• Geomechanics and Engineering
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• v.7 no.6
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• pp.665-678
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• 2014

In discrete element modeling, 2D software has been widely used in order to gain further insights into the fundamental mechanisms with less computational time. The porosities used in 2D DEM studies should be determined with appropriate approaches based on 3D laboratory porosities. This paper summarizes the main approaches for converting porosities from 3D to 2D for DEM studies and theoretical evaluations show that none of the current approaches can be widely used in dealing with soil mechanical problems. Therefore, a parabolic equation and a criterion have been suggested for the determination of 2D porosities in this paper. Moreover, a case study has been used to validate that the 2D porosity obtained from the above suggestion to be rational with both the realistic contact force distribution in the specimen and the good agreement of the DEM simulation results of direct shear tests with the corresponding experimental data. Therefore, the parabolic equation and the criterion are suggested for the determination of 2D porosities in a wide range of polydisperse particle systems, especially in dealing with soil mechanical problems.

• Tunnel and Underground Space
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• v.33 no.1
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• pp.57-69
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• 2023

In this study, we simulated induced seismicity in the Groningen natural gas reservoir using 2D hydro-mechanical coupled discrete element modelling (DEM). The code used is PFC2D (Particle Flow Code 2D), a commercial software developed by Itasca, and in order to apply to this study we further developed 1)initialization of inhomogeneous reservoir pressure distribution, 2)a non-linear pressure-time history boundary condition, 3)local stress field monitoring logic. We generated a 2D reservoir model with a size of 40 × 50 km² and a complex fault system, and simulated years of pressure depletion with a time range between 1960 and 2020. We simulated fault system failure induced by pressure depletion and reproduced the spatiotemporal distribution of induced seismicity and assessed its failure mechanism. Also, we estimated the ground subsidence distribution and confirmed its similarity to the field measurements in the Groningen region. Through this study, we confirm the feasibility of the presented 2D hydro-mechanical coupled DEM in simulating the deformation of a complex fault system by hydro-mechanical coupled processes.

• 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.

• Computers and Concrete
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• v.18 no.1
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• pp.39-51
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• 2016

This paper considers the tensile strength of concrete samples in direct, CTT, modified tension, splitting and ring tests using both of the experimental tests and numerical simulation (particle flow code 2D). It determined that which one of indirect tensile strength is close to direct tensile strength. Initially calibration of PFC was undertaken with respect to the data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, validation of the simulated models in four introduced tests was also cross checked with the results from experimental tests. By using numerical testing, the failure process was visually observed and failure patterns were watched to be reasonable in accordance with experimental results. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Tensile strength of concrete in direct test was less than other tests results. Tensile strength resulted from modified tension test was close to direct test results. So modified tension test can be a proper test for determination of tensile strength of concrete in absence of direct test. Other advantages shown by modified tension tests are: (1) sample preparation is easy and (2) the use of a simple conventional compression press controlled by displacement compared with complicate device in other tests.

• Computers and Concrete
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• v.27 no.2
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• pp.99-109
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• 2021

Experimental and discrete element methods were used to investigate the effects of echelon non-persistent joint on the failure behaviour of joint's bridge area under uniaxial compressive test. Concrete samples with dimension of 150 mm×100 mm×50 mm were prepared. Uniaxial compressive strength and tensile strength of concrete were 14 MPa and 1MPa, respectivly. Within the specimen, three echelon non-persistent notches were provided. These joints were distributed on the three diagonal plane. the angle of diagonal plane related to horizontal axis were 15°, 30° and 45°. The angle of joints related to diagonal plane were 30°, 45°, 60°. Totally, 9 different configuration systems were prepared for non-persistent joint. In these configurations, the length of joints were taken as 2 cm. Similar to those for joints configuration systems in the experimental tests, 9 models with different echelon non-persistent joint were prepared in numerical model. The axial load was applied to the model by rate of 0.05 mm/min. the results show that the failure process was mostly governed by both of the non-persistent joint angle and diagonal plane angle. The compressive strengths of the specimens were related to the fracture pattern and failure mechanism of the discontinuities. It was shown that the shear behaviour of discontinuities is related to the number of the induced tensile cracks which are increased by increasing the joint angle. The strength of samples increase by increasing both of the joint angle and diagonal plane angle. The failure pattern and failure strength are similar in both methods i.e. the experimental testing and the numerical simulation methods.

• Computers and Concrete
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• v.29 no.1
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• pp.31-45
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• 2022

Experimental and numerical simulation were used to investigate the effects of angle and number of T shape non-persistent crack on the shear behaviour of crack's bridge area under uniaxial compressive test. concrete samples with dimension of 150 mm×150 mm×40 mm were prepared. Within the specimen, T shape non-persistent notches were provided. 16 different configuration systems were prepared for T shape non-persistent crack based on two and three cracks. In these configurations, the length of cracks were taken as 4 cm and 2 cm based on the cracks configuration systems. The angle of larger crack related to horizontal axis was 0°, 30°, 60° and 90°. Similar to cracks configuration systems in the experimental tests, 28 models with different T shape non-persistent crack angle were prepared in numerical model. The length of cracks were taken as 4 cm and 2 cm based on the cracks configuration systems. The angle of larger crack related to horizontal axis was 0°, 15°, 30°, 45°, 60°, 75° and 90°. Tensile strength of concrete was 1 MPa. The axial load was applied to the model. Displacement loading rate was controlled to 0.005 mm/s. Results indicated that the failure process was significantly controled by the T shape non-persistent crack angle and crack number. The compressive strengths of the specimens were related to the fracture pattern and failure mechanism of the discontinuities. Furthermore, it was shown that the compressive behaviour of discontinuities is related to the number of the induced tensile cracks which are increased by increasing the crack number and crack angle. The strength of samples decreased by increasing the crack number. In addition, the failure pattern and failure strength are similar in both methods i.e. the experimental testing and the numerical simulation methods (PFC2D).

• 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)).

• 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.

• 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.