Brazilian disc test study on tensile strength-weakening effect of high pre-loaded red sandstone under dynamic disturbance

Tensile failure(spalling or slabbing)often occurs on the sidewall of deep tunnel,which is closely related to the coupled stress state of deep rock mass under high pre-static load and dynamic disturbance.To reveal the mechanism of rock tensile failure caused by this coupled stress mode,the Brazilian disc tests were carried on red sandstone under high pre-static load induced by dynamic disturbance.Based on the pure static tensile fracture load of red sandstone specimen,two static load levels(80%and 90%of the pure static tensile fracture load)were selected as the initial high pre-static loading state,and then the dynamic disturbance load was applied until the rock specimen was destroyed.The dynamic disturbance loading mode adopted a sinusoidal wave(sine-wave)load,and the loading wave amplitude was 20%and 10%of the pure static tensile fracture load,respectively.The dynamic disturbance frequencies were set to 1,10,20,30,40,and 50 Hz.The results show that the tensile failure strength and peak displacement of red sandstone specimens under coupled load actions are lower than those under pure static tensile load,and both parameters decrease significantly with the increase of dynamic disturbance frequency.With the increase of dynamic disturbance frequency,the decrease range of tensile strength of red sandstone increased from 3.3%to 9.4%when the pre-static load level is 80%.While when the pre-static load level is 90%,the decrease range will increase from 7.4%to 11.6%.This weakening effect of tensile strength shows that the deep surrounding rock is more likely to fail under the coupled load actions of pre-static load and dynamic disturbance.In this tensile failure mechanism of the deep surrounding rock,the stress environment of deep sidewall rock determines that the failure mode of rock is a tensile failure,the pre-static load level dominates the tensile failure strength of surrounding rock,and dynamic disturbance promotes the strength-weakening effect and affects the weakening range.

Behaviour of layered sandstone under Brazilian test conditions:Layer orientation and shape effects

The experimental study in this paper focuses on the effects of the layer orientation and sample shape on failure strength and fracture pattern of samples tested under Brazilian test conditions(i.e.diametrical loading of cylindrical discs)for one particular layered sandstone which is from Modave in the south of Belgium.The variations of the strength in combination with the failure patterns are examined as a function of the inclination angle between the layer plane and the loading direction.The experimental,results clearly show that the induced fracture patterns are a combination of tensile and/or shear fractures.In shape effect experiments the layer thickness and the number of layer boundaries are investigated.Different blocks of Modave sandstone are used to prepare samples.The layer thickness is different among the various blocks,but the layer thickness in each studied rock block can be considered to be constant;hence,the number of layer boundaries changes according to the sample diameter for samples of the same block.The experimental study shows that the layer thickness plays a more important role than the number of layer boundaries per sample.

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.

The influence of jaw's curvature on the results of the Brazilian disc test

The general contact problem of a disc squeezed between jaws of arbitrary curvature is considered employing Muskhelishvili’s complex potentials.Taking advantage of the general solution introduced,the closed-form expressions for the stresses along strategic loci(loaded rim,loaded diameter,disc’s center)are obtained,in terms of the ratio r of the disc’s to the jaw’s curvature.Then,the effect of r(as well as that of the relative stiffness of the disc’s and jaw’s materials dictating the contact arc)on the stress distribution along these loci is explored.It is concluded that,for both smooth contact(zero friction)and contact with friction,the role of the jaw’s curvature is significant not only along the disc-jaw contact arc(as it could be expected),but also all along the loaded diameter.On the other hand,it is indicated that the stress field at the disc’s center is more or less insensitive to the jaw’s curvature assuming that r lies within the range(0,0.67)or in other words within the limits defined by the two standardized suggestions,i.e.that of American Society for Testing and Materials(ASTM)(plane loading platens with r ? 0)and that of International Society for Rock Mechanics(ISRM)(curved jaws with r ? 0.67).The upper limit of this range is a kind of compromise between the need to make the stress field at the disc’s center independent of the boundary conditions while keeping at the same time the contact angle large enough to reduce the stress concentration and the risk for premature fracture initiation far from the disc’s center.For jaws with radius of curvature exceeded by that suggested by ISRM,the stress field at the disc’s center is significantly influenced.Especially for jaws with radius approaching that of the disc,the stress field at the disc’s center is dramatically distorted rendering Hondros’ formula inapplicable and the test results erroneous.

3-D distribution of tensile stress in rock specimens for the Brazilian test

It is claimed that the formula used for calculating the tensile strength of a disk-shaped rock specimen in the Brazilian test is not accurate, because the formula is based on the 2-dimensional elastic theory and only suitable for very long or very short cylinders. The Matlab software was used to obtain the 2-dimensional distribution of stress in the rock specimen for Brazilian test. Then the 2-dimensional stress distribution in Brazilian disk was analyzed by the Marc FEM software. It can be found that the results obtained by the two software packages can verify each other. Finally, the 3-dimensional elastic stress in the specimen was calculated. The results demonstrate that the distribution of stress on the cross section of the specimen is similar to that in 2-dimension. However, the value of the stress on the cross section varies along the thickness of the specimen and the stress is bigger when getting closer to the end of the specimen. For the specimen with a height-to-diameter ratio of 1 and a Poisson＇s ratio of 0.25, the tensile strength calculated with the classical 2-D formula is 23.3% smaller than the real strength. Therefore, the classical 2-D formula is too conservative.

Correction of dynamic Brazilian disc tensile strength of rocks under preloading conditions considering the overload phenomenon and invoking the Griffith criterion

Dynamic tensile failure is a common phenomenon in deep rock practices,and thus accurately evaluating the dynamic tensile responses of rocks under triaxial pressures is of great significance.The Brazilian disc(BD)test is the suggested method by the International Society for Rock Mechanics and Rock Engineering(ISRM)for measuring both the static and dynamic tensile strengths of rock-like materials.However,due to the overload phenomenon and the complex preloading conditions,the dynamic tensile strengths of rocks measured by the BD tests tend to be overestimated.To address this issue,the dynamic BD tensile strength(BTS)of Fangshan marble(FM)under different preloading conditions were measured through a triaxial split Hopkinson pressure bar(SHPB).The fracture onset in BD specimen was captured through a strain gage around the disc center.The discrepancy between the traditional tensile strength(TTS,determined by the peak load P_(f) of the BD specimen)and the nominal tensile strength(NTS,obtained from the load P_(i) when the diametral fracture commences in the tested BD specimen)was applied to quantitatively evaluating the overload phenomenon.The Griffith criterion was used to rectify the calculation of the tensile stress at the disc center under triaxial stress states.The results demonstrate that the overload ratio(s)increases with the loading rate(σ)and decreases with the hydrostatic pressure(σ_(s)).The TTS corrected by the Griffith criterion is independent of theσ_(s)due to the overload phenomenon,while the NTS corrected by the Griffith criterion is sensitive to both the andσ.Therefore,it is essential to modify the tensile stress in dynamic confined BD tests using both the overload correction and the Griffith criterion rectification to obtain the accurate dynamic BTS of rocks.

Analysis of stresses at the center of transversely isotropic Brazilian disk

This article presents the stresses at the center of a Brazilian disk(BD)for transversely isotropic rocks.It is shown that the solution of stresses at the center of an anisotropic disk is a function of the disk radius and the magnitude of applied load,as well as the material orientation with respect to the load axis and two dimensionless ratios with specific physical meanings and limitations.These two dimensionless parameters are the ratios of Young’s modulus and apparent shear modulus,although the ratio of apparent shear modulus will be eliminated if the Saint-Venant assumption is considered.Considerable finite element simulations are carried out to find the stresses at the disk center concerning the material orientation and the two dimensionless parameters.Also,an approximate formula obtained from analytical results,previously proposed in the literature for solving the tensile and compressive stresses at the disk center,is re-written and simplified based on these new definitions.The results of the approximate formula fitted to the analytical results are compared to those obtained from numerical solutions,suggesting a good agreement between the numerical and analytical methods.An approximate equation for the shear stress at the disk center is also formulated based on the numerical results.Finally,the influence of the assumptions for simplification of the proposed formula for the tensile,compressive,and shear stresses at the disk center is discussed,and simple and practical equations are proposed as estimations for the stresses at the center of the BD specimen for low to moderate anisotropic rocks.For highly anisotropic rocks,the reference plots can be used for more accuracy.

Effects of 3D deformation and nonlinear stress–strain relationship on the Brazilian test for a transversely isotropic rock

To improve the accuracy of indirect tensile strength for a transversely isotropic rock in the Brazilian test, this study considered the three-dimensional (3D) deformation and the nonlinear stress–strain relationship. A parametric study of a numerical Brazilian test was performed for a general range of elastic constants, revealing that the 3D modeling evaluated the indirect tensile strength up to 40% higher than the plane stress modeling. For the actual Asan gneiss, the 3D model evaluated the indirect tensile strength up to 10% higher and slightly enhanced the accuracy of deformation estimation compared with the plane stress model. The nonlinearity in stress–strain curve of Asan gneiss under uniaxial compression was then considered, such that the evaluated indirect tensile strength was affected by up to 10% and its anisotropy agreed well with the physical intuition. The estimation of deformation was significantly enhanced. The further validation on the nonlinear model is expected as future research.

Tensile strength and failure behavior of rock-mortar interfaces: Direct and indirect measurements

The tensile strength at the rock-concrete interface is one of the crucial factors controlling the failure mechanisms of structures,such as concrete gravity dams.Despite the critical importance of the failure mechanism and tensile strength of rock-concrete interfaces,understanding of these factors remains very limited.This study investigated the tensile strength and fracturing processes at rock-mortar interfaces subjected to direct and indirect tensile loadings.Digital image correlation(DIC)and acoustic emission(AE)techniques were used to monitor the failure mechanisms of specimens subjected to direct tension and indirect loading(Brazilian tests).The results indicated that the direct tensile strength of the rock-mortar specimens was lower than their indirect tensile strength,with a direct/indirect tensile strength ratio of 65%.DIC strain field data and moment tensor inversions(MTI)of AE events indicated that a significant number of shear microcracks occurred in the specimens subjected to the Brazilian test.The presence of these shear microcracks,which require more energy to break,resulted in a higher tensile strength during the Brazilian tests.In contrast,microcracks were predominantly tensile in specimens subjected to direct tension,leading to a lower tensile strength.Spatiotemporal monitoring of the cracking processes in the rock-mortar interfaces revealed that they show AE precursors before failure under the Brazilian test,whereas they show a minimal number of AE events before failure under direct tension.Due to different microcracking mechanisms,specimens tested under Brazilian tests showed lower roughness with flatter fracture surfaces than those tested under direct tension with jagged and rough fracture surfaces.The results of this study shed light on better understanding the micromechanics of damage in the rock-concrete interfaces for a safer design of engineering structures.

Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring

Static and dynamic splitting tests were conducted on ring marble specimens with different internal diameters to study the tensile strength and failure modes with the change of the ratio of internal radius to external radius （ρ） under different loading rates. The results show that the dynamic tensile strength of disc rock specimen is approximately five times its static tensile strength. The failure modes of ring specimens are related to the dimension of the internal hole and loading rate. Under static loading tests, when the ratio of internal radius to external radius of the rock ring is small enough （ρ〈0.3）, specimens mostly split along the diametral loading line. With the increase of the ratio, the secondary cracks are formed in the direction perpendicular to the loading line. Under dynamic loading tests, specimens usually break up into four pieces. When the ratio ρreaches 0.5, the secondary cracks are formed near the input bar. The tensile strength calculated by Hobbs’ formula is greater than the Brazilian splitting strength. The peak load and the radius ratio show a negative exponential relationship under static test. Using ring specimen to determine tensile strength of rock material is more like a test indicator rather than the material properties.

Mutual interference of layer plane and natural fracture in the failure behavior of shale and the mechanism investigation

Shale contains a certain amount of natural fractures,which affects the mechanical properties of shale.In this paper,a bonded-particle model in particle flow code(PFC)is established to simulate the failure process of layered shale under Brazilian tests,under the complex relationship between layer plane and natural fracture.First,a shale model without natural fractures is verified against the experimental results.Then,a natural fracture is embedded in the shale model,where the outcomes indicate that the layer plane angle(marked asα)and the angle(marked asβ)of embedded fracture prominently interfere the failure strength anisotropy and fracture pattern.Finally,sensitivity evaluations suggest that variable tensile/cohesion strength has a changeable influence on failure mechanism of shale,even for sameαor/andβ.To serve this work,the stimulated fractures are categorized into two patterns based on whether they relate to natural fracture or not.Meanwhile,four damage modes and the number of microcracks during the loading process are recognized quantitatively to study the mechanism of shale failure behavior.Considering the failure mechanism determines the outcome of hydraulic fracturing in shale,this work is supposed to provide a significant implication in theory for the engineering operation.

Mechanical anisotropy associated with beddings in shale under Brazilian test conditions:Insights from acoustic emission statistics

A comprehensive understanding of shale’s bedding anisotropy is crucial for shale-related engineering activities,such as hydraulic fracturing,drilling and underground excavation.In this study,seven Brazilian tests were conducted on shale samples at different bedding orientations with respect to the loading direction(0°,45°and 90°)and the disc end face(0°,45°and 90°).An acoustic emission(AE)system was employed to capture the evolution of damage and the temporal-spatial distribution of microcracks under splitting-tensile stress.The results show that the Brazilian tensile strength decreases with increasing bedding inclination with respect to the disc end face,while it increases with the angle between bedding and loading directions.Increasing the bedding inclination with respect to the end face facilitates the reduction in b value and enhances the shale’s resistance to microcrack growth during the loading process.Misalignment between the bedding orientation and the end face suppresses the growth of mixed tensile-shear microcracks,while reducing the bedding angle relative to the loading direction is beneficial for creating mixed tensile-shear and tensile cracks.The observed microscopic failure characteristics are attributed to the competing effects of bedding activation and breakage of shale matrix at different bedding inclinations.The temporal-spatial distribution of microcracks,characterized by AE statistics including the correlation dimension and spatial correlation length,illustrates that the fractal evolution of microcracks is independent of bedding anisotropy,whereas the spatial distribution shows a stronger correlation.The evolution features of correlation dimension and spatial correlation length could be potentially used as precursors for shale splitting failure.These findings may be useful for predicting rock mass instability and analyzing the causes of catastrophic rupture.

Stress-deformed state of cylindrical specimens during indirect tensile strength testing

In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.

Microscopic damage evolution of anisotropic rocks under indirect tensile conditions: Insights from acoustic emission and digital image correlation techniques

The anisotropy induced by rock bedding structures is usually manifested in the mechanical behaviors and failure modes of rocks.Brazilian tests are conducted for seven groups of shale specimens featuring different bedding angles. Acoustic emission (AE) and digital image correlation (DIC) technologies are used to monitor the in-situ failure of the specimens. Furthermore, the crack morphology of damaged samples is observed through scanning electron microscopy (SEM). Results reveal the structural dependence on the tensile mechanical behavior of shales. The shale disk exhibits compression in the early stage of the experiment with varying locations and durations. The location of the compression area moves downward and gradually disappears when the bedding angle increases. The macroscopic failure is well characterized by AE event location results, and the dominant frequency distribution is related to the bedding angle. The b-value is found to be stress-dependent.The crack turning angle between layers and the number of cracks crossing the bedding both increase with the bedding angle, indicating competition between crack propagations. SEM results revealed that the failure modes of the samples can be classified into three types:tensile failure along beddings with shear failure of the matrix, ladder shear failure along beddings with tensile failure of the matrix, and shear failure along multiple beddings with tensile failure of the matrix.

Deformation and Failure of Polymer Bonded Explosives

The deformation and failure of pressed polymer bonded explosives under different types of loads including tension, compression and low velocity impact are presented. Brazilian test is used to study the tensile properties. The microstructure of polymer bonded explosives and its evolution are studied by use of scanning electronic microscopy and polarized light microscopy. Polishing techniques have been developed to prepare samples for microscopic examination. The failure mechanisms of polymer bonded explosives under different loads are analyzed. The results show that interfacial debonding is the predominant failure mode in quasi-static tension, while extensive crystal fractures are induced in compression. With the increase of strain rate, more crystal fractures occur. Low velocity impact also induces extensive crystal fractures.

Dynamic rock tensile strengths of Laurentian granite: Experimental observation and micromechanical model

Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks.Here we examine dynamic tensile strength values of Laurentian granite(LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc(BD) test, and dynamic semi-circular bending(SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.

Strength Developing in Clay-Andesite Brick

The objective of this work was to develop a more and better understanding of the strength developing in clay-andesite fired brick. The purpose was to improve the quality of the clay bricks that are handmade in the southern region of Ecuador to make them suitable for more widespread use in the local construction industry. To achieve our goal, we first physically, chemically, and mechanically characterized the “clayey” and “sandy” materials used in the fabrication of handmade bricks in the region. Second, the optimal mixture (OM): the optimal proportion between the amounts of “clayey” and “sandy” material was sought. Third, clay bricks were prepared using the OM, baked at 950°C, and characterized. In addition, bricks produced by regional artisans were characterized, and the results were compared with the results obtained for the bricks prepared using the OM. Our data reveal that the optimal mixture is 50% “clayey” material and 50% “sandy” material and that with this mixture, an average improvement in brick quality of 300% can be achieved;thus, the use of the OM makes it possible to expand the use of these bricks in the local construction industry and enables an environmentally friendly production process by reducing the intensive exploitation of regional clay deposits. This improvement is achieved by virtue of the anorthite enrichment that occurs in the solid solution, which results from the evolution of andesine. The anorthite contributes to the formation of a stronger matrix among the different grains of the material. Conditions are favorable for this enrichment process to occur when “sandy” materials with high contents of andesite, which is common in Ecuadorian soils, are used.

Acoustic emissions evaluation of the dynamic splitting tensile properties of steel fiber reinforced concrete under freeze-thaw cycling

This study empirically investigated the influence of freeze-thaw cycling on the dynamic splitting tensile properties of steel fiber reinforced concrete(SFRC).Brazilian disc splitting tests were conducted using four loading rates(0.002,0.02,0.2,and 2 mm/s)on specimens with four steel fiber contents(0%,0.6%,1.2%,and 1.8%)subjected to 0 and 50 freeze-thaw cycles.The dynamic splitting tensile damage characteristics were evaluated using acoustic emission(AE)parameter analysis and Fourier transform spectral analysis.The results quantified using the freeze-thaw damage factor defined in this paper indicate that the degree of damage to SFRC caused by freeze-thaw cycling was aggravated with increasing loading rate but mitigated by increasing fiber content.The percentage of low-frequency AE signals produced by the SFRC specimens during loading decreased with increasing loading rate,whereas that of high-frequency AE signals increased.Freeze-thaw action had little effect on the crack types observed during the early and middle stages of the loading process;however,the primary crack type observed during the later stage of loading changed from shear to tensile after the SFRC specimens were subjected to freeze-thaw cycling.Notably,the results of this study indicate that the freeze-thaw damage to SFRC reduces AE signal activity at low frequencies.