• Computers and Concrete
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• v.20 no.1
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• pp.39-47
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• 2017

In this paper, mode I fracture toughness of rock was determined by direct and indirect methods using Particle Flow Code simulation. Direct methods are compaction tension (CT) test and hollow centre cracked quadratic sample (HCCQS). Indirect methods are notched Brazilian disk (NBD) specimen, the semi-circular bend (SCB) specimen, hollow centre cracked disc (HCCD), the single edge-notched round bar in bending (SENRBB) specimen and edge notched disk (END). It was determined that which one of indirect fracture toughness values is close to direct one. For this purpose, initially calibration of PFC was undertaken with respect to data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, the simulated models in five introduced indirect tests were cross checked with the results from direct tests. By using numerical testing, the failure process was visually observed. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Mode I fracture toughness of rock in direct test was less than other tests results. Fracture toughness resulted from semi-circular bend specimen test was close to direct test results. Therefore semi-circular bend specimen can be a proper test for determination of Mode I fracture toughness of rock in absence of direct test.

• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.81-91
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• 2022

The effects of interaction between concrete-gypsum interface and edge crack on the failure behavior of the specimens in senicircular bend (SCB) test were studied in the laboratory and also simulated numerically using the discrete element method. Some quarter circular specimens of gypsum and concrete with 5 cm radii and hieghts were separately prepared. Then the semicircular testing specimens were made by attaching one gypsum and one concrete sample to one another using a special glue and one edge crack is produced (in the interface) by do not using the glue in that part of the interface. The tensile strengths of concrete and gypsum samples were separately measured as 2.2 MPa and 1.3 MPa, respectively. during all testing performances a constant loading rate of 0.005 mm/s were stablished. The proposed testing method showed that the mechanism of failure and fracture in the brittle materials were mostly governed by the dimensions and number of discontinuities. The fracture toughnesses of the SCB samples were related to the fracture patterns during the failure processes of these specimens. The tensile behaviour of edge notch was related to the number of induced tensile cracks which were increased by decreasing the joint length. The fracture toughness of samples was constant by increasing the joint length. The failure process and fracture pattern in the notched semi-circular bending specimens were similar for both methods used in this study (i.e., the laboratory tests and the simulation procedure using the particle flow code (PFC2D)).

• Advances in concrete construction
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• v.14 no.5
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• pp.317-330
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• 2022

This paper investigated computationally and experimentally the interaction here between a notch as well as a micropore under uniaxial compression. Brazilian tensile strength, uniaxial tensile strength, as well as biaxial tensile strength are used to calibrate PFC2d at first. Then, uniaxial compression test was conducted which they included internal notch and micro pore. Experimental and numerical building of 9 models including notch and micro pore were conducted. Model dimensions of models are 10 cm × 10 cm × 5 cm. Joint length was 2 cm. Joints angles were 30°, 45° and 60°. The position of micro pore for all joint angles was 2cm upper than top of the joint, 2 cm upper than middle of joint and 2 cm upper than the joint lower tip, discreetly. The numerical model's dimensions were 5.4 cm × 10.8 cm. The fractures were 2 cm in length and had angularities of 30, 45, and 60 degrees. The pore had a diameter of 1 cm and was located at the top of the notch, 2 cm above the top, 2 cm above the middle, and 2 cm above the bottom tip of the joint. The uniaxial compression strength of the model material was 10 MPa. The local damping ratio was 0.7. At 0.016 mm per second, it loaded. The results show that failure pattern affects uniaxial compressive strength whereas notch orientation and pore condition impact failure pattern. From the notch tips, a two-wing fracture spreads almost parallel to the usual load until it unites with the sample edge. Additionally, two wing fractures start at the hole. Both of these cracks join the sample edge and one of them joins the notch. The number of wing cracks increased as the joint angle rose. There aren't many AE effects in the early phases of loading, but they quickly build up until the applied stress reaches its maximum. Each stress decrease was also followed by several AE effects. By raising the joint angularities from 30° to 60°, uniaxial strength was reduced. The failure strengths in both the numerical simulation and the actual test are quite similar.

• Journal of the Korean Geotechnical Society
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• v.25 no.10
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• pp.17-30
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• 2009

Underground construction such as tunneling can induce damages on the surrounding rock mass, due to the stress concentration of in situ stresses and excessive energy input during construction sequence, such as blasting. The developed damage on the rock mass can have substantial influence on the mechanical and hydraulic behaviors of the rock masses around a tunnel. In this study, investigation on the generation of damage around an opening in a jointed rock model under biaxial compression condition was conducted. The joint dip angles employed are 30, 45, and 60 degrees to the horizontal, and the synthetic rock mass was made using early strength cement and water. From the biaxial compression test, initiation and propagation of tensile cracks at norm to the joint angle were found. The propagated tensile cracks eventually developed rock blocks, which were dislodged from the rock mass. Furthermore, the propagation process of the tensile cracks varies with joint angle: lower joint angle model shows more stable and progressive tensile crack propagation. The development of the tensile crack can be explained under the hypothesis that the rock segment encompassed by the joint set is subjected to the developing moment, which can be induced by the geometric irregularity around the opening in the rock model. The experiment results were simulated by using discrete element method PFC 2D. From the simulation, as has been observed from the test, a rock mass with lower joint angle produces wider damage region and rock block by tensile cracks. In addition, a rock model with lower joint angle shows progressive tensile cracks generation around the opening from the investigation of the interacted tensile cracks.

• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.493-504
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• 2018

In this paper, the tensile failure behaviour of transversally bedding layers was numerically simulated by using particle flow code in two dimensions. Firstly, numerical model was calibrated by uniaxial, Brazilian and triaxial experimental results to ensure the conformity of the simulated numerical model's response. Secondly, 21 circular models with diameter of 54 mm were built. Each model contains two transversely bedding layers. The first bedding layer has low mechanical properties, less than mechanical properties of intact material, and second bedding layer has high mechanical properties, more than mechanical properties of intact material. The angle of first bedding layer, with weak mechanical properties, related to loading direction was $0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$, $60^{\circ}$, $75^{\circ}$ and $90^{\circ}$ while the angle of second layer, with high mechanical properties, related to loading direction was $90^{\circ}$, $105^{\circ}$, $120^{\circ}$, $135^{\circ}$, $150^{\circ}$, $160^{\circ}$ and $180^{\circ}$. Is to be note that the angle between bedding layer was $90^{\circ}$ in all bedding configurations. Also, three different pairs of the thickness was chosen in models; i.e., 5 mm/10 mm, 10 mm/10 mm and 20 mm/10 mm. The result shows that In all configurations, shear cracks develop between the weaker bedding layers. Shear cracks angel related to normal load change from $0^{\circ}$ to $90^{\circ}$ with increment of $15^{\circ}$. Numbers of shear cracks are constant by increasing the bedding thickness. It's to be note that in some configuration, tensile cracks develop through the intact area of material model. There is not any failure in direction of bedding plane interface with higher strength.

• Journal of the Korean GEO-environmental Society
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• v.12 no.7
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• pp.57-65
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• 2011

Numerical simulations by three-dimensional Particle Flow Code($PFC^{3D}$, Itasca) considering distinct element method (DEM) were carried out for prediction of triaxial compression test with sand material. The effect of scale conditions for numerical model and distinct material on final prediction results was analyzed by numerical models under various scale conditions, and following observations were made from the numerical experiments. It is very useful to model the initial material condition without any porosity conversion from 2-D to 3-D DEM. Numerical experiments have shown that in all cases considered, 3D distinct element modeling could provide good agreement on stress-strain behavior, volume change and strength properties with laboratory testing results. It was important thing to assess reasonable scale ratio of numerical model and distinct elements for saving calculation time and securing calculation efficiency under condition with accuracy and appropriateness as numerical laboratory. As results of DEM simulations under various scale conditions, most of results show that shear strength properties as cohesion and internal friction angle are similar in condition of $D_{mod}/D_{gmax}$ < 10. It shows that 3-D distinct element method could be used as efficient tool to assess strength properties by numerical laboratory technique.

• Journal of the Korea Concrete Institute
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• v.20 no.2
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• pp.147-156
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• 2008

In an uniaxial compressive test of a concrete standard specimen (150$\times$300 mm) the crack initiation and extension with the stress increase are the major reason of the failure, which is similar to the breakage of the particle bonding in the simulation by using particle bonded model, especially particle flow code in 3 dimensions (PFC3D) developed by Itasca Consulting Group Inc. That is the main motive to study the possibility of an uniaxial compressive strength test simulation. It is important to investigate the relationship between the micro-parameters and the macro-properties because the 3-dimensional particle bonded model uses the spherical particles to analyze the physical phenomena. Contact bonded model used herein has eight micro-parameters and there are five macro-properties; Young's modulus, Poisson's ratio, uniaxial compressive strength and the crack initiation stress and the ratio concerning the crack propagation with the stress. To simulate the compressive test we made quantitative relationships between the micro-parameters and the macro-properties by using the fractional factorial design and various sensitivity analyses including regression analysis, which result in the good agreement with the previous studies. Also, the stress-stain curve and the crack distribution over the specimen given by PFC3D showed the mechanical behavior of the concrete standard specimen under the uniaxial compression. It is concluded that the particle bonded model can be a good tool for the analyzing the mechanical behavior of concrete under the uniaxial compressive load.

• Tunnel and Underground Space
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• v.7 no.4
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• pp.267-273
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• 1997

Rock fragmentation with plasma blasting technique has advantageous properties in contrast to the conventional blasting method in controlling of flying rocks and ground vibrations, when residents are complaining or surrounding structures stay in protection from blasting operations. The experiences show in urban construction works that the plasma blasting is the most possible method to prevent damages and minimize adverse environmnetal impacts. The fragmentation energy level is evaluated by numerical simulation using PFC-2D for various drill hole pattern and tested accordingly to get the feasibility. The energy output of plasma blasting system has been improved to a level of 1 MJ, which can break a 2~3 ㎥ granite boulder or 1.5 m height bench face. Measurements are carried out to get the ground vibration level and propagation equation, so that the control of the blasting operations can be performed more precisely and safely.

• Proceedings of the Korean Society for Rock Mechanics Conference
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• 2011.09a
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• pp.3-21
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• 2011

Laboratory experiments and numerical simulations using Particle Flow Code (PFC2D) were performed to study the effects of joint separation and joint overlapping on the full failure behavior of rock bridges under direct shear loading. Through numerical direct shear tests, the failure process is visually observed and the failure patterns are achieved with reasonable conformity with the experimental results. The simulation results clearly showed that cracks developed during the test were predominantly tension cracks. It was deduced that the failure pattern was mostly influenced by both of the joint separation and joint overlapping while the shear strength is closely related to the failure pattern and its failure mechanism. The studies revealed that shear strength of rock bridges are increased with increasing in the joint separation. Also, it was observed that for a fixed cross sectional area of rock bridges, shear strength of overlapped joints are less than the shear strength of non-overlapped joints.

• Tunnel and Underground Space
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• v.17 no.5
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• pp.389-410
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• 2007

For moderately jointed to massive rock masses, the failure and deformation behaviors around an excavated opening are absolutely influenced by the initial rock stress and strength of in-situ rock mass. The localized and progressive brittle failure around an opening does not mean whole collapse of an excavated opening. But, for many cases, it may induce temporary stopping of excavation works and reexamination of the current supporting system, which can result in delay of the entire construction works and additional construction cost. In this paper, the characteristics of the brittle failure around an opening with stress level and tunnel shape was studied by the biaxial compressive test using scaled specimen and by the numerical simulation with $PFC^{2D}$. The biaxial test results were well coincided with the stress induced failure patterns around the excavated openings observed and monitored in the in-situ condition. For the circular part of the opening wall, the stress induced cracks initially occurred at the wall surface in the direction of the minimum principal stress and contributed to the localized notch shaped failure region having a certain range of angle. But for the corner and straight part of the opening wall, the cracks initiated at sharp corners were connected and coalesced each other and with existing micro cracks. Further they resulted in a big notch shaped failure region connecting two sharp corners.