of coal under dynamic load were numerically reproduced.The numerical results indicated that the axial fracture is caused directly by the incident compressive stress wave and the lateral fracture is caused by the tensile stress wave reflected from the interface between coal specimen and transmitted bar.Potential application was further conducted to interpret dynamic problems in underground coal mine and it manifested that the lateral and axial fractures of coal constitute the parallel cracks in the coal mass under roof fall and blasting in mining space.

Phenomena and theoretical analysis for the failure of brittle rocks

Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.

Composite wedge failure using photogrammetric measurements and DFN-DEM modelling

Analysis and prediction of structural instabilities in open pit mines are an important design and operational consideration for ensuring safety and productivity of the operation. Unstable wedges and blocks occurring at the surface of the pit walls may be identified through three-dimensional(3D) image analysis combined with the discrete fracture network(DFN) approach. Kinematic analysis based on polyhedral modelling can be used for first pass analysis but cannot capture composite failure mechanisms involving both structurally controlled and rock mass progressive failures. A methodology is proposed in this paper to overcome such limitations by coupling DFN models with geomechanical simulations based on the discrete element method(DEM). Further, high resolution photogrammetric data are used to identify valid model scenarios. An identified wedge failure that occurred in an Australian coal mine is used to validate the methodology. In this particular case, the failure surface was induced as a result of the rock mass progressive failure that developed from the toe of the structure inside the intact rock matrix. Analysis has been undertaken to determine in what scenarios the measured and predicted failure surfaces can be used to calibrate strength parameters in the model.

Mechanism of progressive failure of a slope with a steep joint under the action of freezing and thawing:model test

The stability of slope rock masses is influenced by freeze-thaw cycles in cold region,and the mechanism of stability deterioration is not clear.In order to understand the damage and progressive failure characteristics of rock masses under the action of freezing and thawing,a model test was conducted on slope with steep joint in this study.The temperature,frost heaving pressure and deformation of slope rock mass were monitored in real-time during the test and the progressive failure mode was studied.The experimental results show that the temperature variations of cracking and the rock mass of a slope are different.There are obvious latent heat stages in the temperature-change plot in the crack,but not in the slope rock masses.The frost heaving effect in the fracture is closely related to the constraint conditions,which change with the deformation of the fracture.The frost heaving pressure fluctuates periodically during freezing and continues to decrease during thawing.The surface deformation of the rock mass increases during freezing,and the deformation is restored when it thaws.Freeze-thaw cycling results in residual deformation of the rock mass which cannot be fully restored.Analysis shows that the rock mass at the free side of the steep-dip joint rotates slightly under the frost heaving effect,causing fracture propagation.The fracture propagation pattern is a circular arc at the beginning,then extends to the possible sliding direction of the rock mass.Frost heaving force and fracture water pressure are the key factors for the failure of the slope,which can cause the crack to penetrate the rock mass,and a landslide ensues when the overall anti-sliding resistance of the rock mass is overcome.

Master crack types and typical acoustic emission characteristics during rock failure

Acoustic emission(AE)signals contain substantial information about the internal fracture characteristics of rocks and are useful for revealing the laws governing the release of energy stored therein.Reported here is the evolution of rock failure with diferent master crack types as investigated using Brazilian splitting tests(BSTs),direct shear tests(DSTs),and uniaxial compression tests(UCTs).The AE parameters and typical modes of each fracture type were obtained,and the energy release characteristics of each fracture mechanism were discussed.From the observed changes in the AE parameters,the rock fracture process exhibits characteristics of staged intensifcation.The scale and energy level of crack activity in the BSTs were signifcantly lower than those in the DSTs and UCTs.The proportion of tensile cracks in the BSTs was 65%–75%,while the proportions of shear cracks in the DSTs and UCTs were 75%–85%and 70%–75%,respectively.During the rock loading process under diferent conditions,failure was accompanied by an increased number of shear cracks.The amplitude,duration,and rise time of the AE signal from rock failure were larger when the failure was dominated by shear cracks rather than tensile ones,and most of the medium-and high-energy signals had medium to low frequencies.After calculating the proposed energy amplitude ratio,the energy release of shear cracks was found to exceed that of tensile cracks at the same fracture scale.

Practical application of failure criteria in determining safe mud weight windows in drilling operations

Wellbore instability is reported frequently as one of the most significant incidents during drilling operations.Analysis of wellbore instability includes estimation of formation mechanical properties and the state of in situ stresses.In this analysis,the only controllable parameter during drilling operation is the mud weight.If the mud weight is larger than anticipated,the mud will invade into the formation,causing tensile failure of the formation.On the other hand,a lower mud weight can result in shear failures of rock,which is known as borehole breakouts.To predict the potential for failures around the wellbore during drilling,one should use a failure criterion to compare the rock strength against induced tangential stresses around the wellbore at a given mud pressure.The Mohr–Coulomb failure criterion is one of the commonly accepted criteria for estimation of rock strength at a given state of stress.However,the use of other criteria has been debated in the literature.In this paper,Mohr–Coulomb,Hoek–Brown and Mogi–Coulomb failure criteria were used to estimate the potential rock failure around a wellbore located in an onshorefield of Iran.The log based analysis was used to estimate rock mechanical properties of formations and state of stresses.The results indicated that amongst different failure criteria,the Mohr–Coulomb criterion underestimates the highest mud pressure required to avoid breakouts around the wellbore.It also predicts a lower fracture gradient pressure.In addition,it was found that the results obtained from Mogi–Coulomb criterion yield a better comparison with breakouts observed from the caliper logs than that of Hoek–Brown criterion.It was concluded that the Mogi–Coulomb criterion is a better failure criterion as it considers the effect of the intermediate principal stress component in the failure analysis.

Integrated modeling of fracturing-flowback-production dynamics and calibration on field data:Optimum well startup scenarios

We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.

Failure modes and slabbing mechanisms of hard rock with different height-to-width ratios under uniaxial compression

To determine the relationship between slabbing failure and the specimen height-to-width(H/W)ratio and to analyze the conditions,characteristics,and mechanism of slabbing failure in the laboratory,uniaxial compression tests were conducted using six groups of granite specimens.The entire failure process was recorded using strain gauges and high-speed cameras.The initiation and propagation of fractures in specimens were identified by analyzing the monitoring results of stress,strain,and acoustic emission.The experimental results show that changes in the specimen H/W ratio can transform the macro failure mode.When the H/W ratio is reduced to 0.5,the macro failure mode is dominated by slabbing.Low load-bearing ability is observed in specimens with slabbing failure,and the slabbing fractures are approximately parallel to the loading direction.Moreover,the fracture propagation characteristics and acoustic emission signals of slabbing failure specimens show typical tensile failure characteristics,indicating that slabbing failure is essentially a special tensile failure.