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.

Distinct behavior of electronic structure under uniaxial strain in BaFe_(2)As_(2)

We report a study of the electronic structure of BaFe_(2)As_(2) under uniaxial strains using angle-resolved photoemission spectroscopy and transport measurements. Two electron bands at the MY point, with an energy splitting of 50 meV in the strain-free sample, shift downward and merge into each other under a large uniaxial strain, while three hole bands at theГ point shift downward together. However, we also observed an enhancement of the resistance anisotropy under uniaxial strains by electrical transport measurements, implying that the applied strains strengthen the electronic nematic order in BaFe_(2)As_(2). These observations suggest that the splitting of these two electron bands at the MY point is not caused by the nematic order in BaFe_(2)As_(2).

Predicting uniaxial compressive strength of tuff after accelerated freeze-thaw testing: Comparative analysis of regression models and artificial neural networks

Ignimbrites have been widely used as building materials in many historical and touristic structures in the Kayseri region of Türkiye. Their diverse colours and textures make them a popular choice for modern construction as well. However, ignimbrites are particularly vulnerable to atmospheric conditions, such as freeze-thaw cycles, due to their high porosity, which is a result of their formation process. When water enters the pores of the ignimbrites, it can freeze during cold weather. As the water freezes and expands, it generates internal stress within the stone, causing micro-cracks to develop. Over time, repeated freeze-thaw (F-T) cycles lead to the growth of these micro-cracks into larger cracks, compromising the structural integrity of the ignimbrites and eventually making them unsuitable for use as building materials. The determination of the long-term F-T performance of ignimbrites can be established after long F-T experimental processes. Determining the long-term F-T performance of ignimbrites typically requires extensive experimental testing over prolonged freeze-thaw cycles. To streamline this process, developing accurate predictive equations becomes crucial. In this study, such equations were formulated using classical regression analyses and artificial neural networks (ANN) based on data obtained from these experiments, allowing for the prediction of the F-T performance of ignimbrites and other similar building stones without the need for lengthy testing. In this study, uniaxial compressive strength, ultrasonic propagation velocity, apparent porosity and mass loss of ignimbrites after long-term F-T were determined. Following the F-T cycles, the disintegration rate was evaluated using decay function approaches, while uniaxial compressive strength (UCS) values were predicted with minimal input parameters through both regression and ANN analyses. The ANN and regression models created for this purpose were first started with a single input value and then developed with two and three combinations. The predictive performance of the models was assessed by comparing them to regression models using the coefficient of determination (R2) as the evaluation criterion. As a result of the study, higher R2 values (0.87) were obtained in models built with artificial neural network. The results of the study indicate that ANN usage can produce results close to experimental outcomes in predicting the long-term F-T performance of ignimbrite samples.

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.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

Mechanical behavior of rock under uniaxial tension:Insights from energy storage and dissipation

Many rock engineering projects show that the growth of tensile cracks is often an important cause of engineering disasters,and the mechanical behavior of rocks is essentially the transmission,storage,dissipation and release of energy.To investigate the tensile behavior of rock from the perspective of energy,uniaxial tension tests(UTTs)and uniaxial compression tests(UCTs)were carried out on three typical rocks(granite,sandstone and marble).Different unloading points were set before the peak stress to separate elastic energy and dissipated energy.The input energy density ut,elastic energy density ue,and dissipated energy density ud at each unloading point were calculated by integrating stress-strain curves.The results show that there is a strong linear relationship between the three energy parameters and the square of the unloading stress in UCT,but this linear relationship is weaker in UTT.The ue and ud increase linearly with the increase in ut in UCT and UTT.Based on the phenomenon that ue and ud increase linearly with ut,the applicability of W_(et)^(p) index in UTT was proved and the relative energy storage capacity and absolute energy distribution characteristics of three rocks in UCT and UTT were evaluated.The tensile behavior of marble and sandstone in UTT can be divided into two stages vaguely according to the energy distribution,but granite is not the case.In addition,based on dissipated energy,the damage evolution of three types of rocks in UCT and UTT was discussed.This study provides some new insights for understanding the tensile behavior of rock.

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.

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.

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.

Focused-ion-beam assisted technique for achieving high pressure by uniaxial-pressure devices

Uniaxial pressure or strain can introduce a symmetry-breaking distortion on the lattice and may alter the ground states of a material. Compared to hydrostatic pressure, a unique feature of the uniaxial-pressure measurements is that a tensile force can be applied and thus a “negative” pressure can be achieved. In doing so, both ends of the sample are usually glued on the frame of the uniaxial-pressure device. The maximum force that can be applied onto the sample is sometimes limited by the shear strength of the glue, the quality of the interface between the sample and the glue, etc. Here we use focused ion beam to reduce the width of the middle part of the sample, which can significantly increase the effective pressure applied on the sample. By applying this technique to a home-made piezobender-based uniaxial-pressure device, we can easily increase the effective pressure by one or two orders of magnitude as shown by the change of the superconducting transition temperature of an iron-based superconductor. Our method thus provides a possible way to increase the upper limit of the pressure for the uniaxial-pressure devices.

Strain Rate Effect of AE Characteristics in the Whole Process of Uniaxial Tensile of Mortar

We completed the uniaxial tensile test of mortar in the range of strain rate from 10^(-6)to 10^(-4)s^(-1)in the section containing softening,and carried out acoustic emission monitoring(AE)simultaneously.A series of AE parameters and spectrum analysis methods were used to identify the damage evolution process and cracking mechanism of mortar at different strain rates.The results show that,with the increase of strain rate,the peak stress and tensile elastic modulus of mortar increase obviously,and the stress level corresponding to the starting point of AE activity increases significantly as well,which indicates that the mechanical properties and AE characteristics of mortar have obvious strain rate effect.With the increase of strain rate,the cumulative AE hit decreases gradually,while the average AE hit rate increases significantly,indicating that the increase of strain rate reduces the damage degree of internal microstructure of the specimen,but the crack propagation speed increases.In the pre-peak stress stage,the average of AE ringing count and signal energy decreases with the increase of strain rate,while the average of duration increases;in the post-peak stress stage(f_(t)-30%f_(t)),the average of the three AE parameters all increase with the increase of strain rate,indicating that the strain rate effect on the damage process of mortar is different before and after peak stress,and the damage mechanism represented by different parameters is also different.In the whole process of uniaxial tensile of mortar,with the increase of strain rate,the scatter distribution of AE frequency-amplitude becomes more discrete,and the b-value shows a decreasing trend.In addition,the average level of AE peak frequency decreases with the increase of strain rate,while that of ca8 band wavelet energy spectrum coefficient increases.It is indicated that the increase of strain rate enables the crack propagation state of mortar specimen to become unstable,and the width of macrocrack increases but the proportion decreases.

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%.

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.

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.

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.

Experiment and simulation of creep performance of basalt fibre asphalt mortar under uniaxial compressive loadings

The creep performance of basalt fibre（BF）reinforced in asphalt mortar under uniaxial compressive loadings is investigated. The samples of basalt fibre asphalt mortar（BFAM） with different BF mass fractions（0. 1%,0. 2%, and 0. 5%） and without BF in asphalt mixture are prepared, and then submitted for the compressive strength test and corresponding creep test at a high in-service temperature.Besides, numerical simulations in finite element ABAQUS software were conducted to model the compressive creep test of mortar materials, where the internal structure of the fibre mortar was assumed to be a two-component composite material model such as fibre and mortar matrix. Finally, the influence factors of rheological behaviors of BFAM are further analyzed. Results indicate that compared to the control sample, the compressive strength of BFAM samples has a significant increase, and the creep and residual deformation are decreased. However, it also shows that the excessive fibre, i.e. with the BF content of 0. 5%, is unfavorable to the high-temperature stability of the mortar. Based on the analysis results, the prediction equations of parameters of the Burgers constitutive model for BFAM are proposed by considering the fibre factors.

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.

Investigation on Uniaxial Tensile Instability of USIBOR1500 Steel Sheets at Elevated Temperature

In the sheet forming process with stretch, diffuse instability and localized instability usually occur in the process one after another. The necking rate has a great impact on the instability process and the forming limits of the rate sensitive material, such as USIBOR1500 steel sheets at elevated temperature. The available reports about this steel mainly focus on hot uniaxial tensile, martensitic transformation and forming process, but there are few investigations on instability behavior and forming limits. Based on Inoue Kachiro＇s flow stress constitutive model at elevated temperature, combined with Swift＇s diffuse instability rule and Hill＇s localized instability nile, the relation is theoretically deduced between the diffuse necking rate along with the localized necking rate and the exponent of strain rate sensitivity together with the strain rate in the case of the USIBOR1500 steel sheets at elevated temperature. According to the time-temperature characteristics of the hot stamping process, tensile tests of the steel sheets were carried out on Gleeble3800, and the stress-strain curves were obtained at different temperatures and different strain rates. Then the values of the exponent of strain rate sensitivity and the hardening exponent were obtained through fitting the curves by least squares. The tests also helped to provide the distribution laws of the major strain of the specimens and the uniform strains as well as the necking width. The uniform strains obtained from the tests are matched well with the theoretical calculations.

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°.