A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

Statistical damage constitutive model for concrete materials under uniaxial compression

According to the damage mechanism of concrete material during the uniaxial compressive failure process,this paper further establishes the statistical damage constitutive model of concrete subjected to uniaxial compressive stress based on the statistical damage model under uniaxial tension. The damage evolution law in the direction subjected to pressure is confirmed by the tensile damage evolution process of lateral deformation due to the Poisson effect,and then the compressive stress-strain relationship is defined. The peak nominal stress state and the critical state occurring in the macro longitudinal distributed splitting cracks are distinguished. The whole loading process can be divided into the even damage phase and the local breakage phase. The concrete specimen is divided into the failure process zone and the resting unloading zone. The size effects during the local breakage phase under the uniaxial monotonic compressive process and the hysteretic phenomenon under the cyclic compressive loading process are analyzed. Finally,the comparison between theoretical results and experimental results preliminarily verifies the rationality and feasibility of understanding the failure mechanism of concrete through the statistical damage constitutional law.

The Mechanical Characteristics and Damage Model of Helan Mountain Rock based on Acoustic Emission

With the risk of disappearing for the rock paintings considering long-term exposure in Helan Mountain,the freeze-thaw(F-T)cycling experiments were carried out with 12-hour F-T cycling(0,10,20,30,and 40 F-T cycles)under five kinds of confining pressures(5,10,20,30,and 40 MPa).The acoustic emission(AE)detect technology was used to reveal the rock fracturing characteristics during the triaxial compression test whole process.The stress-strain relation changes along with different confining pressures and F-T cycles.Peak stress and residual stress changes along with different confining pressures and damages,and the variation of axial stress-AE ringing counts-time changes along with different confining pressures and F-T cycles.The damage variable with AE parameter under F-T and force coupling was defined for the first time,and the damages model was established.The experimental results show that the F-T cycles lead to the decrease of rock strength and the gradual transformation of compression failure mode from brittleness to plasticity.The confining pressure provides a certain ability to resist deformation and inhibit crack growth for rock samples after F-T cycles.The temporal and spatial evolution law of AE counts well corresponds to the loading and failure process of the rock samples.The AE 3D positioning technology can accurately capture the development position and direction of internal cracks and pores of rock,and the failure form is conical shear failure.The established damage model has a better fittingness between the theoretical calculation results and the test results,and is reasonable to be used in the future for protection of Helan Mountain rock painting.

Study on Acoustic Emission Characteristics of Self-Compacting Concrete under Uniaxial Compression Test

To study the relationship between acoustic emission characteristic parameters of self-compacting concrete(SCC)and its destruction evolution,under uniaxial compression,acoustic emission(AE)tests are performed on C30 selfcompacting concrete test blocks that are preserved for 7 days and 28 days,the corresponding relationship among energy,amplitude,ring count and different failure stages of the specimens are analyzed by AE experiment,and the spatial distribution of AE in each stage is described by introducing location map.The test shows that there are two rules for the failure of SCC specimens cured for 7 days and 28 days:(1)The first failure law is divided into four stages according to the percentage of the stress value reaching the limit stress:Initial stage:above 10%,the compaction time of test block cured for 28 days is relatively low;Elastic failure stage:30%–35%,the cumulative value of each parameter increases linearly,and the cumulative value of the amplitude is the largest;Crack stable propagation stage:35%–90%,there is a moment that causes local stress concentration in both test blocks;Active stage:above 90%,the cumulative value of the parameter rises sharply,then continues to load the test block instability and damage.(2)The second failure law is divided into five stages according to the percentage of the stress value reaching the limit stress:Initial stage:15%–20%,the cumulative value of each parameter increases with time;Elastic failure stage:20%–40%,the cumulative value of the parameter continues to grow,but the growth curve is approximately parallel;Crack stable propagation stage:40%–60%,all parameters increased sharply and the increase reached the peak of the whole process;A stable state:60–80%,the emission characteristic parameter will become zero,and the stable state of the 28 days curing test block is lagging;Active stage:above 90%,the number of signals increased sharply,but the energy and amplitude are low,and the later test block is completely fractured.(3)In the process of failure,the test block of SCC will form an inverted triangle or landslide failure surface,and the part above the failure surface is prone to failure,and there is a tendency to leave the test block.(4)Under uniaxial compression,the penetration of SCC cracks is mostly shear penetration.

A Damage Model of Acoustic Emission in Rock and Its Initial Application in Seismological Research

The model of the relationship of AE parameter,damage variable and strain is derived by applying the damage theory and micro-element statistical strength theory.The relation between AE characteristics during rock failure and machine stiffness is analyzed under uniaxial compression with the above model.Based on the above analysis,the internal connection among AE activity law and seisraogenic process and earthquake activity is discussed.

Acoustic emission responses and damage estimation of coal with carbon fiber-reinforced polymer confinement under uniaxial compression

Fiber-reinforced polymer(FRP)wrapping is a potential technique for coal pillar reinforcement.In this study,an acoustic emission(AE)technique was employed to monitor coal specimens with carbon FRP(CFRP)jackets during uniaxial compression,which addressed the inability to observe the cracks inside the FRP-reinforced coal pillars by conventional field inspection techniques.The spatiotemporal fractal evolution of the cumulated AE events during loading was investigated based on fractal theory.The results indicated that the AE response and fractal features of the coal specimens were closely related to their damage evolution,with CFRP exerting a significant influence.In particular,during the unstable crack development stage,the evolutionary patterns of the AE count and energy curves of the CFRPconfined specimens underwent a transformation from the slight shockemajor shock type to the slight shockesub-major shockeslight shockemajor shock type,in contrast to the unconfined coal specimens.The AE b-values decreased to a minimum and then increased marginally.The AE spatial fractal dimension increased rapidly,whereas the AE temporal fractal dimension fluctuated significantly during the accumulation and release of strain energy.Ultimately,based on the AE count and AE energy evolution,a damage factor was proposed for the coal samples with CFRP jackets.Furthermore,a damage constitutive model was established,considering the CFRP jacket and the compaction characteristics of the coal.This model provides an effective description of the stressestrain relationship of coal specimens with CFRP jackets.

Uniaxial experimental study of the acoustic emission and deformation behavior of composite rock based on 3D digital image correlation(DIC)

In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3 D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the θ = 0?–45?specimens had obvious plastic deformation during loading, and the brittleness of the θ = 60?–90?specimens gradually increased during the loading process. When the anisotropic angle θincreased from 0?to 90?, the peak strength, peak strain,and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories:tensile fracture across the discontinuities(θ = 0?–30?), slid-ing failure along the discontinuities(θ = 45?–75?), and tensile-split along the discontinuities(θ = 90?). The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the θ = 0?–45?specimens and was almost the same as that of the θ = 60?–90?specimens. As for the strain localization highlighted in the maximum principal strain field, the θ = 0?–30?specimens appeared in the rock matrix approximately parallel to the loading direction,while in the θ = 45?–90?specimens it appeared at the hard and weak rock layer interface.

Investigating the mechanical and acoustic emission characteristics of brittle failure around a circular opening under uniaxial loading

The size of underground openings in rock masses in metal mines is critical to the performance of the openings. In this study, the mechanical and acoustic emission (AE) characteristics of brittle rock-like specimens containing a circular opening with different ratios of opening diameter to sample size λ (λ = 0.1, 0.13, 0.17, 0.2, and 0.23) were investigated under uniaxial compression with AE monitoring. The results indicate that the opening size strongly affected the peak strength and the elastic modulus. Crack initiation first started from the upper surface of the specimens, not from the periphery of the openings. Tensile and shear cracks coexisted on the roof and floor of the specimens, whereas tensile cracks were dominant on the two sides. The fracture mode of samples with openings was partially affected by the relative size of the pillars and openings. The AE response curves (in terms of counts, cumulative energy, cumulative counts, and b-value) show that brittle failure was mainly a progressive process. Moreover, the AE information corresponded well with microcrack evolution in the samples and thus can be used to predict sample failure.

Stress-strain-acoustic responses in failure process of coal rock with different height to diameter ratios under uniaxial compression

Residual coal pillars play an important role in mining the adjacent coal seam safely,managing the gobs and maintaining the stability of abandoned coal mines.The height to diameter ratio(H/D)affects the stability of residual coal pillars.In this study,uniaxial compressive tests of coal specimens with five H/D(2.0,1.5,1.0,0.8 and 0.6)were performed,and the stress,strain and acoustic emission(AE)were monitored.Results show that the uniaxial compressive strength(UCS)and peak strain increase with H/D decreasing.An empirical equation is proposed to calculate the UCS based on the H/D.The AE activities during coal failure process can be separated into four periods.The span of quiet period and rapid decline period shorten with H/D decreasing.The smaller the H/D is,the more complicated the failure characteristics of coal will be.The failure form of coal with H/D of 2.0,1.5,and 1.0 is primarily shear failure,while splitting failure along the axial direction is the mainly mode when H/D is 0.8 or 0.6.The initiation,expansion,aggregation and connection of micro-cracks can be reflected by the real-time spatial evolution of AE event points.

Monitoring damage evolution of steel strand using acoustic emission technique and rate process theory

Utilizing the acoustic emission(AE) technique, an experimental investigation into the damage evolution for steel strand under axial tension was described. The damage evolution model for steel stand relating the damage evolution to acoustic emission parameters was proposed by incorporating the AE rate process theory. The AE monitoring results indicate that damages occur in both elastic and plastic phases of steel strand. In elastic phase, AE signals are mainly sent out from the micro damage due to the surface friction among the wires of steel strand, while in plastic phase, AE signals emitted from the plastic deformation of wires. In addition, the AE cumulative parameters curves closely resemble the loading curve. The AE cumulative parameters curves can well describe the damage evolution process including the damage occurrence and damage development for steel strands. It is concluded that the AE technique is an effective and useful nondestructive technique for evaluating the damage characteristics of steel strand.

Damage evolution law of coal-rock under uniaxial compression based on the electromagnetic radiation characteristics

Based on electromagnetic radiation characteristics, the present research studied the damage evolution of rock under uniaxial compression. Besides, this research built the coal-rock damage evolution model considered residual strength. The applicability and accuracy of the model were verified through experiments. The results show that coal-rock damage evolution consists of four periods. The first period is from the beginning of compression to nearly 20% of the stress peak value, during which the damage variable changes stably about 0.1, and accordingly a few of electromagnetic radiation signals emerge. The second period is from about 20% to 70% of the stress peak value. The damage has stable development, and the parameter of electromagnetic radiation characteristics turns larger continuously with the increase of stress. The third period is when the damage has accelerated development, the coal-rock was broken which result from sharp increasing of the damage variable, meanwhile a great quantity of electromagnetic radiation signals emerge. The fourth period is after the coal-rock fracture, during which the damage variable corresponding to the parameter of electromagnetic radiation characteristics has a stable development. This research has great academic and realistic significance for further studies the electromagnetic radiation characteristics of coal-rock under loading and damage and the forecasting of coal-rock dynamic disasters.

Damage characteristics of thermally treated granite under uniaxial compression: Insights from active and passive ultrasonic techniques

To explore the effects of thermal treatment on cracking processes in granite, granite samples were thermally treated at 25-400 ℃ and then loaded under uniaxial compression. Active ultrasonic testing and passive acoustic emission(AE) monitoring were combined to monitor the damage characteristics of the samples. The uniaxial compression strength(UCS) of the sample treated at 200 ℃ shows no apparent change compared with that of the nonheated sample, while the UCS increases at 300 °C and decreases at 400 ℃. As the temperature increases from 25 to 400 ℃, the initial P-wave velocity(Vp) decreases gradually from 4909 to 3823 m/s, and the initial Vpanisotropy ε increases slightly from 0.03 to 0.09. As the axial stress increases, ε increases rapidly in the crack closure stage and unstable cracking stage. The attenuation of ultrasonic amplitude spectra also shows an obvious anisotropy. Besides, the main location magnitude of AE events decreases after thermal treatment, and low-frequency AE events and high-amplitude AE events increasingly occur. However, there is insufficient evidence that the treatment temperature below 400 ℃ has a significant effect on the temporal characteristics, source locations, and b-values of AE.

Experimental study on mesostructural damage evolution of sandstone subjected to freeze-thaw cycling under uniaxial compression

In perennially frozen or seasonally frozen soil regions,freeze-thaw cycling adversely impacts the mechanical properties of rock mass,resulting in landslides,rock erosion,and other geological disasters.The microscopic damage evolution law of loaded sandstone under the freeze-thaw cycle is analyzed by conducting Nuclear Magnetic Resonance(NMR)and uniaxial compression acoustic emission(AE)experiments.The experimental results have shown that:(1)Freeze-thaw cycling increases sandstone's internal pores,enlarges the pore size,and modifies the original pore distribution.(2)The damage due to freeze-thaw cycling is positively correlated with the initial damage to the rock,and the damage on the rock surface is more severe than inside the rock sample.(3)Freeze-thaw cycling negatively impacts the mechanical properties of sandstone,and the elastic deformation stage of sandstone gradually decreases as the number of freeze-thaw cycles increases and gradually transitions from brittle failure to ductile failure.(4)The characteristic parameters of AE ringing count and accumulated energy can reveal the severity of freeze-thaw damage and the dynamic evolution process,and the damage development rate exhibits abrupt changes at critical moments.After five freeze-thaw cycles,the damage development rate rises suddenly,as manifested by a sharp increase in the frequency and energy of AE events.High-energy AE events frequently occur during the rapid expansion period of damage,which can be adopted as an essential reference for damage propagation and aggravation.

Mechanical responses and acoustic emission behaviors of coal under compressive differential cyclic loading(DCL):a numerical study via 3D heterogeneous particle model

The stability of coal walls(pillars)can be seriously undermined by diverse in-situ dynamic disturbances.Based on a 3D par-ticle model,this work strives to numerically replicate the major mechanical responses and acoustic emission(AE)behaviors of coal samples under multi-stage compressive cyclic loading with different loading and unloading rates,which is termed differential cyclic loading(DCL).A Weibull-distribution-based model with heterogeneous bond strengths is constructed by both considering the stress-strain relations and AE parameters.Six previously loaded samples were respectively grouped to indicate two DCL regimes,the damage mechanisms for the two groups are explicitly characterized via the time-stress-dependent variation of bond size multiplier,and it is found the two regimes correlate with distinct damage patterns,which involves the competition between stiffness hardening and softening.The numerical b-value is calculated based on the mag-nitudes of AE energy,the results show that both stress level and bond radius multiplier can impact the numerical b-value.The proposed numerical model succeeds in replicating the stress-strain relations of lab data as well as the elastic-after effect in DCL tests.The effect of damping on energy dissipation and phase shift in numerical model is summarized.

Fracture evolution around pre-existing cylindrical cavities in brittle rocks under uniaxial compression

The development of fracture around pre-existing cylindrical cavities in brittle rocks was examined using physical models and acoustic emission technique. The experimental results indicate that when granite blocks containing one pre-existing cylindrical cavity are loaded in uniaxial compression condition, the profiles of cracks around the cavity can be characterized by tensile cracking （splitting parallel to the axial compression direction） at the roof-floor, compressive crack at two side walls, and remote or secondary cracks at the perimeter of the cavity. Moreover, fracture around cavity is size-dependent. In granite blocks containing pre-existing half-length cylindrical cavities, compressive stress concentration is found to initiate at the two sidewalls and induce shear crack propagation and coalescence. In granite blocks containing multiple parallel cylindrical cavities, the adjacent cylindrical cavities can influence each other and the eventual failure mode is determined by the interaction of tensile, compressive and shear stresses. Experimental results show that both tensile and compressive stresses play an important role in fracture evolution process around cavities in brittle rocks.

Damage and failure rule of rock undergoing uniaxial compressive load and dynamic load

For understanding the damage and failure rule of rock under different uniaxial compressive loads and dynamic loads, tests on red sandstone were carried out on Instron 1342 electro-servo controlled testing system with different uniaxial compressive loads of 0, 2, 4 and 6 MPa. It is found that peak stress, peak strain, elastic modulus and total strain energy decrease with the increase of static compressive stress. Based on the test results, the mechanism on damage and failure of rock was analyzed, and according to the equivalent strain hypothesis, a new constitutive model of elastic-plastic damage was established, and then the calculated results with the established model were compared with test results to show a good agreement. Furthermore the rule of releasing ratio of damage strain energy was discussed.

Effect of heterogeneity on mechanical and acoustic emission characteristics of rock specimen

The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks.The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC 3D software.Five schemes were adopted to investigate the influence of heterogeneity.The results demonstrate that as the homogeneity increases,the peak strength and brittleness of rocks increase,and the macro elastic modulus improves as well.Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0.The volume expansion is not so obvious when the homogeneity increases.As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock.When the homogeneity coefficient is high,the cumulative acoustic emission events-axial strain curve is gentle before the rock failure.The numerical results agree with the previously numerical results and earlier experimental measurements.

Spatial correlation-based characterization of acoustic emission signal-cloud in a granite sample by a cube clustering approach

To extract more in-depth information of acoustic emission(AE)signal-cloud in rock failure under triaxial compression,the spatial correlation of scattering AE events in a granite sample is effectively described by the cube-cluster model.First,the complete connection of the fracture network is regarded as a critical state.Then,according to the Hoshen-Kopelman(HK)algorithm,the real-time estimation of fracture con-nection is effectively made and a dichotomy between cube size and pore fraction is suggested to solve such a challenge of the one-to-one match between complete connection and cluster size.After,the 3D cube clusters are decomposed into orthogonal layer clusters,which are then transformed into the ellip-soid models.Correspondingly,the anisotropy evolution of fracture network could be visualized by three orthogonal ellipsoids and quantitatively described by aspect ratio.Besides,the other three quantities of centroid axis length,porosity,and fracture angle are analyzed to evaluate the evolution of cube cluster.The result shows the sample dilatancy is strongly correlated to four quantities of aspect ratio,centroid axis length,and porosity as well as fracture angle.Besides,the cube cluster model shows a potential pos-sibility to predict the evolution of fracture angle.So,the cube cluster model provides an in-depth view of spatial correlation to describe the AE signal-cloud.