Analysis of the stress ratio of anisotropic rocks in uniaxial tests

The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relationship between σ_(cd) and the uniaxial peak strength σ_(ucs) of anisotropic rocks for different orientations 8 of the isotropy planes with respect to the loading directions were investigated theoretically and experimentally.A theoretical relation of σ_(cd)/σ_(ucs) with the function of the shape parameter m was established.Additionally,uniaxial compression tests of shale samples were conducted for several inclinations θ.The test result of σ_(cd)/σ_(ucs) was close to the theoretical value for a given orientation.Furthermore,both experimental results and theoretical solutions of σ_(cd)/σ_(ucs) were independent of the inclination θ while σ_(cd) andσ_(ucs) were strongly affected by θ.The strength ratio σ_(cd)/σ_(ucs) may therefore be an intrinsic property of anisotropic rocks and could be used to predict the failure of rock samples.

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.

Biomechanical behavior of grass roots at different gauge lengths

Gauge length influences the biomechanical properties of herbaceous roots such as tensile resistance,tensile strength and Young’s modulus.However,the extent to which and how these biomechanical properties of herbaceous roots are influenced remain unknown.To better understand the behavior of roots in tension under different conditions and to illustrate these behaviors,uniaxial tensile tests were conducted on the Poa araratica roots as the gauge length increased from 20 mm to 80 mm.Subsequently,ANOVA was used to test the impact of the significant influences of gauge length on the biomechanical properties,nonlinear regression was applied to establish the variation in the biomechanical properties with gauge length to answer the question of the extent to which the biomechanical properties are influenced,and Weibull models were subsequently introduced to illustrate how the biomechanical properties are influenced by gauge length.The results reveal that(1)the variation in biomechanical properties with root diameter depends on both the gauge length and the properties themselves;(2)the gauge length significantly impacts most of the biomechanical properties;(3)the tensile resistance,tensile strength,and tensile strain at cracks decrease as the gauge length increases,with values decreasing by 20%-300%,while Young’s modulus exhibits the opposite trend,with a corresponding increase of 30%;and(4)the Weibull distribution is suitable for describing the probability distribution of these biomechanical properties;the Weibull modulus for both tensile resistance and tensile strain at cracks linearly decrease with gauge length,whereas those for tensile strength and Young’s modulus exhibit the opposite trend.The tensile resistance,tensile strength,and tensile strain at the cracks linearly decrease with increasing gauge length,while the tensile strength and Young’s modulus linearly increase with increasing gauge length.

Effect of height-diameter ratio on the mechanical characteristics of shale with different bedding orientations

Geological exploration cores obtained from shale gas wells several kilometers deep often show different height-diameter ratios(H/D)because of complex geological conditions(core disking or developed fractures),which makes further standard specimen preparation for mechanical evaluation of reservoirs difficult.In multi-cluster hydraulic fracturing,shale reservoirs between planes of hydraulic fractures with different lengths could be simplified to have different H/D ratios.Discovering the effect of H/D on the mechanical characteristics of shale specimens with different bedding orientations will support mechanical evaluation tests of reservoirs based on disked geological cores and help to optimize multicluster fracturing programs.In this study,we performed uniaxial compression tests and acoustic emission(AE)monitoring on cylindrical Longmaxi shale specimens under five bedding orientations and four H/D ratios.The experimental results showed that both the H/D-dependent mechanical properties and AE parameters demonstrated significant anisotropy.Increasing H/D did not change the uniaxial compressive strength(UCS)evolution versus bedding orientation,demonstrating a V-shaped relationship,but enhanced the curve shape.The stress level of crack damage for the specimens significantly increased with increasing H/D,excluding the specimens with a bedding orientation of 0°.With increasing H/D,the cumulative AE counts of the specimens with each bedding orientation tended to exhibit a stepped jump against the loading time.The proportion of low-average-frequency AE signals(below 100 kHz)in specimens with bedding orientations of 45°and 60°increased to over 70%by increasing H/D,but it only increased to 40%in specimens with bedding orientations of 0°,30°,and 90°.Finally,an empirical model that can reveal the effect of H/D on anisotropic UCS of shale reservoir was proposed,the anisotropic proportion of tensile and shear failure cracks in specimens under four H/D ratios was classified based on the AE data,and the effect of H/D on the anisotropic crack growth of specimens was discussed.

Failure behavior and strength model of blocky rock mass with and without rockbolts

To better understand the failure behaviours and strength of bolt-reinforced blocky rocks,large scale extensive laboratory experiments are carried out on blocky rock-like specimens with and without rockbolt reinforcement.The results show that both shear failure and tensile failure along joint surfaces are observed but the shear failure is a main controlling factor for the peak strength of the rock mass with and without rockbolts.The rockbolts are necked and shear deformation simultaneously happens in bolt reinforced rock specimens.As the joint dip angle increases,the joint shear failure becomes more dominant.The number of rockbolts has a significant impact on the peak strain and uniaxial compressive strength(UCS),but little influence on the deformation modulus of the rock mass.Using the Winkler beam model to represent the rockbolt behaviours,an analytical model for the prediction of the strength of boltreinforced blocky rocks is proposed.Good agreement between the UCS values predicted by proposed model and obtained from experiments suggest an encouraging performance of the proposed model.In addition,the performance of the proposed model is further assessed using published results in the literature,indicating the proposed model can be used effectively in the prediction of UCS of bolt-reinforced blocky rocks.

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.

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.

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.

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.

Micro-failure process and failure mechanism of brittle rock under uniaxial compression using continuous real-time wave velocity measurement

In this study,the micro-failure process and failure mechanism of a typical brittle rock under uniaxial compression are investigated via continuous real-time measurement of wave velocities.The experimental results indicate that the evolutions of wave velocities became progressively anisotropic under uniaxial loading due to the direction-dependent development of micro-damage.A wave velocity model considering the inner anisotropic crack evolution is proposed to accurately describe the variations of wave velocities during uniaxial compression testing.Based on which,the effective elastic parameters are inferred by a transverse isotropic constitutive model,and the evolutions of the crack density are inversed using a self-consistent damage model.It is found that the propagation of axial cracks dominates the failure process of brittle rock under uniaxial loading and oblique shear cracks develop with the appearance of macrocrack.

Experimental study on complete stress-deformation curves of larger-size concrete specimens subjected to uniaxial tension

In order to provide parameters for numerical analyses of the huge Three-Gorge concrete dam (2309 m long by 175 m height), complete tensile stress-deformation curves for large-size plain concrete specimens were measured and studied by per-forming uniaxial tensile tests on large-size unnotched specimens (250 mm×250 mm×1400 mm). The specimens were prepared with the three-graded-aggregate materials provided by the client of the Three-Gorge project. To prevent a failure occurring near the ends of the unnotched specimens, both the ends of each specimen (450 mm in length) were cast using a higher-strength concrete than the middle part (i.e., active part). Tensile tests were completed on a specially-designed tensile testing machine, which can be easily re-assembled to accommodate different-size specimens. To make the specimens fail stably, a cyclic loading scheme was adopted after the peak strength was reached. Four of five tests in this study were successful, and four complete tensile stress-deformation curves were obtained. It was found that the post-peak curve of the large-size specimens used in this study is more gradual than those for the small-size specimens reported in the literature.

Correlations between direct and indirect strength test methods

The difficulties associated with performing direct compression strength tests on rocks lead to the development of indirect test methods for the rock strength assessment. Indirect test methods are simple, more economical, less time-consuming, and easily adaptable to the field. The main aim of this study was to derive correlations between direct and indirect test methods for basalt and rhyolite rock types from Carlin trend deposits in Nevada. In the destructive methods, point load index, block punch index, and splitting tensile strength tests are performed. In the non-destructive methods, Schmidt hammer and ultrasonic pulse velocity tests are performed. Correlations between the direct and indirect compression strength tests are developed using linear and nonlinear regression analysis methods. The results show that the splitting tensile strength has the best correlation with the uniaxial compression strength.Furthermore, the Poisson's ratio has no correlation with any of the direct and indirect test results.

Assessment of inherent heterogeneity effect on continuous mechanical properties of shale via uniaxial compression and scratch test methods

Shale reservoirs have been a significant focus of hydrocarbon production over the past few decades,and the mechanical assessment of target shale reservoirs has been critical to successful field operations,especially in hydraulic fracturing and well completions.The Unconfined compressive strength(UCS)and Poisson's ratio(ν)are critical mechanical properties in shale reservoir assessment.The estimation and measurement of shale mechanical properties are often erroneous by not accounting for their heterogeneous and pre-existing features,which yield variability of shale mechanical properties along their lithostratigraphy.Thus,there is a need to investigate the degree of correlation and accuracy in multiscale mechanical evaluations of heterogeneous shales,and the correlation between such micromechanical and macromechanical measurements.This study investigated the impact of inherent heterogeneity on the measurement of continuous micromechanical and macromechanical properties of shale reservoirs using scratch test(ST)and uniaxial compression test(UCT)methods,and the degree of correlation(correlation coefficient,r)of measurements in shale was further assessed for the variability of their measured properties.Shale core samples from three distinct shale formations were utilized and studied,and the core samples were subjected to ST and UCT,respectively.The results from this study showed that despite inherent heterogeneous anomalies and natural fractures in the shale samples analyzed,there is a good degree of correlation(UCS:r=0.73;ν:r=0.89)in the micro-and macro-mechanical properties of shales using two independent experimental tests(ST and UCT).This study provides insights for improving the accuracy of mechanical evaluations and numerical modeling in shales with a high degree of heterogeneity and pre-existing natural fractures.The results indicate that when considering the structural complexity and heterogeneity of unconventional reservoirs such as shales,the ST method can provide a better continuous micromechanical assessment of shales.In contrast,the UCT can provide a better bulk macromechanical measurement of shales.

Analysis of axial strain in one-dimensional loading by different models

Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presented and used to describe the material inelastic deformation in uniaxial test. Agreement of the models with experimental results and with the theoretical concepts and physical realities is the criterion of choosing the most appropriate formulation for uniaxial test. A model is thus proposed in which plastic deformation, primary creep and secondary creep contribute to the inelastic deformation. However, it is believed that the hardening parameter is composed of plastic and primary creep parts. Accordingly, the axial plastic strain in a uniaxial test may no longer be considered as the hardening parameter. Therefore, a proportionality concept is proposed to calculate the plastic contribution of deformation.

Circumferential variation in mechanical characteristics of porcine descending aorta

Arterial characterization of healthy descending thoracic aorta(DTA)is indispensable in determining stress distributions across wall thickness and different regions that may be responsible for aorta inhomogeneous dilation,rupture,and dissection when aneurysm occurs.Few studies have shown the inhomogeneity of DTA along the aorta tree considering changes in circumferential direction.The present study aims to clarify the circumferential regional characterization of DTA.Porcine DTA tissues were tested according to region and orientation using uniaxial tension.For axial test,results show that the difference in circumferential direction was mainly in collagen fiber modulus,where the anterior collagen fiber modulus was significantly lower than the posterior quadrant.For circumferential test,the difference in circumferential direction was mainly in the recruitment parameter,where the circumferential stiffness is significantly higher in the posterior region at physiological maximum stress.The proximal posterior quadrant and left quadrant showed significantly lower axial collagen fiber stiffness than the right and anterior quadrants,which may be a factor in aneurysm development.Furthermore,the constitutive parameters for similar detailed regions can be used by biomedical engineers to investigate improved therapies and thoroughly understand the initial stage of aneurysm development.The regional collagen fiber modulus can help improve our understanding of the mechanisms of arterial dilation and aortic dissection.

Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method

A user-defined three-dimensional （3D） discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete （AC）. The 3D discrete element method （DEM） model of AC was constructed employing a user-defined computer program developed using the ＂Fish＂ language in PFC3D. Important microstructural features of AC were modeled, including aggregate gradation, air voids and mastic. The irregular shape of aggregate particle was modeled using a clump of spheres. The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test, based on which the dynamic modulus and phase angle were calculated from the output stress- strain relationship. The effects of air void content, aggregate stiffness and volumetric fraction on AC modulus were further investigated. The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies. The user- defined 3D model also demonstrated significant improvement over the general existing two-dimensional models.

An investigation into the effects of lime on compressive and shear strength characteristics of fiber-reinforced clays

To meet the ever-increasing construction demands around the world during recent years,reinforcement and stabilization methods have been widely used by geotechnical engineers to improve the performances and behavior of fine-grained soils.Although lime stabilization increases the compressive strength of soils,it reduces the soil ductility at the same time.Recent research shows that random fiber inclusion modifies the brittleness of soils.In the current research,the effects of lime and polypropylene(PP)fiber additions on such characteristics as compressive and shear strengths,failure strain,secant modulus of elasticity(E50)and shear strength parameters of mixtures were investigated.Kaolinite was treated with 1%,3% and 5% lime by dry weight of soil and reinforced with 0.1% monovalent PP fibers with the length of 6 mm.Samples were prepared at optimum conditions and cured at 35℃ for 1 d,7 d and 28 d at 90% relative humidity and subsequently subjected to uniaxial and triaxial compression tests(UCT and TCT)under cell pressures of 25 kPa,50 kPa and 100 kPa.Results showed that inclusion of random PP fibers to clay-lime mixtures increases both compressive and shear strengths as well as the ductility.Lime content and curing period were found to be the most influential factors.Scanning electron microscopy(SEM)analysis showed that lime addition and the formation of cementitious compounds bind soil particles and increase soil/fiber interactions at interface,leading to enhanced shear strength.The more ductile the stabilized and reinforced composition,the less the cracks in roads and waste landfill covers.

Effect of waste concrete with different strength on mechanical properties of recycled fine aggregate mortar

The influence of source concrete (SC) with different compression strengths on the workability and mechanical properties of recycled mortar made with river sand substituted by 100% fine recycled concrete aggregates (FRCA) is experimentally investigated. The basic physical performance test shows that with the increase in SC strength, FRCA exhibit lower water absorption and crushing index, meanwhile keeping higher densities. Mechanical property tests, including compressive strength, flexural strength and uniaxial compressive stress-strain tests, show that compressive strength,flexural strength and elasticity modulus of recycled sand mortars increase roughly with the increase in SC strength. The proposed mixture design method demonstrates that all of the components can be kept as the same as those in natural mortar mixture design and FRCA must be pre-wetted before making mortar mixture. Meanwhile, the reuse of higher strength SC can ensure that recycled mortar mixtures are able to achieve similar mechanical performance when compared to natural mortar designs.

Evaluation of granule structure and strength properties of green packed beds in iron ore sintering using high-resolution X-ray tomography and uniaxial compression testing

The strength properties of green sinter beds,including the Young’s modulus and maximum bed strain,were evaluated using uniaxial compression tests.The green-sinter-bed samples were scanned using X-ray computed tomography(XCT),and the geometry characteristics of the granules were quantified by XCT image analysis.The orthogonal array method was applied to determine the concomitant effects of the moisture,hydrated lime,and concentrate contents on the bed strength characteristics.Less bed strain was observed when the granules had a thin adhering layer and increased interlock contacts,which had a great capacity to resist the applied load collectively.The optimal combination for decreasing the bed maximum strain was 5.8%moisture,2%hydrated lime,and 0%concentrate.The moisture and concentrate contents were the most significant factors determining the green bed strength.Increasing the moisture and concentrate contents produced granules with a thicker and more deformable adhering layer,resulting in a more compact bed.The addition of hydrated lime inhibited rearrangement,deformation,and fracture of the granules in green sinter bed during compression.