Determining elastic constants of transversely isotropic rocks using Brazilian test and iterative procedure

Chou, Yen Chin; Chen, Chao Shi

doi:10.1002/nag.619

Cited by 33 publications

(10 citation statements)

References 10 publications

(22 reference statements)

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“…For static elastic property measurements, the standard methodology has been to apply an elastic axial load to a strain-gauged cylindrical specimen and then use the applied load and axial and radial strains to calculate the Young's modulus and Poisson's ratio, from which the other elastic parameters can be calculated if isotropy is assumed. It is difficult to characterize even transverse isotropy (with radial symmetry) using static measurements, and even then, several cores in different directions are required [e.g., Amadei, 1996;Liao et al, 1997b;Chou and Chen, 2008;Kim et al, 2012]. For dynamic elastic properties, only the P and S wave velocity in one direction is required to determine the elastic properties of an isotropic sample.…”

Section: Introductionmentioning

confidence: 99%

The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

Blake

Faulkner

2016

JGR Solid Earth

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Elastic properties are key parameters during the deformation of rocks. They can be measured statically or dynamically, but the two measurements are often different. In this study, the static and dynamic bulk moduli (Kstatic and Kdynamic) were measured at varying effective stress for dry and fluid‐saturated Westerly granite with controlled fracture densities under isotropic and differential stress states. Isotropic fracturing of different densities was induced in samples by thermal treatment to 250, 450, 650, and 850°C. Results show that fluid saturation does not greatly affect static moduli but increases dynamic moduli. Under isotropic loading, high fracture density and/or low effective pressure results in a low Kstatic/Kdynamic ratio. For dry conditions Kstatic/Kdynamic approaches 1 at low fracture densities when the effective pressure is high, consistent with previous studies. Stress‐induced anisotropy exists under differential stress state that greatly affects Kstatic compared to Kdynamic. As a result, the Kstatic/Kdynamic ratio is higher than that for the isotropic stress state and approaches 1 with increasing axial loading. The effect of stress‐induced anisotropy increases with increasing fracture density. A key omission in previous studies comparing static and dynamic properties is that anisotropy has not been considered. The standard methods for measuring static elastic properties, such as Poisson's ratio, Young's and shear modulus, involve subjecting the sample to a differential stress state that promotes anisotropy. Our results show that stress‐induced anisotropy resulting from differential stress state is a major contributor to the difference between static and dynamic elasticity and is dominant with high fracture density.

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Section: Introductionmentioning

confidence: 99%

The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

Blake

Faulkner

2016

JGR Solid Earth

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“…Therefore, to determine tensile strength, indirect tensile tests are developed, for example Brazilian test, ring test, hoop test, bending test, etc. Brazilian test which is much more popular among those carried out has been proved as a satisfactory technique for determining the tensile strength of many rocks . Brazilian test measures tensile strength indirectly by developing tension across the diameter of a rock disc that is subjected to compression through a vertical load .…”

Section: Introductionmentioning

confidence: 99%

Modeling of tensile strength of rocks materials based on support vector machines approaches

Ceryan

Okkan

Samui

et al. 2012

Num Anal Meth Geomechanics

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In the predicting of geological variables, artificial neural networks (ANNs) have some drawbacks including possibility of getting trapped in local minima, over training, subjectivity in the determining of model parameters and the components of its complex structure. Recently, support vector machines (SVM) has been found to be popular in prediction studies due to its some advantages over ANNs. Because the least squares SVM (LS-SVM) provides a computational advantage over SVM by converting quadratic optimization problem into a system of linear equations, LS-SVM method is also tried in study. The main purpose of this study is to examine the capability of these two SVM algorithms for the prediction of tensile strength of rock materials and to compare its performance with ANN and linear regression (MLR) models. Total porosity, sonic velocity, slake durability index and aggregate impact value were used as input in modeling applications. Favorite performance evaluation measures were employed to assess developed models. The results determined in study indicate that the SVM, LS-SVM and ANN methods are successful tools for prediction of tensile strength variable and can give good prediction performances than MLR model. Although these three methods are powerful artificial intelligence techniques, LS-SVM makes the running time considerably faster with the higher accuracy. In terms of accuracy, the LS-SVM model resulted in error reductions relative to that of the other models.Tensile strength was used for different geotechnical aims, and laboratory and full-scale studies were carried out to explore the possible relationship between fine production and water content of rock material [11]. Results of the laboratory work showed that the percentage of fines fraction produced by a cone crusher machine was a function of the type of rock tested and the tensile strength of individual specimens [11].There are mainly two methods for determining the tensile strength of rock materials. One of the methods is laboratory tests including direct uniaxial tensile test and indirect tensile tests (direct method) or making use of the previously derived empirical equations from literature called as indirect method. Direct uniaxial tensile test have some disadvantages and limitations. This test, which is theoretically the simplest and most effective method for the determination of tensile strength, is in fact difficult to carry out in practice for rock material and the difficulty in specimen preparation [4,9,[12][13][14][15][16]. Therefore, to determine tensile strength, indirect tensile tests are developed, for example Brazilian test, ring test, hoop test, bending test, etc. Brazilian test which is much more popular among those carried out has been proved as a satisfactory technique for determining the tensile strength of many rocks [6,[8][9][10][11][17][18][19][20]. Brazilian test measures tensile strength indirectly by developing tension across the diameter of a rock disc that is subjected to compression through a vertical load [8]. Testing proc...

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“…Thereinto, the closed-form solution of stress distribution was proposed using the linear elastic theory, and the connotative assumption is that the influence of anisotropy on stress distribution is ignored. In 1957, Lekhnitskij proposed the elastic solution of stress distribution for an anisotropic medium [66,67], but only the stress distributions that were located on some key points/lines were obtained, due to their studies mainly focusing on the determination of anisotropic elastic constants and anisotropic indirect tensile strength [13,32,57,[68][69][70][71]. In the present paper, the isotropic closed-form solution was used to simplify the complexity of the modeling.…”

Section: Discussionmentioning

confidence: 99%

Brazilian Tensile Strength of Anisotropic Rocks: Review and New Insights

Peng

Zhu

et al. 2018

Energies

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Strength anisotropy is one of the most distinct features of anisotropic rocks, and it also normally reveals strong anisotropy in Brazilian test Strength ("BtS"). Theoretical research on the "BtS" of anisotropic rocks is seldom performed, and in particular some significant factors, such as the anisotropic tensile strength of anisotropic rocks, the initial Brazilian disc fracture points, and the stress distribution on the Brazilian disc, are often ignored. The aim of the present paper is to review the state of the art in the experimental studies on the "BtS" of anisotropic rocks since the pioneering work was introduced in 1964, and to propose a novel theoretical method to underpin the failure mechanisms and predict the "BtS" of anisotropic rocks under Brazilian test conditions. The experimental data of Longmaxi Shale-I and Jixi Coal were utilized to verify the proposed method. The results show the predicted "BtS" results show strong agreement with experimental data, the maximum error is only~6.55% for Longmaxi Shale-I and~7.50% for Jixi Coal, and the simulated failure patterns of the Longmaxi Shale-I are also consistent with the test results. For the Longmaxi Shale-I, the Brazilian disc experiences tensile failure of the intact rock when 0 • ≤ β w ≤ 24 • , shear failure along the weakness planes when 24 • ≤ β w ≤ 76 • , and tensile failure along the weakness planes when 76 • ≤ β w ≤ 90 • . For the Jixi Coal, the Brazilian disc experiences tensile failure when 0 • ≤ β w ≤ 23 • or 76 • ≤ β w ≤ 90 • , shear failure along the butt cleats when 23 • ≤ β w ≤ 32 • , and shear failure along the face cleats when 32 • ≤ β w ≤ 76 • . The proposed method can not only be used to predict the "BtS" and underpin the failure mechanisms of anisotropic rocks containing a single group of weakness planes, but can also be generalized for fractured rocks containing multi-groups of weakness planes.

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Determining elastic constants of transversely isotropic rocks using Brazilian test and iterative procedure

Cited by 33 publications

References 10 publications

The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

Modeling of tensile strength of rocks materials based on support vector machines approaches

Brazilian Tensile Strength of Anisotropic Rocks: Review and New Insights

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