Rectangular Prismatic Specimens Research Articles

Rockburst characteristics of several hard brittle rocks: A true triaxial experimental study

Abstract Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation. Rock lithology is a control factor of rockburst. In this paper, rockburst tests were conducted on rectangular prismatic specimens of six types of intact hard brittle rocks, i.e. granodiorite, granite, marble, basalt, sandstone and limestone, under one-free-face true triaxial loading conditions. With the use of high-speed cameras, an acoustic emission (AE) system and a scanning electron microscope (SEM), rockburst of different rocks was investigated. The results show that the strainbursts of granodiorite, granite and marble were accompanied by tensile splitting near the free face, and consequently were relatively strong with a large amount of fragment ejection and kinetic energy release. For basalt, sandstone and limestone, failure was primarily dominated by shear rupture. The strainbursts of basalt and sandstone were relatively small with minor fragment ejection and kinetic energy release; while no burst failure occurred on limestone due to its relatively low peak strength. Rock strength, fracturing and fragmentation characteristics, and failure modes of different rocks can significantly affect rockburst proneness and magnitude. The AE evolution coupled with SEM analysis reveals that the differences in the inherent microstructures and fracture evolution under loading are the primary factors accounting for different rockbursts in various rock types.

High strain rate compressive behaviour of wood on the transverse plane

The high strain rate compressive behaviour of Pinus pinaster Ait. wood along the radial and tangential material axes was addressed in this work. Both quasi-static and dynamic tests were considered for comparation purposes. The quasi-static compression tests were performed on rectangular prismatic specimens along the radial and tangential directions coupled with digital image correlation. The high strain rate tests were carried out using a classical split-Hopkinson pressure bar coupled with a high-speed imaging system allowing independent kinematic measurements through digital image correlation. From these tests and material symmetry orientations, the constitutive curves were determined from which the Young modulus, Poisson’s ratio and yield stress were evaluated and compared over the two different regimes over the strain rate spectrum. The mechanical properties observed for this species under quasi-static compression loading agree with reference values. A qualitative comparison between quasi-static and high strain rate regimes reveals a significant increase of some mechanical properties by increasing the strain rate. Quantitatively, by comparing mean values at the two strain rates, it was found that, in the radial direction, the modulus of elasticity increased by 6.3%, the yield stress showed an increase of 130.3% and the Poisson’s ratio is slightly higher by 3.0%. Furthermore, in the tangential direction, it was found that the modulus of elasticity increased by 21.9% while the value of the yield stress showed an increase of 111.8%, and finally the Poisson‘s ratio presented a reduction of 24.3%.

Experiment on Rockburst Process of Borehole and Its Acoustic Emission Characteristics

In the present study, structural model test using rectangular prismatic granite specimen 200 mm × 200 mm × 200 mm with a horizontal central circular hole of 78 mm diameter was conducted to investigate a rockburst process of borehole. Strain measurement system and high-speed camera were used to capture the rock responses during rockburst. Acoustic emission (AE) system was adopted to monitor the associated AE signals during the rockburst process, and to locate the positions of micro-cracks and subsequently quantitatively investigate the cracking mechanisms. In addition, scanning electron microscope (SEM) was also used to identify the micro-cracks of fragments. The experimental results indicate that rockburst process is characterized by significant spatial distribution and structural responses. As the circumferential stress of surrounding rocks increase, there are some local rockbursts interlacing at different regions of compressive stress concentration along the opening axis direction before overall rockburst. These local rockbursts continued to develop and coalesce, eventually forming overall rockburst. A local rockburst in the present test can be composed of several bursts and persist for a longer period of time than that in true-triaxial tests using rectangular prismatic specimen. Hoop effect, stress gradient around the opening, and last V-shaped bands were accurately simulated. According to AE analysis results, quiet period characterized by few AE hits with high amplitude and a sharp increase in AE energy can be used as an early warning signal for overall rockburst. The time and position of rockburst are related to the spatiotemporal distribution of AE event density, which can be used as a potential indicator for rockburst prediction. During the rockburst process, tensile cracks occupied most of the total micro-cracks, and tensile splitting dominated the failure process. Shear cracks due to tensile cracks interaction initiated at 67% of the spalling strength (tangential stress for spalling failure at the opening boundary) of the borehole.

Characteristic Stress Levels and Brittle Fracturing of Hard Rocks Subjected to True Triaxial Compression with Low Minimum Principal Stress

In this study, true triaxial compression tests were carried out on three types of hard rocks (i.e., granite, marble and sandstone) using rectangular prismatic specimens (50 × 50 × 100 mm3) with low minimum principal stress σ3, and various intermediate principal stresses σ2. The main purposes were to establish the relationship between the characteristic stress levels (i.e., crack initiation stress, crack damage stress and peak stress) and the corresponding principal stresses and to investigate the brittle fracturing process of hard rocks near excavation boundaries. The test results indicated that the stress–strain curves were primarily characterized by the linear-elastic–brittle behavior. The failure planes of the specimens in the tests were found to be adjacent to the σ3 loading surface, and almost parallel to the σ1–σ2 plane, which were analogous to the spalling of the surrounding rock. With the aid of scanning electron microscopy, it was shown that cleavage fractures accounted for the majority of the fracture morphology in the sandstone specimens. Two revised methods were developed to determine the crack initiation stress of hard rocks under true triaxial compression, and these characteristic stress levels could be appropriately fitted by utilizing both the parabolic and power functions. Although the power function achieved better fitting results, the parameters in the parabolic function could be associated with the tensile cracks induced during the loading process. The influence of intermediate principal stress on the strength, deformation and failure was significant. In addition, the brittle fracturing process could be illustrated by the crack-induced strains in three principal stress directions.

On necessary precautions when measuring solid polymer linear viscoelasticity with dynamic analysis in torsion

Solid polymer linear viscoelasticity in shear is often characterized by applying torsion and using the Saint-Venant solution when rectangular prismatic specimens are considered. It is shown that experimental dynamic torsion tests can show a dependency of the storage modulus and damping factor on the dimensions of the rectangular prismatic specimen when linear temperature ramps are applied. While the discrepancy of damping factor is explained by temperature heterogeneities and can be corrected easily by applying temperature steps, the inconsistency of storage modulus is due to an invalid application of the Saint-Venant solution. Finite element simulations allowed definition of the sample dimensions for which the Saint-Venant solution provides a good approximation, and a coefficient is given to correct the results obtained with commercial instruments when other sample dimensions are used.

An Experimental and Numerical Study on Cracking Behavior of Brittle Sandstone Containing Two Non-coplanar Fissures Under Uniaxial Compression

To understand the fracture mechanism in all kinds of rock engineering, it is important to investigate the fracture evolution behavior of pre-fissured rock. In this research, we conducted uniaxial compression experiments to evaluate the influence of ligament angle on the strength, deformability, and fracture coalescence behavior of rectangular prismatic specimens (80 × 160 × 30 mm) of brittle sandstone containing two non-coplanar fissures. The experimental results show that the peak strength of sandstone containing two non-coplanar fissures depends on the ligament angle, but the elastic modulus is not closely related to the ligament angle. With the increase of ligament angle, the peak strength decreased at a ligament angle of 60°, before increasing up to our maximum ligament angle of 120°. Crack initiation, propagation, and coalescence were all observed and characterized from the inner and outer tips of pre-existing non-coplanar fissures using photographic monitoring. Based on the results, the sequence of crack evolution in sandstone containing two non-coplanar fissures was analyzed in detail. In order to fully understand the crack evolution mechanism of brittle sandstone, numerical simulations using PFC2D were performed for specimens containing two non-coplanar fissures under uniaxial compression. The results are in good agreement with the experimental results. By analyzing the stress field, the crack evolution mechanism in brittle sandstone containing two non-coplanar fissures under uniaxial compression is revealed. These experimental and numerical results are expected to improve the understanding of the unstable fracture mechanism of fissured rock engineering structures.

Stick–slip behavior of Indian gabbro as studied using a NIED large-scale biaxial friction apparatus

This paper reports stick–slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention (NIED), Tsukuba, Japan. The apparatus consists of the existing shaking table as the shear-loading device up to 3,600 kN, the main frame for holding two large rectangular prismatic specimens with a sliding area of 0.75 m2 and for applying normal stresses σ n up to 1.33 MPa, and a reaction force unit holding the stationary specimen to the ground. The shaking table can produce loading rates v up to 1.0 m/s, accelerations up to 9.4 m/s2, and displacements d up to 0.44 m, using four servocontrolled actuators. We report results from eight preliminary experiments conducted with room humidity on the same gabbro specimens at v = 0.1–100 mm/s and σ n = 0.66–1.33 MPa, and with d of about 0.39 m. The peak and steady-state friction coefficients were about 0.8 and 0.6, respectively, consistent with the Byerlee friction. The axial force drop or shear stress drop during an abrupt slip is linearly proportional to the amount of displacement, and the slope of this relationship determines the stiffness of the apparatus as 1.15 × 108 N/m or 153 MPa/m for the specimens we used. This low stiffness makes fault motion very unstable and the overshooting of shear stress to a negative value was recognized in some violent stick–slip events. An abrupt slip occurred in a constant rise time of 16–18 ms despite wide variation of the stress drop, and an average velocity during an abrupt slip is linearly proportional to the stress drop. The use of a large-scale shaking table has a great potential in increasing the slip rate and total displacement in biaxial friction experiments with large specimens.

Influence of a repeated preheating procedure on mechanical properties of three resin composites.

The aim of this study was to assess the flexural strength, flexural elastic modulus and Vickers microhardness of three resin composites prepared at room temperature or cured after one or repeated preheating cycles to a temperature of 39°C. Three resin composites were evaluated: Enamel Plus HFO (Micerium), Opallis (FGM), and Ceram X Duo (Dentsply DeTrey). For each trial, one group of specimens of each material was fabricated under ambient laboratory conditions, whereas in the other groups, the composites were cured after 1, 10, 20, 30, or 40 preheating cycles to a temperature of 39°C in a preheating device. Ten rectangular prismatic specimens (25 × 2 × 2 mm) were prepared for each group (N=180; n=10) and subjected to a three-point bending test for flexural strength and flexural modulus evaluation. Vickers microhardness was assessed on 10 cylindrical specimens from each group (N=180; n=10). Statistical analysis showed that, regardless of the material, the number of heating cycles was not a significant factor and was unable to influence the three mechanical properties tested. However, a significant main effect of the employed material on the marginal means of the three dependent variables was detected.

Resistencia a corte paralela a la tensión de la fibra de la madera, por medio de la prueba de punzonamiento propuesta

This research aims to propose a method for testing the shear strength of wood parallel to fiber and compare with other proposed methods. The method proposed by NBR 7190/1997 Brazilian Standard, that is similar to ASTM D 143-09/2010, the uses a rectangular prismatic specimen with an indentation to prevent its rotation, which it is caused by the asymmetry in the application of force that promotes the shear. In order to eliminate this asymmetry, the proposed procedure applies shear stress by punching a simple prismatic test specimen without cuts, with the distribution of shear section symmetrically in relation to a point. There upon, it's developed a male and female tool adapted to a universal test press for force application. Once the consistency of the method is verified, it's been carried out a series of tests with three different wood species (Pinus sp, Erisma uncinatum and Mezilaurus itauba), distinguished by their mechanical strength, inspecting the method by Santos Neto (1999) under the NBR 7190/1997 Brazilian Standard, and comparing it with the proposed method - punching. The outcomes showed that the testing with NBR 7190/1997 Brazilian Standard methods and the proposed method displayed similar and close results between them. Rev. ing. constr. [online]. 2014, vol.29, n.1, pp. 46-60. ISSN 0718-5073. http://dx.doi.org/10.4067/S0718-50732014000100003

A Failure Criterion for Rocks Based on True Triaxial Testing

Mean effective normal stress acting on thefailure planec Cohesion/ Angle of internal frictionA, n, a, b Material constants1 DescriptionThe failure criterion based on true triaxial testing considersthe effect of all three principal stresses on rock compres-sive strength, and is entirely based on true triaxial testsconducted on rectangular prismatic specimens subjected tothree independent principal stresses. The failure criterion iscommonly expressed in terms of the octahedral shear stressas a monotonically increasing function of the mean effec-tive normal stress acting on the plane of failure. In testsconducted thus far the function best fitting experimentaldata is the one obeying the power law. This criterion wasfirst derived by Mogi (1971) and confirmed for severalother rocks by Haimson and Chang (2000), Chang andHaimson (2000), Oku et al. (2007) and Lee and Haimson(2011).2 BackgroundThe significant observation by Murrell (1963) and Handinet al. (1967) that rock compressive strength in experi-ments conducted in conventional triaxial extension(r

Local and global instabilities in nanosize rectangular prismatic gold specimens

Abstract We use molecular mechanics simulations with the tight-binding potential to study local and global instabilities in initially defect-free nanosize rectangular prismatic specimens of gold deformed in tension/compression and simple tension/compression. Whereas in simple tension/compression atoms on end faces are constrained to move axially but are free to move laterally and the cross-sectional dimensions of end faces can change, in tension/compression all three components of displacements of atoms on end faces are prescribed and the cross-section of an end face does not change. The three criteria used to delineate local instabilities in a specimen are: (i) a component of second-order spatial partial derivatives of the displacement field has large value relative to its average value in the body, (ii) the minimum eigenvalue of the Hessian of the potential energy of an atom is negative, (iii) a relatively high value of the common neighborhood parameter. A specimen becomes globally unstable when its potential energy decreases noticeably with a small increase in its deformations. It is found that the three criteria for local instability are met essentially simultaneously at the same atomic position. Deformations of interior points of a specimen are different when it is deformed in simple tension/compression from those in tension/compression. It is found that the initial unloaded configuration (or the reference configuration) of the minimum potential energy has significant in-plane stresses on the bounding surfaces and non-zero normal stresses at interior points. This initial stress distribution satisfies Cauchy’s equilibrium equations for a continuum. In deformations of a nanobar studied here, the yield stress defined as the average axial stress when the average axial stress vs. the average axial strain curve exhibits a sharp discontinuity depends upon the specimen size. It is shown possibly for the first time that deformations of the specimen are reversible if it is unloaded prior to yielding but have a permanent strain if unloaded after it has yielded. Because of residual stresses in the reference configuration, the average axial stress at yield in compression is nearly one-half of that in tension. The slope of the average axial stress vs. the average axial strain curve during unloading after it has yielded is the same as that during initial loading up to the yield point.

An experimental study on the brittle failure under true triaxial conditions

When a tunnel or an underground structure is excavated in a highly stressed rock mass, rock damaged zone is formed around the tunnel due to the stress concentration resulting from stress redistribution. Recent studies on the rock damaged zone revealed its importance to structural stability around deep underground openings. In order to evaluate the characteristics of the rock damaged zone by brittle failure, physical model test and numerical model tests have been conducted. For this study, a new true triaxial chamber has been designed and fabricated. It is possible to load highly in all three orthogonal directions. All three independent stresses applied to rectangular prismatic specimens, 30x30x30cm in size, are servo-controlled. The test models, made with cement mortar, have an opening of 6cm in diameter and 15cm in length. The experiments were conducted under true triaxial test using new testing system. The experimental results indicate that the shape of the failure zone around the opening is V-shape and the extent is affected by the magnitude of applied stress. However, the numerical predictions using general failure criteria, Mohr-Coulomb criteria, are found to be different from the experiments results. These differences call for further investigation on understanding the brittle failure and developing new criteria for predicting the brittle failure. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.

Analysis of Shear Banding in True Triaxial Tests on Sand

A series of true triaxial tests have been performed on rectangular prismatic specimens of Santa Monica Beach sand at three different relative densities to study the occurrence of failure, mechanisms that create failure, and soil behavior in the vicinity of failure. One mechanism is smooth peak failure, in which the soil continues to behave as a continuum with uniform strains, and smooth peak failure is followed by strain softening. Another mechanism is shear banding, whose occurrence in the plastic hardening regime limits the strength of the soil. Presented here are analyses based on theoretical conditions for localization and subsequent shear banding and on the results of the true triaxial tests. Thus, the strength increases as b [=(σ2 − σ3)/(σ1 − σ3)] increases from 0 to about 0.18, remains almost constant until b reaches 0.85, and then decreases slightly at b = 1.0. Shear banding initiates in the hardening regime for b-values of 0.18–0.85. Thus, peak failure is caused by shear banding in this middle range of b-values, and a smooth, continuous 3D failure surface is therefore not generally obtained for soils. The experimental results agree with the theoretical conditions for the occurrence of shear banding and its consequent effect on the 3D failure stress states for soil.

Effets de plaques dans l'essai de flexion 3 points

The rectangular prismatic specimens which are used in bending tests are usually approximated as a beam. In this study, the beam-plate limit is evaluated and the validity of the beam approximation for the usual specimen geometry is discussed.

A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite

Abstract A new true triaxial cell has been designed, fabricated, calibrated, and successfully tested. Its main feature is very high loading capability in all three orthogonal directions, enabling the testing to failure of hard crystalline rocks subjected to large least and intermediate principal stresses. All three principal stresses applied to rectangular prismatic specimens, 19×19×38 mm in size, are servo controlled. The cell was used to conduct an extensive series of tests in Westerly granite. A new true triaxial strength criterion for the rock was obtained that takes into account the effect of the intermediate principal stress. This turns out to be so significant that it raises serious questions about the suitability of criteria such as those named after Mohr, Coulomb, Griffith, and others. Measurements of strain in all three principal directions revealed that the onset of dilatancy relative to the major principal stress at failure rises substantially as the intermediate principal stress increases. The true triaxial tests also demonstrate that for the same least horizontal stress the main fracture dip angle in Westerly granite increases as a function of the intermediate principal stress, suggesting a strengthening effect. Limited thin section and SEM study shows that microcrack propagation, crack localization, and main fracture characteristics are basically similar to those observed in common triaxial tests.

Deformation characteristics of a sedimentary soft mudstone from triaxial compression tests using rectangular prism specimens

A new triaxial testing system has been developed for accurately evaluating the deformation characteristics of soft rock. Axial and lateral strains were measured locally along the surfaces of a rectangular prismatic specimen by using, in total, four pairs of local deformation transducers. Sedimentary mudstone samples retrieved by block sampling at Sagamihara Test Site were first compressed isotropically to the field overburden pressure level, followed by drained triaxial compression at different axial strain rates. A series of small unload/reload cycles was applied to define elastic and plastic deformation properties at intermediate loading stages. Very large bedding errors were observed at both the top and bottom ends and at the lateral surfaces of specimens during isotropic compression, and at the ends during triaxial compression. Local strains showed approximately isotropic deformation during isotropic compression. From the results of the drained triaxial compression tests, the Young's modulus and Poisson's ratio, defined for elastic and total strain increments, and their dependences on shear stress level and strain rate were quantified. Un nouveau systeème d'essais triaxiaux a été mis au point pour l'évaluation précise des caractéristiques de déformation des roches tendres. Les contraintes axiales et latérales ont été mesurées localement sur les surfaces d'une éprouvette rectangulaire prismatique à l'aide de quatre paires de capteurs de déformation locale. Des échantillons d'argilite sédimentaire prélevés par échantillonnage par blocs sur le terrain d'essai de Sagamihara ont d'abord été comprimés de façon isotrope jusqu'à la pression des mortsterrains avant de subir des essais de compression triaxiale drainés à différents taux de contrainte axiale. On a eu recours à une série de petits cycles décharge=recharge pour déÆnir les propriétés de déformation élastique et plastique aux stades de chargement intermédiaires. On a observé une grande erreur de litage aux extrémite s supérieure et inférieure et aux surfaces latérales de l'éprouvette pendant la compression isotrope, ainsi qu'à l'extrémité supérieure pendant la compression triaxiale. Les contraintes locales ont produit une déformation approximativement isotrope pendant la compression isotrope. A partir des résultats des essais de compression triaxiale drainée, on a quantifié le module de Young et le coefficient de Poisson, définis pour les écarts de contrainte élastique et totale, et la facçon dont ils dépendent du cisaillement et de l'état de contrainte.

Measuring Anisotropic Elastic Properties of Sand Using a Large Triaxial Specimen

Abstract An advanced automated triaxial testing system developed to characterize elastic behavior of soils is described. Small axial and lateral strains of a large rectangular prismatic specimen were measured locally at various stress states along a specified stress path, which was achieved by automatically controlling axial load and confining pressure. Elastic deformation was measured by applying very small cycles of axial or lateral stress at each given neutral stress state. Typical test data for air-dried sand are presented. It is observed that the elastic Young's modulus is a rather unique function of the normal stress in the direction of the major principal strain increment, and therefore elastic deformation characteristics of sand become anisotropic under anisotropic stress conditions.

Preparation of Rectangular Prismatic Specimens of Bismuth Telluride and Attachment of Fine Potential Leads

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