Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

Uniaxial Compressive Strength Prediction for Rock Material in Deep Mine Using Boosting-Based Machine Learning Methods and Optimization Algorithms

Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining environments under high in-situ stress.Thus,this study aims to develop an advanced model for predicting the UCS of rockmaterial in deepmining environments by combining three boosting-basedmachine learning methods with four optimization algorithms.For this purpose,the Lead-Zinc mine in Southwest China is considered as the case study.Rock density,P-wave velocity,and point load strength index are used as input variables,and UCS is regarded as the output.Subsequently,twelve hybrid predictive models are obtained.Root mean square error(RMSE),mean absolute error(MAE),coefficient of determination(R2),and the proportion of the mean absolute percentage error less than 20%(A-20)are selected as the evaluation metrics.Experimental results showed that the hybridmodel consisting of the extreme gradient boostingmethod and the artificial bee colony algorithm(XGBoost-ABC)achieved satisfactory results on the training dataset and exhibited the best generalization performance on the testing dataset.The values of R2,A-20,RMSE,and MAE on the training dataset are 0.98,1.0,3.11 MPa,and 2.23MPa,respectively.The highest values of R2 and A-20(0.93 and 0.96),and the smallest RMSE and MAE values of 4.78 MPa and 3.76MPa,are observed on the testing dataset.The proposed hybrid model can be considered a reliable and effective method for predicting rock UCS in deep mines.

Microscopic cracking behaviors of rocks under uniaxial compression with microscopic multiphase heterogeneity by deep learning

Cracking behaviors of rocks significantly affect the safety and stability of the explorations of underground space and deep resources.To understand deeply the microscopic cracking process and mechanical property of rocks,X-ray micro-computed tomography(X-μCT)is applied to capture the rock microstructures.The digital color difference UNet(DCD-UNet)-based deep learning algorithm with 3D reconstruction is proposed to reconstruct the multiphase heterogeneity microstructure models of rocks.The microscopic cracking and mechanical properties are studied based on the proposed microstructure-based peridynamic model.Results show that the DCD-UNet algorithm is more effective to recognize and to represent the microscopic multiphase heterogeneity of rocks.As damage characteristic index of multiphase rocks increases,transgranular cracks in the same grain phase,transgranular and intergranular cracks of pore-grain phase,intergranular and secondary transgranular cracks and transgranular crack between different grains propagate.The ultimate microscopic failure modes of rocks are mainly controlled by the transgranular cracks-based T1-shear,T3-shear,T1-tension,T2-tension and T3-tension failures,and the intergranular cracks-based T1-tension,T1-shear and T3-shear failures under uniaxial compression.

Effects of mineralogical composition on uniaxial compressive strengths of sedimentary rocks

Figuring out rock strength plays essential roles in the sub ground mining activities,such as oil and gas well drilling and hydraulic fracturing,coal mining,tunneling,and other civil engineering scenarios.To help understand the effects of the mineralogical composition on evaluating the rock strength,this research tries to establish indirect prediction models of rock strength by specific input mineral contents for common sedimentary rocks.Using rock samples collected from the outcrops in the Sichuan Basin,uniaxial compression tests have been conducted to sandstone,carbonate,and shale cores.Combining with statistical analysis,the experimental data prove it true that the mineralogical composition can be utilized to predict the rock strength under specific conditions but the effects of mineralogical composition on the rock strength highly depend on the rock lithologies.According to the statistical analysis results,the predicted values of rock strengths by the mineral contents can get high accuracies in sandstone and carbonate rocks while no evidences can be found in shale rocks.The best indicator for predicting rock strength should be the quartz content for the sandstone rocks and the dolomite content for the carbonate rocks.Especially,to improve the evaluation accuracy,the rock strengths of sandstones can be obtained by substituting the mineral contents of quartz and clays,and those of carbonates can be calculated by the mineral contents of dolomite and calcite.Noticeably,the research data point out a significant contrast of quartz content in evaluating the rock strength of the sandstone rocks and the carbonate rocks.Increasing quartz content helps increase the sandstone strength but decrease the carbonate strength.As for shale rocks,no relationship exists between the rock strength and the mineralogical composition(e.g.,the clay fractions).To provide more evidences,detailed discussion also provides the readers more glances into the framework of the rock matrix,which can be further studied in the future.These findings can help understand the effects of mineralogical composition on the rock strengths,explain the contrasts in the rock strength of the responses to the same mineral content(e.g.,the quartz content),and provide another indirect method for evaluating the rock strength of common sedimentary rocks.

Extraction and identifcation of spectrum characteristics of coal and rock hydraulic fracturing and uniaxial compression signals

Microseismic(MS)events generated during coal and rock hydraulic fracturing(HF)include wet events caused by fracturing fuid injection,in addition to dry events caused by stress perturbations.The mixture of these two events makes efective fracturing MS events pickup difcult.This study is based on physical experiments of diferent coal and rock HF and uniaxial compression.The diferences of waveform characteristic parameters of various coal and rock ruptures were analyzed using the Hilbert–Huang transform,leading to some useful conclusions.The phase characteristics of the acoustic emission(AE)energy difered signifcantly and responded well to the pumping pressure curve.The AE waveforms of HF exhibit similar energy and frequency distribution characteristics after Empirical mode decomposition.The main frequency bands for coal,sandstone,and shale samples are 100–300 kHz,while the mudstone sample is in the range of 50–150 kHz.The decay ratios for coal,sandstone,shale and mudstone samples are 0.78,0.83,0.67 and 0.85,respectively.When compared to the uniaxial compression test,the main frequency bands of HF were reduced for coal,sandstone and mudstone samples,whereas shale remained essentially unchanged.The duration,instantaneous energy,and total energy of the HF waveform are smaller than those of uniaxial compression,while the decay ratio is greater,especially for the mudstone samples.The waveform characteristic parameters,trained using the multilayer perceptron neural network,can efectively identify HF and uniaxial compression events with an accuracy of 96%.

Heterogeneity induced strain localization in block-in-matrix-soils subjected to uniaxial loading using real-time CT scanning

Block-in-matrix-soils(bimsoils)are geological mixtures that have distinct structures consisting of relatively strong rock blocks and weak matrix soils.It is still a challenge to evaluate the mechanical behaviors of bimsoils because of the heterogeneity,chaotic structure,and lithological variability.As a result,only very limited laboratory studies have been reported on the evolution of their internal deformation.In this study,the deformation evolution of bimsoils under uniaxial loading is investigated using real-time X-ray computed tomography(CT)and image correlation algorithm(with a rock block percentage(RBP)of 40%).Three parameters,i.e.heterogeneity coefficient(K),correlation coefficient(CC),and standard deviation(STD)of displacement fields,are proposed to quantify the heterogeneity of the motion of the rock blocks and the progressive deformation of the bimsoils.Experimental results show that the rock blocks in bimsoils are prone to forming clusters with increasing loading,and the sliding surface goes around only one side of a cluster.Based on the movement of the rock blocks recorded by STD and CC,the progressive deformation of the bimsoils is quantitatively divided into three stages:initialization of the rotation of rock blocks,formation of rock block clusters,and formation of a shear band by rock blocks with significant rotation.Moreover,the experimental results demonstrate that the meso-motion of rock blocks controls the macroscopic mechanical properties of the samples.

A comparative study for determining rock joint normal stiffness with destructive uniaxial compression and nondestructive ultrasonic wave testing

Rock joints are one of the vital discontinuities in a natural rock mass.How to accurately and conveniently determine joint normal stiffness is therefore significant in rock mechanics.Here,first,seven existing methods for determining joint normal stiffness were introduced and reviewed,among which MethodⅠ(the indirect measurement method),MethodⅡ(the direct determination method),MethodⅢ(the across-joint strain gauge measurement method)and MethodⅣ(the deformation measuring ring method)are via destructive uniaxial compression testing,while MethodⅤ(the best fitting method),MethodⅥ(the rapid evaluation method)and MethodⅦ(the effective modulus method)are through wave propagation principles and nondestructive ultrasonic testing.Subsequently,laboratory tests of intact and jointed sandstone specimens were conducted following the testing requirements and pro-cedures of those seven methods.A comparison among those methods was then performed.The results show that Method I,i.e.the benchmark method,is reliable and stable.MethodⅡhas a conceptual drawback,and its accuracy is acceptable at only very low stress levels.Relative errors in the results from MethodⅢare very large.With MethodⅣ,the testing results are sufficiently accurate despite the strict testing environment and complicated testing procedures.The results from MethodⅤare greatly unstable and significantly dependent on the natural frequency of the transducers.The joint normal stiffness determined with MethodⅥis stable and accurate,although data processing is complex.MethodⅦcould be adopted to determine the joint normal stiffness corresponding to the rock elastic deformation phase only.Consequently,it is suggested that MethodsⅠ,ⅣandⅥshould be adopted for the mea-surement of joint normal stiffness.The findings could be helpful in selecting an appropriate method to determine joint normal stiffness and,hence,to better solve discontinuous rock mass problems.

Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

A coupled thermo-mechanical peridynamic model for fracture behavior of granite subjected to heating and water-cooling processes

Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects.This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures.The laboratory uniaxial compression experiments were also conducted.Then,a coupled thermo-mechanical ordinary state-based peridynamic(OSB-PD)model and corresponding numerical scheme were developed to simulate the damage of rocks after the heating and cooling processes,and the change of crack evolution process was predicted.The results demonstrate that elevated heating temperatures exacerbate the thermal damage to the specimens,resulting in a decrease in peak strength and an increase in ductility of granite.The escalating occurrence of thermal-induced cracks significantly affects the crack evolution process during the loading phase.The numerical results accurately reproduce the damage and fracture characteristics of the granite under different final heating temperatures(FHTs),which are consistent with the test results in terms of strength,crack evolution process,and failure mode.

Statistical analysis of physico-mechanical parameters of sandstones occurring in orogenic settings

In northeastern Sicily(Italy),sandstone rock masses widely crop out as cover deposits over crystalline terrains belonging to the orogenic belt.Despite being part of the same geological formation,these sandstones are characterized by highly different features in terms of texture and physico-mechanical properties.This poses a scientific question on the possibility of tracing these rocks to a single statistical model,which could be representative of their main engineering geological properties.Therefore,it is worth investigating on the possible reasons of such differences,that should be searched either in the current geographical sandstone distribution or in the rock texture.For this study,sandstone samples were collected from different sites and were analyzed at both the hand and thin section scales.Three sandstone types were recognized,characterized by a different texture.Then,the laboratory characterization allowed estimating their main physico-mechanical and ultrasonic properties,such as porosity,density,mechanical strength,deformability,and ultrasonic velocities.The rock mechanical strength proved linked to the rock compactness and to the presence of lithic fragments,while pores and a pseudo-matrix between grains represent weakening features.Rock data were also statistically analyzed by grouping the specimens according to a geographical criterion,with respect to their sampling area,but no link was found between location and rock properties.Finally,with the aim of achieving mathematical laws that could be used to predict some rock properties from others,useful for practical purposes when dealing with such a high property variability,single and multiple regression analyses were carried out.Results show that the Uniaxial Compressive Strength,porosity,and P-wave velocity are the best predictors for a quick,indirect estimation of the main physico-mechanical parameters.The methodological approach developed for this research can be taken as reference to study other worldwide cases,involving rocks characterized by a wide range of physico-mechanical properties and covering large regional territories.

Three-dimensional finite element simulation and reconstruction of jointed rock models using CT scanning and photogrammetry

The geometry of joints has a significant influence on the mechanical properties of rocks.To simplify the curved joint shapes in rocks,the joint shape is usually treated as straight lines or planes in most laboratory experiments and numerical simulations.In this study,the computerized tomography (CT) scanning and photogrammetry were employed to obtain the internal and surface joint structures of a limestone sample,respectively.To describe the joint geometry,the edge detection algorithms and a three-dimensional (3D) matrix mapping method were applied to reconstruct CT-based and photogrammetry-based jointed rock models.For comparison tests,the numerical uniaxial compression tests were conducted on an intact rock sample and a sample with a joint simplified to a plane using the parallel computing method.The results indicate that the mechanical characteristics and failure process of jointed rocks are significantly affected by the geometry of joints.The presence of joints reduces the uniaxial compressive strength (UCS),elastic modulus,and released acoustic emission (AE) energy of rocks by 37%–67%,21%–24%,and 52%–90%,respectively.Compared to the simplified joint sample,the proposed photogrammetry-based numerical model makes the most of the limited geometry information of joints.The UCS,accumulative released AE energy,and elastic modulus of the photogrammetry-based sample were found to be very close to those of the CT-based sample.The UCS value of the simplified joint sample (i.e.38.5 MPa) is much lower than that of the CT-based sample (i.e.72.3 MPa).Additionally,the accumulative released AE energy observed in the simplified joint sample is 3.899 times lower than that observed in the CT-based sample.CT scanning provides a reliable means to visualize the joints in rocks,which can be used to verify the reliability of photogrammetry techniques.The application of the photogrammetry-based sample enables detailed analysis for estimating the mechanical properties of jointed rocks.

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints.In this study,numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method(FEM)with the intrinsic cohesive zone model(ICZM).Then,the uniaxial compressive and wave propagation simulations were performed.The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models.The uniaxial compressive strength(UCS)and wave velocity of rock masses decrease monotonically as the joint number increases.However,the wave velocity grows monotonically as the joint dip angle increases.When the joint dip angle is 45°–60°,the UCS of the rock mass is lower than that of other dip angles.The wave velocity parallel to the joints is greater than that perpendicular to the joints.When the dip angle of joints remains unchanged,the UCS and wave velocity are positively related.When the joint dip angle increases,the variation amplitude of the UCS regarding the wave velocity increases.To reveal the effect of the joint distribution on the velocity,a theoretical model was also proposed.According to the theoretical wave velocity,the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results.Furthermore,a theoretical indicator(i.e.fabric tensor)was adopted to analyze the variation of the wave velocity and UCS.

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.

Effect of the layer orientation on mechanics and energy evolution characteristics of shales under uniaxial loading

The uniaxial compression tests were conducted on the cylindrical shale specimens with bedding plane inclined at 0° and 90° to the axial loading direction, respectively. Effect of the bedding orientation on the mechanical property and energy evolution characteristics of shales was revealed. The failure mechanisms of the specimens with layers in 0° orientation showed splitting failure along weak bedding, while the specimens with layers in 90° orientation were failed by shearing sliding. The values of compressive strength, elastic modulus and shear modulus of samples at 0° were higher than those of samples at 90°and there was little difference of Poisson's ratio between samples at 0° and 90°. The analysis of the stress–strain energy and acoustic emission(AE) energy indicated that the growth rate of absorbed energy density and elastic energy density at 0° was significantly faster than that at 90°, hence their final values at 0°were relatively larger than the latter. Moreover, higher energy release was observed for specimens at 0°.The energy release and rapid growth of energy dissipation also appeared more early at 0°. The stress ratio63% was a critical point of energy distribution at which differences started to arise between samples at 0°and 90°. These results indicated that the failure of shale at 0° was more violent and devastative than the failure of shale at 90°.

Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression

Failure of rock mass that is subjected to compressive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research investigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the preexisting flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: primary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour.

Specimen aspect ratio and progressive field strain development of sandstone under uniaxial compression by three-dimensional digital image correlation

The complete stress-strain characteristics of sandstone specimens were investigated in a series of quasistatic monotonic uniaxial compression tests.Strain patterns development during pre-and post-peak behaviours in specimens with different aspect ratios was also examined.Peak stress,post-peak portion of stress-strain,brittleness,characteristics of progressive localisation and field strain patterns development were affected at different extents by specimen aspect ratio.Strain patterns of the rocks were obtained by applying three-dimensional(3D) digital image correlation(DIC) technique.Unlike conventional strain measurement using strain gauges attached to specimen,3D DIC allowed not only measuring large strains,but more importantly,mapping the development of field strain throughout the compression test,i.e.in pre-and post-peak regimes.Field strain development in the surface of rock specimen suggests that strain starts localising progressively and develops at a lower rate in pre-peak regime.However,in post-peak regime,strains increase at different rates as local deformations take place at different extents in the vicinity and outside the localised zone.The extent of localised strains together with the rate of strain localisation is associated with the increase in rate of strength degradation.Strain localisation and local inelastic unloading outside the localised zone both feature post-peak regime.

Comparative evaluation of different statistical tools for the prediction of uniaxial compressive strength of rocks

In this study,uniaxial compressive strength(UCS),unit weight(UW),Brazilian tensile strength(BTS),Schmidt hardness(SHH),Shore hardness(SSH),point load index(Is50)and P-wave velocity(Vp)properties were determined.To predict the UCS,simple regression(SRA),multiple regression(MRA),artificial neural network(ANN),adaptive neuro-fuzzy inference system(ANFIS)and genetic expression programming(GEP)have been utilized.The obtained UCS values were compared with the actual UCS values with the help of various graphs.Datasets were modeled using different methods and compared with each other.In the study where the performance indice PIat was used to determine the best performing method,MRA method is the most successful method with a small difference.It is concluded that the mean PIat equal to 2.46 for testing dataset suggests the superiority of the MRA,while these values are 2.44,2.33,and 2.22 for GEP,ANFIS,and ANN techniques,respectively.The results pointed out that the MRA can be used for predicting UCS of rocks with higher capacity in comparison with others.According to the performance index assessment,the weakest model among the nine model is P7,while the most successful models are P2,P9,and P8,respectively.

Inconsistency of changes in uniaxial compressive strength and P-wave velocity of sandstone after temperature treatments

It is generally accepted that the uniaxial compressive strength(UCS)and P-wave velocity of rocks tend to decrease simultaneously with increasing temperature.However,based on a great number of statistical data and systematic analysis of the microstructure variation of rocks with temperature rising and corresponding propagation mechanism of elastic wave,the results show that(1)There are three different trends for the changes of UCS and P-wave velocity of sandstone when heated from room temperature(20C or 25C)to 800C:(i)Both the UCS and P-wave velocity decrease simultaneously;(ii)The UCS increases initially and then decreases,while the P-wave velocity decreases continuously;and(iii)The UCS increases initially and then fluctuates,while the P-wave velocity continuously decreases.(2)The UCS changes at room temperaturee400C,400Ce600C,and 600Ce800C are mainly attributed to the discrepancy of microstructure characteristics and quartz content,the transformation plasticity of clay minerals,and the balance between the thermal cementation and thermal damage,respectively.(3)The inconsistency in the trends of UCS and P-wave velocity changes is caused by the change of quartz content,phase transition of water and certain minerals.

Shape ratio effects on the mechanical characteristics of rectangular prism rocks and isolated pillars under uniaxial compression

Isolated pillars in underground mines are subjected to uniaxial stress,and the load bearing cross-section of pillars is commonly rectangularly shaped.In addition,the uniaxial compression test(UCT)is widely used for determining the basic mechanical properties of rocks and revealing the mechanism of isolated pillar disasters under unidimensional stress.The shape effects of rock mechanical properties under uniaxial compression are mainly quantitatively reflected in the specific shape ratios of rocks.Therefore,it is necessary to study the detailed shape ratio effects on the mechanical properties of rectangular prism rock specimens and isolated pillars under uniaxial compressive stress.In this study,granite,marble and sandstone rectangular prism specimens with various height to width ratios(r)and width to thickness ratios(u)were prepared and tested.The study results show that r and u have a great influence on the bearing ability of rocks,and thin or high rocks have lower uniaxial compressive strength.Reducing the level of r can enhance the u effect on the strength of rocks,and increasing the level of u can enhance the r effect on the strength of rocks.The lateral strain on the thickness side of the rock specimen is larger than that on the width side,which implies that crack growth occurs easily on the thickness side.Considering r and u,a novel strength prediction model of isolated pillars was proposed based on the testing results,and the prediction model was used for the safety assessment of 179 isolated pillars in the Xianglu Mountain Tungsten Mine.

Effect of Relative Stress on Post-Peak Uniaxial Compression Fracture Energy of Concrete

Fracture energy in strain softening regime was investigated analytically by considering microstructures interaction and interplay.Based on gradient-dependent plasticity, the thickness of localized band was determined completely and strictly by characteristic length in relation to average grain diameter.After obtaining the plastic shear displacement of the band,the formula on axial response of concrete was proposed and the analytical post-peak fracture energy was deduced.A comparison between present theoretical results and earlier experimental results was carried out and the analytical result is reasonable and has a plausible foundation as considering the localized failure theoretically.Decreasing the relative stress leads to increasing the fracture energy non-linearly.The larger the shear elastic modulus and shear softening modulus,the lower the post-peak fracture energy.A larger fracture energy is caused by a larger thickness of shear band or a larger characteristic length of concrete material.If the inclination angle of the shear band and the compressive strength are not concerned with structural size of specimen,the post-peak fracture energy is size independent.