• Structural Engineering and Mechanics
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• v.66 no.4
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• pp.445-452
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• 2018

In this paper the effects of particle size and model scale of concrete have been investigated on point load index, tensile strength, and the failure processes using a PFC2D numerical modeling study. Circular and semi-circular specimens of concrete were numerically modeled using the same particle size, 0.27 mm, but with different model diameters of 75 mm, 54 mm, 25 mm, and 12.5 mm. In addition, circular and semi-circular models with the diameter of 27 mm and particle sizes of 0.27 mm, 0.47 mm, 0.67 mm, 0.87 mm, 1.07 mm, and 1.27 mm were simulated to determine whether they can match the experimental observations from point load and Brazilian tests. The numerical modeling results show that the failure patterns are influenced by the model scale and particle size, as expected. Both Is(50) and Brazilian tensile strength values increased as the model diameter and particle sizes increased. The ratio of Brazilian tensile strength to Is(50) showed a reduction as the particle size increased but did not change with the increase in the model scale.

• Structural Engineering and Mechanics
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• v.69 no.1
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• pp.51-67
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• 2019

In this paper, the anisotropy of tensile behaviours of layered rocks consisting internal notch has been investigated using particle flow code. For this purpose, firstly calibration of PFC2D was performed using Brazilian tensile strength. Secondly Brazilian test models consisting bedding layer was simulated numerically. Thickness of layers was 10 mm and layered angularity was $90^{\circ}$, $75^{\circ}$, $60^{\circ}$, $45^{\circ}$, $30^{\circ}$, $15^{\circ}$ and $0^{\circ}$. The strength of bedding interface was too high. Each model was consisted of one internal notch. Notch length is 1 cm, 2 cm and 4 cm and notch angularities are $60^{\circ}$, $45^{\circ}$, $30^{\circ}$, $15^{\circ}$ and $0^{\circ}$. Totally, 90 model were tested. The results show that failure pattern was affected by notch orientation and notch length. It's to be noted that layer angle has not any effect on the failure pattern. Also, Brazilian tensile strength is affected by notch orientation and notch length.

• Explosives and Blasting
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• v.38 no.1
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• pp.30-37
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• 2020

In this study the split ring (SR) test was investigated for its applicability to the measurement of the tensile strength of rock specimen of NX size. The concept of the SR test is the same as the half ring (HR) test (Choi et al., 2019) except that the expected fracture plane is perpendicular to the loading direction. Because of this perpendicularity, however, it was believed that the SR test could be more accurate than the HR test. Like the HR specimen, the SR specimen is a curved prismatic bar with a uniform section. Appealing to a basic bending theory in strength of materials, the tensile strength for the special bar can be calculated analytically. Numerical simulations using LS-DYNA revealed, as expected, that the strength errors were 1% and 5% for the tensional and compressional SR tests, respectively, which were much lower than that (12%) of the HR test. To identify the performance of the two SR tests, laboratory experiments were conducted. The HR and Brazilian tests were also performed for comparison. The experiments showed that the ratios of the tensional and compressional SR to Brazilian strengths were 1.2~1.4 and 1.1~1.2, respectively, which are too small compared to empirical values in ordinary bend tests. Consequently, it is concluded that the SR test is not appropriate for use in tensile strength test of rock specimen of NX size. But the ratio of the HR to Brazilian strengths was within 1.7~2.0 for both the previous and present studies, showing a good consistency in their test results.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.537-547
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• 2018

This research presents the effect of anisotropy of the hollow disc mode under Brazilian test using PFC3D. The Brazilian tensile strength test was performed on the hollow disc specimens containing the bedding layers and then these specimens were numerically modeled by using the two dimensional discrete element code (PFC3D) to calibrate this computer code for the simulation of the cracks propagation and cracks coalescence in the anisotropic bedded rocks. The thickness of each layer within the specimens varied as 5 mm, 10 mm and 20 mm and the layers angles were changed as $0^{\circ}$, $25^{\circ}$, $50^{\circ}$, $75^{\circ}$ and $90^{\circ}$. The diameter of internal hole was taken as 15 mm and the loading rate during the testing process kept as 0.016 mm/s. It has been shown that for layers angles below $25^{\circ}$ the tensile cracks produce in between the layers and extend toward the model boundary till interact and break the specimen. The failure process of the specimen may enhance as the layer angle increases so that the Brazilian tensile strength reaches to its minimum value when the bedding layers is between $50^{\circ}$ and $75^{\circ}$ but its value reaches to maximum at a layer angle of $90^{\circ}$. The number of tensile cracks decreases as the layers thickness increases and with increasing the layers angle, less layer mobilize in the failure process.

• Structural Engineering and Mechanics
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• v.69 no.1
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• pp.43-50
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• 2019

In this research, the effect of bedding layer on the tensile failure mechanism of rocks has been investigated using PFC2D. For this purpose, firstly calibration of PFC2d was performed using Brazilian tensile strength. Secondly Brazilian test was performed on the bedding layer. Thickness of layers were 5 mm, 10 mm and 20 mm. in each thickness layer, layer angles changes from $0^{\circ}$ to $90^{\circ}$ with increment of $15^{\circ}$. Totally, 21 model were simulated and tested by loading rate of 0.016 mm/s. The results show that when layer angle is less than 15, tensile cracks initiates between the layers and propagate till coalesce with model boundary. Its trace is too high. With increasing the layer angle, less layer mobilizes in failure process. Also, the failure trace is very short. It's to be noted that number of cracks decrease with increasing the layer thickness. Also, Brazilian tensile strength is minimum when bedding layer angle is between $45^{\circ}$ and $75^{\circ}$. The maximum one is related to layer angle of $90^{\circ}$.

• Geomechanics and Engineering
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• v.12 no.6
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• pp.871-882
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• 2017

Indirect measure of the tensile strength of laboratory samples is an important topic in rock engineering. One of the most important tests, the Brazilian strength test is performed to obtain the tensile strength of rock, concrete and other quasi brittle materials. Because the measurements are provided indirectly and the inspected rock materials may have heterogeneous properties, uncertainty quantification is required for a reliable test evaluation. In addition to the conventional measurement evaluation uncertainty methods recommended by the Guide to the Expression of Uncertainty in Measurement (GUM), such as Taylor's and Monte Carlo Methods, a fuzzy set-based approach is also proposed and resulting uncertainties are discussed. The results showed that when a tensile strength measurement is measured by a laboratory test, its uncertainty can also be expressed by one of the methods presented.

• Tunnel and Underground Space
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• v.23 no.3
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• pp.212-218
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• 2013

Tuff specimens were thermally treated with predetermined temperatures of 200, 400 and $600^{\circ}C$ to construct specimens simulating weathered tuff rocks. Specific gravity, absorption ratio, elastic wave velocity, uniaxial compressive strength, Brazilian tensile strength, Young's modulus, Poisson's ratio and slake-durability index were measured for pre-heated specimens. Heating of rock specimens entailed the degradation of material properties except for slake-durability index. It was found that correlations among P-wave velocity, uniaxial compressive strength, Brazilian tensile strength, Young's modulus and absorption ratio are high. Regression equations which use the P-wave velocity as an independent variable were presented to evaluate uniaxial compressive strength, Brazilian tensile strength, Young's modulus and absorption ratio.

• Tunnel and Underground Space
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• v.22 no.5
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• pp.339-345
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• 2012

Information on the deformation behavior and fracture strength of rocks subjected to dynamic loadings is important to stability analyses of underground openings underground vibration due to rock blasts, earthquakes and rock bursts. In this study, Split Hopkinson Pressure Bar (SHPB) system was applied to estimate dynamic compressive and tensile fracture strengths of limestone and also examine deformation behavior of limestones under dynamic loadings. A micro-focus X-ray CT scanner was used to observe non-destructively inside the impacted limestone specimens. From the dynamic tests, it was revealed that the limestone have over 140MPa dynamic compressive strength and the strain-rate dependency of the strength. Dynamic Brazilian tensile strength of the limestone exceeds 21MPa and shows over 3 times static Brazilian tensile strength.

• Advances in concrete construction
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• v.3 no.4
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• pp.269-282
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• 2015

In this paper, a compression to tensile load converter device was developed to determine the anisotropic tensile strength of concrete. The samples were made from a mixture of water, fine sand and cement, respectively. Concrete samples with a hole at its center was prepared and subjected to tensile loading using the compression to tensile load converter device. A hydraulic load cell applied compressive loading to converter device with a constant pressure of 0.02 MPa per second. Compressive loading was converted to tensile stress on the sample because of the overall test design. The samples have three different configurations related to loading axis; 0, $45^{\circ}$, $-45^{\circ}$. A series of finite element analysis were done to analyze the effect of hole diameter on stress concentration of the hole side along its horizontal axis to provide a suitable criterion for determining the real tensile strength of concrete. Concurrent with indirect tensile test, Brazilian test and three point loading test were also performed to compare the results from the three methods. Results obtained by this device were quite encouraging and show that the tensile strengths of concrete were similar in different directions because of the homogeneity of bonding between the concrete materials. Also, the indirect tensile strength was clearly lower than the Brazilian test strength and three point loading test.

• Structural Engineering and Mechanics
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• v.60 no.6
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• pp.939-952
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• 2016

A compression to tensile load transforming (CTT) device was developed to determine indirect tensile strength of concrete material. Before CTT test, Particle flow code was used for the determination of the standard dimension of physical samples. Four numerical models with different dimensions were made and were subjected to tensile loading. The geometry of the model with ideal failure pattern was selected for physical sample preparation. A concrete slab with dimensions of $15{\times}19{\times}6cm$ and a hole at its center was prepared and subjected to tensile loading using this special loading device. The ratio of hole diameter to sample width was 0.5. The samples were made from a mixture of water, fine sand and cement with a ratio of 1-0.5-1, respectively. A 30-ton hydraulic jack with a load cell applied compressive loading to CTT with the compressive pressure rate of 0.02 MPa per second. The compressive loading was converted to tensile stress on the sample because of the overall test design. A numerical modeling was also done to analyze the effect of the hole diameter on stress concentrations of the hole side along its horizontal axis to provide a suitable criterion for determining the real tensile strength of concrete. Concurrent with indirect tensile test, the Brazilian test was performed to compare the results from two methods and also to perform numerical calibration. The numerical modeling shows that the models have tensile failure in the sides of the hole along the horizontal axis before any failure under shear loading. Also the stress concentration at the edge of the hole was 1.4 times more than the applied stress registered by the machine. Experimental Results showed that, the indirect tensile strength was clearly lower than the Brazilian test strength.